R-modes of accreting hyperon stars as persistent sources of gravitational waves

我渴望成为天文学家的英语作文Title: The Starry Dream of Becoming an AstronomerBeneath the vast expanse of the night sky, sprinkled with stars like shimmering grains of sand, there lies within my heart a fervent desire—to become an astronomer. This ambition, alight in my soul since the tender years of my childhood, gleams brighter than the most luminous of celestial bodies.My yearning is not merely for the scientific exploration of the cosmos but for the profound connection to the universe that astronomers seem to possess. It is a longing to decipher the mysteries etched in the heavens, to unlock the ancient tales told by galaxies, to witness the birth and death of stars, and to seek answers to questions that have perplexed mankind since the dawn of time.The allure of astronomy lies not in the distant, cold beauty of the stars but in their intimate relationship to our very existence. The realization that the elements within our bodies were forged in stellar alchemy connects us to the universe in a way that is both humbling and awe-inspiring. The pursuit of astronomy is a quest for understanding our place in the cosmos, for tracing the threads that bind us to the great tapestry of existence.To be an astronomer is to embrace a life of perpetual wonder and ceaseless learning. It demands a dedication to peering through telescopes, not merely to gaze at the beauty before us but to scrutinize, to analyze, and to interpret the language of the heavens. It is a commitment to a journey of the mind, where each discovery is akin to unearthing a treasure, each theory a key to unlocking the secrets of creation.With this passion burning within me, I envision a future where my days are spent amidst colleagues who share this zeal for the unknown. Together, we would stand on the frontiers of knowledge, pushing the boundaries of our understanding. In observatories, under the watchful gaze of the night, we would labor to unravel the fabric of space and time.The path to becoming an astronomer is fraught with challenges, requiring not only intellectual prowess but also resilience and tenacity. The studies are daunting, the competition fierce, and the hours spent in research and experimentation, exhaustive. Yet, it is a path illuminated by the light of distant suns, guided by the same curiosity that led explorers of old to set sail into uncharted waters.As I stand on the cusp of my journey, I am filled with a hopeful anticipation. Like a compass pointing true north, my desire steers me toward this noble goal. Every star I observe, every book I read, every equation I solve brings me closer to realizing the dream of calling the universe my realm of exploration.In the infinite darkness sprinkled with sparkling diamonds, I find my purpose. To become an astronomer is not just a professional aspiration; it is a spiritual quest, a romance with the cosmos. It is to engage in a never-ending conversation with the stars, to seek answers that lie beyond our world, and to contribute to the story of humanity's endeavor to understand its place within the vast, beautiful universe.Indeed, the starry dream of becoming an astronomer burns brightly within me, guiding my path and illuminating my nights. With every passing moment, I draw closer to embracing the endless expanse, not as an observer from afar, but as a scholar among the stars.。

