下载文档原格式
Leave Out All The Rest （抛下其他的一切）I dreamed I was missing, you were so scared我在梦中迷失自我，你恐惧万分But no one would listen, cause no one else cared没有人倾听，因为没有人在意After my dreaming, I woke with this fear梦醒了，恐惧依然没有消散What am I leaving when I'm done here? 该怎么面对我所做的一切？So if you're asking me, I want you to know当你问我的时候，我只想让你明白When my time comes, forget the wrong that I've done当我逝去之时，忘记我所犯过的错Help me leave behind some reasons to be missed让我远离那些迷失的理由Don't resent me, and when you're feeling empty请不要在怨恨我，当你寂寞时Keep me in your memory, leave out all the rest让我留在你的记忆中剩下的一切都不要考虑Leave out all the rest剩下的一切都不要考虑Don't be afraid不要害怕I've taken my beating, I've shared what I've made我会面对挫折，我们一起承当I'm strong on the surface, not all the way through表面上坚强的我并没有把一切做好I've never been perfect, but neither have you我从未完美过，但是你也一样So if you're asking me, I want you to know当你问我时，只想让你明白When my time comes, forget the wrong that I've done当我逝去之时，忘记我犯过的错Help me leave behind some reasons to be missed让我远离那些让我迷失的理由Don't resent me, and when you're feeling empty请不要在怨恨我，当你觉得寂寞的时候Keep me in your memory, leave out all the rest让我留在你的记忆中，剩下的一切都不要考虑Leave out all the rest剩下的一切都不要考虑Forgetting all the hurt inside that you've learned to hide so well遗忘你心中深藏的伤痕Pretending someone else can come and save me from myself当作总有别人能将我解救I can't be who you are我无法变得和你一样When my time comes, forget the wrong that I've done当我逝去之时,忘记我所犯过的错Help me leave behind some reasons to be missed让我远离那迷失的理由Don't resent me, and when you're feeling empty请不要在怨恨我，当你觉得寂寞的时候Keep me in your memory, leave out all the rest让我留在你的记忆中，剩下的一切都不用去考虑Leave out all the rest剩下的一切都不用去考虑Forgetting all the hurt inside you've learned to hide so well遗忘你心中深藏的伤痕Pretending someone else can come and save me from myself当作总有别人能将我解救I can't be who you are我无法变得和你一样I can't be who you are我无法变得和你一样END...Burning In The Skies （在天空燃烧）I use the dead would to make the fire rise 我用死者祭奠升起火焰The blood of innocence burning in the skies 看那圣洁之血在空中燃烧I filled my cup with the rising of the sea 潮起的的海注满我的杯子And poured it out in an ocean of derby 用它浇注德比之海Oh…I'm swimming in the smoke 我在烟雾中穿游Of bridges I have burned就在炸毁那桥的烟雾中So don't apologize 不用道歉I'm losing what I don't deserve 我配不上我失去的东西What I don't deserve 配不上MUSIC音乐~~~~~~~~~~~~~~~We held my breath as clouds began to fall 即使在云也形成的时候我们一息尚存But you were lost in the beating of the storm 但你却在风暴中迷失But in the end we were meant to be apart 最终我们会分离In separate chambers of the human heart 在人心另外的密室里No…I'm swimming in the smoke我在烟雾中穿游Of bridges I have burned 就在炸毁那桥的烟雾中So don't apologize 不用道歉I'm losing what I don't deserve 我不值得拥有我所拥有的东西It's in the black and bolds它的黑色在增加Of bridges I have burned 就在炸毁那桥的烟雾中So don't apologize 不用道歉I'm losing what I don't deserve 我不值得拥有我所拥有的东西What I don't deserve 不值MUSIC音乐~~~~~~~~~~~~~~~I'm swimming in the smoke 我在烟雾中穿游Of bridges I have burned 就在炸毁那桥的烟雾中So don't apologize 不用道歉I'm losing what I don't deserve 我不值得拥有我所拥有的东西The blame is mine alone 此罪为吾所有For bridges I have burned 因为我炸毁此桥So don't apologize 不用道歉I'm losing what I don't deserve 我不值得拥有我所拥有的东西What I don't deserve…不值What I don't deserve… (For oh~) 不值What I don't deserve…不值I use the dead would to make the fire rise 我用死者祭奠升起火焰The blood of innocence burning in the skies 看那圣洁之血在空中燃烧END…Remember the Name-Fort Minor You ready? Let's go!Yeah, for those of you that want to know what we're all aboutIt's like this y'all (come!)This is ten percent luckTwenty percent skillFifteen percent concentrated power of willFive percent pleasureFifty percent painAnd a hundred percent reason to Remember the NameMikeHe doesn't need his name up in lightsHe just wants to be heard whether it's the beat or the micHe feels so unlike everybody else, aloneIn spite of the fact that some people still think that they know himBut fuck meHe knows the codeIt's not about the salaryIt's all about reality and makin' some noiseMakin' the storyMakin' sure his clique stays upThat means when he puts it down Tak's pickin' it up(Let's go!)Who the hell is he anyway?He never really talks muchNever concerned with status but still leavin' them star struckHumbled through opportunities given to him despite the factThat many misjudge him because he makes a livin' from writin rapsPut it together himself, now the picture connectsNever askin for someone's help, to get some respectHe's only focused on what he wrote, his will is beyond reachAnd now when it all unfolds, the skill of an artistThis is twenty percent skillEighty percent beerBe one hundred percent clear 'cause Ryu is illWho would've thought that he'd be the one to set the west in flames And I heard him wreckin' with The Crystal Method, Name Of The Game Came back dropped Megadef, took 'em to churchI like 'bleach, man, why you have the stupidest verse?This dude is the truth, now everybody be givin' him guest spots His stock's through the roof I heard he fuckin' with S-Dot!This is ten percent luckTwenty percent skillFifteen percent concentrated power of willFive percent pleasureFifty percent painAnd a hundred percent reason to Remember the NameThey call him Ryu, he’s sickAnd he’s spittin fire with MikeGot him out the dryer he's hotFound him in Fort Minor with TakWhat a fuckin’ nihilist porcupineHe's a prick, he's a cockThe type women want to be withAnd rappers hope he get shotEight years in the makin'Patiently waitin to blowNow the record with Shinoda's takin' over the globeHe's got a partner in crime his shit is equally dopeYou won't believe the kind of shit that comes out of this kid's throat TakHe's not your everyday on the blockHe knows how to work with what he's gotMakin' his way to the topHe often gets a comment on his namePeople keep askin him was it given at birthOr does it stand for an acronym?No, he's livin' proofGot him rockin' the boothHe'll get you buzzin' quicker than a shot of vodka with juiceHim and his crew are known around as one of the best Dedicated to what they do and give a hundred percentForget MikeNobody really knows how or why he works so hardIt seems like he's never got timeBecause he writes every note and he writes every lineAnd I've seen him at work when that light goes on in his mindIt’s like a design is written in his head every timeBefore he even touches a key or speaks in a rhymeAnd those motherfuckers he runs with, those kids that he signed Ridiculous, without even tryin', how do they do it?This is ten percent luckTwenty percent skillFifteen percent concentrated power of willFive percent pleasureFifty percent painAnd a hundred percent reason to Remember the NameThis is ten percent luckTwenty percent skillFifteen percent concentrated power of willFive percent pleasureFifty percent painAnd a hundred percent reason to Remember the NameYeahFort Minor, M. ShinodaStyles of BeyondRyu, TakbirMachine Shop林肯公园——Faint （中文歌词）我有一点孤单，有一点冷漠，有一些抱怨，这些对事情没有什么好处，每个人都能看到这些伤痕。
