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介绍黑洞的引言英文作文Introduction to Black Holes。
Black holes, one of the most fascinating objects in the universe, have been a subject of scientific research for decades. These mysterious objects are formed when a massive star collapses under its own gravity, creating a region in space where the gravitational pull is so strong that nothing, not even light, can escape. The concept of black holes was first proposed by the physicist John Michell in 1783 and was later refined by Albert Einstein's theory of general relativity in 1915.Black holes are invisible to the naked eye, as they do not emit any light or radiation. However, their presence can be detected by observing the effects of their immense gravitational pull on nearby stars and gas. The area surrounding a black hole is known as the event horizon, which marks the point of no return. Anything that crosses the event horizon is pulled into the black hole and is lostOne of the most intriguing aspects of black holes is their ability to distort time and space. The intensegravity near a black hole causes time to slow down, and space to be warped and stretched. This phenomenon, known as gravitational time dilation, has been confirmed by observations of stars orbiting black holes.Black holes come in different sizes, ranging from a few times the mass of the sun to billions of times the mass of the sun. Supermassive black holes, found at the centers of galaxies, are thought to play a crucial role in the evolution of galaxies, as they can influence the motion of stars and gas.Despite their mysterious nature, black holes have become a topic of intense research in astrophysics and cosmology. Scientists are using a variety of techniques, such as gravitational wave detection and observations of the effects of black holes on nearby objects, to study these enigmatic objects and unlock the secrets of theIn conclusion, black holes are one of the most intriguing and mysterious objects in the universe. They are formed by the collapse of massive stars and have a gravitational pull so strong that nothing can escape. Their ability to distort time and space and influence the motion of nearby objects makes them a subject of intense research in astrophysics and cosmology.。
黑洞介绍英语作文初一Title: Exploring the Mysteries of Black Holes。
Introduction:Black holes are one of the most intriguing and enigmatic phenomena in the universe. They are regions in space where gravity is so strong that nothing, not even light, can escape from them. In this essay, we will delve into the fascinating world of black holes, exploring their characteristics, formation, and significance in the cosmos.Characteristics of Black Holes:Black holes come in various sizes, from small ones with masses comparable to that of a mountain to supermassive ones found at the centers of galaxies, with masses millions or even billions of times that of our Sun. Despite their differences in size, all black holes share certain common characteristics.Firstly, every black hole has a boundary called the event horizon. Once an object crosses this boundary, it is trapped within the black hole's gravitational pull and cannot escape. Beyond the event horizon lies the singularity, a point of infinite density where the laws of physics, as we understand them, break down.Formation of Black Holes:Black holes can form through different processes, but the most common way is through the gravitational collapse of massive stars at the end of their life cycles. When a massive star exhausts its nuclear fuel, it can no longer sustain the outward pressure generated by nuclear fusion, causing its core to collapse under its own gravity. If the core's mass exceeds a certain threshold, it collapses into a black hole.Another way black holes can form is through the merger of two smaller black holes. When galaxies collide, their black holes can also merge, creating even larger blackholes in the process.Significance in the Cosmos:Black holes play a crucial role in the evolution of galaxies and the universe as a whole. They influence the dynamics of galaxies, shaping their structure and influencing the distribution of stars within them. Supermassive black holes, found at the centers of galaxies, are believed to play a significant role in regulating the growth of galaxies by emitting powerful jets of radiation and matter.Furthermore, black holes serve as natural laboratories for testing the fundamental laws of physics, particularly the theory of general relativity proposed by Albert Einstein. By studying the behavior of matter and light around black holes, scientists can gain insights into the nature of space, time, and gravity in the extreme conditions near a singularity.Conclusion:In conclusion, black holes are captivating cosmic phenomena that continue to astound and intrigue scientists and enthusiasts alike. With their immense gravitationalpull and mysterious properties, black holes challenge our understanding of the universe and inspire us to explore its deepest mysteries. As we continue to study and unravel the secrets of black holes, we come one step closer to unlocking the secrets of the cosmos itself.。
黑洞介绍英语作文带翻译Title: Exploring the Enigma of Black Holes。
Introduction。
Black holes have long captured the imagination of scientists and the public alike. These enigmatic cosmic entities, formed from the collapse of massive stars, possess gravitational forces so intense that not even light can escape their grasp. In this essay, we will delve into the fascinating world of black holes, exploring their properties, formation, and the profound implications they hold for our understanding of the universe.Properties of Black Holes。
At the heart of every black hole lies a singularity, a point of infinite density where the laws of physics, as we currently understand them, break down. Surrounding this singularity is the event horizon, the boundary beyond whichnothing can escape the black hole's gravitational pull. It is this event horizon that gives black holes their name, as it appears "black" to outside observers.Formation of Black Holes。
英语关于黑洞的作文The Mysterious and Fascinating Black Holes.In the vast and enigmatic universe, black holes standas one of the most intriguing and perplexing phenomena. These regions of space, characterized by their intense gravity and complete absence of light, have captivated the imagination of scientists and laypeople alike for centuries. Despite their otherworldly nature, black holes play acrucial role in understanding the evolution and structureof our universe.The concept of black holes emerged in the late 18th century, with the pioneering work of scientists like John Michell and Pierre-Simon Laplace. They theorized the existence of objects so massive that not even light could escape their intense gravitational pull. However, it wasnot until the 20th century that astronomers began to gather evidence that supported the existence of these mysterious objects.One of the most significant milestones in the study of black holes was the work of Albert Einstein. His theory of general relativity provided a mathematical framework to describe the behavior of gravity and its interaction with matter. This theory laid the foundation for understanding the properties of black holes, including their formation, evolution, and interaction with their environment.Black holes are formed when a massive star collapses under its own weight at the end of its life cycle. This collapse compresses the star's matter into a tiny, ultra-dense region known as a singularity. The gravity around this singularity is so intense that nothing, including light, can escape its pull. The boundary of this region, known as the event horizon, marks the point where the escape velocity exceeds the speed of light.There are two main types of black holes: stellar-mass black holes and supermassive black holes. Stellar-mass black holes are formed when a star of about 10 to 30 times the mass of the Sun collapses. These black holes have adiameter of only a few kilometers but possess a mass comparable to that of a small star. On the other hand, supermassive black holes have masses ranging from millionsto billions of times the mass of the Sun. They are believed to reside at the centers of most galaxies, including ourown Milky Way.The study of black holes has revealed much about the structure and dynamics of the universe. For instance, black holes play a crucial role in the evolution of galaxies. By accreting matter and emitting radiation, they can significantly impact the star formation and gas dynamics of their host galaxies. Additionally, the merging of black holes, a common occurrence in the universe, can emit gravitational waves, ripples in the fabric of spacetimethat can be detected by advanced telescopes like the Laser Interferometer Gravitational-Wave Observatory (LIGO).Despite their otherworldly nature, black holes are not entirely devoid of life. In fact, there are theories that suggest the existence of accretion disks around black holes. These disks are formed when matter from a nearby star orgas cloud is attracted to the black hole and begins toorbit it. As the matter spirals inward, it heats up and emits radiation, creating a bright and energetic environment.The study of black holes also holds the key to understanding some of the most fundamental questions about our universe. For instance, black holes provide a unique laboratory to test the limits of Einstein's theory of general relativity. By studying the behavior of matter and light near the event horizon, scientists can gain insights into the nature of gravity and its interaction with quantum mechanics.In conclusion, black holes are one of the most mysterious and fascinating phenomena in the universe. They challenge our understanding of gravity, matter, and the structure of the cosmos. As we continue to explore and study these enigmatic objects, we may unlock the secrets of the universe and gain a deeper understanding of our placein the cosmos.。
克莱汤普森g660分作文英语Title: Exploring the Wonders of the UniverseIn the vast expanse of the universe lie countless mysteries waiting to be unraveled and marvels to be discovered. As human beings, our insatiable curiosity propels us to explore the unknown depths of outer space. From the twinkling stars to the enigmatic black holes, the universe continues to captivate our imaginations and push the boundaries of our understanding. This essay delves into the wonders of the universe and highlights some of the most intriguing phenomena.At the heart of our solar system, the Sun reigns supreme. This gigantic ball of glowing gas provides light, warmth, and sustenance to all life on planet Earth. The Sun's mesmerizing dance of fusing hydrogen atoms into helium generates an incredible amount of energy, fueling our existence. Itsintense heat and gravity create beautiful phenomena such as solar flares and sunspots. Furthermore, the Sun's enormous magnetic field gives rise to the awe-inspiring auroras that illuminate the polar skies.The planets of our solar system, each unique in its own way, also captivate our attention. Mercury, the closest planet to the Sun, is a barren and desolate world with extreme temperature variations. Venus, on the other hand, is shrouded in a thick layer of toxic clouds, making it the hottest planet in our solar system. Mars, often referred to as the "Red Planet," has piqued our interest as a potential habitat for future human colonization. The gas giants, such as Jupiter with its mesmerizing stripes and the iconic Great Red Spot, and Saturn with its spectacular rings, showcase the sheer beauty and grandeur of the outer planets.Beyond our solar system lies the vastness of the Milky Way galaxy. With over 100 billion stars swirling in amagnificent cosmic dance, it is a testament to the incomprehensible scale of the universe. Within our galaxy, there are numerous celestial objects that continue to astound astronomers. Nebulas, enormous clouds of gas and dust, give birth to new stars and offer a glimpse into the cosmic creation process. Supernovae, the explosive deaths of massive stars, release energy equivalent to billions of nuclear bombs and forge elements essential for life.Exploring farther into the universe, we encounter galaxies other than our own. The Andromeda galaxy, our closest galactic neighbor, is a spiraling beauty housing billions of stars similar to our Sun. Collisions between galaxies often produce breathtaking displays of cosmic fireworks, shaping their morphologies and giving birth to new stars. The supermassive black holes residing at the centers of galaxies intrigue scientists with their immense gravitational pull and the potential to bend space and time.The study of exoplanets has also deepened our understanding of the universe. These planets, orbiting stars outside our solar system, offer insights into the possibility of life beyond Earth. From gas giants with scorching atmospheres to rocky planets with potential habitable conditions, each new discovery brings us closer to answering the age-old question: Are we alone in the universe?In conclusion, the wonders of the universe are vast and encompassing. From the blazing Sun to the captivating planets, the breathtaking galaxies, and the mysteries of exoplanets,the universe unfolds its secrets, enticing us to explore its depths. As we continue to push the boundaries of scientific knowledge, we embark on an incredible journey of discoveryand revelation, humbled by the sheer magnificence that awaits us in the cosmic abyss.。
关于太空的英语作文初二英文回答：Beyond the confines of our planet, an abyss of cosmic wonders awaits. The vast expanse of space, with its enigmatic celestial bodies, has captivated the human imagination for centuries.Stars: The night sky is adorned with celestial orbsthat ignite our wonder. Stars are massive balls of incandescent gas, powered by nuclear fusion reactions. They emit prodigious amounts of energy, illuminating the cosmic tapestry. Our sun, a yellow dwarf star, is the anchor of our solar system.Galaxies: Stars congregate in sprawling cosmic structures known as galaxies. The Milky Way, our home galaxy, is a vast spiral system containing billions of stars. Galaxies range in size, shape, and stellar density, and their study provides insights into the evolution of theuniverse.Black Holes: These enigmatic cosmic entities possess gravitational forces so formidable that nothing, not even light, can escape their clutches. Black holes form when massive stars collapse under their own gravity. They are believed to reside at the centers of most galaxies and exert a profound influence on their surroundings.Nebulae: These celestial nurseries are vast clouds of gas and dust where new stars are born. As massive stars within nebulae emit intense radiation, they excite the surrounding gas, creating vibrant and ethereal structures. Nebulae provide a glimpse into the birthplaces of celestial bodies.Cosmic Microwave Background: This faint radiation permeating the universe is a relic of the Big Bang, the cataclysmic event that gave birth to our cosmos. Its study helps scientists understand the origins and evolution of the universe.Exoplanets: Beyond our solar system, astronomers have discovered a myriad of planets orbiting distant stars. These exoplanets exhibit a wide range of characteristics, including gas giants, rocky worlds, and even potentially habitable environments. The exploration of exoplanets offers the tantalizing prospect of discovering life beyond Earth.中文回答：太空，无限的奥秘。