a r X i v :g r -q c /9812019v 4 19 M a r 1999To appear in the Astrophysical JournalWhere are the r-modes of isentropic stars?Keith H.Lockitch and John L.FriedmanUniversity of Wisconsin-Milwaukee,P.O.Box 413,Milwaukee,WI 53201lockitch@,friedman@ABSTRACTAlmost none of the r-modes ordinarily found in rotating stars exist,if the starand its perturbations obey the same one-parameter equation of state;and rotatingrelativistic stars with one-parameter equations of state have no pure r-modes at all,no modes whose limit,for a star with zero angular velocity,is a perturbation with axialparity.Similarly (as we show here)rotating stars of this kind have no pure g-modes,no modes whose spherical limit is a perturbation with polar parity and vanishingperturbed pressure and density.Where have these modes gone?In spherical stars of this kind,r-modes and g-modes form a degenerate zero-frequency subspace.We find that rotation splits the degeneracy to zeroth order in thestar’s angular velocity Ω,and the resulting modes are generically hybrids,whose limitas Ω→0is a stationary current with axial and polar parts.Lindblom and Ipser haverecently found these hybrid modes in an analytic study of the Maclaurin spheroids.Since the hybrid modes have a rotational restoring force,they call them “rotationmodes”or “generalized r-modes”.Because each mode has definite parity,its axial and polar parts have alternatingvalues of l .We show that each mode belongs to one of two classes,axial-led orpolar-led,depending on whether the spherical harmonic with lowest value of l thatcontributes to its velocity field is axial or polar.We numerically compute these modesfor slowly rotating polytropes and for Maclaurin spheroids,using a straightforwardmethod that appears to be novel and robust.Timescales for the gravitational-wavedriven instability and for viscous damping are computed using assumptions appropriate to neutron stars.The instability to nonaxisymmetric modes is,as expected,dominatedby the l =m r-modes with simplest radial dependence,the only modes which retaintheir axial character in isentropic models;for relativistic isentropic stars,these l =mmodes must also be replaced by hybrids of the kind considered here.Subject headings:instabilities —stars:neutron —stars:oscillations —stars:rotation1.IntroductionA recently discovered instability of r-modes of rotating stars(first found in numerical study by Andersson(1998),and analytically verified by Friedman and Morsink(1998))has gained the attention of a number of authors(Kojima1998;Lindblom,Owen,and Morsink1998;Owen et al.1998;Andersson,Kokkotas and Schutz1998;Kokkotas and Stergioulas1998;Andersson, Kokkotas and Stergioulas1998;Lindblom and Ipser1998;Madsen1998;Spruit1999;Beyer and Kokkotas1999;Lindblom et al.1999).These modes have axial parity(see below)and their frequency is proportional to the star’s angular velocity.Neutron stars that are rapidly rotating at birth are likely to be unstable to nonaxisymmetric perturbations driven by gravitational waves; estimates of growth times and viscous damping times(Lindblom et al1998,Owen et al.1998, Andersson et al1998,Kokkotas and Stergioulas1998,Lindblom et al.1999)suggest that r-modes dominate the spin-down of such stars for several months,until a superfluid transition shuts offthe instability.Unstable r-modes may thus set the upper limit on the spin of young neutron stars,and gravitational waves emitted during the initial spin-down might be detectable.The recent discovery by Marshall et al(1998)of a pulsar in the supernova remnant N157B implies the existence of a class of neutron stars that are rapidly rotating at birth and whose spin is plausibly limited by the gravitational-wave driven instability.Perturbations of a spherical star can be divided into two classes,axial and polar,depending on their behavior under parity.Where polar tensorfields on a2-sphere can be constructed from the scalars Y m l and their gradients∇Y m l(and the metric on a2-sphere),axialfields involve the pseudo-vectorˆr×∇Y m l,and their behavior under parity is opposite to that of Y m l.That is,axial perturbations of odd l are invariant under parity,and axial perturbations with even l change sign. If a mode varies continuously along a sequence of equilibrium configurations that starts with a spherical star and continues along a path of increasing rotation,the mode will be called axial if it is axial for the spherical star.Its parity cannot change along the sequence,but l is well-defined only for modes of the spherical configuration.It is useful to further divide stellar perturbations into subclasses according to the physics dominating their behaviour.In perfectfluid stellar models,the polar parity perturbations consist of the f-,p-and g-modes;the f-and p-modes having pressure as their dominant restoring force and the g-modes having gravity as their dominant restoring force(Cowling1941).The axial parity perturbations are dominated by the Coriolis force in rotating stars and were called“r-modes”by Papaloizou and Pringle(1978)because of their similarity to the Rossby waves of terrestrial meteorology.For slowly rotating stars,the r-modes have frequencies which scale linearly with the star’s angular velocity and in the spherical limit they become time-independent convective currents.Despite the sudden interest in these modes,however,they are not yet well-understood for stellar models in which both the star and its perturbations are governed by a one-parameter equation of state,p=p(ρ);we shall call such stellar models isentropic,because isentropic modelsand their adiabatic perturbations obey the same one-parameter equation of state.For stars with more general equations of state,the r-modes appear to be complete for perturbations that have axial parity.However,this is not the case for isentropic models.Onefinds that the only purely axial modes allowed in isentropic stars are the physically interesting l=m r-modes with simplest radial behavior(Papalouizou and Pringle1978;Provost et al.19781;Saio1982;Smeyers and Martens1983).The disappearance of the purely axial modes with l>m occurs for the following reason.In spherical isentropic stars the gravitational restoring forces that give rise to the g-modes vanish and they,too,become time-independent convective currents with vanishing perturbed pressure and density.Thus,the space of zero frequency modes,which generally consists onlyof the axial r-modes,becomes larger for spherical isentropic stars to include the polar g-modes. This large degenerate subspace of zero-frequency modes is split by rotation to zeroth order in the angular velocity,and the corresponding modes of rotating isentropic stars are hybrids whose spherical limits are mixtures of axial and polar perturbations.These hybrid modes have already been found analytically for the uniform-density Maclaurin spheroids by Lindblom and Ipser(1998) who point out that since their dominant restoring force is the Coriolis force,it is natural to refer to them as rotation modes,or generalized r-modes.Although isentropic Newtonian stars do retain a vestigial set of purely axial modes(those having l=m),it appears that rotating relativistic stars of this type have no pure r-modes,no modes whose limit for a spherical star is purely axial(Andersson,Lockitch and Friedman,1999). For nonisentropic relativistic stars,Kojima(1998)has derived an equation governing purely axial perturbations to lowest order in the star’s angular velocity.2For the isentropic case,however, wefind a second,independent equation for these perturbations that appears to give inconsistent radial behaviour for purely axial modes(Andersson,Lockitch and Friedman,1999).This second equation is obtained from an angular component of the curl of the relativistic Euler equation and is simply the relativistic generalization of the equations presented in Sect.III of this paper(Eq.(36),for example).Kojima’s equation is one from which polar-parity perturbations have been excluded,and,as the present paper makes clear,one cannot assume that axial and polar parity modes decouple for slowly rotating isentropic stars.Instead,we expect the Newtonian l=mr-modes to become discrete axial-led hybrids of the corresponding relativistic models.In this paper we examine the hybrid rotational modes of rotating isentropic Newtonian stars. We distinguish two types of modes,axial-led and polar-led,and show that every mode belongs to one of the two classes.We then turn to the computation of eigenfunctions and eigenfrequencies for modes in each class,adopting what appears to be a method that is both novel and robust.Forthe uniform-density Maclaurin spheroids,these modes have been found analytically by Lindblom and Ipser in a complementary presentation that makes certain features transparent but masks properties that are our primary concern.We examine the eigenfrequencies and corresponding eigenfunctions to lowest nontrivial order in the angular velocityΩ.We then examine the frequencies and modes of n=1polytropes,finding that the structure of the modes and their frequencies are very similar for the polytropes and the uniform-density configurations.The numerical analysis is complicated by a curious linear dependence in the Euler equations,detailed in Appendix B.The linear dependence appears in a power series expansion of the equations about the origin.It may be related to difficulty other groups have encountered in searching for these modes.Finally,we examine unstable modes,computing their growth time and expected viscous damping time.The pure l=m=2r-mode retains its dominant role,but the3≤l=m∼<10 r-modes and some of the fastest growing hybrids may contribute to the gravitational radiation and spin-down.2.Spherical StarsWe consider a static spherically symmetric,self-gravitating perfectfluid described by a gravitational potentialΦ,densityρand pressure p.These satisfy an equation of state of the formp=p(ρ),(1) as well as the Newtonian equilibrium equations∇a(h+Φ)=0(2)∇2Φ=4πGρ,(3) where h is the specific enthalpy in a comoving frame,h= dpthe perturbed Euler equation,δ (∂t+£v)v a+∇a(h−1ρ=dpρ.(10)Because Eq.(7)forδv a decouples from Eqs.(8),(9)and(10)for(δρ,δΦ),any solution to Eqs.(7)-(10)is a superposition of a solution(0,0,δv a)and a solution(δρ,δΦ,0).This is the claimed decomposition.The theorem that any static self-gravitating perfectfluid is spherical implies that the solution (δρ,δΦ,0)is spherically symmetric,to within the assumptions that the static perturbation equations have no spurious solutions(“linearization stability”)3.Thus,under the assumption of linearization stability we have shown that all stationary non-radial perturbations of a spherical,isentropic star haveδρ=δp=δΦ=0and a velocityfield δv a that satisfies Eq.(7).A perturbation with axial parity has the form(Friedman and Morsink1998),δv a=U(r)ǫabc∇b Y m l∇c r,(11) and automatically satisfies Eq.(7).A perturbation with polar parity perturbation has the form,δv a=W(r)dr(rρW)−l(l+1)ρV=0.(13)These perturbations must satisfy the boundary conditions of regularity at the center,r=0 and surface,r=R,of the star.Also,the Lagrangian change in the pressure(defined in the next section)must vanish at the surface of the star.These boundary conditions result in the requirement thatW(0)=W(R)=0;(14) however,apart from this restriction,the radial functions U(r)and W(r)are undetermined.Thus,a spherical,isentropic,Newtonian star admits a class of zero frequency convectivefluid motions of the forms(11)and(12).Because they are stationary,these modes do not couple to gravitational radiation.43.Rotating Isentropic StarsWe consider perturbations of an isentropic Newtonian star,rotating with uniform angular velocityΩ.No assumption of slow rotation will be made until we turn to numerical computations in Sect.IV.The equilibrium of an axisymmetric,self-gravitating perfectfluid is described by the gravitational potentialΦ,densityρ,pressure p and a3-velocityv a=Ωϕa,(15) whereϕa is the rotational Killing vectorfield.We will use a Lagrangian perturbation formalism(Friedman and Schutz1978a)in which perturbed quantities are described in terms of a Lagrangian displacement vectorξa that connects fluid elements in the equilibrium and perturbed star.The Eulerian changeδQ in a quantity Q is related to its Lagrangian change∆Q by∆Q=δQ+£ξQ,(16) with£ξthe Lie derivative alongξa.Thefluid perturbation is then determined by the displacementξa:∆v a=∂tξa(17)∆p=−∇aξa(18)ρSince the equilibrium spacetime is stationary and axisymmetric,we may decompose our perturbations into modes of the form5e i(σt+mϕ).The corresponding Eulerian changes areδv a=i(σ+mΩ)ξa(19)δρ=−∇a(ρξa)(20)dpδp=W l Y m l∇a r+V l∇a Y m l−iU lǫabc∇b Y m l∇c r e iσt,(23)rand examine the perturbed Euler equation.The Lagrangian perturbation of Euler’s equation is0=∆[(∂t+£v)v a+∇a(h−1v2+Φ)],(24)2and its curl,which expresses the conservation of circulation for an isentropic star,is0=q a≡i(σ+mΩ)ǫabc∇b∆v c,(25) or0=q a=i(σ+mΩ)ǫabc∇bδv c+Ωǫabc∇b(£δvϕc).(26) Using the spherical harmonic expansion(23)ofδv a we can write the components of q a as10=q r=5We will always choose m≥0since the complex conjugate of an m<0mode with frequencyσis an m>0mode with frequency−σ.Note thatσis the frequency in an inertial frame.0=qθ=1r Y m l−2Ω∂r V l cosθsinθ∂θY m l+2Ωm2V lrsinθ∂θY m l e iσt,(28)and0=qϕ=ir[m2−l(l+1)sin2θ]Y m l−2mΩ∂r V l cosθY m l+ (σ+mΩ) ∂r V l−W l r sinθ∂θY m l e iσt.(29) These components are not independent.The identity∇a q a=0,which follows from equation(25), serves as a check on the right-hand sides of(27)-(29).Let us rewrite these equations making use of the standard identities,sinθ∂θY m l=lQ l+1Y m l+1−(l+1)Q l Y m l−1(30)cosθY m l=Q l+1Y m l+1+Q l Y m l−1(31) whereQ l≡ (l+m)(l−m)2.