木星和土星的英文诗句Jupiter and Saturn's Poetic VerseThe celestial dance of Jupiter and Saturn has captivated the imaginations of stargazers and poets alike for millennia. These two majestic gas giants, each with their own unique charms, have inspired countless works of art and literature across cultures and throughout history. In the realm of poetry, their splendor has been immortalized in verses that celebrate their grandeur, their mysteries, and the awe they inspire in all who gaze upon them.Jupiter the Mighty stands tall in the night sky, its swirling storms and vibrant hues a testament to the sheer power and scale of the cosmos. Its Great Red Spot, a perpetual hurricane larger than our own planet, is a symbol of the raw, untamed forces that shape the universe. Yet amidst this turbulence, Jupiter also exudes a sense of regal elegance, a proud and commanding presence that has drawn comparisons to the mightiest of ancient gods.One poet, captivated by Jupiter's majesty, pens these words "O mighty Jove, your crimson cloak unfurls, a tapestry of storms that shake the heavens. Your steady gaze, a beacon in the night, guidesus through the vastness of the skies." The author's reverence for this colossal world is palpable, each line evoking the awe and wonder inspired by this celestial giant.Saturn, in contrast, is a world of delicate beauty, its iconic rings a testament to the intricate dance of gravity and matter that governs the heavens. This ringed wonder, with its serene and contemplative aura, has long been a source of fascination for poets and philosophers alike. They see in its graceful form a reflection of the harmony and balance that underpins the very fabric of the universe.One such poet muses "O Saturn, your rings a shimmering veil, a celestial lace that whispers of mysteries untold. Your moons, like silent sentinels, guard the secrets of your realm, inviting us to ponder the rhythm of the cosmos." The poet's words capture the sense of tranquility and wonder that Saturn evokes, a world of subtle beauty that invites contemplation and deeper understanding.Yet these gas giants are not merely passive observers in the grand cosmic dance. They are dynamic, ever-changing worlds, their atmospheres and orbital patterns constantly in flux, responding to the gravitational interplay between them and the other denizens of the solar system. This interplay has inspired poets to explore the relationship between these two giants, weaving intricate tapestries of verse that capture the delicate balance and tension that existsbetween them.One such poet writes "Jupiter and Saturn, celestial partners in the eternal ballet, their gravitational embrace a symphony of celestial movements. They dance across the heavens, their rhythmic motions shaping the destiny of worlds, their influence felt throughout the solar system." The poet's words evoke a sense of the grand cosmic drama that unfolds between these two titans, a drama that has captivated the human imagination for eons.But the poetry inspired by Jupiter and Saturn is not limited to their physical forms and celestial interactions. These worlds have also come to symbolize deeper philosophical and spiritual truths, serving as metaphors for the great mysteries of existence. Poets have seen in these giants reflections of the human condition, with all its complexities, contradictions, and eternal questions.One poet, contemplating the vastness of these worlds, writes "Jupiter and Saturn, twin guardians of the cosmos, remind us of our smallness and our grandeur. In their endless dance, we see the rhythm of life and death, the cycle of creation and destruction that governs all things." The poet's words suggest that these giants, for all their immensity, also hold the keys to understanding our own place in the universe, our own significance and insignificance.Another poet, struck by the timeless quality of these worlds, pens these lines "Jupiter and Saturn, ageless sentinels of the night, bear witness to the rise and fall of empires, the birth and death of stars. They stand as monuments to the eternal, reminding us that our own fleeting existence is but a heartbeat in the grand symphony of the cosmos." The poet's words invoke a sense of humility and reverence, reminding us that we are but transient visitors in the grand scheme of the universe.Through the power of poetry, Jupiter and Saturn have been elevated to the realm of the mythic and the archetypal. They have become symbols of the great mysteries and truths that underlie the universe, touchstones for the human search for meaning and understanding. And in this, they continue to inspire and captivate, their celestial dance a source of endless fascination and wonder for all who gaze upon them.。
卡尔·萨根英文名句卡尔·萨根是一位美国天文学家、天体物理学家、宇宙学家、科幻作家，以下是一些他的英文名句及意思：1. "Somewhere, something incredible is waiting to be known." - 某处，有一些不可思议的事情正等待被发现。
这句话表达了卡尔·萨根对未知世界的探索精神和对科学发现的信念。
2. "The universe is not only stranger than we imagine, it is stranger than we can imagine." - 宇宙不仅比我们想象的更奇怪，而且比我们能够想象的更奇怪。
这句话强调了宇宙的复杂性和神秘性，以及人类认知的有限性。
3. "We are a way for the cosmos to know itself." - 我们是宇宙了解自身的一种方式。
这句话表达了人类在探索宇宙中的重要性，以及人类与宇宙的紧密联系。
4. "Science is not only a cerebral pursuit; it is also a spiritual quest." - 科学不仅是一种智力追求，也是一种精神追求。
这句话强调了科学对人类精神层面的影响和意义。
5. "The earth is a very small stage in a vast cosmic arena." - 地球在广阔的宇宙舞台上只是一个非常小的舞台。
这句话表达了宇宙的宏大和人类的渺小，提醒人们要保持谦虚和开放的心态。
这些名句展示了卡尔·萨根对科学、宇宙和人类的深刻思考，他的思想和作品对科学界和公众产生了广泛的影响。
黑格尔仰望星空名言英文1. "To be capable of looking upwards at the stars is to possess the essence of humanity."2. "The grandeur of the universe reflects the infinite potential within each of us."3. "Staring at the starry night, one realizes the vastness of existence and the insignificance of our troubles."4. "In the face of the cosmos, all divisions and conflicts seem trivial."5. "Lift your eyes to the heavens and discover the boundless power of dreams."6. "The stars remind us of our own mortality and the importance of making our lives count."7. "Each star is a reminder of the countless stories and mysteries waiting to be explored."8. "Gazing at the stars reminds us of the interconnectedness of all life and the shared human experience."9. "The beauty of the night sky awakens a sense of wonder and awe that transcends ordinary existence."10. "The silent stars speak to the depths of our souls, carrying messages of hope and inspiration."11. "In the starry expanse, past and future merge, reminding us of the eternal cycle of life."12. "The vastness of the universe humbles us and reminds us of our responsibility to safeguard our planet."13. "In the dark night, the stars act as beacons of light, guiding us towards our true purpose."14. "The stars illuminate the darkness, teaching us to endure and find strength even in the most challenging times."15. "We are all stardust, connected to the cosmos in ways we cannot fully comprehend."16. "The starry sky evokes a sense of transcendence, awakening our inherent desire to reach for the heavens."17. "Gazing up into the vastness of space, we are filled with a sense of awe and reverence for the cosmic order."18. "The stars remind us that even in our darkest moments, there is always light shining through."19. "Staring at the stars, we gain perspective, realizing that our problems are small compared to the grand tapestry of the universe."20. "The stars guide us on a journey of self-discovery, helping us find our place in the universe."。