innumberable英译-回复"Innumerable" in English refers to a large or countless number of something. Here is a step-by-step response to the topic of "innumerable," consisting of a 1500-2000 word article:Title: Exploring the Innumerable Wonders of the UniverseIntroduction (150 words):The universe is a vast expanse filled with innumerable wonders that have captivated human imagination for centuries. From the billions of stars in the night sky to the countless galaxies swirling around us, the scale and mysteries of the cosmos seem unfathomable. In this article, we will embark on a journey to explore some of these innumerable wonders and understand their significance in unraveling the secrets of the universe.1. The Immensity of Space (200 words):The first awe-inspiring aspect of the universe is its sheer immensity. It encompasses an innumerable number of stars, planets, and galaxies, stretching billions of light-years in every direction. Looking up at the night sky, it becomes difficult to comprehend the countless trillions of stars that exist. Further, recent discoverieshave revealed the existence of over two trillion galaxies, each containing billions of stars. The vastness of space is both humbling and exhilarating, challenging us to contemplate our place in the cosmos.2. Galaxies: Cosmic Island Chains (300 words):Within the universe, galaxies are the building blocks of cosmic structure. These vast systems consist of stars, planets, gas, dust, and dark matter, all held together by gravity. The most common type of galaxy is the spiral galaxy, characterized by its rotating arms and central bulge. Examples include our own Milky Way and the Andromeda Galaxy. However, other types, such as elliptical and irregular galaxies, are also innumerable in number.3. Black Holes: Cosmic Monsters (350 words):Black holes are one of the most mysterious and captivating objects in the universe. These gravitational powerhouses are formed from the remnants of massive stars that have exhausted their nuclear fuel. Their gravity is so strong that nothing, not even light, can escape their gravitational pull. Black holes are thought to be innumerable in number, ranging in sizes from stellar black holes to supermassive ones that exist at the centers of galaxies. Their studyprovides insights into the nature of spacetime and the behavior of matter under extreme conditions.4. Exoplanets: Homes Beyond Our Solar System (350 words):The discovery of exoplanets, or planets orbiting stars outside our solar system, has revolutionized our understanding of the universe. The exoplanet population is believed to be innumerable, with an estimated hundreds of billions in just our Milky Way galaxy alone. These distant worlds come in all shapes and sizes, some resembling Earth and potentially harboring conditions suitable for life as we know it. Understanding exoplanets is crucial in our quest to find extraterrestrial life and expand human exploration beyond our celestial neighborhood.5. Dark Matter: The Invisible Enigma (400 words):Dark matter is perhaps the greatest unsolved mystery in modern astrophysics. It is called "dark" because it neither emits nor absorbs light, making it invisible. Nevertheless, its gravitational effects have been observed throughout the universe, shaping the formation of galaxies and large-scale structures. Despite its innumerable presence, dark matter's nature and composition remain largely unknown, baffling scientists. Unlocking the secrets of dark matterwill provide a deeper understanding of the cosmos and the invisible forces that govern it.Conclusion (200 words):The universe is an ever-expanding tapestry of innumerable wonders, challenging our comprehension and pushing the boundaries of human knowledge. From the vastness of space to the mesmerizing beauty of galaxies, the existence of black holes, the discovery of exoplanets, and the enigma of dark matter, each aspect unravels a distinct piece of the cosmic puzzle. As we continue to explore and study these wonders, we inch closer to unraveling the mysteries of the universe and understanding our place within it. The only limit to our knowledge of the universe is our ability to imagine and inquire, urging us to continue the journey of discovery and exploration of the innumerable marvels that lie beyond our planet Earth.。
关于天文的英语句子The Enigma of the Cosmos: A Journey Through the Depths of Space.As we gaze up at the night sky, our minds are drawn to the vastness of the universe and the mysteries it holds. The night sky, with its countless stars and constellations, has fascinated humans for centuries, sparking curiosity and wonder. Astronomy, the study of celestial objects and phenomena, has been a crucial part of human civilization, helping us understand our place in the universe.From the ancient astronomers who used simple devices like the astrolabe to track the movements of the stars to the modern-day telescopes that allow us to peer into the farthest reaches of space, the journey of astronomy has been remarkable. Each discovery, each breakthrough, has added a new layer to our understanding of the universe.One of the most fascinating aspects of astronomy is thediversity of celestial objects it encompasses. From planets and moons to galaxies and quasars, each type of object presents its own set of challenges and mysteries. The study of planets, for instance, has revealed much about their composition, atmosphere, and potential for harboring life. The discovery of exoplanets, planets orbiting stars other than our Sun, has further expanded our understanding of planetary systems and the possibilities of extraterrestrial life.Galaxies, on the other hand, are vast collections of stars, dust, and gas held together by gravity. Studying galaxies allows us to understand the structure and evolution of the universe. The identification of dark matter and dark energy, which account for a significant portion of the universe's mass and energy, has been a crucial milestone in our understanding of galactic and cosmic evolution.Quasars, extremely luminous and energetic objects at the centers of some galaxies, are another fascinating aspect of astronomy. Their intense brightness and energyoutput challenge our understanding of physics and Astrophysics. Studying quasars can provide insights intothe extreme conditions that exist in the cores of galaxies and the mechanisms that power them.In addition to the study of individual objects, astronomy also involves the exploration of larger-scale phenomena like supernovae, gamma-ray bursts, and black holes. These phenomena, though rare and transient, offer unique insights into the extreme physics that govern the universe. The detection of gravitational waves, a predicted but long-sought-after phenomenon, has opened a new window into the universe, allowing us to study its most violentand energetic events.The future of astronomy is exciting and filled with promise. With the advent of new telescopes and technologies, we are poised to make even more groundbreaking discoveries. The James Webb Space Telescope, successor to the Hubble Space Telescope, is expected to revolutionize our understanding of the early universe and the formation of stars and galaxies. The Square Kilometre Array, a radiotelescope under construction in Australia and South Africa, will allow us to peer deeper into the cosmos and study the properties of dark matter and dark energy in unprecedented detail.As we continue to explore the universe, it is important to remember that each discovery and breakthrough is a testament to the curiosity and perseverance of human beings. Astronomy, more than just a science, is a journey of discovery and understanding that has the potential to transform our view of the world and our place in it. As we gaze up at the night sky, let us remember that themysteries of the universe are still vast and unending, waiting to be uncovered by the next generation of astronomers.。
黑洞介绍英语作文带翻译标题，Exploring the Mysteries of Black Holes。
Introduction:Black holes have long been a subject of fascination and wonder for scientists and laypeople alike. These enigmatic cosmic phenomena, characterized by their immense gravitational pull and ability to devour everything intheir path, continue to captivate our imagination. In this essay, we will delve into the depths of black holes, exploring their formation, properties, and the profound impact they have on the universe.正文：1. What are Black Holes?Black holes are regions in space where thegravitational pull is so strong that nothing, not evenlight, can escape from them. They are formed when massive stars undergo gravitational collapse at the end of theirlife cycle. As the star's core runs out of fuel, it can no longer support its own weight against gravity, causing itto collapse in on itself. This collapse creates a singularity—a point of infinite density—surrounded by an event horizon, beyond which no information can escape.1. 黑洞的形成。
探索黑洞英语作文高中Exploring Black Holes。
Black holes are one of the most mysterious and fascinating objects in the universe. They are formed when a massive star collapses under its own gravity, creating a region of space where the gravitational pull is so strong that nothing, not even light, can escape. This makes black holes invisible to the naked eye, but scientists have been able to study them through indirect methods.One way scientists have explored black holes is through observing their effects on nearby objects. For example, if a black hole is close to a star, it can pull gas from the star and create a disk of material around the black hole. As the gas falls into the black hole, it heats up and emits X-rays, which can be detected by telescopes. By studying the X-rays emitted by these accretion disks, scientists can learn about the properties of the black hole, such as its mass and spin.Another way scientists have explored black holes is through gravitational waves. These are ripples in thefabric of spacetime that are created when two massive objects, such as black holes, collide and merge. In 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected the first gravitational waves from a black hole merger. Since then, several more black hole mergers have been detected, providing scientists with valuable information about the properties of black holes.Despite these advances, there is still much we don't know about black holes. One of the biggest mysteries is what happens at the event horizon, the point of no return where the gravitational pull is so strong that nothing can escape. According to Einstein's theory of general relativity, anything that crosses the event horizon will be pulled into the black hole and crushed into a singularity, a point of infinite density. However, some scientists believe that there may be other possibilities, such as a firewall of high-energy particles that would destroy anything that crosses the event horizon.In order to answer these questions, scientists are planning to launch new missions to study black holes. One of these is the Event Horizon Telescope, a network of telescopes around the world that will work together to create the first direct image of a black hole's event horizon. Another is the Laser Interferometer Space Antenna (LISA), a space-based gravitational wave detector that will be able to detect mergers of supermassive black holes in the centers of galaxies.In conclusion, black holes are some of the most fascinating objects in the universe, and scientists are constantly exploring new ways to study them. Through observations of their effects on nearby objects and the detection of gravitational waves, we have learned a great deal about these mysterious objects. However, there isstill much we don't know, and new missions such as the Event Horizon Telescope and LISA will help us to unlock the secrets of black holes.。
我想玩黑洞的作文英语Title: A Journey into the Depths: Exploring the Enigma of Black Holes。
In the vast expanse of the cosmos, there exists a phenomenon so mysterious and captivating that it defies the laws of conventional physics: the black hole. A black hole is a region in space where gravity is so strong that nothing, not even light, can escape from its grasp. It is a cosmic enigma, shrouded in darkness and intrigue, beckoning humanity to explore its depths and unravel its secrets.The concept of black holes has fascinated scientists and astronomers for centuries, sparking countless theories and debates about their nature and behavior. One of the most intriguing aspects of black holes is their formation. They are born from the remnants of massive stars that have exhausted their nuclear fuel and undergone gravitational collapse. As the star collapses inward, it creates a singularity—a point of infinite density—surrounded by anevent horizon, beyond which no information can escape.Venturing into the realm of black holes is akin to embarking on a journey into the unknown—a journey fraught with peril and uncertainty. Yet, it is also a journeyfilled with the promise of discovery and enlightenment. The study of black holes has led to profound insights into the nature of space, time, and the universe itself.One of the most iconic features of black holes is their event horizon—the point of no return. Once an object crosses the event horizon, it is inexorably drawn towards the singularity at the center of the black hole, where the laws of physics as we know them break down. This raises profound questions about the nature of reality and the limits of our understanding.Despite their mysterious nature, black holes emit radiation known as Hawking radiation, named after the renowned physicist Stephen Hawking. This radiation is believed to be generated by quantum effects near the event horizon, causing black holes to slowly evaporate over time.The discovery of Hawking radiation has profoundimplications for our understanding of black holes and the fundamental laws of physics.The study of black holes has also provided valuable insights into the dynamics of galaxies and the evolution of the universe. Supermassive black holes, which reside at the centers of galaxies, play a crucial role in shaping their structure and influencing the motion of stars and gaswithin them. Understanding the behavior of these cosmic behemoths is essential for unraveling the mysteries of galaxy formation and evolution.In recent years, astronomers have made significant strides in observing black holes directly, thanks to advancements in observational techniques and technology. The Event Horizon Telescope, a global network of radio telescopes, made headlines in 2019 with the first-ever image of a black hole's event horizon in the galaxy M87. This groundbreaking achievement marked a new era in our quest to understand these enigmatic cosmic phenomena.As we continue to probe the depths of space and push the boundaries of our knowledge, the study of black holes remains one of the most exciting and challenging frontiers in astrophysics. Each new discovery brings us closer to unraveling the mysteries of these cosmic giants and shedding light on the fundamental nature of the universe.In conclusion, the exploration of black holes represents a journey into the unknown—a journey fueled by curiosity, driven by passion, and guided by the relentless pursuit of knowledge. It is a journey that challenges our perceptions, expands our horizons, and ultimately deepens our understanding of the cosmos and our place within it. As we gaze into the abyss of a black hole, we are reminded of the boundless wonders that await us in the universe, beckoning us to venture forth and explore the mysteriesthat lie beyond.。