(32) Defining a dimensionless comoving frequencyκ≡(σ+mΩ)2κl(l+1)−m]U l Y m l+(W l−lV l)(l+2)Q l+1Y m l+1−[W l+(l+1)V l](l−1)Q l Y m l−1 ,(34)qθ=0becomes0=∞l=m −Q l+1Q l+2 lV′l−W′l Y m l+2−Q l+1 (m−1r Y m l+1+ 12κm W l r Y m l−Q l m +1r Y m l −1+Q l −1Q l (l +1)V ′l +W ′l Y m l −2(35)and q ϕ=0becomes0=∞ l =m −lQ l +1Q l +2 U ′l −(l +1)U l 2κl −m )V ′l +mlV l 2κl W l2κm +(l +1)Q 2l−lQ 2l +1U ′l + m 2−l (l +1) 1−Q 2l −Q 2l +1 U l2κ(l +1)+m V ′l +m (l +1)V l2κ(l +1)W l rY m l −2 (36)where ′≡d 6When m =0there exists a set of modes with parity +1that may be designated as “axial-led hybrids”since δv a receives contributions only from axial terms with l =1,3,5,...and polar terms with l =2,4,6,....7When m =0there exist two sets of modes that may be designated as “polar-led hybrids.”One set has parity −1and δv a receives contributions only from polar terms with l =1,3,5,...and axial terms with l =2,4,6,....The other set (which includes the radial oscillations)has parity +1and δv a receives contributions only from polar terms with l =0,2,4,...and axial terms with l =1,3,5,....if δv a receives contributions only frompolar terms with l =m,m +2,m +4,...andaxial terms with l =m +1,m +3,m +5,....Such a mode has parity (−1)m .Let us rewrite the equations one last time using the orthogonality relation for spherical harmonics, Y m ′l ′Y ∗m l d Ω=δll ′δmm ′,(37)where d Ωis the usual solid angle element.From equation (34)we find thatq r Y ∗m l d Ω=0gives0=[12κ(l −1)]U ′l −1−m (l −1)U l −12κm +(l +1)Q 2l−lQ 2l +1 V ′l +1r−m 2V l 2κ(l +2)]U ′l +1+m (l +2)U l +1r +(l +3)Q l +2Q l +1 U ′l +2+(l +2)U l +22κm +(l +1)Q 2l −lQ 2l +1U ′l + m 2−l (l +1) 1−Q 2l −Q 2l +1 U l 2κ(l −1)−m ]V ′l −1+m (l −1)V l −12κ(l −1)W l −12κ(l +2)+m ]V ′l +1+m (l +2)V l +12κ(l +2)W l +1TheΩ→0limit of such a perturbation is a sum of the zero-frequency axial and polar perturbations considered in Sect.II.Note that,although the relative orders ofδρandδv a are physically meaningful,there is an arbitrariness in their absolute order.If(δρ,δv a)is a solution to the linearized equations,so is(Ωδρ,Ωδv a).We have chosen the order(41)to reflect the existenceof well-defined,nontrivial velocity perturbations of the spherical model.Other authors(e.g., Lindblom and Ipser(1998))adopt a convention in whichδv a=O(Ω)andδρ=O(Ω2).To lowest order,the equations governing these perturbations are the perturbed Euler equations(38)-(40)and the perturbed mass conservation equation,(7),which becomesrW′l+ 1+rρ′ρ =1R i,(44)and about r=R as ρ′R∞k=−1˜πk 1−rBecause(38)relates U l(r)algebraically to W l±1(r)and V l±1(r),we may eliminate U l′(r)(all l′)from(39)and(40).We then need only work with one of equations(39)or(40)since the equations(38)through(40)are related by∇a q a=0.We next replaceρ′/ρ,W l′,and V l′in equations(39)or(40)by their series expansions.We eliminate the U l′(r)from either(39)or(40)and,again,substitute for the W l′(r)and V l′(r). Finally,we write down the matching condition at the point r0equating the series expansions about r=0to the series expansions about r=R.(Explicitly one equates(B6)and(B7)of Appendix B for axial-led modes or(B13)and(B14)for polar-led modes).The result is a linear algebraic system which we may represent schematically asAx=0.(46) In this equation,A is a matrix which depends non-linearly on the parameterκ,and x is a vector whose components are the unknown coefficients in the series expansions for the W l′(r)and V l′(r). In Appendix B,we explicitly present the equations making up this algebraic system as well as the forms of the regular series expansions for W l′(r)and V l′(r).To satisfy equation(46)we mustfind those values ofκfor which the matrix A is singular,i.e., we mustfind the zeroes of the determinant of A.We truncate the spherical harmonic expansion ofδv a at some maximum index l max and we truncate the radial series expansions about r=0and r=R at some maximum powers i max and k max,respectively.The resultingfinite matrix is band diagonal.Tofind the zeroes of its determinant we use standard rootfinding techniques combined with routines from the LAPACK linear algebra libraries (Anderson et al.1994).Wefind that the eigenvalues,κ0,computed in this manner converge quickly as we increase l max,i max and k max.The eigenfunctions associated with these eigenvalues are determined by the perturbation equations only up to normalization.Given a particular eigenvalue,wefind its eigenfunction by replacing one of the equations in the system(46)with the normalization condition thatV m(r=R)=1for polar-hybrids,or that(47)V m+1(r=R)=1for axial-hybrids.Since we have eliminated one of the rows of the singular matrix A in favor of this condition,the result is an algebraic system of the form˜Ax=b,(48) where˜A is now a non-singular matrix and b is a known column vector.We solve this system for the vector x using routines from LAPACK and reconstruct the various series expansions from this solution vector of coefficients.5.The Eigenvalues and EigenfunctionsWe have computed the eigenvalues and eigenfunctions for uniform density stars and for n=1polytropes,models obeying the polytropic equation of state p=Kρ2,where K is a constant.Our numerical solutions for the uniform density star agree with the recent results of Lindblomand Ipser(1998)whofind analytic solutions for the hybrid modes in rigidly rotating uniformdensity stars with arbitrary angular velocity-the Maclaurin spheroids.Their calculation uses thetwo-potential formalism(Ipser and Managan1985;and Ipser and Lindblom1990)in which theequations for the perturbation modes are reformulated as coupled differential equations for afluidpotential,δU,and the gravitational potential,δΦ.All of the perturbedfluid variables may beexpressed in terms of these two potentials.The analysis follows that of Bryan(1889)who foundthat the equations are separable in a non-standard spheroidal coordinate system.The Bryan/Lindblom-Ipser eigenfunctionsδU0andδΦ0turn out to be products of associatedLegendre polynomials of their coordinates.This simple form of their solutions leads us to expectthat our series solutions might also have a simple form-even though their unusual spheroidalcoordinates are rather complicated functions of r andθ.In fact,we dofind that the modes ofthe uniform density star have a particularly simple structure.For any particular mode,both theangular and radial series expansions terminate at somefinite indices l0and i0(or k0).That is,thespherical harmonic expansion(23)ofδv a contains only terms with m≤l≤l0for this mode,andthe coefficients of this expansion-the W l(r),V l(r)and U l(r)-are polynomials of order i0.For alll0≥m there exist a number of modes terminating at l0.In Tables1to4we present the functions W l(r),V l(r)and U l(r)for all of the axial-andpolar-led hybrids with m=1and m=2for a range of values of the terminating index l0.(Seealso Figure1.)For given values of m>0and l0there are l0−m+1modes.(When m=0there are l0modes.See equation(50)below.)We alsofind that the last term in the expansion(23),theterm with l=l0,is always axial for both types of hybrid modes.This fact,together with the factthat the parity of the modes is,(49)π= (−1)m for polar-led hybrids(−1)m+1for axial-led hybrids,(for m>0)implies that l0−m+1must be even for polar-led modes and odd for axial-led modes.The fact that the various series terminate at l0,i0and k0implies that Equations(46)and(48)will be exact as long as we truncate the series at l max≥l0,i max≥i0and k max≥k0.Tofind the eigenvalues of these modes we search theκaxis for all of the zeroes of thedeterminant of the matrix A in equation(46).We begin byfixing m and performing the searchwith l max=m.We then increase l max by1and repeat the search(and so on).At any given valueof l max,the searchfinds all of the eigenvalues associated with the eigenfunctions terminating atl0≤l max.In Table5,we present the eigenvaluesκ0found by this method for the axial-and polar-ledhybrid modes of uniform density stars for a range of values of l0and m.Observe that manyof the eigenvalues,(marked with a∗)satisfy the conditionσ(σ+mΩ)<0.[Recall that the mode frequency in an inertial frame isσ=(κ0−m)Ω].The modes whose frequencies satisfy this condition are subject to a gravitational radiation driven instability in the absence of viscosity.The modes having l0=m>0(or l0=1for m=0)are the purely axial r-modes.Their frequencies were found by Papalouizou and Pringle(1978)and are given byκ0=2/(m+1)(orκ0=0for m=0).Wefind that there are no purely polar modes satisfying our assumptions(41)in these stellar models.We have compared these eigenvalues with those of Lindblom and Ipser(1998).To lowest non-trivial order inΩtheir equation for the eigenvalue,κ0,can be expressed in terms of associated Legendre polynomials8(see Lindblom and Ipser’s equation6.4),as(4−κ20)d2)−2mP m l0+1(κ0rδv r+2cotθδvθ+iκδvϕ ,(52)it is straightforward numerically to construct this quantity from the components of ourδv a and compare it with the analytic solutions forδU given by Lindblom and Ipser(see their equation 7.2).We have compared these solutions on a20×40grid in the(r−θ)plane and found that they agree(up to normalization)to better than1part in109for all cases checked.Because of the use of the two-potential formalism and the unusual coordinate system used in their analysis,the axial or polar hybrid character of the Bryan/Lindblom-Ipser solutions is not obvious.Nor is it evident that these solutions have,as theirΩ→0limit,the zero-frequency convective modes described in Sect.II.The comparison of their analytic results with our numerical work has served the dual purpose of clarifying these properties of the solutions and of testing the accuracy of our code.The computational differences are minor between the uniform densitycalculation and one in which the star obeys a more realistic equation of state.Thus,this testing gives us confidence in the validity of our code for the polytrope calculation.As a further check, we have written two independent codes and compared the eigenvalues computed from each.One of these codes is based on the set of equations described in Appendix B.The other is based on the set of second order equations that results from using the mass conservation equation,(42),to substitute for all the V l(r)in favor of the W l(r).For the n=1polytrope we will consider and,more generally,for any isentropic equationof state,the purely axial r-modes are independent of the equation of state.In both isentropic and non-isentropic stars,pure r-modes exist whose velocityfield is,to lowest order inΩ,an axial vectorfield belonging to a single angular harmonic(and restricted to harmonicswith l=m in the isentropic case).The frequency of such a mode is given(to orderΩ)byκΩ=(σ+mΩ)=2mΩ/l(l+1)(Papalouizou and Pringle1978)and is independent of the equation of state.In isentropic stars,only those modes having l=m(or l=1for m=0)exist,and for these modes the eigenfunctions are also independent of the(isentropic)equation of state9.This independence of the equation of state occurs for the r-modes because(to lowest order inΩ)fluid elements move in surfaces of constant r(and thus in surfaces of constant density and pressure). For the hybrid modes,however,fluid elements are not confined to surfaces of constant r and one would expect the eigenfrequencies and eigenfunctions to depend on the equation of state.Indeed,wefind such a dependence.The hybrid modes of the n=1polytrope are not identical to those of the uniform density star.On the other hand,the modes do not appear to be very sensitive to the equation of state.We have found that the character of the polytropic modes is similar to the modes of the uniform density star,except that the radial and angular series expansions do not terminate.For each eigenfunction in the uniform density star there is a corresponding eigenfunction in the polytrope with a slightly different eigenfrequency(See Table6.) For a given mode of the uniform density star,the series expansion(23)terminates at l=l0.For the corresponding polytrope mode,the expansion(23)does not terminate,but it does converge quickly.The largest terms in(23)with l>l0are more than an order of magnitude smaller than those with l≤l0and they decrease rapidly as l increases.Thus,the terms that dominate the polytrope eigenfunctions are those that correspond to the non-zero terms in the corresponding uniform density eigenfunctions.In Figures1and2we display the coefficients W l(r),V l(r)and U l(r)of the expansion(23)for the same m=2axial-led hybrid mode in each stellar model.For the uniform density star(Figure 1)the only non-zero coefficients for this mode are those with l≤l0=4.These coefficients are presented explicitly in Table3and are low order polynomials in r.For the corresponding mode in the polytrope,we present in Figure2thefirst seven coefficients of the expansion(23).Observethat those coefficients with l≤4are similar to the corresponding functions in the uniform density mode and dominate the polytrope eigenfunction.The coefficients with4<l≤6are an order of magnitude smaller than the dominant coefficients and those with l>6are smaller still.(Since they would be indistinguishable from the(r/R)axis,we do not display the coefficients having l>6for this mode.)Just as the angular series expansion fails to terminate for the polytrope modes,so too do the radial series expansions for the functions W l(r),V l(r)and U l(r).We have seen that in the uniform density star these functions are polynomials in r(Tables1through4).In the polytropic star,the radial series do not terminate and we are required to work with both sets of radial series expansions-those about the center of the star and those about its surface-in order to represent the functions accurately everywhere inside the star.In Figures3through11we compare corresponding functions from each type of star.For example,Figures3,4,and5show the functions W l(r),V l(r)and U l(r)(respectively)for l≤6for a particular m=1polar-led hybrid mode.In the uniform density star this mode has eigenvalue κ0=1.509941,and in the polytrope it has eigenvalueκ0=1.412999.The only non-zero functions in the uniform density mode are those with l≤l0=2and they are simple polynomials in r(see Table2).Observe that these functions are similar,but not identical to,their counterparts in the polytrope mode,which have been constructed from their radial series expansions about r=0and r=R(with matching point r0=0.5R).Again,note the convergence with increasing l of the polytrope eigenfunction.The mode is dominated by the terms with l≤2and those with l>2 decrease rapidly with l.(The l=5and l=6coefficients are virtually indistinguishable from the (r/R)axis.)Because the polytrope eigenfunctions are dominated by their l≤l0terms,the eigenvalue search with l max=l0willfind the associated eigenvalues approximately.We compute these approximate eigenvalues of the polytrope modes using the same search technique as for the uniform density star.We then increase l max and search near one of the approximate eigenvalues for a corrected value,iterating this procedure until the eigenvalue converges to the desired accuracy. We present the eigenvalues found by this method in Table6.As a further comparison between the mode eigenvalues in the polytropic star and those in the uniform density star we have modelled a sequence of“intermediate”stars.By multiplying the expansions(44)and(45)for(ρ′/ρ)by a scaling factor,ǫ∈[0,1],we can simulate a continuous sequence of stellar models connecting the uniform density star(ǫ=0)to the polytrope(ǫ=1). Wefind that an eigenvalue in the uniform density star varies smoothly as function ofǫto the corresponding eigenvalue in the polytrope.。