我心目中的科学家英语作文范文In my view, scientists are akin to modern-day alchemists, weaving intricate narratives of discovery within the fabric of the universe. They are the navigators of the unknown, wielding curiosity as their compass and reason as their sail. Let me take you on a journey through the corridors of my mind, where the portrait of a scientist unfolds in vibrant hues of intellect and ingenuity.Imagine a world where equations dance across chalkboards like cosmic ballets, where the language of atoms whispers secrets only the keenest ears can decipher. This is the realm of the scientist, where every question is a breadcrumb leading to the banquet of knowledge. They are the architects of understanding, building bridges between the tangible and the intangible.At the heart of scientific inquiry lies a relentlesspursuit of truth. It is a quest fueled not by ego, but by an insatiable hunger to unravel the mysteries of existence. From the microscopic dance of particles to the grandorchestration of galaxies, scientists peer through the veil of ignorance, seeking to illuminate the darkness with the torch of reason.Yet, amidst the chaos of experimentation and the labyrinth of data, there exists a quiet humility. For every answer uncovered reveals a dozen new questions, each more tantalizing than the last. The scientist is a humble pilgrim, journeying ever deeper into the unknown, guided by the twin beacons of curiosity and skepticism.But make no mistake, theirs is not a solitary endeavor. Science is a tapestry woven from the threads of collaboration and cooperation. Across continents and disciplines, scientists join hands in a symphony of discovery, harmonizing their efforts to conquer the frontiers of knowledge. In this global chorus, no voice is too small, no contribution too insignificant. For it is in diversity that the true power of science resides, drawing strength from the myriad perspectives that illuminate the path forward.And yet, for all their brilliance, scientists are not immune to the foibles of humanity. Egos clash like tectonic plates, and dogma can obscure the light of reason. But in the crucible of debate and discourse, truth emerges triumphant, tempered by the fire of scrutiny.So, what then defines the essence of a scientist? Is it the accolades adorning their walls or the equations etched in their minds? Perhaps it is neither, but rather the spark of curiosity that ignites their soul. For in the end, it isnot the destination that defines us, but the journey we undertake in pursuit of understanding.In my eyes, the scientist is more than a mere mortal; they are the custodians of curiosity, the stewards of skepticism, and the architects of enlightenment. They are the poets of the cosmos, crafting verses of truth in the language of the universe. And as long as there are questions left unanswered, their quest shall endure, a testament to the indomitable spirit of human intellect.。
小王子equation插曲英文The Little Prince Equation InterludeIn the midst of his journey through the stars, the Little Prince stumbled upon a peculiar equation that seemed to defy all logic and reason. It was a perplexing formula that lay hidden within the fabric of the universe, waiting to be uncovered by someone with an open heart and a curious mind.The equation itself was simple yet enigmatic, written in symbols that danced across the page like notes in a cosmic symphony. It spoke of love and loss, of joy and sorrow, of all the emotions that make us human. As the Little Prince pondered its meaning, he was struck by a sudden realization – that the answer to life's greatest mysteries could be found in the smallest of details.With a sense of wonder and awe, the Little Prince set out to explore the equation further, determined to unlock its secrets and unravel its mysteries. He searched high and low, traveling from planet to planet in search of the elusive solution. Along the way, he encountered a myriad of characters, each with their own interpretations of the equation.From the wise old astronomer who saw it as a gateway to the stars, to the lonely flower who saw it as a reflection of her own beauty, everyone had their own unique perspective on the equation. But it was the Little Prince himself who ultimately discovered the true meaning behind the symbols – that love is the greatest equation of all.As he gazed upon the equation one final time, the Little Prince felt a sense of peace and serenity wash over him. For in that moment, he understood that the answers to life's greatest questions were not to be found in the stars above, but in the beating of his own heart.And with that realization, the Little Prince bid farewell to the equation and continued on his journey through the cosmos, forever changed by the beauty and wonder of the universe.。
八大行星英语歌-回复题目：八大行星英语歌Introduction:The solar system is a fascinating place with its many celestial bodies, including eight major planets. In this article, we will explore each of these planets and delve into their characteristics, captivating facts, and memorable aspects reflected in an English song. Let's embark on this celestial journey!Mercury:Mercury is the closest planet to the Sun. It is small and rocky with a scorching hot surface. The song begins with a lively tune, introducing Mercury's speedy orbit around the Sun. Lyrics like "Mercury, fastest of them all, dancing around the Sun in a blazing ball" reflect its quick revolution and breathtaking environment.Venus:Next, we encounter Venus, often referred to as Earth's twin due to their similar size and composition. The song takes on a romantic tone as it highlights Venus's beauty. The lyrics "Venus, shining bright, a jewel in the night" capture its radiant appearance in theevening sky. Additionally, the song emphasizes Venus's scorching-hot atmosphere with lines like "Venus, burning fierce, surface's temperature fierce."Earth:Moving further, we reach the third planet from the Sun, our own home - the Earth. The song's tone becomes nostalgic and uplifting as it celebrates our planet's diversity. Lyrics such as "Earth, our precious sphere, where life blossoms year by year" encapsulate the beauty and wonder of our home. The song also touches on the importance of preserving Earth, with lines like "Earth, we must take care, for future generations to share."Mars:Known as the "Red Planet" due to its rusty hue, Mars is the fourth planet in our solar system. The song adopts a catchy tune, reflecting the planet's intrigue and potential for human exploration. Lines such as "Mars, future frontier, reach for the stars, we'll conquer our fears" inspire the listener to dream of interplanetary travel and Mars colonization.Jupiter:As we venture deeper into the solar system, we encounter the largest planet, Jupiter. Its colossal size is emphasized by the grandiose melody of the song. Lyrics like "Jupiter, king of them all, a mighty gas giant standing tall" accentuate its dominance. The song also mentions Jupiter's iconic feature, the Great Red Spot, with lines like "Jupiter, with a storm so grand, the Great Red Spot, it commands."Saturn:Saturn, renowned for its beautiful and distinct ring system, takes center stage in the song. The melody adopts a whimsical tone, mirroring the enchantment of its rings. Lyrics such as "Saturn, with rings so bright, like jewels in the night" encapsulate its spectacular appearance. The song also mentions Saturn's many moons, highlighting their diversity and potential for exploration.Uranus:Uranus, the seventh planet from the