Using gravitational "lenses" in space, University of Utah astronomers discovered that the centers of the biggest galaxies are growing denser -- evidence of repeated collisions and mergers by massive galaxies with 100 billion stars. "We found that during the last 6 billion years, the matter that makes up massive elliptical galaxies is getting more concentrated toward the centers of those galaxies. This is evidence that big galaxies are crashing into other big galaxies to make even bigger galaxies," says astronomer Adam Bolton, principal author of the new study."Most recent studies have indicated that these massive galaxies primarily grow by eating lots of smaller galaxies," he adds. "We're suggesting that major collisions between massive galaxies are just as important as those many small snacks."The new study -- published recently in The Astrophysical Journal -- was conducted by Bolton's team from the Sloan Digital Sky Survey-III using the survey's 2.5-meter optical telescope at Apache Point, N.M., and the Earth-orbiting Hubble Space Telescope.The telescopes were used to observe and analyze 79 "gravitational lenses," which are galaxies between Earth and more distant galaxies. A lens galaxy's gravity bends light from a more distant galaxy, creating a ring or partial ring of light around the lens galaxy.The size of the ring was used to determine the mass of each lens galaxy, and the speed of stars was used to calculate the concentration of mass in each lens galaxy.Bolton conducted the study with three other University of Utah astronomers -- postdoctoral researcher Joel Brownstein, graduate student Yiping Shu and undergraduate Ryan Arneson -- and with these members of the Sloan Digital Sky Survey: Christopher Kochanek, Ohio State University; David Schlegel, Lawrence Berkeley National Laboratory; Daniel Eisenstein, Harvard-Smithsonian Center forAstrophysics; David Wake, Yale University; Natalia Connolly, Hamilton College, Clinton, N.Y.; Claudia Maraston, University of Portsmouth, U.K.; and Benjamin Weaver, New York University.利用引力透镜”的空间，犹他大学的天文学家发现的最大的星系的中心，越来越密集的恒星的星系——100000000000多次的碰撞和合并的证据。
a rXiv:as tr o-ph/4262v13Fe b24E+A Galaxies and the Formation of Early Type Galaxies at z ∼01Yujin Yang,Ann I.Zabludoff,and Dennis Zaritsky Steward Observatory,University of Arizona,Tucson,AZ 85721yyang@,azabludoff@,dennis@ Tod uer National Optical Astronomy Observatories,Tucson,AZ 85726lauer@ J.Christopher Mihos 2Department of Astronomy,Case Western Reserve University,10900Euclid Ave,Cleveland,OH 44106hos@ ABSTRACT E+A galaxies,whose spectra have deep Balmer absorption lines but no significant [OII]emis-sion,are the best candidates for an evolutionary link between star-forming,gas-rich galaxies and quiescent,gas-poor galaxies.Yet their current morphologies are not well known.We present HST /WFPC2observations of the five bluest E+A galaxies (z ∼0.1)in the Zabludoffet al.sam-ple to study whether their detailed morphologies are consistent with late-to-early type evolution and to determine what drives that evolution.The morphologies of four galaxies are disturbed,indicating that a galaxy-galaxy merger is at least one mechanism that leads to the E+A phase.Two-dimensional image fitting shows that the E+As are generally bulge-dominated systems,even though at least two E+As may have underlying disks.In the Fundamental Plane,E+As stand apart from the E/S0s mainly due to their high effective surface brightness.Fading of the young stellar population and the corresponding increase in their effective radii will cause these galaxies to migrate toward the locus of E/S0s.E+As have profiles qualitatively like those of normal power-law early-type galaxies,but have higher surface brightnesses.This result provides the first direct evidence supporting the hypothesis that power-law ellipticals form via gas-richmergers.In total,at least four E+As are morphologically consistent with early-type galaxies.We detect compact sources,possibly young star clusters,associated with the galaxies.These sources are much brighter (M R ∼−13)than Galactic globular clusters,have luminosities consis-tent with the brightest clusters in nearby starburst galaxies,and have blue colors consistent with the ages estimated from the E+A galaxy spectra (several 108yr).Further study of such young star cluster candidates might provide the elusive chronometer needed to break the age/burst-strength degeneracy for these post-merger galaxies.Subject headings:galaxies:evolution —galaxies:interactions —galaxies:starburst —galaxies:star clusters —galaxies:stellar content1.IntroductionIf galaxies evolve morphologically from late to early types,then some may be now changing from star-forming,gas-rich,disk-dominated objects into quiescent,gas-poor spheroidals.Spectroscopic surveys have identified at least one set of candidates for such a transformation:“E+A”galaxies1,whose spectra have deep Balmer absorption lines but no significant[OII]emission,indicating that star formation ceased abruptly in these galaxies within the last∼Gyr.In general,E+A galaxies lack significant amounts of HI gas(Chang et al.2001)and have hot,pressure-supported kinematics(Norton et al.2001),suggesting that these galaxies are indeed evolving—somehow—from late to early types.However,we do not yet know whether their current morphologies are consistent with late-to-early type evolution or what drives E+A evolution.While the mechanism(or mechanisms)that causes galaxies to pass through an E+A phase is not understood,there are several clues.First,E+A spectra suggest a recent burst of star formation that required the rapid consumption or dispersal of a gas reservoir.Second,although they werefirst studied in distant clusters(Dressler&Gunn1983),E+As—at least at low redshifts(z∼0.1)—lie mostly in low density environments(Zabludoffet al.1996;Quintero et al.2003).Third,in low-resolution POSS images,some E+As have features suggestive of tidal tails(Zabludoffet al.1996).Could E+As be the result of disk galaxy mergers,which are both common in thefield and known to enhance star formation?In the merger hypothesis, E+As are further along the“Toomre sequence”(Toomre,A.1977)and thus more relaxed than systems like the Antennae,whose morphology and kinematics are in such disarray that it is nearly impossible to constrain its endproduct.E+As may thus teach us considerably more about the endpoints of galaxy-galaxy mergers.We cannot test this picture of E+A formation,or whether the E+A phase is a bonafide late-to-early type transition,without detailed morphological information.Simulations predict that well-evolved major mergers have a hybrid morphology,including fading,low surface brightness tidal tails at large radii,a more relaxed spheroid-dominated core,and a population of young star clusters(Barnes1988;Barnes&Hernquist 1996;Ashman&Zepf1992;Mihos&Hernquist1994).Identifying such low surface brightness or small scale features,even at low redshifts,requires spatial resolution on the order of100pc and low sky background levels.Therefore,Hubble Space Telescope imaging of nearby E+As is required.In this paper,we present the detailed HST/WFPC2morphologies of thefive bluest E+A galaxies in the Zabludoffet al.(1996)sample.We review the sample and the data reduction methods in§2.We describe the qualitative morphologies of these galaxies in§3.1,discussing the observed tidal features and the implications for E+A origin.We address the question of whether E+As are consistent with evolution into early types by fitting two-dimensional,surface brightness models to each image and deriving structural parameters such as bulge-to-disk ratio,effective radius,and central surface density(§3.2).In§3.4,we examine the color gradients in the E+As and compare them with the expectations from disk merger models.We compare the results with the fundamental plane for early type galaxies and with the surface brightness profiles of the nearby elliptical galaxies in§3.5and§3.6,respectively.In§3.7,we search for star clusters in the E+As and ask whether their properties are consistent with late-to-early type galaxy evolution.We discuss the implications of our results for higher redshift galaxy surveys in§3.8,cautioning that bulge-to-disk decompositions,quantitative measures of asymmetry,and tests to uncover tidal features may mislead.Section4summarizes our results.2.Observations and Data ReductionOur HST imaging sample is a subset of the20nearby E+A galaxies2that were spectroscopically identified from11,113galaxy spectra in the Las Campanas Redshift Survey(LCRS)with redshifts between 0.07and0.18(Zabludoffet al.1996).These E+As are selected by requiring that their spectra have strong Balmer absorption features(average equivalent width H of Hβ,Hγand Hδ>5.5˚A)and little if any[OII] emission(EW[OII]<2.5˚A).Three-quarters of the E+As in the sample are in thefield,well outside rich cluster environments.The number of each E+A(e.g.,EA1)is from Zabludoffet al.(1996)and increases with increasing4000˚A break(D4000)strength.D4000is related to the galaxy’s color—bluer galaxies have smaller D4000.EA1through EA5,the focus of our HST study,have the smallest D4000’s,and therefore are more dominated by the young stellar population than the other E+As.This dominance can arise either because they have had the most recent or strongest bursts.For the remainder of this paper,we refer to each galaxy by its assigned number.Table1summarizes the basic data offive galaxies:coordinates,redshift, and environment.Throughout this paper,we assume H0=70km s−1Mpc−1,ΩM=0.3,andΩΛ=0.7.We obtained high resolution images of thefive nearby(z∼0.08−0.12)E+A galaxies with the Hubble Space Telescope Wide Field Planetary Camera2(WFPC2).Because our sample is at relatively low redshift (typically z∼0.1,for which0.5′′=∼1kpc),it is possible to study the LCRS sample in ways that are not possible for the more classic E+As discovered in distant clusters.We take advantage of this benefit to obtain spatially-resolved spectroscopy(Norton et al.2001)and sub-kpc imaging here.We observed the sample using the F702W(λeff=6997˚A)and F439W(λeff=4292˚A)filters and obtained three CR-split700s exposures for each object.Stacked images were generated by summing the three individual images for each galaxy andfilter.The pointing was identical for each image,so no shifting or interpolation was required. We rejected CR events by comparing deviant pixels within the stack to a WFPC2noise model.We adopt photometric zero points of the HST/WFPC2from Holtzman et al.(1995)after correcting for the gain=7.0and the nominal infinite aperture.Our values are the same as given in the HST Data Handbook. For the Planetary Camera,F439W and F702W magnitude zero points are20.884and22.428,respectively. We adopt Galactic extinction corrections from Schlegel et al.(1998),assuming an R V=3.1extinction curve.A F702W and A F439W are calculated from the relative extinction table in the Appendix(Schlegel et al.1998). The value for F439W is not available in the Appendix,so we use the extinction appropriate for the LandoltB magnitude.To compare the magnitudes of galaxies within certainfilters across a range of redshifts,or to photometric models,we apply K-corrections.In principle,the K-correction can be calculated by using the spectral energy distribution(SED)of an object with full spectral coverage and high S/N.Unfortunately,flux-calibrated spectra with full spectral coverage and high S/N are not available for our sample.The SEDs of E+As strongly depend both on the stellar mass formed during the starburst and on the time elapsed since the burst. To account for this variation in stellar populations,we examine both extremes—a pure A type and a pure K type stellar spectrum.We use A dwarf and K giant templates from the Gunn-Stryker spectrophotometric atlas(Gunn&Stryker1983),which covers the wavelength range3130to10800˚A.We artificially redshift the template spectra to(1+z)and measure the magnitude differences in the F702W and F439Wfilters using the CALCPHOT routine within the IRAF/SYNPHOT package.In the F702W band the difference between the corrections for the two populations is within∼0.19−0.31magnitudes.In contrast,the difference in thecorrections is larger than0.62magnitudes for F439W because the F439Wfilter band includes the Balmer jump.A slight shift of the spectra can cause a large change in measured brightness.We list both sets of corrections in Table3,but adopt the correction calculated for an A star with the justification that these are the bluest,most A-like,of the E+As in the Zabludoffet al.(1996)sample.Because the K correction is the major source of uncertainty in our error budget,the global photometric quantities,especially colors, possibly harbor significant systematic errors.The sense of any relative colors within a galaxy is not affected, although the numerical values may be.3.Results and DiscussionThe HST images provide a wealth of information on the small and large scale structure of these galaxies. With the goal of understanding the origin of the E+A phenomenon and into what these systems will evolve, we investigate the morphologies of these systems,their color profiles,their location on the Fundamental Plane(Jorgensen et al.1996)of elliptical galaxies,and their relationship to“core”and“power-law”ellipticals (Faber et al.1997).We also discover a population of associated point sources(possibly young star clusters). Finally,we review the implications of our results,obtained for low-redshift E+As,for the identification and study of such systems at higher redshifts.The reader is referred to Tables2-5for a summary of the quantitative results discussed in this section.3.1.Morphologies:First ImpressionsFigure1shows the WFPC2mosaic and PC images of ourfive E+A galaxies at different contrast levels. The full mosaic images(80′′×80′′)are in the left column.The center of each E+A is located in the PC, which is in the upper right corner of each mosaic.Tidal features that extend into the other CCDs are evident in EA1-3.The middle and right columns contain the F702W(24′′×24′′)and F439W(12′′×12′′)PC images, respectively,on a logarithmicflux scale.HST/WFPC2observations are relatively insensitive in the bluer band so that the signal in the F439W images typically extends out only to∼3kpc,25%of the red coverage, and even there it is of low signal-to-noise.Thesefive E+As exhibit a variety of morphologies ranging from a highly complex system(EA1)to what could visually be classified as a barred S0galaxy(EA5),even though they have been uniformly selected using spectroscopic criteria,i.e.,“k+a”type spectra from the LCRS.EA1stands apart from the other four E+As.It is composed of two components that are separated spatially by∼3kpc and another companion with a projected separation of14kpc(assuming the companion is at the redshift of EA1).The association is supported by an asymmetric feature emanating from the companion that could be tidal material and a faint bridge that appears to connect