五年级星空与宇宙英语阅读理解30题1<背景文章>The solar system is a wonderful and vast place, consisting of the sun and eight planets. The eight planets in order from the sun are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.Mercury is the closest planet to the sun. It is a relatively small planet. It has a very thin atmosphere. Venus is the second planet. It is about the same size as the Earth. It has a thick atmosphere which is mainly composed of carbon dioxide.The Earth is our home planet. It is a beautiful blue planet. It has a suitable atmosphere for living things. Mars is the fourth planet. It is smaller than the Earth. It also has an atmosphere, but it is much thinner than that of the Earth.Jupiter is the largest planet in the solar system. It has a very thick atmosphere. Saturn is famous for its beautiful rings. It is also a large planet with a thick atmosphere. Uranus and Neptune are the outermost planets in the solar system. They are both very cold and have their own unique atmospheres.1. <问题1>Which planet is the closest to the sun?A. VenusB. MercuryC. MarsD. Earth答案：B。

小学下册英语第1单元期中试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.What do we call the planet we live on?A. MarsB. VenusC. EarthD. Jupiter答案:C2.The capital of Kenya is _______.3. A ________ (航空港) is where planes take off and land.4.________ (观赏植物) are often used in landscaping.5.What do you call a person who works with metal?A. BlacksmithB. CarpenterC. ElectricianD. Mason答案:A6. A hydrate is a compound that contains ______ molecules.7.What is 15 + 10?A. 20B. 25C. 30D. 358. A _____ (蚂蚁) works hard to gather food for winter.9.What do we call a sweet food made from cocoa?A. CandyB. ChocolateC. CakeD. Biscuit答案:B10.I can play with my ________ (玩具类型) anywhere.11. A halogen is an element found in group ______ of the periodic table.12.What do we call a person who repairs shoes?A. TailorB. CobblerC. SeamstressD. Artisan答案:B13.What is the name of the first artificial satellite launched into orbit?A. Sputnik 1B. Explorer 1C. Vanguard 1D. Luna 114.What is the season after spring?A. WinterB. SummerC. FallD. Autumn答案:B15.The ancient Sumerians are known for creating the first ________ (城市).16.I found a _______ (古老的) coin.17.Which animal has a long neck?A. ElephantB. GiraffeC. DogD. Cat答案:B18.I like to watch ________ (纪录片) about animals.19.The ice cream is ___. (melting)20.The sunset is _______ (动人的).21.She is wearing a cute ___. (outfit)22.The car is _____ (fast/slow).23. A ______ is a type of bird that can mimic sounds.24.What is 10 - 4?A. 5B. 6C. 7D. 8答案:B25.The rain is ______ on the roof. (falling)26. A _____ (草坪) is perfect for picnics in the park.27.What is the color of an orange?A. BlueB. OrangeC. PurpleD. Green28. A ________ (植物知识普及) can inspire others.29.What do you call a person who plays a musical instrument?A. PainterB. SingerC. MusicianD. Dancer答案:C30.The _______ of a solution tells us how concentrated it is. (浓度)31.What is the main ingredient in falafel?A. LentilsB. ChickpeasC. BeansD. Rice32.The hamster stores food in its ______ (脸颊).33.We enjoy visiting the ___. (aquarium)34. A shooting star is actually a _______ that burns up in the atmosphere.35. A ______ is an animal that can be found in the ocean.36.What is the name of the famous American holiday celebrated on the fourth Thursday in November?A. ThanksgivingB. ChristmasC. New Year'sD. Independence Day答案:A37.Which animal has a long trunk?A. GiraffeB. ElephantC. ZebraD. Lion答案:B38. A solution that can dissolve more solute is called a _______ solution.39.The ________ was a significant movement for women's rights.40.My mom loves to _______ on weekends.41.We have math _____ today. (class)42. A _____ (生态平衡) is essential for a healthy environment.43.The ice cream is ___. (melting)44. A baby cat is called a __________.45.How many days are in a leap year?A. 365B. 366C. 367D. 364答案:B46.What do you call the person who teaches you in school?A. DoctorB. TeacherC. ChefD. Engineer答案:B47.I enjoy planting _____ in the garden.48.Which animal is known as "man's best friend"?A. CatB. DogC. BirdD. Fish49.I can ________ a message.50.__________ are used in the construction industry for insulation.51.What is the name of the fairytale character who climbed a beanstalk?A. JackB. PeterC. HanselD. Gretel52.The __________ (历史的启发性思维) drives innovation.53.I want to ___ a great cook. (become)54.What is the term for the distance light travels in one year?A. Light-YearB. Astronomical UnitC. ParsecsD. Cosmic Yard55.What is the name of the famous volcano in Italy?A. Mount EtnaB. Mount VesuviusC. Mount FujiD. Mount St. Helens答案:B56.The __________ helps to protect the brain.57.What is the name of the fictional land where Peter Pan lives?A. NeverlandB. WonderlandC. OzD. Narnia答案:A58.What is the capital of Portugal?A. LisbonB. MadridC. RomeD. Paris答案:A59.I have a ___ (dream) to travel the world.60.Which flower is known for being red?A. TulipB. RoseC. DaisyD. Sunflower答案:B61.What is the capital of Switzerland?A. ZurichB. GenevaC. BernD. Basel答案:C62.What is the name of the famous American singer known for her powerful voice?A. AdeleB. Whitney HoustonC. Mariah CareyD. Beyoncé答案:B63.What do we call a baby cat?A. KittenB. PuppyC. CubD. Foal答案:A64.The process of making biodiesel involves _______ oils.65.What color is a ripe banana?A. GreenB. YellowC. RedD. Blue66.The dog is _____ with its favorite toy. (playing)67.The ancient Greeks held _______ to honor their gods. (运动会)68.小鱼) plays with its friends in the tank. The ___69.The ______ communicates through sounds.70.What do you call a baby platypus?A. PuggleB. KitC. CalfD. Pup答案:A71.Cleopatra was the last active ruler of the __________ (埃及) dynasty.72.The bird is singing a ______ (happy) song.73.I can ______ (坚持) my beliefs.74.Light pollution makes it difficult to see the stars in an urban _______.75.What is the name of the famous American author known for "Beloved"?A. Toni MorrisonB. Maya AngelouC. Alice WalkerD. Zora Neale Hurston答案:A76.What do you call the hot liquid inside a volcano?A. MagmaB. LavaC. AshD. Gas答案:A77.What is the sound of a sheep?A. MeowB. BarkC. BaaD. Moo答案:C78.What is the name of the famous festival held in Rio de Janeiro?A. CarnivalB. OktoberfestC. DiwaliD. Holi答案:A Carnival79.We can _______ (一起学习) for the exam.80.My best friend is my loyal _______ who always supports me.81.Cosmic rays are high-energy particles that travel through ______.82. A _____ (植物文化交流) fosters appreciation for diversity.83. (Russian) Revolution led to the establishment of the Soviet Union. The ____84.The children are ________ in the playground.85.The ice cream is _____ (cold/warm) and delicious.86.The capital of Canada is _____.87.The _____ (大象) communicates with low-frequency sounds.88.What is the capital of Sri Lanka?A. ColomboB. KandyC. GalleD. Jaffna答案:A89.My sister's name is . (我妹妹的名字是。