Sun, is known for its unique sideways rotation and pale blue color. The song embraces a mesmerizing melody reminiscent of the planet's mysterious nature. Lyrics like "Uranus, spinning on its side, its pale blue hue, a cosmic ride" reflect its distinct characteristics. The song also touches uponUranus's icy composition and extreme cold with lines like "Uranus, frozen realm, with temperatures overwhelming and helms."Neptune:Finally, we reach the outermost planet in our solar system, Neptune. The song adopts a dreamy, ethereal tune, mirroring the planet's distant and mysterious persona. Lyrics such as "Neptune, farthest of them all, an azure beauty, captivating and tall" highlight its distant location and enchanting atmosphere. The song also mentions Neptune's winds, which are the strongest in the solar system, with lines like "Neptune, stormy reign, winds howl and wane."Conclusion:The eight major planets of our solar system each possess unique and awe-inspiring characteristics that are intriguing to explore. Through an English song, we have delved into the remarkable aspects of each planet, immersing ourselves in their celestial wonders. As we continue to gaze at the night sky, may we carry the melodies and knowledge of these eight planets in our hearts.。
卡尔·萨根是20世纪最杰出的科学家之一，也是一位著名的天文学家、宇宙学家和科普作家。
他以丰富的想象力和深邃的见解，向世人展示了宇宙的壮丽和神秘。
在他的著作《宇宙》中，留下了许多经典的句子，激发了无数人对宇宙的思考和探索。
以下是一些卡尔·萨根《宇宙》中的经典句子的英文原文及其对应的中文翻译：1. "The universe is not required to be in perfect harmony with human ambition."- "宇宙不必与人类的野心完全和谐。
"2. "The cosmos is within us. We are made of star-stuff. We are a way for the universe to know itself."- "宇宙就在我们之中。
我们是由星辰构成的。
我们是让宇宙认识自己的一种方式。
"3. "Somewhere, something incredible is w本人ting to be known."- "在某个地方，有些令人难以置信的东西正等待被发现。
"4. "For small creatures such as we the vastness is bearable only through love."- "对于像我们这样的小生物来说，唯有通过爱才能承受宇宙的浩瀚。
"5. "Imagination will often carry us to worlds that never were. But without it we go nowhere."- "想象力往往会带领我们去到从未存在的世界。
但没有想象力，我们一无所得。
黑格尔仰望星空名言英文-回复1. "The stars are the embodiment of absolute beauty and infinite wisdom."2. "Looking up at the stars, I am reminded of the boundless potential of the human spirit."3. "In the vastness of the night sky, we find solace and inspiration for our own dreams."4. "To gaze at the stars is to connect with the grandeur and mysteries of the universe."5. "Stars are the eternal beacons that guide us towards our own purpose and destiny."6. "The stars remind us that we are part of something much greater than ourselves."7. "In the darkness of night, the stars illuminate our path and show us the way forward."8. "Stars symbolize the timeless and unchanging truth in anever-changing world."9. "As we look up at the stars, we realize that our problems are minuscule in the grand scheme of things."10. "The stars teach us humility, for they remind us of our insignificance in the vastness of the cosmos."11. "The beauty of the stars is a reflection of the beauty withinourselves."12. "Stars inspire us to dream big and reach for the impossible."13. "At night, when we see the stars, we are reminded of the wonders of creation."14. "Looking at the stars, we are reminded of the infinite possibilities that lie ahead."15. "The stars whisper secrets of the universe to those who are willing to listen."16. "Stars are the celestial poetry that speaks to the depths of our souls."17. "The stars remind us that even in the darkest of times, there is always a glimmer of hope."18. "To gaze at the stars is to witness the eternal dance of light and darkness."19. "Stars are the windows through which we glimpse the majesty and greatness of the cosmos."20. "In the beauty of the stars, we find a reflection of our own inner light."。
He deals the cards as a meditationAnd those he plays never suspectHe doesn't play for the money he winsHe don't play for respectHe deals the cards to find the answerThe sacred geometry of chanceThe hidden law of a probable outcomeThe numbers lead a danceI know that the spades are the swords of a soldier I know that the clubs are weapons of warI know that diamonds mean money for this artBut that's not the shape of my heartThe shape of my heartAnd if I told you that I loved youYou'd maybe think there's something wrongI'm not a man of too many facesThe mask I wear is oneThose who speak know nothingAnd find out to their costLike those who curse their luck in too many places And those who fear a lossI know that the spades are the swords of a soldier I know that the clubs are weapons of warI know that diamonds mean money for this artBut that's not the shape of my heartThe shape of my heartI know that the spades are the swords of a soldier I know that the clubs are weapons of warI know that diamonds mean money for this artBut that's not the shape of my heart在牌局中运筹帷幄是他冥想的方式他从不会质疑自己所打出的每一张牌他打牌的目的绝非利益也更不是为了获得尊重他打牌只为寻找人生的答案蕴藏在无尽可能之中神圣的几何形状看似偶然的结局掩藏着的亘古不变的规律简单的数字也可融合成一支炫目的舞蹈我深知黑桃来自士兵手中无情的利刃（黑桃源自士兵长矛的形状）也明白梅花象征战争中最危险的武器（梅花可能源自三叶草的形状，代表幸福）更知道方块正如同这圣洁艺术中肮脏的金钱（方块源自钻石的形状）但那牌上画着的绝非我心（红桃）的形状我心的形状若我告诉你我爱你你肯定会认为有什么事出了问题我并非擅用面具伪装自己的男人我今生所戴的面具不过只有我自己的面容喧哗者往往一无所知他们会斤斤计较着短浅的利益就像那些抱怨命运不公的人戚戚然患得患失我深知黑桃来自士兵手中无情的利刃也明白梅花象征战争中最危险的武器更知道方块正如同这圣洁艺术中肮脏的金钱但那牌上画着的绝非我心的形状我心的形状我深知黑桃来自士兵手中无情的利刃也明白梅花象征战争中最危险的武器更知道方块正如同这圣洁艺术中肮脏的金钱但那牌上画着的绝非我心的形状。
OSSERVATORIOASTRONOMICOdi PADOVA16.9.1997 Are the Bulge C–stars in the Sagittarius dwarf galaxy?Yuen K.NgPadova Astronomical Observatory,Vicolo dell’Osservatorio5,I-35122Padua,Italy(Yuen@astrpd.pd.astro.it)Received21March1997/Accepted10July1997Abstract.Part of the mystery around the Bulge carbon stars from Azzopardi et al.(1991)is solved,if they are re-lated to the Sagittarius dwarf galaxy.The carbon stars are in that case not metal-rich as previously thought,but they have a metallicity comparable to the LMC,with an age be-tween0.1–1Gyr.A significant fraction of the carbon stars still have luminosities fainter than the lower LMC limit of M bol –3.m5.A similar trend is present among some of the carbon stars found in other dwarf spheroidals,but they do not reach a limit as faint as M bol –1.m4foundfor the SMC.At present,the TP-AGB models cannot ex-plain the origin of carbon stars with M bol>–3.m5through a single-star evolution scenario,even if they form imme-diately after entering the TP-AGB phase.Mass transfer through binary evolution is suggested as a possible sce-nario to explain the origin of these low luminosity carbon stars.Key words:Stars:carbon stars–evolution–Hertzsprung-Russell(HR)diagram—galaxies:individ-ual:Sagittarius dwarf–Local Group–Galaxy center1.Introduction1.1.Bulge carbon starsFor a long time carbon stars are searched in the direction of the Galactic Centre.From a low dispersion,near in-frared grism survey a total offive carbon stars were found amid2187M-giants(Blanco et al.1978,McCarthy et al. 1983and Blanco&Terndrup1989).The stars are mainly identified by the CN bands at7945,8125,and8320˚A. Azzopardi et al.(1985ab;1986)demonstrated that addi-tional,especially blue carbon stars can be found with the strong Swan C2bands(4737and5165˚A)in the spec-tral range4350–5300˚ing this technique,Azzopardi et al.