it to EA1.EA2and EA3also exhibit highly disturbed morphologies,although EA3could be visually classified as a normal face-on spiral galaxy in the low contrast PC image.This ambiguity in visual classification is discussed in more detail in§3.8.EA2has tidal tail that extends to at least50kpc.EA4and EA5appear less disturbed,although EA4has somewhat irregular outer isophotes,some lopsidedness(in the F439Wfilter image),and shell-like structures closer to the center that are visible in the PC image.The mechanism or mechanisms responsible for the spectral E+A phenomenon produce a variety of morphologies.Whether all of these systems will evolve into a somewhat more homogeneous population—for example,early-type galaxies—is yet unclear.3.2.Morphologies:Bulge-Disk DecompositionsWhile EA2-5appear to have significant spheroidal components,EA3and EA4,at least,also seem to have aflattened,or perhaps disk-like,morphology.Understanding the fate of these systems requires a quantitative estimate of the relative importance of the dynamically hot and cold stellar components.Measuring the surface brightness profile for asymmetric,disturbed systems is challenging.To mitigate potential systematic problems,we use two different algorithms.First,to obtain photometric parameters,r e andµe,we use the two-dimensional imagefitting algorithm GALFIT(Peng et al.2002)designed to extract structural parameters directly from the galaxy image.GALFIT assumes a two-dimensional model profile for the galaxy.The functional form of the models we choose tofit include combinations of an r1/4-law,a S´e rsic r1/n-law,an exponential disk profile,and a spatially constant sky background.Wefit the following:the (x,y)position of the center,M tot(the total magnitude of the component),r e(the effective radius),n(the S´e rsic index),q(the axis ratio defined as b/a),the major axis position angle,and c(the diskiness/boxiness index,where c>0indicates boxy).This index c plays the same role as the cos4θFourier coefficient term used often in isophote analysis(Rix&Zaritsky1995).As GALFIT explores parameter space,it convolves the model image with a point-spread function(PSF)and compares it to the data for each parameter set.The model PSFs are generated for each galaxy by the TinyTim(Krist&Hook1999)software for the WFPC2. Although convolution is computer intensive,the advantage of the convolution process is that it preserves the noise characteristics of the images and can be applied to low signal-to-noise images.Because GALFIT begins with a very specific,smooth model,which may be a poor representation of such distorted galaxies,we also measure surface brightness profiles using the IRAF/ELLIPSE algorithm. This approach allows the center,major axis position angle,and ellipticity of each ellipse to change,but does not enforce a model radial profile.To accurately recover the surface brightness profiles without recourse to ad hoc models,we applied20iterations of Richardson-Lucy deconvolution(Richardson1972;Lucy1974). Lauer et al.(1998)showed that the WFPC2PSF can depress the brightness profile as far out as0′′.5from the galaxy center.Richardson-Lucy deconvolution allows the intrinsic brightness profile to be recovered to the few percent level down to r∼0′′.05,with adequate exposure levels(S/N∼50in the galaxy center). With reduced S/N and only20deconvolution cycles,the central(r=0)point in the profile may remain slightly-depressed,dependent on the(unknown)intrinsic structure of the galaxy center.Because EA1is too disturbed to be reasonably modeled by a simple disk+bulge model,we restrict our analysis to EA2-5.For each galaxy,wefit three different light distributions:r1/4law,r1/n S´e rsic law,and r1/4+exponential disk law.For EA2,we do notfit the r1/4+exponential disk law model because we might be seeing this galaxy close to edge-on(see the linear residuals in Figure2),and it is hard for GALFIT tofit an edge-on disk with an extended tail.The structural parameters and the reducedχ2ν’s of these three GALFIT models are listed in Tables4and5.With the exception of one case,1<χ2ν<2.These values ofχ2νare somewhat larger than statistically acceptable,due presumably to the presence of asymmetric components, as can be seen in Figure2.Of the three profiles we consider,only the S´e rsic profile has theflexibility to model either a spheroidal or disk-like system by varying the parameter n.Therefore the best-fit value of n can guide our conclusions about the nature of the galaxy.An exponential disk corresponds to a value of n=1,while the classic de Vaucouleurs profile corresponds to n=4.However,the correspondence between disk system,spheroid,andn is not quite this simple—fitting S´e rsic profiles to SDSS galaxies,Blanton et al.(2003)show a peak at n=1corresponding to disky systems,but no peak at n=4.Instead,spheroidal systems show a range of n values.This result is further complicated when one factors in differences in radial rangesfit—for example,fitting the inner slope of cuspy power-law ellipticals(e.g.,Lauer et al.1995)will give a much higher n value than willfits at larger radii.With these caveats in mind,wefind that a single S´e rsic profilefit yields n>5for all our galaxies, demonstrating that the light is dominated by a spheroidal component.Indeed,the high values for n indicate a very high concentration of the light,even more than expected for a classic de Vaucouleurs profile.Such high concentrations are consistent with the idea that central starbursts have raised the central luminosity density(e.g.,Mihos&Hernquist1994).For example,in the case of EA4,masking the inner kpc and refitting the Sersic law results in a value of n=3.6,much more typical of a normal elliptical.This is not always the case,however—in EA3,the high S´e rsic value persists even when the nucleus is masked out.For EA3the fitted value(n=8.7)is unusually high compared to normal ellipticals(e.g.,Kelson et al.2000;Graham et al.2001;Graham2002).An additional complication to the interpretation of thesefits is that,while the light appears to be dominated by a concentrated spheroid,some of the galaxies appear to contain an additional disk-like component that would affect any dynamical model of a merger and its aftermath.To determine whether these galaxies do indeed contain a disk component,we alsofit models with two components.The resulting radial profiles for EA3and4(Figure3)and the significant decrease inχ2ν(an improvement in thefit at the99%confidence level)demonstrate that a pure spheroid model is not the preferred model for these two systems.To avoid the degeneracies present infitting disk and bulge simultaneously,we alsofit single S´e rsic profiles just to the outer parts of the ing the effective radii of the bulges calculated from the two-componentfit,we mask pixels inside a chosen radius,vary that radius to be∼3−5r e and refit a single component.We mark the effective radii and disk scale lengths with circles in Figure2.For EA3,the best-fit S´e rsic indicies are n=2.5,1.6and1.3for masks corresponding to 3r e,4r e,and5r e,respectively.For EA4,we measure n=0.93and0.86when we apply3r e and4r e masks, respectively.In both of these cases,the S´e rsic index beyond several r e is as expected for an exponential disk and thefit spans4to5disk scale lengths.Although we cannot discriminate tidal material from a possible underlying disk,we conclude that in EA3and EA4there is material beyond that described by a spheroid and that it is consistent with an underlying disk.EA3and EA4appear to be sufficiently relaxed that no significant dynamical evolution is expected,so they may become S0’s.We also hypothesize that their progenitors may have included a disk that was significantly heated but not completely destroyed during an intermediate mass ratio merger(e.g.,Naab2000;Bendo&Barnes2000).Even though no disturbed tidal structure is apparent in EA5,the modeling is complicated by the presence of a strong bar-like structure.The presence of a bar-like feature suggests an underlying disk.When viewed at the different contrasts in Figure4,EA5is composed of at least three distinct components,a extended light distribution in outer part(axis ratio q∼0.8),a compact and elliptical bar structure(q∼0.4−0.5), and a very bright blue central nucleus.The three-componentfit gives the S´e rsic index n=1.1for the central nucleus,n=0.5(Gaussian)for the bar,and n=1.5for the outer disk-like region.This three-component S´e rsic profilefit(Figure4)is acceptable and suggests the presence of disk.For mask sizes2.5r e,3r e and 3.5r e,the bestfit S´e rsic indicies n are2.0,1.8,and1.8,respectively.However,unlike for EA3and EA4,we do thisfit in a limited region and cannot conclude that EA5has a distinct exponential disk component.The presence of a bar-like feature also suggests an underlying disk.For the E+As that may contain a disk component,we calculate a bulge-to-total light ratio(B/T)to quantify the relative importance of the bulge and disk-like components.B/T for EA3and EA4is0.56and0.62,respectively.These values are larger than the typical B/T for Sa galaxies(0.45)and comparable to the median for S0’s(0.63;Kent1985).Despite the complications offitting EA5,various modes offitting the galaxy produce B/T∼0.7.Unless the bulge and any underlying disk-like component fade at dramatically different rates,which is unlikely given the relatively weak large-scale population gradients in these galaxies (Norton et al.2001),the descendants of these galaxies must be early type(S0or E,if the disk-like material is tidal debris that disperses or collapses onto the central component).Given the asymmetric features,how reliable are thesefits?There are several ways to check the results for possible systematic errors.First,we compare thefitted analytical profiles to the radial surface brightness profiles obtained from the isophotefitting procedure.In Figure3,we plot the radial surface brightness profiles of a chosen model for each galaxy:r1/4profile for EA2and EA5,r1/4+exponential disk profile for EA3and EA4,and the profiles obtained from the isophotefitting.The differences between the data (ELLIPSE)and models(GALFIT)range mostly between±0.5mag/arcsec2,are not global,and reflect local asymmetric components.Second,we examine the residual images obtained by subtracting the smooth and symmetric models from the data(see Figure2).In all cases we see evidence for components beyond the bulge+disk model.We then calculate how much light remains in the residual images to quantify the goodness of thefit.The relative asymmetric light—excess(deficit)—within a10′′radius is16(8)%, 6(5)%,8(9)%,9(8)%of the symmetric model components for EA2-5,respectively.Most(50%to80%)of the under(over)subtracted light comes from the central region within0.5′′,where the even a small amount of fractional deviation from the data can dominate the residualflux over the outer faint parts.Except for EA2, the global under(over)subtractions are roughly the same and localizedfluctuations dominate the residuals, so we conclude that our globalfits are reliable.In the case with the most residual light(EA2),24%of the light cannot be explained by a symmetric model and the positive residuals dominate all over the galaxy. Therefore,we cannot exclude the possibility that we are looking right along the interaction plane(the tidal debris are quite linear).The point sources near the E+A bulges in the residual images are discussed in§3.7.3.3.Morphologies:Asymmetric ComponentsSo far we havefit symmetric smooth models with moderate success,but have found that asymmetric features are quite common in our sample.Asymmetry,in particular lopsidedness,has been used to measure disturbances in local“normal”disk galaxies(Rix&Zaritsky1995;Zaritsky&Rix1997)and correlates with recent star formation(Zaritsky&Rix1997;Rudnick&Rix1998).There are multiple ways in which one can quantify asymmetry,but here we choose to follow what was done for local spirals by Rix&Zaritsky (1995).This measurement is based on the azimuthal Fourier decomposition of the surface brightness along elliptical isophotes.For the two most disk-like of the E+As(EA3and4),we calculate the Fourier decomposition of the F702W band surface brightness distribution.We use a grid with24azimuthal and36radial bins from semi-major axes of4to200pixels.The center of the azimuthal grid is identified as the brightest central point in the galaxy image.Figure5shows the amplitudes of the variousfirst Fourier terms as a function of radius. Infield spirals,A1>0.2is identified as strong lopsidedness,found in∼20%of the cases,and interpreted as the result of a recent interaction(other explanations,such as halo-induced disk sloshing have since been suggested;e.g.,Levine&Sparke1998;Kornreich et al2002).EA3has A1≪0.2at all radii except in the transition region between the inner spiral arms and the tidal tails at∼3−6kpc and at large radii where the uncertainties are large.Although EA4has large A1within3kpc,which is consistent with the appearance of the residual image(Figure2),A1<0.2for1.5<r d<2.5,the range used in the study offield spirals.Thelopsidedness of EA3and EA4is consistent with that of normal spiral galaxies despite the cataclysmic event that occurred∼Gyr ago indicated by the spectra.This result has two possible interpretations:either these galaxies have had sufficient time to relax and“smooth out”interaction-induced asymmetries(e.g.,Mihos 1995),or they are the result of encounters not strong enough to cause major dynamical damage.Of course, the latter possibility runs into the problem of how to trigger such a massive starburst without dynamically disturbing the galaxy.3.4.Color GradientsThe color gradients of E+As are constraints on merger models and clues as to what these galaxies will ultimately become.In Figure6,we show the F702W−F439W color profiles of EA2-5,which are obtained by using the results from the ELLIPSE task and include the A-type K-correction.Because of the shallow exposure in F439W band,the color profiles are limited to r 2−3kpc,which is only25%of the radial coverage available in the red.To derive the color profiles within the most central region(<0.5′′),we use the deconvolved images.However,because deconvolution can produce large artificialfluctuations in low signal-to-noise data,we cannot use the deconvolved F439W profiles in the outer regions of the galaxy.We compromise by using the deconvolved images for r<0.5′′and the non-deconvolved images for r>0.5′′.The overall colors of E+As are relatively blue globally due to the recent star formation(bottom panel of Figure6).The radial extent of the blue colors confirms previous observations(Franx1993;Caldwell et al.1996;Norton et al.2001)that the recent star formation region is not confined within the innermost regions.However,the color gradients,especially within1kpc of the centers,are as diverse as the overall morphologies.While,EA3and EA5have blue nuclei and become redder going outward,EA2becomes bluer with radius,and EA4shows a relativelyflat profile.The colors are the result of the complicated interplay between age,metallicity and dust.The lack of HI in these systems(Chang et al.2001;Miller&Owen2001)and of any patchiness in the images of EA2-5argue against high levels of dust(but it is still possible that high density pockets of dust are present,particularly toward the nucleus of some of these systems).With the exception of EA1,none of the E+As show the irregular,filamentary structures expected from strong dust lanes.We thus conclude that the variety of color gradients within the inner few hundred parsecs reflects variations of the spatial distribution of the young population,which in some systems appears to be preferentially located near the center of the galaxy and in others appears to avoid the center.Perhaps this reflects differences in the types of encounter involved and its ability to drive true nuclear starbursts—e.g.,differences between prograde and retrograde encounters (Barnes&Hernquist1996),major versus minor mergers(Hernquist&Mihos1995),or differences in the structural properties of the progenitor galaxies(Mihos&Hernquist1996).3.5.Relationship to Fundamental PlaneTo investigate whether E+As can evolve into E/S0galaxies,we compare the stellar kinematics and structural parameters of E+As with“normal”early type galaxies.Norton et al.(2001)found that the old component of E+A galaxies is offset(brighter by∼0.6mag)from the the local Faber-Jackson relation. Using the structural parameters that can only be measured using HST imaging,we extend this comparison to various projections of the Fundamental Plane(hereafter FP)in Figure7.To compare our results with the FP of Jorgensen et al.(1996),we correct these observables to our adopted cosmology(H0=70km s−1Mpc−1,。