TPO63阅读-2Structure and Composition of Comets原文 (1)译文 (3)题目 (4)答案 (7)背景知识 (8)原文Structure and Composition of Comets①Astronomers now have a fairly good idea of what a comet really is.When it is far from the Sun,it is a very small object only a few kilometers across.It consists mainly of ices(water,methane,ammonia)with bits of dust embedded in it-a kind of dirty ice ball.As it approaches the Sun,radiation from the Sun vaporizes the icy matter and releases some of the dust.This forms a gigantic halo around the ice ball. This halo-called the coma extends out tens of thousands of kilometers from the icy core,which is the nucleus of the comet.Sunlight reflected off the dust particles makes the coma visible to observers on Earth.Ultraviolet radiation from the Sun breaks down the vapor molecules into their constituents.These components can be excited by absorbing radiation from the Sun.In returning to lower-energy states, the excited atoms and ions emit light,contributing to the luminosity of the coma.②When the comet gets even closer to the Sun,one of its most spectacular parts begins to form-the tail.Actually,there are two kinds of tails:the dust tail and the ion tail.The dust tail is produced by the light from the Sun reflecting off the dust particles in the coma.A photon carries momentum.In bouncing off a dust particle, it imparts a tiny,but perceptible,momentum change to the dust particle,driving it away from the coma.As the comet sweeps along its orbit,it leaves a curving trail of dust behind in its path.This visible dust tail can extend for tens or hundreds of millions of kilometers out from the nucleus.The dust tail is characterized by its gently curving shape and its yellowish color.③A different mechanism is responsible for the ion tail.Near the Sun,ultraviolet radiation from the Sun(solar wind)ionizes and excites the atoms in the coma.Asthe solar wind sweeps through the coma,the high-velocity charged particles of the solar wind interact with the electrically charged excited ions in the coma,driving them away from the head of the comet.In returning to lower-energy states,these excited ions emit photons and form a luminous,bluish-colored tail extending out from the comet directly away from the Sun.Since both kinds of tails are produced by radiation streaming out from the Sun,they extend out from the coma in the general direction away from the Sun.A comet may exhibit several tails of each kind.④Although the nucleus is of the order of a few kilometers in size,the diameter of the coma may be tens or hundreds of thousands of kilometers;the tails typically extend out tens or hundreds of millions of kilometers away from the coma.⑤A comet leaves a trail of matter behind it as it moves through the inner solar system.Some of this debris may get strewn across Earth's orbit around the Sun. When Earth passes through this part of its annual path,it sweeps through the dust trail.The particles enter Earth's atmosphere at high velocity.The air friction can cause one of these bits of matter to produce a brief streak of light as it burns up in the atmosphere.⑥Since a comet loses matter on each pass by the Sun,eventually it will be depleted to the point where it is no longer ets that approach the Sun have finite lifetimes.Given the typical sizes of comets and the typical rates at which they lose matter,astronomers have concluded that the lifetimes of comets with orbits that bring them near enough to the Sun to be seen from Earth are very much shorter than the age of the solar system.Where do the new comets come from to replace the old ones that dissipate and vanish from view?⑦Dutch astronomer Jan Oort proposed that a giant cloud of matter left over from the formation of the solar system surrounds the Sun and extends out to about 50,000astronomical units.This cloud contains large chunks of matter like the nuclei of comets.The gravitational influence of a passing star can be sufficient to perturb the orbit of one of these chunks to send it toward the inner solar system and bring it near the Sun.译文彗星的结构和组成①天文学家现在对彗星的真正含义有了相当好的了解。