(1985b,1988;the latter is hereafter referred to as ALR88)found33carbon stars in8differentfields of the Galactic Bulge.Near-IR photometry and medium-low res-olution spectra have been obtained for these carbon stars (Azzopardi et al.1991–hereafter referred to as ALRW91, Tyson&Rich1991,Westerlund et al.1991).These stars show similarities with the low-to medium bolometric lu-minosity SMC carbon stars,but the galactic carbon stars have stronger NaD doublets.Various studies suggest that a wide metallicity range is present in the bulge(Whit-ford&Rich1983,Rich1988&1990,Geisler et al.1992, McWilliam&Rich1994,Ng1994,Bertelli et al.1995, Ng et al.1995&1996,Sadler et al.1996).According to ALR88the carbon stars are expected to be metal-rich if they belong to the Bulge.1.2.Sagittarius dwarf galaxyThe serendipitous identification of the Sagittarius dwarf galaxy(SDG)was made by Ibata et al.(1994,1995; hereafter respectively referred to as IGI94and IGI95). It is the closest dwarf spheroidal and moves away from us at about160km/s.Accurate distance determinations from RR Lyrae stars belonging to this galaxy range from 22.0–27.3kpc(Alcock et al.1997;Alard1996;Mateo et al.1995ab,1996;Ng&Schultheis1997–hereafter re-ferred to as NS97).The photometric metallicity estimates made thus far depend heavily on the assumed age and the values for[Fe/H]range from–0.5to–1.8.The mean age (10–12Gyr)and metallicity([Fe/H]=–1.5)adopted is a trade-off,such that the age conveniently allows for the presence RR Lyrae and carbon stars(Ibata et al.1997). IGI95identified four carbon stars belonging to this galaxy, Whitelock et al.(1996,hereafter referred to as WIC96) performed a near-IR study of26candidates,and NS97 identified one more carbon star in the outer edge of the dwarf galaxy.The next section deals with how the Bulge carbon stars mentioned above are related to the(candi-date)carbon stars from the dwarf galaxy.1.3.A clue?A supposedly high metallicity lead Tyson&Rich(1991) and Westerlund et al.(1991)to suggest that the Bulge carbon stars should be old and posses a mass of about 0.8M ,while evolutionary calculations(Boothroyd et al.2Yuen K.Ng:Are the Bulge carbon stars in the the Sagittarius dwarf galaxy?1993,Groenewegen&de Jong1993,Groenewegen et al.1995,Marigo et al.1996ab)demonstrate that the initial mass of carbon stars is at least1.2M (t<∼4Gyr)for Z=0.008.Furthermore,the initial mass increases towardshigher metallicity and decreases towards lower metallicity (Lattanzio1989).The Bulge carbon stars are a mystery (Lequeux1990,Tyson&Rich1991,Westerlund et al.1991, Chiosi et al.1992,Azzopardi1994),because they are in bolometric luminosity about2.m5too faint to be regarded as genuine AGB(Asymptotic Giant Branch)stars,if lo-cated in the metal-rich Bulge.NS97compiled a catalogue of candidate RR lyrae and long period variables(LPVs)in the outer edge of the SDG. After de-reddening of the K-band magnitudes for the can-didate LPVs,the period-K0relation for the Mira variables from the Sgr Ifield in the Bulge from Glass et al.(1995) put these stars at25.7kpc.This distance is in good agree-ment with the distance obtained from the RR Lyrae stars found in the samefield.One of the LPVs is a carbon star. The difference between the distance modulus of the dwarf galaxy and the Galactic Centre at8kpc is∼2.m5.This lead to the suggestion that the Bulge carbon stars could actually be located in the dwarf galaxy,whose presence was unknown at the time the carbon stars were identified. This would solve the standing question about the origin of the‘bulge’carbon stars.The possibility that the‘bulge’carbon stars could be member of the SDG is analyzed.The organization of the paper is as follows.In Sect.2the formerly Bulge carbon from ALRW91are placed in a CMD(colour-magnitude diagram)at the distance of the SDG.A comparison is made with the near-IR magnitudes and colours from ac-tual and candidate carbon star members from the dwarf galaxy(WIC96,NS97).In Sect.3isochrones are placed in the CMD and it is demonstrated that the majority of the ALRW91carbon stars are still fainter than the tip of the red giant branch.A discussion of the results is given in Sect.4.Some stars are too faint,even if carbon stars are formed immediately after they enter the TP-AGB phase, and a possible binary evolution origin is suggested for some of the carbon stars fainter than the red giant branch tip.Arguments are given that the expected number of car-bon stars related to the SDG is at least two times larger. The results are summarized in Sect.5.2.Data and method2.1.Near-infrared photometryThe near-IR photometry of the Bulge carbon stars pre-sented by ALRW91was reduced to the standards from the homogenized ESO photometric system proposed by Koornneef et al(1983ab).Bouchet et al.(1991)found in this system no systematic differences in the magni-tudes from the standards observed at ESO in the period 1983–1989.Fig. 1.The distance of the Sagittarius dwarf galaxy deter-mined for various galactic latitudes.The dashed line refers to an unweighted linear least squaresfit for the points,while the long-dashed line shows a two sectionfit drawn through the pointsThe near-IR photometry from WIC96with the SAAO 1.9m telescope is appropriately transformed to the ESO system(Hron et al.1997).Note,that in general many transformations from SAAO to the ESO near-IR system refer to the transformation from the system defined by Glass(1974)or Carter(1990)to an older ESO system defined by Engels et al.(1981)and Wamsteker(1981). 2.2.Extinction and distanceThe extinction for the Bulge carbon stars is not homoge-neous.For eachfield defined by ALRW91a general correc-tion is applied to all stars.Instead of A V=1.m87(Glass et al.1995)an extinction of A V=1.m71is adopted for the Sgr Ifield.It is the average value from Walker&Mack (1986)and Terndrup et al.(1990).For Baade’s Window field around NGC6522A V=1.m50.This value was ob-tained by Ng et al.(1996)from the(V,V–I)CMD ob-tained by the OGLE(Optical Gravitational Lensing Ex-periment,see Paczy´n ski et al.1994for details)and is in good agreement with average value E(B–V)=0.m49 determined for thisfield.For the extended clear region around and near NGC6558the same value as used by ALR88,E(B–V)=0.m41or A V=1.m27from Zinn(1980), is adopted.No actual determinations of the extinction are found for thefield intermediate to NGC6522and NGC6558and A V=1.m38is adopted.For the remain-ing Bulgefields(b<−8.◦0)a relation(Blommaert1992, Schultheis et al.1997)based on the reddening map con-structed by Wesselink(1987)from the colour excess of the RR Lyrae stars at minimum light,is used:A V= 0.104b+1.58,where b is the galactic latitude.The value A V=0.m48obtained by Mateo et al.