小学上册英语第一单元真题试卷(含答案)考试时间：80分钟（总分:140）B卷考试人：_________题号一二三四五总分得分一、综合题(共计100题共100分)1. 填空题：I think it’s important to ________ (保持冷静).2. 填空题：I enjoy watching a _______ (小狐狸) in the wild.3. 选择题：How many players are on a soccer team?A. FiveB. SixC. SevenD. Eleven4. 填空题：A ferret can be quite ______ (顽皮) and energetic.5. 听力题：The core of the Earth is made mostly of ______.6. 听力题：Galaxies are huge systems of stars, gas, and ______.7. 填空题：The ancient Egyptians built _______ to honor their pharaohs. (金字塔)8. 选择题：Who is the main character in "Harry Potter"?A. HermioneB. RonC. HarryD. Draco答案：CWhat is the main ingredient in apple pie?A. ApplesB. PeachesC. BerriesD. Bananas10. 填空题：A _____ (植物活动) can promote environmental awareness.11. ts are _____ (edible) and can be eaten. 填空题：Some pla12. 选择题：Which of these is a type of flower?A. OakB. RoseC. PineD. Maple13. 填空题：________ (草原动物) graze on grasses.14. 听力题：My friend is a ______. He enjoys learning about space.15. 听力题：The capital of Thailand is ________.16. 填空题：The water is ________ (清澈).17. 填空题：The _____ (水獺) plays in the river and slides on the ice.水獺在河里玩耍，并在冰上滑行。
a r X i v :a s t r o -p h /0206243v 1 14 J u n 2002Submitted to The Astrophysical JournalPreprint typeset using L A T E X style emulateapj v.14/09/00LENSING AND THE CENTERS OF DISTANT EARLY-TYPE GALAXIESCharles R.Keeton 1Astronomy and Astrophysics Department,University of Chicago,5640S.Ellis Ave.,Chicago,IL 60637Submitted to The Astrophysical JournalABSTRACTGravitational lensing provides a unique probe of the inner 10–1000pc of distant galaxies (z ∼0.2–1).Lens theory predicts that every strong lens system should have a faint image near the center of the lens galaxy,which should be visible in radio lenses but have not been observed.We study these “core”images using models derived from the stellar distributions in nearby early-type galaxies.We find that realistic galaxies predict a remarkably wide range of core images,with lensing magnifications spanning some six orders of magnitude.More concentrated galaxies produce fainter core images,although not with any simple,quantitative,model independent relation.Some real galaxies have diffuse cores and predict bright core images (magnification µcore 0.1),but more common are galaxies that predict faint core images (µcore 0.001).Thus,stellar mass distributions alone are probably concentrated enough to explain the lack of observed core images,and may require observational sensitivity to improve by an order of magnitude before detections of core images become common.Two-image lenses will tend to have brighter core images than four-image lenses,so they will be the better targets for finding core images and exploiting these tools for studying the central mass distributions of distant galaxies.Subject headings:galaxies:elliptical and lenticular,cD —galaxies:nuclei —galaxies:structure —gravitational lensing1.introductionGalaxy centers are interesting places to study dynamics and galaxy formation.Their short crossing times make them sensitive to dynamical processes such as relaxation and binary black hole heating (e.g.,Ebisuzaki,Makino &Okumura 1991;Milosavljevic &Merritt 2001).Their deep potential wells collect remnants of the galaxy forma-tion process such as the cores of accreted galaxies (e.g.,de Zeeuw &Franx 1991;Barnes &Hernquist 1992).Their dark matter content provides clues to the interaction be-tween baryons and dark matter by adiabatic compression during galaxy formation (e.g.,Blumenthal et al.1986),and may even reveal properties of the dark matter parti-cle such as cross sections for self-interactions (e.g.,Spergel &Steinhardt 2000).Nearby,galaxy centers can be studied directly with high spatial resolution observations.Hubble Space Telescope imaging of early-type galaxies shows that,contrary to the-oretical expectations (e.g.,Tremaine 1997),the luminos-ity profiles diverge at small radii (e.g.,Faber et al.1997;Ravindranath et al.2001;Rest et al.2001).The profiles seem to fall into two classes:“core”galaxies have a dis-tinct transition between a steep outer profile and a shallow inner core that has I ∝R −γwith γ 0.3;while “power law”galaxies show no such break and have steep central cusps with γ 0.5.Interestingly,the global properties of the galaxies seem to correlate well with the centers.Core galaxies tend to be luminous,slowly rotating systems with boxy or elliptical isophotes,while power law galaxies tend to be faint,rapidly rotating systems with disky isophotes.Although the division may not be as sharp as originally thought (see Ravindranath et al.2001;Rest et al.2001),it still puts strong constraints on the formation process.In hierarchical merging scenarios,simple models cannot eas-ily explain why the large galaxies are so much less dense1Hubble Fellowthan their small progenitors (see §7of Faber et al.1997,and references therein),and some additional process such as heating by binary black holes may be required (e.g.,Milosavljevic &Merritt 2001;Milosavljevic et al.2001).For distant galaxies,we cannot directly resolve 10–100parsec scales,but we can instead turn to a unique indi-rect probe offered by gravitational lensing.Lens theory predicts that if the central mass distribution is shallower than ρ∝r −2then any multiply-imaged gravitational lens must have an odd number of images (Burke 1981;Schnei-der,Ehlers &Falco 1992).Standard image configurations 2have two or four bright images lying ∼3–10kpc from the center of the lens galaxy,with the remaining image just 10–100pc from the center and much fainter than the others.Because the “core”image is very sensitive to the central surface density of the lens galaxy,with a higher density corresponding to a fainter image,it offers a unique way to constrain the density on scales that cannot be directly resolved.This probe of galaxy centers can in principle be applied to all lens galaxies,which now number more than 60and are predominantly early-type galaxies spanning the redshift range z ∼0.3–1(e.g.,Kochanek et al.2000).It is conceptually equivalent to using radial arcs to constrain the central profiles of lensing clusters (e.g.,Mellier,Fort &Kneib 1993;Smail et al.1996;Molikawa &Hattori 2001;Oguri,Taruya &Suto 2001).The best observational data on core images come from radio lenses,because the lack of radio emission from most lens galaxies enables sensitive searches for core images.The Cosmic Lens All-Sky Survey found 18radio lenses but no core images,based on radio maps where the dy-2The rare exception is a configuration where the source lies in a naked cusp (e.g.,Schneider et al.1992);among more than 60known lenses,APM 08279+5255is the only candidate naked cusp lens (Lewis et al.2002).The only other exception is B1359+154,a unique lens where three lens galaxies jointly produce six bright im-ages,and models predict three additional core images (Rusin et al.2001).2namic range is typically several tens to several hundreds but reaches1200for B1030+074and2000for B0218+357 (Rusin&Ma2001;Norbury et al.2002).Several other radio lenses have candidate core images(MG1131+0456, Chen&Hewitt1993;PMN J1632-0033,Winn et al.2002) although the hypothesis that the central radioflux origi-nates in the lens galaxy cannot be ruled out.At optical and near-infrared wavelengths,APM08279+5255has an odd number of images(Ibata et al.1999;Egami et al. 2000),but its interpretation is not clear.The third image may be a core image,in which case it indicates a large low-density core in the lens galaxy(Ibata et al.1999;Egami et al.2000;Mu˜n oz,Kochanek&Keeton2001),or it may be a case of a“naked cusp”image configuration,in which case it contains no information about the center of the lens galaxy(Lewis et al.2002).No other optical core im-ages have been seen,although the searches are of course hindered by light from the lens galaxies.The apparent discrepancy between data and theory pro-vides the desired opportunity to learn about the centers of distant galaxies.Motivated both by theoretical expecta-tions(see Tremaine1997)and by ease of use,many anal-yses have assumed models with afinite density core and obtained limits on lens galaxy core radii(e.g.,Narayan, Blandford&Natyananda1984;Narasimha,Subramanian &Chitre1986;Blandford&Kochanek1987;Hinshaw& Krauss1987;Narayan&Schneider1990;Wallington& Narayan1993;Kochanek1996;Evans&Hunter2002). Rusin&Ma(2001)instead used power law models and obtained a lower limit on the power law index,γ>0.8 at90%confidence for a surface densityΣ∝R−γ.The question remained,though,whether these two classes of models were realistic enough to provide robust,model in-dependent conclusions about lens galaxy centers.Mu˜n oz et al.(2001)introduced double power law models where the core region is allowed to have a power law cusp whose index is independent of the density profile at large radii. They found that the lack of a core image in B1933+503 robustly impliesγ 0.6for that one galaxy.Keeton (2001)studied core images statistically using models with cuspy stellar components,treated as generalized Hernquist (1990)models,embedded in dark matter halos.He found that the models were inconsistent with the data,perhaps because generalized Hernquist models may not accurately represent the stellar components of galaxies on10–100pc scales.The goal of this paper is to reconsider the core image problem using more realistic models derived from nearby galaxies,and more generally to discuss using core images as tools for studying the centers of distant(z∼0.3–1) galaxies.Nearby early-type galaxies have surface bright-nesses that can be modeled as a Nuker law(Lauer et al. 1996;Byun et al.1996),and in§2we discuss lensing by such galaxies.In§3we consider in a general way what physical properties of lens galaxies determine core images properties,or conversely what we can learn about lens galaxies by studying core images.In§4we study in de-tail the core images predicted by a sample of realistic lens galaxies.Finally,in§5we offer a summary and conclu-sions.We assume the popularΛCDM cosmology with matter densityΩM=0.3,cosmological constantΩΛ=0.7, and Hubble constant H0=75km s−1Mpc−1.2.nuker law lensesThe lensing properties of a galaxy with projected mass densityΣare given by the lensing potentialφthat satis-fies the two-dimensional Poisson equation∇2φ=2Σ/Σcr. HereΣcr=(c2D os)/(4πGD ol D os)is the critical surface density for lensing,where D ol,D os,and D ls are angular diameter distances between the observer(“o”),the lens (“l”),and the source(“s”).We consider afiducial lens-ing situation with a lens galaxy at redshift z l=0.5and a source at redshift z s=2,which yields a critical density of Σcr=2230M⊙pc−2for our adoptedΛCDM cosmology. The lensing deflection is given byα=∇φ,and the mag-nification depends on the second derivatives ofφ.See the book by Schneider et al.(1992)for a full discussion of lens theory.Because lensing selects galaxies by mass,the sample of observed lens galaxies is dominated by early-type galaxies. In many nearby early-type galaxies the surface brightness distribution is well described by a Nuker law(Lauer et al. 1995;Byun et al.1996),I(R)=2(β−γ)/αI b R r b α (γ−β)/α,(1) whereγandβare the inner and outer power law indices, respectively,r b is the radius where the break in the power law occurs,αgives the sharpness of the break,and I b is the surface brightness at the break radius.If the luminosity distribution has circular symmetry and the mass-to-light ratio isΥ,the lensing deflection isαgal(R)=21+(β−γ)/αr b1−γ(2)×2F1 2−γα,1+2−γr b α ,whereκb=ΥI b/Σcr is the surface mass density at the break radius in units of the critical density for lensing, and2F1is the hypergeometric function.If the stellar dis-tribution has ellipsoidal symmetry,the lensing deflection must be computed numerically using the formalism given by,e.g.,Schramm(1990).Most galaxies contain central,supermassive black holes (e.g.,Magorrian et al.1998),so we consider adding them to the model.The deflection from a black hole isαbh(R)= R2E/R where the black hole’s Einstein radius is(in angular units)R E= 4GM•D ol D os 1/2.(3)We normalize the black holes using the observed corre-lation between the black hole mass M•and the velocity dispersionσof the parent galaxy(Gebhardt et al.2000; Merritt&Ferrarese2001).The net deflection is simply the sum of the deflections from the Nuker component and the black hole.As an example we consider the nearby galaxy NGC4486, which has Nuker parametersα=2.82,β=1.39,and γ=0.25and is a fairly typical(albeit massive)exam-ple of the early-type galaxies in the sample studied by Faber et al.(1997).We imagine a lens galaxy obtained by moving NGC4486to a typical lens redshift z l=0.5. The deflection profileα(R)for the resulting lens is shown3Fig. 1.—The deflection profile for a mock lens galaxy obtained by taking the nearby galaxy NGC4486and moving it to redshift z l =0.5.The vertical dotted line indicates the Nuker break radius r b .The dots mark the critical radii R ein and R rad .The top panel shows the result for the Nuker galaxy alone,while the bottom panel adds a central black hole normalized by the M •–σrelation from Gebhardt et al.(2000).The mean core image magnification µcore is computed with the method presented in §3.in Fig.1.The asymptotic behavior is α(R )∝R 1−γfor R ≪r b (if there is no black hole),and α(R )∝R 1−βfor R ≫r b .Typical galaxies have γ<1and β>1,so the deflection is zero at the origin,rises to some finite peak,then slowly declines.There are two important radii cor-responding to the “critical curves,”or curves along which the lensing magnification is infinite.The tangential crit-ical curve lies at the Einstein radius R ein ,which is the solution to α(R ein )=R ein .The radial critical curve lies at the radius R rad which is the solution to dα/dR =1.The radial critical curve maps to a caustic atu max =α(R rad )−R rad .