关于太空宇宙的英语作文三句或四句I. IntroductionThe universe, an immense expanse teeming with celestial wonders, has long captivated human imagination and driven our insatiable quest for knowledge. From the twinkling stars that adorn our night skies to the enigmatic black holes lurking in the darkness, the cosmos is a realm of unfathomable beauty and mystery. This vast, ever-expanding entity, comprised of billions of galaxies, each housing countless stars and their planetary systems, represents the ultimate frontier for scientific inquiry.II. The Observable Universe: A Glimpse into Infinity Our observable universe, extending approximately 93 billion light-years in diameter, is but a tiny fraction of what may lie beyond. It contains a staggering array of celestial bodies, ranging from blazing stars in various stages of life to the ethereal, ghostly remnants of exploded stars known as supernovae. Furthermore, it is threaded by invisible forces, such as gravity and dark matter, which shape the cosmic web and govern the dance of galaxies. The cosmic microwave background radiation, theresidual heat left over from the Big Bang, whispers tales of our universe's fiery birth and subsequent expansion.III. The Search for Extraterrestrial LifeAs we peer deeper into this celestial tapestry, one question looms large: Are we alone in the universe? The discovery of thousands of exoplanets orbiting distant stars has fueled optimism that Earth might not be the sole cradle of life. These alien worlds, some found within the "habitable zones" where liquid water can exist, beckon us to ponder the possibility of extraterrestrial organisms thriving under different conditions. Ongoing missions, such as NASA's James Webb Space Telescope and the search for biosignatures, aim to unveil whether these seemingly habitable planets indeed harbor life, thus rewriting our understanding of our place in the cosmos.IV. Challenges and Future ProspectsExploring the universe is an audacious endeavor fraught with challenges, including the vast distances involved, harsh space environments, and the limitations of current technology. However, advancements in fields like astrophysics, aerospace engineering, and artificial intelligence hold promise for surmounting these obstacles.Space telescopes with unprecedented resolution will enable us to observe the universe in greater detail, while interstellar travel concepts like nuclear fusion propulsion and light sails could potentially revolutionize our ability to traverse the cosmos. Moreover, the pursuit of establishing permanent human settlements on other planets, such as Mars, signifies our aspirations to become a multi-planetary species and secure humanity's future among the stars.In conclusion, the universe, a boundless expanse of celestial marvels and profound mysteries, continues to entice and challenge us. As we delve deeper into its secrets, we not only broaden our understanding of the cosmos but also gain invaluable insights into our own existence. The quest to explore and comprehend this magnificent realm reflects our innate curiosity and unyielding spirit of exploration, promising a future filled with groundbreaking discoveries and paradigm-shifting revelations about the universe we call home.。