(1995)is adopted for the stars in the SDG observed by WIC96.The extinction in the near-IR passbands is determined under the assumption that A J/A V=0.282,A H/A V=0.175,and A K/A V=0.112(Rieke&Lebofsky1985).Yuen K.Ng:Are the Bulge carbon stars in the the Sagittarius dwarf galaxy?3Fig.2.Panel (a &b )The ALRW91carbon stars placed at the distance of the Sagittarius dwarf galaxy (open circles;small open circles are used to indicate a larger uncertainty in the extinction adopted),together with the carbon stars from IGI95(filled triangles).Open triangles and crosses are used for respectively the candidate carbon stars and giant branch stars of the dwarf galaxy observed by WIC96.The open square indicates the carbon stars S283found by NS97among the variables studied by Plaut (1971)and Wesselink (1987).The dotted horizontal line indicates the observational lower LMC limit at which carbon stars are found,while the lower magnitude limit corresponds with the SMC limit (Azzopardi 1994).The difference between panel (a )and (b )is the method used to assign a distance to each star,see Sect.2.3.Panel (c )shows the stars which are possibly located in the Bulge.The open crosses indicate the giant branch stars observed by WIC96,the open square is a carbon star (L199,unpublished)found among the variables studied by Plaut (1971)and Wesselink (1987),and the dots show for comparison the location of the semiregular and Mira variables selected from respectively Schultheis et al.(1997)and Blommaert (1992).The isochrones (Bertelli et al.1994;only for log T eff<3.70)displayed in the three panels are as follows:a )10Gyr RGBs for Z =0.0004,0.004,0.008,and 0.020;b )1and 10Gyr AGBs for Z =0.001(long-dashed line)and 0.1and 1Gyr AGBs for Z =0.008(dotted line);and c )5and 10Gyr AGBs for Z =0.004(dotted and solid line)and Z =0.02(dot-dashed and dashed line).See Sect.3.1for additional details about the magnitude and the colour transformations.Note that the left vertical axes in each panel give the K-magnitude scale,while the right vertical axes indicate the M bol -scaleThe distance determined with RR Lyrae stars for theSDG ranges from 22.0–27.3kpc.Figure 1shows thatthese distances are actually correlated with the galac-tic latitude at which they were determined.Additionaldistance determinations (Sarajedini&Layden 1995–here-after referred to as SL95,Fahlman et al.1996)obtainedwith other methods were added to this figure.An un-weighted linear least squares fit through those distancesgives D (kpc)=21.83−0.25b .Figure 1also shows a twosection line drawn through these points.2.3.Colour-magnitude diagramFigure 2a shows the de-reddened CMD.A distance cor-rection with the linear least squares line was applied to allthe stars to reduce the scatter due to differential distanceeffects.Figure 2b shows the diagram with the distancescorrected with the two section line.There is no signifi-cant difference between the Figs.2a &2b.Some stars are very bright.In SDG their M bol would range from –6.m 0to –7.m 0.They could be bright members of SDG or they could be located in the Bulge and have a lower luminosity.For a graphical purpose those stars are placed in Fig.2c at a distance of 8.0kpc.A sample of LPVs from Schultheis et al.(1997)are included in panel 2c.The dotted line in Figs.2a –c is the lower LMC limit at which carbon stars are found,while the lower magnitude boundary cor-responds with the SMC limit.Figures 2a &b show that three of the four IGI95car-bon stars observed by WIC96form an extension to the ALRW91sequence of carbon stars.This clearly is a strong indication that the ALRW91carbon stars belong to the SDG.The fourth carbon star (star C1from WIC96)ap-pears to be redder and located in the parallel sequence formed by the giant branch stars.It is not clear if this is due to a mis-identification in the photometry with an-other redder,nearby star.The finding chart provided from WIC96does not rule out this possibility.The figure fur-4Yuen K.Ng:Are the Bulge carbon stars in the the Sagittarius dwarf galaxy?ther shows that eight(#s1–3,5,6,12,15,21)out of the 26stars from WIC96are highly eligible carbon star candi-dates,because they are located on the combined ALRW91 &WIC96carbon star sequence.A significant number of the ALRW91carbon stars are located below the LMC limit at which carbon stars are found.This limit might be related to a low metallicity of the stars,but in Sect.4.1it is argued that this is not the case.A similar trend is present among some of the carbon stars found in other dwarf spheroidals(see Fig.2b from WIC96).However,Azzopardi et al.(1997)found car-bon stars with M bol –1.m2in the Fornax dwarf galaxy, assuming(m–M)0=21.m0.This is even fainter than the present limit M bol –2.m0for the‘bulge’carbon stars iflocated in the SDG and M bol –1.m4for the SMC carbon stars(Azzopardi1994;Westerlund et al.1993,1995). Four LPVs,most likely belonging to the dwarf galaxy (NS97),are included in thisfigure.Note that they are the first Mira and the semiregular variables found belonging to the SDG.In fact,they are thefirst LPVs discovered in a dwarf spheroidal galaxy.Two LPVs are located in-side the carbon star sequence,while the other two form at M K<–7.m5a blue extension to the carbon sequence.3.Models3.1.Conversion:theoretical−→observational planeThe transformation of the bolometric magnitude to the K-magnitude scale in Fig.2is obtained from the period-luminosity(PL-and PK-)relation of carbon Miras (Groenewegen&Whitelock1996,hereafter referred to as GW96).Transformed to the ESO photometric system this gives:M K=1.37M bol–1.58.The actual transforma-tion from the bolometric magnitude to a K-magnitude in the models shown in Fig.2is achieved with the relation provided by Suntzeffet al.(1993):M K=M bol−BC K,BC K=1.00+2.076(J−K)0−0.463(J−K)20.The relation is valid for0.m3<(J−K)<2.m3and was ob-tained from afit to the(J–K,BC K)relation given by Fro-gel et al.(1980).The bolometric magnitude was obtained from the numerical integration of the broadbandflux dis-tributions of the galactic carbon stars observed by Men-doza&Johnson(1965).The same bolometric corrections are applied to non-carbon stars.Figure2from Frogel et al.(1980)shows that the differences are at most∼0.m2.The conversion from log T effto(J–K)0is established from an empirical relation derived by Ng et al.(1997), based on giant stars with a spectral type ranging from late G to late M.The effective temperatures for these stars were obtained from angular diameter measurements. The empirical log T eff/(J–K)0relation takes into account a small shift in colour as a function of metallicity.The rela-tions,provided for the metallicity Z=0.004and Z=0.024,are logarithmically interpolated for Z≥0.004and the Z=0.004relation is applied for lower metallicities.Al-though some uncertainty is present due to the fact that this relation is not based on carbon stars,the differences will not be too large as long as the colours are not too red.The empirical relation covers conveniently the observed colour range of the carbon stars.3.2.IsochronesIn Figs.2a–c some isochrones from Bertelli et al.