(4)This caustic bounds the multiply-imaged region;sources with u <u max are multiply-imaged,while sources with u >u max are not.The core images are always contained in the region bounded by the radial critical curve.The radii R ein and R rad are marked in Fig.1.If the galaxy has a steep central cusp with γ>1,the deflection diverges at the origin and is a monotonically decreasing function of radius.In this case,the radial crit-ical curve does not exist and the lens never produces a core image.If the galaxy contains a central black hole,the black hole causes the deflection to diverge at the ori-gin and suppresses some of the core images (Mao,Witt &Koopmans 2001).However,the black hole changes the deflection only at very small radii,so it has little effect on the critical radii R ein and R rad or on the mean core image magnification µcore (see Fig.1).Adding a dark matter halo to the lens galaxy would raise the outer deflection profile and make it approximately flat,but it would have little effect on the central deflection profile that determines the properties of the core images unless it were muchmoreFig. 2.—Cumulative distributions of magnification factors for the core images predicted by the NGC4486mock lens galaxy.(a)Total distributions plotted for a circular (solid line)or flattened (dashed line)lens galaxy.(b)Distributions plotted separately for lenses with two or four bright images (doubles or quads),for a lens galaxy with ellipticity e =0.5.There is more statistical uncertainty in the curve for quads than for doubles,because of the 7917random source positions we examined only 238of them corresponded to quads.centrally concentrated than the light.To characterize the core images expected in this lens,we study the core image magnification distribution.The dis-tribution can be computed fairly rapidly using inverse ray shooting (e.g.,Kayser,Refsdal &Stabell 1986;Wambs-ganss 1997).Fig.2a shows the distribution for circular and flattened lens galaxies.The distribution is broad,span-ning more than two orders of magnitude,with a median value µcore =0.0019and a mean value µcore =0.0053for the circular case.Making the galaxy flattened shifts the magnification distribution to higher values;but even for ellipticity e =0.5the shift is only 0.05dex,so the core image magnification distribution is largely insensitive to ellipticity in the lens galaxy.(We would see more of an ef-fect if we described core images by their flux ratio relative to the bright images,µcore /µbright ,because µbright is quite sensitive to ellipticity.)Ellipticity is important in one respect.If the lens galaxy is non-spherical,some source positions correspond to lenses with two bright images (doubles),while others correspond to lenses with four bright images (quads).(See,e.g.,Schnei-der et al.1992.)Fig.2b shows the core image magnifica-tion distributions for quads and doubles separately.Be-cause the source lie closer to the origin for quads than for doubles,and the core image magnification increases with the distance of the source from the origin,quads tend to have smaller core image magnifications than doubles.The quantitative details depend on the ellipticity,on any exter-nal tidal perturbation (shear)that may affect the lens,and on the stellar profile of the galaxy,but the general result is robust:quads to tend have smaller µcore than doubles.The ellipticity effect combines with an observational se-4lection effect.Quads generally have larger total magnifi-cations than doubles,so the sources in quads tend to be intrinsically fainter than the sources in doubles.Together, their fainter sources and smaller core image magnifications suggest that quads will tend to have fainter core images than doubles.The lack of core images in observed quads should therefore be less surprising than in doubles.Con-versely,doubles should be better systems than quads for searching for core images.Thus,while ellipticity in the lens galaxy is important in understanding differences between quads and doubles, it is not very important in the overall distribution of core image magnifications.In the remainder of the paper we therefore neglect ellipticity and use circular lens galaxies.3.what do core images probe?In order to derive meaningful conclusions from observa-tional constraints on core images,it is important to under-stand how core images depend on the physical properties of lens galaxies.(Merely understanding the parameter de-pendencies in parametric lens models does not allow strong physical conclusions.)Although the full distributions of core images predicted for a particular lens galaxy must be computed numerically,the mean magnification µcore can be studied analytically.Moreover,in§4we argue that this quantity is actually a good way to characterize the distri-bution.Hence,in this section we study µcore in general terms.Formally,we haveµcore = multµcore(u)d umult d u.(6)Thefirst line is simply the definition of the average,where the integral extends over the multiply-imaged region of the source plane.In the second line,the integral in the numerator extends over the“core”region in the image plane,defined to be the region within the radial critical curve;this equality holds becauseµcore=|∂x/∂u|is the Jacobian of the transformation between the source and image planes.In words,eq.(6)says that the mean core image magnification is equal to the area within the radial critical curve divided by the lensing cross section(the area of the multiply-imaged region in the source plane).For circularly symmetric lenses,µcore =(R rad/u max)2.(7) For non-circular lenses,Fig.2suggests that this is still a good approximation,because theµcore distribution is not terribly sensitive to ellipticity.These relations werefirst given by Keeton(2001).Now we focus on circularly symmetric lenses.Given the definition of u max from eq.(4),we can write eq.(7)asµcore =[α(R rad)/R rad−1]−2,(8)=( κ Rrad−1)−2,(9) where κ R is the mean surface density within radius R, in units of the critical density for lensing.The second equality holds because by the definition of the deflection,α(R)R2 R0ξκ(ξ)dξ= κ R.(10)Alternatively,returning to eq.(8)and using the identitiesα(R)dR=2κ(R),(11)dα4[κ(R rad)−1]−2.(13) Eqs.(9)and(13)indicate that the mean core image mag-nification is given very simply from either the surface mass density at the radial critical curve R rad or the mean surface mass density within R rad.What remains is to understand what physical proper-ties of the galaxy determine the radial critical curve R rad. Equating eqs.(9)and(13),wefind that R rad is the solu-tion to2κ(R rad)= κ Rrad+1.(14) This relation implies that the radial critical curve is related to the concentration of galaxy’s(projected)mass distri-bution.We expectκ(R)to be a decreasing function,so κ R≥κ(R)for all R.Ifκ(R)is steep(the mass is con-centrated),then κ is large and we must go to largeκ(small R)to satisfy eq.(14);eq.(13)then implies faint core images.3Conversely,ifκ(R)is shallow then eq.(14) is satisfied at smallerκ(larger R),and the core images are brighter.These results can be demonstrated with two simple ex-amples.First,consider a softened isothermal sphere with surface mass densityκ(R)=(b/2)(s2+R2)−1/2,where s is a core radius and b is a scale radius that equals the Einstein radius in the case s=0.The critical radii and mean core image magnification areR ein=[b(b−2s)]1/2,(15)R rad=14(ξ+ζ)1/2(ξ−3ζ)3/2,(17) µcore = 2ζγ−12.(21)Increasingγ(making the profile steeper)decreases µcore . These expressions are valid only for1<γ<2,because forγ>2the density profile is so steep that the radial 3This result also explains how adding a central black hole affects the mean core image magnification.The black hole suppresses some core images,reducing µcore (Mao et al.2001).In the language of our analysis,the black hole increases κ R without changingκ(R), so we must move to largerκ(smaller R)to keep eq.(14)satisfied.5 critical curve does not exist and the model does not pro-duce core images.Previous studies used models like theseto understand the inverse relation between the brightnessof core images and the concentration of the lens galaxy,but eqs.(13)and(14)now give it in a general,modelindependent form.4.core images in realistic galaxies4.1.The sampleTo understand core images in realistic galaxies,we studymodels constructed from a sample of observed galaxies.This approach ensures that we examine the region of pa-rameter space occupied by real systems.We seek galaxieswith well resolved luminosity profiles,plus measured ve-locity dispersions as mass indicators.Faber et al.(1997),Carollo et al.(1997),Carollo&Stiavelli(1998),and Ravin-dranath(2001)have published samples of nearby early-type galaxies observed with high-resolution Hubble SpaceTelescope imaging at optical or near-infrared wavelengths.4Together the samples comprise73distinct galaxies with both Nuker lawfits and velocity dispersions,which are summarized in Table1.The different samples use differ-ent passbands:V for the Faber sample,H for the Ravin-dranath sample,and V and I for the Carollo sample.How-ever,we can check for wavelength dependence and other systematic effects because some of the galaxies appear in more than one sample:six galaxies in both the Faber and Ravindranath samples,five galaxies in both the Faber and Carollo samples,six galaxies in both the Ravindranath and Carollo samples,and ten galaxies with multiple passbands in the Carollo sample.(No galaxies appear in all three samples.)We use this sample to construct mock lens galaxies by moving each galaxy to a typical lens redshift z l=0.5, and assuming a typical source redshift z s=2.Following Faber et al.(1997),we compute the mass-to-light ratio for each galaxy using a spherical and isotropic dynami-cal model.Faber et al.(1997)give mass-to-light ratios for their sample,providing a check for our calculations. We then compute the lensing properties of the mock lens galaxies,which are summarized in Table1.As discussed in§2we focus on circularly symmetric galaxies because ellipticity has little effect on the over-all distribution of core image magnifications.We consider only the Nuker components of the galaxies,neglecting any nuclear components that may be indicated byfits to the surface brightness distribution.This is a conservative ap-proach to our problem,because any additional mass con-centration would decrease the predicted core image mag-nifications and bring the models closer to agreement with the data.We also neglect dark matter halos.Dark matter does not appear to be dynamically important in the inner 5–10kpc of elliptical galaxies(e.g.,Gerhard et al.2001). While it is important for lensing(because lensing depends on the projected mass;e.g.,Treu&Koopmans2002),dark matter would have little effect on the projected mass distri-butions on the 200pc scales important for core images unless it were substantially more concentrated than the light.We can check that our mock lenses are reasonable in sev-4Rest et al.(2001)give a similar sample,but without velocity dis-persions.Fig. 3.—Relation between the velocity dispersionσand Einstein radius R ein for the mock lens galaxies.Crosses and boxes indicate galaxies in the Faber and Ravindranath samples,respectively.The dotted line shows the relation R ein∝σ2;thefitted zero point is −4.84(in log units),compared with a predicted value of−4.74for comparable Singular Isothermal Spheres.eral ways.First,we compute the Einstein radius for each galaxy and compare it to the velocity dispersion in Fig.3; this tests whether the lensing and dynamical masses are consistent.For comparison,a simple Singular Isothermal Sphere(SIS)lens has the scaling R ein∝σ2,with a zero point of−4.74(in log units)for z l=0.5and z s=2in our adoptedΛCDM cosmology(see Schneider et al.1992). The mock galaxies are consistent with this scaling and a fitted zero point of−4.84,although with a scatter of0.16 dex.The fact that the mock galaxies lie on average0.1 dex below the expected SIS relation may be related to our neglect of dark matter halos.Still,the dynamical and lensing properties are related in a sensible way suggesting that the mock lens galaxies are not unreasonable.As a second check,we consider the galaxies that ap-pear in more than one of the original samples.For ex-ample,for each galaxy that was observed and modeled by both Faber et al.(1997)and Ravindranath et al.(2001), we compute the lensing properties using both models and compare them.In this way we test whether the use of dif-ferent modeling techniques and different passbands affects our lensing results.Fig.4compares the Einstein radii and mean core image magnifications for all of the duplicate galaxies.There is fair agreement in the Einstein radii, although with some scatter because different studiesfind somewhat different values of the outer slopeβ;the main outlier is NGC524,where dust is known to affect the lu-minosity profile at optical wavelengths(Lauer et al.1995; Ravindranath et al.2001).There is good agreement in the mean core image magnification,so our conclusions about the properties of core images are not sensitive to whose data we use.For the remainder of the paper,we adopt as our main sample all of the Ravindranath galaxies plus the Faber galaxies that are not in the Ravindranath sample.6Fig. 4.—A comparison of the Einstein radii (top)and mean core image magnifications (bottom)for galaxies that appear in more than one of the original samples.Filled boxes indicate galaxies in both the Faber and Ravindranath samples,open boxes the Faber and Carollo samples,and crosses the Ravindranath and Carollo samples.Open circles indicate galaxies in both the V-band and I-band Carollo samples.4.2.A plethora of core imagesFig.5a shows the core image magnification distributions for nine of the mock lens galaxies to illustrate the range of effects.Each mock lens galaxy has a distribution of core image magnifications that spans some two orders of magnitude,and the complete set of mock lenses spans six orders of magnitude in µcore .Realistic lens galaxies predict a remarkably wide range of core images.Studying the full µcore distribution for each mock lens galaxy is impractical,so we would like to describeeachFig. 5.—Cumulative core image magnification distributions for nine of the mock lens galaxies:the three with the lowest non-zero values for µcore (dotted lines;NGC221,NGC3377,NGC4621);the three with values for µcore at the median of the sample (solid lines;NGC4570,NGC5982,NGC4649);and the three with the largest val-ues for µcore (dashed lines;NGC4239,NGC6166,NGC5273).(a)Distributions of the core image magnification µcore .(b)Distribu-tions of the normalized magnification µcore / µcore .galaxy by a single characteristic quantity.We propose to use the mean core image magnification µcore as a good characteristic value,partly because this quantity is easy to compute (see §3),and partly because Fig.5b sug-gests that it is indeed characteristic of the overall distribu-tion.Specifically,when plotted in terms of the normalized quantity µcore / µcore the distributions for a wide range of galaxies all lie on top of each other.Although there are differences in the shapes of the distributions at the faint end,the distributions at the bright end are remarkably similar.Hence,we believe that µcore is a useful charac-terization of the distribution of core image magnifications for a particular galaxy,especially at the bright end.Fig.6shows a histogram of the µcore values for the 73mock lens galaxies.(The values are given in Table 1.)Note that the histogram is intended only to show the broad range of core image properties in our sample;it should not be interpreted as a global distribution of µcore values,because our sample is not a statistical sample of galaxies.Still,the histogram is instructive in illustrating that the mean values µcore span more than four orders of magnitude,from µcore =1.8×10−5for NGC221to µcore =0.19for NGC5273—plus two galaxies that never produce core images (NGC1172and NGC4742).Again we see the wide range of core image properties in realistic lens galaxies;some lenses should have bright,detectable core images,while others should have core images that are es-sentially invisible.In principle the central supermassive black holes that are common in galaxies can suppress core images (Mao et al.2001),but in practice they have little effect.Table 1gives the values for µcore when the galaxies contain black holes。