高二英语天文联想单选题40题1. Astronomers often use telescopes to observe ______, which is the largest planet in our solar system.A. VenusB. JupiterC. MarsD. Earth答案：B。

解析：太阳系中最大的行星是木星Jupiter。

选项A金星Venus，选项C火星Mars，选项D地球Earth都不符合题意。

2. The ______ is at the center of our solar system, providing light and heat to all the planets.A. moonB. starC. sunD. comet答案：C。

解析：在太阳系中心，为所有行星提供光和热的是太阳sun。

选项A月亮moon是地球的卫星，选项B恒星star概念太宽泛，选项D彗星comet不符合题意。

3. Many satellites orbit around ______, which is our home planet.A. MarsB. EarthC. SaturnD. Neptune答案：B。

解析：地球Earth是我们的家园星球，很多卫星围绕地球运转。

选项A火星Mars、选项C土星Saturn、选项D海王星Neptune 不符合题意。

4. We can see a beautiful ring around ______ through a powerful telescope.A. JupiterB. UranusC. SaturnD. Venus答案：C。

解析：通过强大的望远镜我们能看到土星Saturn周围有美丽的环。

选项A木星Jupiter、选项B天王星Uranus、选项D金星Venus没有这样的特征。

5. ______ is known as the "Red Planet" because of its reddish appearance.A. MarsB. MercuryC. VenusD. Jupiter答案：A。