(1994) are displayed.Fig.2a shows the RGB for an age of10Gyrfor various metallicities and Fig.2b&2c show the AGB for different age and metallicities.Figure2a demonstratesthat if one assumes afixed age then a large metallic-ity spread could be present among the SDG stars.Given the uncertainties,the GB stars likely have a metallicityof Z=0.008,comparable to the LMC.Figure2b demon-strates that difficulties are present to distinguish1& 10Gyr isochrones for the AGBs with Z=0.001from thosewith a0.1&1gyr age for Z=0.008.The isochrones in Fig2c show that the colour difference between5and10Gyr populations with the same metallicity is quite small compared to the colour difference due to a large metallicity range.4.Discussion4.1.Metallicity and ageThe isochrones in Fig.2a indicate that the metallicity of the old population in the SDG is Z 0.008.This isquite high,but within the uncertainties comparable with [Fe/H]=–0.52±0.09obtained by SL95from a photomet-ric study of a(V,V–I)CMD.This is in contrast with val-ues[Fe/H]<∼–0.7obtained with different methods(IGI94, IGI95,Ibata et al.1997,Fahlman et al.1996,Mateo et al.1995&1996,WIC96,Marconi et al.1997).SL95found an indication of the possible existence of a[Fe/H]=–1.3(i.e.Z=0.001)component in the dwarf galaxy.With such a metallicity the age of the carbon stars is somewhere between1and10Gyr,see Fig.2b. Figure2a already shows that there is an old component with Z=0.008and an age around10Gyr.If there is a rather smooth age range present for Z=0.001,then why are the younger stars absent among the RGB stars with Z=0.008?Furthermore,why should the metallicity de-creases towards younger age?From a close box model one expects an increasing metallicity towards younger age.All together this does not favour a metallicity of Z=0.001. If on the other hand,the metallicity for the carbon stars is Z=0.008then we are apparently dealing with two differ-ent age populations.The carbon stars would in this case reflect a very recent star formation burst in this galaxy, while the major stellar population has an age∼10Gyr. An almost zero metallicity enrichment is in agreementYuen K.Ng:Are the Bulge carbon stars in the the Sagittarius dwarf galaxy?5Fig. 3.CMD of SDG stars in field 1from Marconi et al.(1997)with an overlay of Z =0.008isochrones of 0.1Gyr(solid line)and 1Gyr (dashed line)from Bertelli et al.(1994).The dashed line between (V,V–I)=(14.m 0,0.m 0)and(V,V–I)=(23.m 0,–0.m 2)is the white dwarf cooling sequencefrom the 1Gyr isochrone.An extinction of A V =0.m 48anda distance modulus of 17.m 02(Mateo et al.1995)have beenadopted for the isochroneswith the multiple starburst Carina dwarf spheroidal stud-ied by Schmecker-Hane et al.(1996).A young age could be independently confirmed throughthe detection of Cepheids in the SDG.Mateo et al.(1995)report the possible detection of an anomalous Cepheidand suggest that the SDG might contain a considerablenumber of these stars.Just as in this study,SL95would not be able to dis-tinguish from their CMD the difference between a veryyoung Z =0.008population from an older Z =0.001pop-ulation.So the present interpretation is not in contradic-tion with their results.An indication that we are indeeddealing with young stellar populations is present in theCMDs from Marconi et al.(1997).In Fig.3(i.e.Mar-coni’s et al.Fig.2)the 0.1Gyr and 1.0Gyr isochronesdemonstrate clearly the presence of a young populationabove the main sequence turn-offof the old stellar popu-lation from the SDG.It is not clear though,why the twodistinct age populations advocated above are not presentin the CMDs analyzed by Fahlman et al.(1996).Possiblythe number of stars involved are too small to be conclusiveand the analysis has to be repeated with a larger numberof stars in the background of the globular clusters.From the considerations outlined above it is concludedthat the metallicity of the SDG stars is Z 0.008.Theage of the ALRW91carbon stars is with thismetallic-Fig.4.The course of the Sagittarius dwarf galaxy projected on the x −z plane.The radial velocity of the galaxy indicates that it is moving away from us.Together with the indicated course this implies that the galaxy crossed quite recently the galactic disc.The position of the Sun is indicated by ity younger than 1Gyr.A second distinct population is present with an age around 10Gyr.If a star formation burst is related with a passage through the galactic disc then an age as young as 0.1Gyr would confirm the assertion that the SDG already passed through the disc and is currently moving away from our Galaxy (Alcock et al.1997,NS97).Figure 4indicates that this should indeed be the case.The absence of populations with intermediate ages separated by approximately 1Gyr appears to rule out the orbital period suggested by John-ston et al.(1995),Vel´a zquez &White (1995)and Ibata et al.(1997).Johnston et al.however pointed out that the existing observations were not sufficient to put limits on the orbit or initial state of the SDG.4.2.Are the ‘bulge’carbon stars on the TP-AGB ?In the current understanding of stellar evolution theory carbon stars are formed at the third dredge-up at the TP-AGB (thermally pulsing asymptotic giant branch)phase,in which the stellar surface is enriched with 12C.Car-bon stars cannot be formed before the TP-AGB phase.In the LMC the majority of the stars are located above the tip of the RGB (red giant branch),but they can be located ∼1.m 0below RGB tip for 20%–30%of its inter-pulse period (see Marigo et al.1996ab and references cited therein).At the distance of the SDG a considerable fraction of the ALRW91carbon stars are located well below the tip of the RGB.Figure 5demonstrates that even if carbon stars can form directly after they enter the TP-AGB phase,the presence of a fraction of those carbon stars cannot be explained.These stars are likely formed through another mechanism not accounted for in the ‘standard theory’for the formation of carbon stars in the TP-AGB phase.The sequence of carbon stars parallel to the giant branch sug-gest that they are either RGB or early AGB stars.It ap-6Yuen K.Ng:Are the Bulge carbon stars in the the Sagittarius dwarfgalaxy?Fig.5.Four solid lines are displayed for the LMC,indicatingthe start of the E-AGB,TP-AGB,the transition from M-toC-type stars and the end of the AGB evolution (see Marigo etal.1996b for details).Above the dotted line carbon stars withmasses in the range 1.2–3.0M have a 90%detection prob-ability.M i is the initial mass of the carbon star.The dashed,horizontal line is the limiting magnitude for the SDG carbonstars and the dashed,vertical lines indicate the age range forthe SDG stars (see Sect.4.1)if Z 0.008.The shaded area in-dicate the region in which the presence of carbon stars cannotbe explained with a TP-AGB star,see Sect.4.2parently contradicts our theoretical understanding aboutthe formation process of carbon stars.ALR88suggested two possible scenarios.Westerlundet al.(1991)favoured the scenario where a very effec-tive mixing occurs at an early phase on the ascend tothe TP-AGB.Since this cannot be the case for even thefaintest carbon stars related to the SDG,the scenario ofmass transfer through binary evolution is favoured for theformation of the low luminosity carbon stars.The samescenario explains the observations of dwarf carbon stars(see Green 1997and references cited therein).In case of mass transfer through binary evolution,theprimary star evolved through the TP-AGB phase andtransferred a significant part of its 12C enriched enve-lope to the secondary.The primary evolved away fromthe AGB and is a white dwarf now and the secondaryis the presently observed carbon star.The fully convec-tive envelope of stars at the RGB or AGB would dilute12C/13C ratio.The dilution is proportional to the timeelapsed since the primary deposited part of its envelope onthe secondary star.The dilution should increase towardslarger distances from the galactic disc (see Figs.1&4).The NaD equivalent width and the CN line strength ob-tained from spectra for the carbon stars by Tyson &Rich (1991,see their Fig.3)would support this assertion.For comparable envelope masses the dilution will be at least a factor 2.If the metallicity is about Z =0.008then the mass transfer should have occurred recently,indicating that the difference of the initial mass between the primary and sec-ondary is very small.A metallicity of Z =0.008is in addi-tion high enough to explain the strong NaD features found present among the carbon stars.McClure (1984)showed that CH stars are binaries,some of them are long-period systems.Suntzeffet al.