a rXiv:as tr o-ph/96155v214Oct1997THE CENTERS OF EARLY-TYPE GALAXIES WITH HST .IV.CENTRAL PARAMETER RELATIONS 1S.M.F aber UCO/Lick Observatory,Board of Studies in Astronomy and Astrophysics,University of California,Santa Cruz,CA 95064Electronic mail:faber@ Scott Tremaine CIAR Cosmology and Gravity Program,Canadian Institute for Theoretical Astrophysics University of Toronto,60St.George St.,Toronto M5S 3H8,Canada Electronic mail:tremaine@cita.utoronto.ca Edward A.Ajhar Kitt Peak National Observatory,National Optical Astronomy Observatories 2,P.O.Box 26732,Tucson,AZ 85726Electronic mail:ajhar@ Yong-Ik Byun 3Institute for Astronomy,University of Hawaii,2680Woodlawn Dr.,Honolulu,HI 96822Electronic mail:byun@.tw Alan Dressler The Observatories of the Carnegie Institution,813Santa Barbara St.,Pasadena,CA 91101Electronic mail:dressler@ Karl Gebhardt 4Department of Astronomy,University of Michigan,Ann Arbor,MI 48109Electronic mail:gebhardt@ Carl Grillmair 5UCO/Lick Observatory,Board of Studies in Astronomy and Astrophysics,University of California,Santa Cruz,CA 95064Electronic mail:carl@John KormendyInstitute for Astronomy,University of Hawaii,2680Woodlawn Dr.,Honolulu,HI96822 Electronic mail:kormendy@Tod uerKitt Peak National Observatory,National Optical Astronomy Observatories2,P.O.Box26732,Tucson,AZ85726Electronic mail:lauer@Douglas RichstoneDepartment of Astronomy,University of Michigan,Ann Arbor,MI48109Electronic mail:dor@Received;RevisedABSTRACTWe analyze Hubble Space Telescope surface-brightness profiles of61elliptical galaxies and spiral bulges(hereafter“hot”galaxies).The profiles are parameterized by break radius r b and break surface brightness I b.These are combined with central velocity dispersions, total luminosities,rotation velocities,and isophote shapes to explore correlations among central and global properties.Luminous hot galaxies(M V<−22)have cuspy cores with steep outer power-law profiles that break at r≈r b to shallow inner profiles I∝r−γwithγ≤0.3.Break radii and core luminosities for these objects are approximately proportional to effective radii and total luminosities.Scaling relations are presented for several core parameters as a function of total luminosity.Cores follow a fundamental plane that parallels the global fundamental plane for hot galaxies but is30%thicker.Some of this extra thickness may be due to the effect of massive black holes(BHs)on central velocity dispersions.Faint hot galaxies(M V>−20.5)show steep,largely featureless power-law profiles that lack cores.Measured values of r b and I b for these galaxies are limits only.At a limiting radius of10pc,the centers of power-law galaxies are up to 1000times denser in mass and luminosity than the cores of large galaxies.At intermediate magnitudes(−22<M V<−20.5),core and power-law galaxies coexist,and there is a range in r b at a given luminosity of at least two orders of magnitude.Here,central properties correlate strongly with global rotation and shape:core galaxies tend to be boxy and slowly rotating,whereas power-law galaxies tend to be disky and rapidly rotating.A search for inner disks was conducted to test a claim in the literature,based on a smaller sample,that power laws originate from edge-on stellar disks.Wefind only limited evidence for such disks and believe that the difference between core and power-law profiles reflects a real difference in the spatial distribution of the luminous spheroidal component of the galaxy. The dense power-law centers of disky,rotating galaxies are consistent with their formation in gas-rich mergers.The parallel proposition,that cores are the by-products of gas-free stellar mergers,is less compelling for at least two reasons:(1)dissipationless hierarchical clustering does not appear to produce core profiles like those seen;(2)core galaxies accrete small,dense,gas-free galaxies at a rate sufficient tofill in their low-density cores if the satellites survived and sank to the center(whether the satellites survive is still an open question).An alternative model for core formation involves the orbital decay of massive black holes(BHs)that are accreted in mergers:the decaying BHs may heat and eject stars from the center,eroding a power law if any exists and scouring out a core.An average BH mass per spheroid of0.002times the stellar mass yields cores in fair agreement with observed cores and is consistent with the energetics of AGNs and the kinematic detection of BHs in nearby galaxies.An unresolved issue is why power-law galaxies also do not have cores if this process operates in all hot galaxies.1.INTRODUCTIONThe Hubble Space Telescope(HST)allows us to study the centers of nearby galaxies with a resolution of a few parsecs.The centers of galaxies are interesting for several reasons: (1)some galaxy centers harbor AGNs and QSOs;(2)many or most galaxy centers may contain massive black holes that are the remnants of dead QSOs;(3)dynamical processes such as relaxation are more rapid near galaxy centers than elsewhere in the galaxy;thus interesting dynamical phenomena are likely to occurfirst near the center;(4)galaxy centers are to galactic astronomy as middens are to archaeologists:centers are the bottoms of potential wells and debris such as gas and dense stellar systems settle there,providing a record of the past history of the galaxy.The systematic properties of the centers of ellipticals and spiral bulges(hereafter “hot galaxies”)were described by Lauer(1983,1985a)and Kormendy(1982a,1984,1985, 1987a,b).They detected inner regions in many galaxies where the slope of the surface-brightness profileflattens out,which they termed cores.They measured the size and surface brightness of these cores and demonstrated central parameter relations that linked core properties with one another and with global properties such as luminosity and effective radius.In particular,cores in brighter galaxies were larger and of lower density.The most recent version of the central parameter relations using ground-based data was presented by Kormendy and McClure(1993).A major goal of this paper is to revisit the central parameter relations using new HST data on61galaxies.We shall show that HST broadly supports the ground-based scaling relations but elaborates upon them in important ways.Historically,the existence of cores in hot galaxies has been accepted as“normal”—probably because familiar dynamical models for galaxies such as the isothermal sphere and King models possess cores.In the absence of a central compact mass,it is plausible that all physical variables should vary smoothly near the origin and hence be expandable in a Taylor series with only even powers of r.In particular,the surface brightness may be writtenI(r)=I0+I1r2+O(r4),(1) where r is projected ing the conventional definition of core radius,a galaxy satisfying Eq.(1)would exhibit a core of radius r c such that I(r c)=1So far,cores have been found only in luminous ellipticals.The division between core and non-core galaxies is fairly sharp.Surface-brightness profiles eitherflatten out to form cores or continue to rise steeply into the resolution limit—few galaxies are in between (Kormendy et al.1994;Jaffe et al.1994;Paper I;Kormendy et al.1996a).Statistical analysis of non-parametrically derived space density profiles indicates the existence of two groups(core and non-core)at the90%confidence level(Paper III).Paper I introduced the term power laws to describe the steeply rising,featureless profiles that lack cores.5It is possible that the power-law category as we have drawn it may be oversimplified:At present the category contains a number of low-luminosity galaxies whose upper limits on core size are larger than those predicted by extrapolation of the core-luminosity relationship defined by brighter galaxies.In other words,some of the low-luminosity power-law galaxies may really be part of a core sequence extending to lower luminosity.Recent WFPC2images in fact show tiny cores in a few power-law galaxies(Lauer et al.1997).Nevertheless,the upper limits on core size for brighter power-law galaxies are already well below the core sequence for galaxies of similar luminosity,and thus clearly differentiate them.Future results may compel some revision of the power-law category,but the present simple core/power-law division is a useful working hypothesis.Lauer(1985a)emphasized that the central properties of hot galaxies do not correlate perfectly with total luminosity and sought an explanation in terms of a second parame-ter.The present data suggest that this second parameter is related to global rotation and isophote shape.So far,cores have been found only in luminous,slowly rotating ellipticals with boxy isophotes6,while power laws are found in faint,rapidly rotating galaxies with disky isophotes.A link between central profile type and global shape/rotation was sug-gested by Nieto et al.(1991a)based on ground-based images,and further evidence was presented by Jaffe et al.(1994)and Ferrarese et al.(1994)based on HST images of14Virgo galaxies.The present database is considerably larger and permits a critical examination of this link and its relation to hot galaxy formation.Our point of view differs importantly from that of Jaffe et al.,who ascribe many of the differences between the two profile types to inclination effects connected with a small inner disk seen either face-on or edge-on. In contrast,we—like Nieto et al.—believe that the spheroidal light distributions are intrinsically different in the two types and would look the same from any viewing angle. These differences in viewpoint are discussed in Section5and Appendix A.The results we have described raise several theoretical issues:why are there two types of profile and how did each type form?Why do the two types have different global rotation and shape?Why are cores non-analytic?And what do central profiles tell us about hot galaxy formation and evolution?The second,more speculative,part of this paper addresses these issues.We suggest in Section7that the power-law profiles of disky galaxies indicate dissipation and are therefore consistent with formation in gas-rich mergers.The parallel suggestion—that the cores ofboxy galaxies are the by-products of purely stellar,gas-poor mergers—is more problematic. For example,luminous core galaxies are expected to accrete small dense satellites.The rate of such accretions appears sufficient to graduallyfill in all low-density cores if such satellites survived and sank to the center.An unresolved issue is whether the satellites do survive,and thus whether some other process is needed to defend low-density cores against in-fill.Even if the data do notfirmly require such a mechanism,there is strong and growing evidence for a widespread population of massive central black holes(BHs)in hot galaxies (Kormendy&Richstone1995).The presence of these objects must be taken into account in standard merger-based models for forming hot galaxies(Section8).The BHs associated with the merging galaxies form binaries whose orbits then decay.The orbital decay heats the surrounding stars,erodes a power law if one exists,and scours out a core.Accreted satellites will also tend to be ripped apart,thus preventing core in-fill.BHs with plausible masses(as estimated in Appendix B)seem able to produce cores of roughly the right size and scaling versus galaxy luminosity.In this way,the presence of central BHs might “rescue”the dissipationless,gas-poor model for cores and boxy galaxies.However,models of core formation based purely on massive BHs leave several questions open,notably how power-law profiles escape similar disruption.Whether or not these speculations about galaxy formation are correct,the updated relations between central and global galaxy parameters that are presented in this paper appear to provide important new constraints on hot galaxy formation.2.CENTRAL PROFILE TYPESMajor collections of HST central profiles include Crane et al.(1993),Jaffe et al.(1994), Forbes et al.(1995),and Paper I.An assortment of representative surface-brightness profiles of55ellipticals and spiral bulges is given in Fig. 1.The following summary is based on the data and discussion in Paper I.We distinguish two types of hot galaxy:(1)Core galaxies have“broken”power-law surface-brightness profiles that change slopesignificantly at a“break radius”r b.To identify a galaxy as having a core,we re-quire that the absolute value of the inner logarithmic slope,γ≡−d log I/d log r,be shallower than0.3.Nearly all core galaxies appear to haveγ>0,which indicatesa cusp in the central surface brightness and an even stronger cusp in the luminositydensity.Paper III concluded that,even with errors taken into account,only2out of 15known core galaxies could admit an analytic core(γ=0).Core galaxies as a class are luminous objects with M V<∼−20.5(H0=80km s−1Mpc−1).They range from brightest cluster galaxies down to the intermediate-massfield elliptical NGC3379.(2)Power-law galaxies show fairly steep surface-brightness profiles with no significantbreak within10′′(at Virgo).Their average surface-brightness slope isγ≃0.8±0.3 at the smallest resolvable radius.Power-law galaxies are generally fainter than core galaxies(M V>−22),but their luminosity densities at10pc are10–1000times higher than those of cores(Paper I).Profile shapes within0′′.1are generally not known,though recent WFPC2images suggest small cores inside some power laws.Power-law galaxies include M32(NGC221),small Virgo ellipticals,and bulges of disk galaxies.Both profile types are wellfit by the following equation(the“Nuker”law,Papers I and II):I(r)=I b2(β−γ)/α r b r b α (γ−β)/α.(2)The asymptotic logarithmic slope inside r b is−γ,the asymptotic outer slope is−β,and the parameterαparameterizes the sharpness of the break.The break radius r b is the point of maximum curvature in log-log coordinates.“Break surface brightness,”I b,is the surface brightness at r b.Equation(2)is intended tofit only over radii accessible to the HST Planetary Camera,i.e.,<10′′.For typicalfitted values ofβ,there must be a further turndown in the profile at larger radii for the total luminosity to befinite.Nuclei are identified when excess light above the prediction of Eq.(2)is visible within the inner few tenths of an arcsec.Nuclei with varying degrees of prominence are illustrated in Paper I(Fig.14).Objects with prominent nuclei are always systems of low luminosity and are probably nucleated dSph or dE galaxies.Nuclei are assumed to be star clusters (or possibly unresolved tiny stellar disks),but direct spectral confirmation is often lacking.A stellar nucleus in NGC3115has been resolved in recent WFPC2images(Kormendy et al.1996b).Non-thermal central point sources exist in four galaxies in our sample:M87 (NGC4486),NGC6166,Abell2052(Paper I)and NGC4594(Kormendy et al.1996c). We call these AGNs to distinguish them from nuclei.So far,no nuclei(as opposed to AGNs)have been found within cores(Kormendy&Djorgovski1989;Paper I).Resolution plays an important role in classifying profiles and estimating central prop-erties.This is illustrated in Fig.2,which shows M31(NGC224)and M32(NGC221)as seen at their actual distances and as they would be seen24times further away just beyond Virgo(for future reference,we call these artificially positioned galaxies M31-in-Virgo and M32-in-Virgo).Up close,M31shows a two-component profile that is clearly divided into a bulge and a nucleus,the latter showing a small core.The entire profile shows too much substructure tofit comfortably into either the core or power-law category.In contrast, M31-in-Virgo shows only a trace of a nucleus,and its profile and degree of nucleation are similar to those of several other galaxies that we have classed as power laws(see Fig. 14in Paper I for a collection of power laws with varying degrees of nucleation).M31 implies that many power-law galaxies,particularly those with hints of nuclei,may contain significant substructure,including nuclei and tiny cores.M32is similarly ambiguous.Seen up close,M32’s profile in Fig.2breaks from a power law near0′′.5,curving gently downward into the resolution limit.M32-in-Virgo shows a nearly perfect power law with only a small bend at the equivalent nearby radius of 70′′.Thus M32does notfit Eq.(2)very well either,because of multiple breaks that yield different values of r b depending on what portion of the profile isfitted.M32shows that values of r b in power-law galaxies are not robust and that similar breaks at small radii could exist in other distant power-law galaxies,even those that apparently show clean power laws at the present resolution.Because thefitted values of r b in power-law galaxies are less robust than those for core profiles,which reflect real features,we regard them as less fundamental.As explained below,we treat thefitted values of r b differently in analyzing the two types of galaxy.3.GALAXY SAMPLE AND DATABASEThe database used in this paper is contained in Tables1,2,and3.A brief overview is given here,and additional details are provided in the table notes.The heart of the sample consists of42normal ellipticals and bulges taken from Paper I(NGC4150,NGC4826,and NGC5322were excluded due to strong nuclear dust).To these were added images of14 E’s and bulges from the WFPC1GTO programs(some unpublished).Five more normal E’s,mostly Virgo galaxies from Jaffe et al.,were located in the HST public archive as of June1993,for a total of61galaxies.The original GO/GTO program and references to published HST profiles are listed in Table1.All images were taken using the Planetary Camera in Cycles1and2and consequently suffer spherical aberration.They were observed throughfilter F555W,which approximates the V band,and usually have a peak signal of ≥104photons in the central pixel.All images were processed as described in Paper I and deconvolved with the same Lucy-Richardson procedure used there.Power-law galaxies with identified nuclei are divided into two types:“moderately”and “severely”nucleated,indicated in Table1by“+”and“++”.M31-in-Virgo is adopted as the dividing line between the two types(cf.Fig.2here and Fig.14of Paper I).In severely nucleated galaxies and in galaxies with AGNs,fits to the nuker law ignore the innermost pixels affected by the nuclear light.Table1presents observed quantities such as Hubble type,distance,magnitude,color, and nuker-law parameters from Paper II.A few galaxies not treated in Paper II have been similarlyfit and the results are given here.M31and M32appear twice,as seen nearby and near Virgo(labeled with a“V”).For core-type profiles,we accept the nuker-lawfits as given forθb andµb.7For power-law galaxies,no core is resolved,and we use the separate upper limits on core size and surface brightness provided by Paper I.These limits(forpower laws only)are calledθlimb andµlimbin Table1.For a few power-law galaxies notcontained in Paper I,these limits were obtained from a visual estimate of the steepness of the innermost part of the profile.The distance to each galaxy(in km s−1)has been estimated using a variety of methods as summarized in the notes to Table1,and the adopted value and its conversion to Mpc (based on H0=80km s−1Mpc−1)are given there.These distances are used to convert the apparent quantities in Table1to absolute quantities in Table2.B-band magnitudes are converted to the V band to be consistent with the HST profiles.Data taken from the literature include central velocity dispersion,σ0,an inner velocity dispersion gradient defined as Rσ≡σ0/σ(10′′),dimensionless rotation parameter(v/σ)∗,isophote shape a4/a, global(effective)radius r e,and global surface brightnessµe,defined as the mean surface brightness within r e.Details and sources are given in the notes.Table3presents several derived quantities based on spherical,isotropic dynamical modelsfitted to the nuker-law light profile.The mass-to-light ratio of each model has been determined by normalizing toσ0from Table1,assuming constant M/L with radius and equatingσ0to the light-weighted rms line-of-sight dispersion in a centered2′′by2′′aperture(corrections for1′′FWHM seeing are at most a few percent and are not included). Mass-related quantities are blank ifσ0is not available.Quantities tabulated at0′′.1include the luminosity density,peak Maxwellian phase-space density,two-body relaxation time, and predicted projected velocity dispersion.Total luminosity and mass within a sphere of the same radius are also parison to the non-parametric densities in Paper III indicates that nuker-lawfitted luminosity densities are10%too low on average but otherwise show little scatter for non-and moderately nucleated galaxies(severe nuclei were ignored infitting nuker laws,and as a result nuker-law densities in these galaxies are about a factor of2lower than the non-parametric inversions).Several quantities are repeated for r=10pc,but for many galaxies this is well inside the resolution limit of0′′.1 and requires an inward extrapolation of the nuker-lawfit.An impression of the division into core and power-law galaxies is provided by Fig.3, which plots inner power-law slopeγversus observed break radiusθb(orθlimbfor power-law galaxies)in arcsec.Profiles withθb≥0′′.16(logθb≥−0.8)are reasonably well resolved by HST.They divide into two groups,those withγ≤0.25(cores)and those withγ>0.5 (power laws)—the valley in between is empty.This is the division that motivated the two profile types in Paper I,later analyzed statistically in Paper III.The rectangular box in Fig.3encloses galaxies that we are fairly sure contain real cores.Galaxies above the box are definitely power laws at current resolution.Galaxies to the left of the box are classed as power laws although some contain a hint of an incipient core.The effect of limited resolution is apparent for M31and M32;both galaxies are plotted twice,as seen nearby and at Virgo.The plotted positions differ appreciably, reflecting features of their inner profiles that cannot be probed in more distant galaxies.Galaxies within the box in Fig.3comprise the“Core”sample used in the following section.All others are classed as power laws.4.CENTRAL PARAMETER RELATIONSThe data in Tables1and2are used to plot new central parameter diagrams like those of Lauer(1983,1985a)and Kormendy(1985,1987a,b).We begin with plots versus absolute magnitude in Figs.4a,b,c,d.The symbols have the following meanings:(1)Core galaxies are plotted withfilled circles(•)using values of r b andµb from Table2.(2)Power laws are plotted with open circles(◦)using the limits r limb andµlimbfrom Table2.(3)M31and M32are plotted twice,as seen at their actual distance(asterisks)and inVirgo(end of vector).The length and direction of these vectors illustrate the possible effect of changing resolution on other power-law galaxies.Their direction is opposite to the limitflags that are attached to all power-law galaxies.(4)Special objects:The S0galaxy NGC524is the only core profile that is found withina bulge(all others are in ellipticals).NGC524is roughly face-on and showsflocculentdusty disk arms(Paper I)and a blue center(Kormendy,private communication);it is plotted with a small square.Fornax A(NGC1316)is a probable recent merger remnant(Schweizer1980)with a peculiar morphology(RC3).It has an abnormally small core for a galaxy of its luminosity(Kormendy1987b).NGC4486B shows a double nucleus like M31’s in WFPC2images(Lauer et al.1996)but continues to have a clearly defined core.The new plots show the same broad trends versus galaxy luminosity that were seen in ground-based data(Kormendy&McClure1993).Core galaxies are luminous objects that extend down to M V=−20.5.All normal ellipticals brighter than M V=−22show cores, with cores of brighter galaxies being larger and lower in surface brightness and density. The new central parameters of core galaxies correlate well with previous values measured from the ground(Kormendy et al.1994).The parameter relations for core galaxies are fairly narrow;for example,the rms scatter in r b versus M V about the best-fitting line is only0.25dex(Fornax A omitted).Ferrarese et al.(1994)have questioned whether the trends in core properties versus absolute magnitude are an artifact created by adding brightest cluster galaxies(BCGs) to smaller,trendless galaxies.They argue that,aside from M87,all cores in their Virgo sample are of similar size,and trends appear only when M87is added.Although M87 does not strictly qualify as a BCG(that distinction in Virgo is held by NGC4472),it does share certain properties with BCGs such as high luminosity and central location within a subcluster.From our larger sample,it seems clear that trends in core properties versus M V are real and are not an artifact of adding BCGs.The present sample could be truncated at M V=−22.2to eliminate all BCGs(including those in small groups as well as Abell clusters),yet trends among the11remaining core galaxies between M V=−20.5and−22 would still be present.In all plots,core properties of BCG galaxies appear to be a normal extension of the cores in smaller core ellipticals.Power-law galaxies in Fig.4are low-to-intermediate luminosity systems that extend in luminosity up to M V=−22.They overlap with core galaxies at intermediate magnitudes in the range−20.5>M V>−22.Despite an increase in angular resolution by a factor of10with HST,we have generally failed tofind cores in these objects,and thus their distribution in Fig.4a is ratherflat,reflecting the constant HST resolution limit of∼0.1 arcsec.For systems fainter than M V≈−19,this limit is uninteresting since it equals or exceeds predictions based on extrapolation from core galaxies.However,at intermediate magnitudes in the range M V=−20.5to−22,power-law and core galaxies coexist,and it is clear that the scatter in break radius is real and large.Core/power-law pairs that illustrate extremes of r b atfixed luminosity include NGC3379and NGC1023,whose break radii differ by more than a factor of40while their absolute magnitudes differ by less than 0.5mag,and NGC4168and NGC4594,for which the ratio of break radii is over100 even though their absolute magnitudes are almost identical.This is not a resolution effect wherein cores are detected in nearby galaxies but not in distant ones.Figure5plots break radius versus distance and shows that most of the sample,containing both small and largecores,resides in a narrow range of distance near that of Virgo.More distant galaxies are actually more likely to show cores because their cores are intrinsically larger.The large scatter in break radii near M V=−20.5to−22might atfirst sight be taken as a manifestation of the two-dimensional,planar distribution of the global structural parameters of hot galaxies,i.e.,the fundamental plane(Dressler et al.1987;Djorgovski &Davis1987;Faber et al.1987).Two-coordinate projections of this two-dimensional distribution commonly exhibit scatter depending on whether they show the plane edge-on or face-on.The basic coordinates for the global plane(see Section6)are r e,µe,andσ0, from which L V can be derived as L V=2πµe r2e.A plot of radius versus magnitude is thus a projection of the fundamental plane,and scatter might be expected in r b versus M V that is comparable to that seen in r e versus M V,provided r b and r e are well correlated.This hypothesis is tested by substituting r e for r b in Fig.4d.The scatter there proves to be small,demonstrating that the combination of radius versus L shows the global plane rather close to edge-on.The much larger scatter of Fig.4a therefore suggests a real decoupling of central properties from global ones,as emphasized by Lauer(1985a).In Section5we examine this scatter in more detail and show that it correlates with global rotation and isophote shape,in the sense that power-law galaxies(which have small r b) are disky and rotate rapidly,while cores(which have large r b)are boxy and rotate slowly.Bulges are distributed in Fig.4like ellipticals of small-to-intermediate size.None (except for M31-nearby)shows a core.The resemblance of bulges to small and intermediate ellipticals is not surprising since the two classes of galaxy share several traits,including similar global size,high rotation,flattening by rotation rather than anisotropy,and disky subsystems(Bender,Burstein&Faber1992).Before drawing further conclusions from Fig.4,we consider whether the trends shown there are affected by the particular sample of galaxies chosen.The present sample is a mixture taken from different authors,but we have been careful to retain only objects that are morphologically normal and free of dust.Our own sample from Paper I(comprising 42out of the61total objects in this paper)was specifically chosen to probe the full range of parameters covered by the ground-based central parameter relations(Lauer1985a; Kormendy&McClure1993).We strove hard to sample the widest possible magnitude range and,at intermediate magnitudes,to sample galaxies with both large and small apparent cores.Thus,it is possible that the present sample somewhat exaggerates the total spread in break radii at middle magnitudes.Another point is that most objects studied here had previous ground-based data,and thus some prior clue as to core size.Since ground data typically agree well with HST data (especially for large galaxies,Kormendy et al.1994),the present sample does not provide a truly fresh look at galaxy centers.A sample to do this with completely new galaxies has been observed in Cycle5and is now being analyzed.What the present sample does is fairly probe galaxies that had previously been examined from the ground.Are the claimed correlations robust for core galaxies specifically?Although Fornax A has been included in the diagrams for interest,it is strongly peculiar and its center is contaminated by dust(Shaya et al.1996).It does not qualify for our sample of normal, massive E’s,and its high residuals should not count against the correlations.Six more core ellipticals with ground-based data could also be added to bolster the HST data;these。