(1993)argue that the CH stars in the LMC,with M bol ranging from –5.m 3to –6.m 5,have an age near 0.1Gyr.Some of the CH stars could well be the predecessors of the SDG carbon stars.If L199is a CH star and the four giant stars observed by WIC96are related to the SDG they have M bol 6.m 5.A binary nature of those stars would strongly support the evolution scenario outlined above.In Fig.6the near-infrared photometry of the ‘bulge’carbon stars are compared with the photometry for the obtained for a sample of SMC carbon stars (Wester-lund et al.1995).For the SMC carbon stars we adopted (m–M)0=18.m 9and E(B–V)=0.m 09(Westerlund 1997).Westerlund et al.(1991,1993,1995)noted that the most luminous ‘bulge’and SMC carbon stars have comparable C 2and CN values,whereas the fainter ‘bulge’stars are more similar to the main bulk of faint SMC carbon stars.This result is not surprising anymore if,as argued in this paper,the ‘bulge’carbon stars are indeed related to the SDG.Figure 6indicates that the former ‘bulge’carbon stars have luminosities almost comparable to the SMC carbon stars.The ALRW91carbon stars form a parallel sequence with the SMC stars.As argued in Sect.4.1the ALRW91carbon stars likely have a metallicity Z 0.008,while the SMC carbon stars are expected to be metal poorer.The SMC sequence ought to be bluer than the SDG sequence,if the carbon stars have a similar age.This however is not the case and the carbon stars therefore do not originate from a population with a similar age.The colours of both sequences can be explained when the SMC carbon stars evolved from an older stellar population.4.3.Are there more SDG carbon stars ?It is an important issue to check if more carbon stars from the dwarf galaxy can be found in other fields.From NS97a crude estimate of about 1/2is found for the ratio of LPVs versus the RR Lyrae stars of Bailey type ab .About one out of six LPVs could be a carbon star.This is however a lower limit,because the sample from NS97is biased towards the brighter stars.The observations were mainly limited due to the instrumental setup and the telescope size and no reliable data was obtained for some of the fainter,suspected carbon stars in the sample.About 29more carbon stars with M K <∼–6.m5mightbe found among the long period variables in the DUOYuen K.Ng:Are the Bulge carbon stars in the the Sagittarius dwarf galaxy?7Fig.6.A comparison between the ‘bulge’carbon stars (sym-bols as in Fig.2)if located in the SDG and the SMC carbonstars (Westerlund et al.1995;filled dots)(Disc Unseen Objects;see Alard 1996and references citedtherein),MACHO (Massive Astrophysical Compact HaloObjects;see references in Alcock 1997),and even theOGLE (see references in Paczy´n ski et al.1994)databases.However,considerably more candidate carbon might bepresent among the stars with –6.m 5<M K <–4.m 0.Ex-trapolating the carbon star PK-relation from GW96indi-cates that if some of these stars are variables,they mightbe found among the variables with periods in the rangefrom 40–130days.An additional result would be a signif-icant increase of the number of LPVs related to the SDG.Another way to estimate the expected number of car-bon stars for the SDG is through the fuel consumptiontheorem (see Renzini &Buzzoni 1983,1986for details).For a population of young stars we have the relation:N ∗=5×10−12×∆t ×L bol ,where L bol ∼4×107L(Mateo et al.1996;L bol 2L V )and ∆t 5×105yr .About 100carbon stars are thus expected.The number isa lower limit,because the full extent of the SDG has notbeen taken into account and the bolometric luminosityhas therefore been underestimated.Moreover,the dura-tion over which carbon stars can be observed is prolongedthrough mass transfer from binary evolution.All togetherthe expected number of SDG carbon stars might be about10times larger than hitherto found.4.4.What about the RR Lyrae stars ?A significant amount of RR Lyrae stars have been foundand have been used to constrain the distance towards theSDG,see Sect.2.2.As mentioned in Sect.1.3the distance of the LPVs is consistent with the RR Lyrae found in the same field (NS97).The LPVs likely have an age compa-rable to the age of the carbon stars and a metallicity of Z 0.008.The metallicity of the RR Lyrae stars are expected to be considerably smaller,say between Z =0.0004–0.001.The GB stars from the parent population appears to be absent in Fig.2a.This could be due to a bias in the selection of the GB stars,confusion of an old,metal-poor popu-lation with the GB from a 0.1–1.0Gyr population with Z =0.008,or the parent population of the RR Lyrae stars has a metallicity close to Z =0.008.In addition,it is not clear how the SDG RR Lyrae stars are related to,or even might originated from the four globular clusters located at the SDG distance (Da Costa &Armandroff1995).The present situation is rather confusing.It is not clear at all what the actual metallicity of the parent population of the SDG RR Lyrae stars is.A thorough analysis of deep CMDs,similar to those from Marconi et al.(1997),with a significant number of stars near the main sequence turn-offis required to determine the age and metallicity of the oldest population in the SDG.4.5.A twist of fate ?4.5.1.Radial velocities The radial velocities of the ‘bulge’carbon stars would pro-vide an independent verification of the photometric anal-ysis presented here,concerning membership of the SDG.Tyson &Rich (1991)determined the radial velocities for 33stars from the ALRW91sample.Their radial velocities would support only for a small number of stars the sugges-tion that the ALRW91carbon stars are actually located in the SDG,while the majority of the stars are moving towards us and could be Bulge members.The spectroscopic results related to the CN line strength and the NaD equivalent width would support membership to the SDG combined with a binary evolu-tion scenario for these stars.Membership of the Bulge does not make sense,because there is in that case no trace of a predecessor,i.e.a brighter population of carbon stars (see Azzopardi 1994,Fig.2).One could argue that an indepen-dent verification of the radial velocities,with a zeropoint based on other stars than the one template star ROA 153used by Tyson &Rich (1991),might shed some light on the present contradictory results.However,if both the photometric and spectroscopic anal-ysis are correct then the ALRW91carbon stars are related to the SDG.Some stars move away from us in the same direction as the SDG,while others move towards us,away from the SDG.This does not necessarily imply that we observe the ongoing disruption of the SDG.It is not clear if an encounter of the SDG with the galactic disc could result in the bifurcation of the radial velocity distribution for stars formed or located in the tidal tail.The numeri-。