2024年牛津版英语初一上学期期中复习试卷及解答参考一、听力部分（本大题有20小题，每小题1分，共20分）1、Listen to the conversation and choose the correct answer. What does the boy want to do this weekend?A. Go to the cinemaB. Visit his grandparentsC. Play footballAnswer: C. Play footballExplanation: In the conversation, the boy expresses his desire to play football with his friends over the weekend. The other options are not mentioned or chosen by the boy in the dialogue.2、What time does the girl’s train leave?A. At 6:30B. At 7:00C. At 7:30Answer: B. At 7:00Explanation: The dialogue mentions that the girl’s train is scheduled to depart at 7 o’clock. It’s important to pay attention to the specific timesgiven in the conversation to select the correct answer.3、What are the speakers discussing in this conversation?A. The weather forecast for the weekend.B. The new student orientation at the school.C. The upcoming sports competition.Answer: BExplanation: The conversation revolves around the new student orientation, which is a typical topic for a school event, indicating that the speakers are discussing the school’s welcome and introduction activities for new students. The mention of “orientation” in the conversation confirms option B as the correct answer.4、How does the woman describe her favorite book?A. It’s a mystery novel that keeps her guessing.B. It’s a historical fiction that takes her back in time.C. It’s a science fiction that’s both entertaining and thought-provoking.Answer: BExplanation: The woman in the conversation expresses her fondness for a book that “takes me back to a different time and place,” which is a characteristic of historical fiction. This description aligns with option B, making it the correct answer. The other options describe different genres, but the woman’s specific comments about time and place suggest she is referring to historical fiction.5、What does the boy want to drink?A. WaterB. JuiceC. MilkRecording: Girl: “What would you like to drink?” Boy: “I’m thirsty. Please give me some water.”Answer: A. WaterExplanation: The boy clearly states that he would like some water because he is thirsty.6、Where did the girl lose her hat?A. At schoolB. In the parkC. At the mallRecording: Girl: “Have you seen my hat? I can’t find it anywhere.” Boy: “Did you check the park where we played yesterday?”Answer: B. In the parkExplanation: The boy suggests that the girl check the park where they played the day before, implying that it’s likely she lost her hat there.7、What are the speakers mainly discussing?A. The weather forecast for the next week.B. The importance of studying English.C. The differences between English and Chinese.Answer: BExplanation: The speakers are talking about the importance of studying English, emphasizing its global significance and the need for it in the modern world. The conversation does not focus on weather or language differences.8、How does the man prefer to learn English?A. By reading books only.B. By watching English movies.C. By attending a language class.Answer: BExplanation: The man mentions that he prefers to learn English by watching English movies, as it helps him improve his listening and speaking skills. He does not mention reading books or attending a language class as his preferred method.9、What subject does Tom say is his favorite?•A) Mathematics•B) English•C) History•Answer: B) English•Explanation: In the dialogue, Tom mentions that he enjoys reading and writing, which indicates that English is his favorite subject.10、How does Mary feel about Science?•A) She finds it boring.•B) She thinks it’s too difficult.•C) She loves experimenting in class.•Answer: C) She loves experimenting in class.•Explanation: Mary expresses her enthusiasm for practical lessons in the conversation, specifically mentioning how much she enjoys doingexperiments during Science class.Note: This section is based on hypothetical dialogue and should be used as an example only.This would typically be followed by the actual audio material which isn’t provided here. The students would listen to the recording and then answer the questions accordingly.11.You hear a conversation between two students, Alice and Bob, talking about their weekend plans. Listen carefully and answer the question.Question: What does Bob plan to do on Saturday afternoon?A. He plans to visit his grandparents.B. He plans to go to the movies.C. He plans to play soccer with his friends.Answer: B. He plans to go to the movies.Explanation: In the conversation, Bob says, “I’m going to see a new movie this weekend. It’s really exciting!” This indicates that he plans to go to the movies on Saturday afternoon.12.You hear a monologue by a teacher talking about the importance of exercise. Listen carefully and answer the question.Question: According to the teacher, what are the benefits of regular exercise?A. It helps students improve their academic performance.B. It helps students stay healthy and fit.C. It helps students make new friends.Answer: B. It helps students stay healthy and fit.Explanation: In the monologue, the teacher says, “Regular exercise is crucial for our health. It helps us stay fit, reduces stress, and improves our overall well-being.”This indicates that the benefits of regular exercise are to help students stay healthy and fit.13、You will hear a conversation between two friends talking about their weekend plans. What activity are they going to do together on Saturday?A)Go to the cinemaB)Visit a museumC)Have a picnic in the parkAnswer: C) Have a picnic in the parkExplanation: In the conversation, one friend suggests having a picnic because the weather forecast predicts a sunny day, and the other agrees enthusiastically, mentioning they can also play frisbee in the park.14、Listen to the announcement from the school’s principal. What special event is being organized at the school next Friday?A) A sports competitionB) A science fairC) A charity bake saleAnswer: B) A science fairExplanation: The principal announces that there will be a science fair next Friday, where students will have the opportunity to present their projects and experiments. It is mentioned that this is a great chance for students to showcase their creativity and scientific knowledge.15.You are listening to a conversation between two students at a school canteen.A. Student A: I heard you’re going to the science fair next month.B. Student B: Yeah, I am. I’m really excited about it.Question: What is Student B’s plan for next month?A. To go to the science fair.B. To have a science class.C. To study for an exam.Answer: AExplanation: The correct answer is A because Student B explicitly mentions that they are going to the science fair next month, indicating it is their plan.16.You are listening to a teacher explaining the rules of a school competition.A. Teacher: Remember, the competition starts at 9 am sharp. Be on time.B. Teacher: All participants must wear their school uniform. No exceptions.C. Teacher: The competition will be held in the school gymnasium. Please meet there.Question: Where will the school competition be held?A. In the classroom.B. In the school library.C. In the school gymnasium.Answer: CExplanation: The correct answer is C because the teacher specifically states that the competition will be held in the school gymnasium.17.You are listening to a conversation between two students discussing their school project.Question: What is the project about?A. A science experimentB. A history presentationC. A music concertD. A sports eventAnswer: B. A history presentationExplanation: The conversation mentions that they are working on a presentation about famous historical figures. Therefore, the correct answer isB. A history presentation.18.You are listening to a dialogue between a teacher and a student discussing the student’s upcoming test.Question: What subject is the student most likely studying?A. MathematicsB. ScienceC. EnglishD. Physical EducationAnswer: C. EnglishExplanation: The student mentions that they are preparing for the upcoming English test. The teacher also asks about the student’s progress in English. Thus, the correct answer is C. English.19.You hear a conversation between two students at a library. The first student is asking for help finding a book. Listen and answer the question.What is the title of the book the first student is looking for?A)The Art of LivingB)Science and TechnologyC)The World of HistoryD)English for BeginnersAnswer: D) English for BeginnersExplanation: In the conversation, the first student mentions they need a book for learning English, which corresponds to option D.20.You listen to a short lecture about the solar system. The speaker mentions some key facts about the planets.Which of the following is NOT mentioned by the speaker?A)Jupiter is the largest planet in the solar system.B)Earth is located between Venus and Mars.C)Saturn has a ring system.D)Mars is often referred to as the Red Planet.Answer: B) Earth is located between Venus and Mars.Explanation: The speaker discusses Jupiter, Saturn, and Mars, including their unique features. However, the location of Earth in relation to Venus and Mars is not mentioned in the lecture.二、阅读理解（30分）Title: The Magic of the MoonThe moon has always been a source of fascination for humans. Throughout history, people have looked up at the sky and seen the moon’s changing phases, from a crescent to a full moon. This celestial body has inspired countless stories, songs, and even entire mythologies. In this article, we will explore the magic of the moon and its impact on our lives.One of the most intriguing aspects of the moon is its phases. The moon goes through a cycle of phases every 29.5 days, which is known as the synodic month. The phases are caused by the moon’s position in relation to the Earth and the sun. When the moon is between the Earth and the sun, we see the new moon. As the moon moves around the Earth, more of its surface becomes illuminated, leading to the first quarter, full moon, and last quarter phases.The full moon is often associated with various cultural and folk beliefs. For example, in some cultures, it is believed that the full moon affects the behavior of animals and humans. People often report feeling more emotional orrestless during a full moon. However, scientific evidence does not support these claims.Another fascinating aspect of the moon is its impact on the ocean’s tides. The gravitational pull of the moon and the sun causes the tides to rise and fall. This natural phenomenon has a significant impact on marine life and human activities such as fishing and shipping.The moon also plays a crucial role in space exploration. The Apollo missions in the 1960s and 1970s were a major step forward in human space exploration. Astronauts landed on the moon’s surface and brought back samples, providing valuable information about our solar system’s early history.Questions:1.How long does it take for the moon to go through a complete cycle of phases?A) 24 hoursB)29.5 daysC)30 daysD) 1 year2.What is the term used to describe the moon’s position between the Earth and the sun?A) New moonB) Full moonC) Last quarterD) First quarter3.Which of the following statements about the full moon is NOT supported by scientific evidence?A) It affects the behavior of animals.B) It causes more accidents on the road.C) It affects the human sleep cycle.D) It influences the tides.Answers:1.B) 29.5 days2.A) New moon3.B) It causes more accidents on the road.三、完型填空（15分）Three idiom completions:Read the following passage and choose the best word or phrase to complete each blank.When we think of a “black sheep,” we often imagine someone who doesn’t fit in with the rest of the family or group. This idiom comes from an old English proverb that says, “As sure as God made little green apples, there’s a black sheep in ever y flock.”1.The black sheep in the family was always the one who___________from the rest of the family.a.stuck outb.kept upc.fit ind.followed2.The idiom “black sheep” is used to describe someone who is ___________.a.kind-heartedb.generousc.rebelliousd.cooperative3.According to the proverb, every group has a black sheep, which means they are ___________.a.not noticeableb.differentc.similarmon4.The black sheep is often considered to be the___________one in the group.a.most popularb.most rebelliousc.most responsibled.most friendly5.Even though the black sheep might cause some trouble, they are still an important part of the ___________.a.familymunityc.countryd.groupAnswers:1.a. stuck out2.c. rebellious3.b. different4.b. most rebellious5.d. group四、语法填空题（本大题有10小题，每小题1分，共10分）1、My favorite sport is playing _______.A. footballB. the footballC. footballs答案：B解析：此题考查冠词的用法。

小学上册英语第5单元真题[含答案]英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1. A __________ is formed through the interaction of multiple geological processes.2.I have a wonderful . (我有一个美好的。

)3.The bird sings sweet ______.4. A __________ is a natural feature that allows water to flow through the land.5.What is the name of the flower that is red and symbolizes love?A. DaisyB. RoseC. TulipD. Lily答案:B6.The ______ (狮子) roars loudly in the wild.7.What is the name of the fairy tale with a girl and a glass slipper?A. Little Red Riding HoodB. CinderellaC. Beauty and the BeastD. The Frog Prince8.She has a ___ (happy/sad) look.9.The _____ (植物群落) is diverse and vibrant.10.My favorite animal is a ______ (小狗). It loves to play and run around the ______ (公园).11.Newton's laws describe the relationship between _______ and motion.12.My favorite toy is a ____. (玩具名称)13.The flamingo stands on one leg to _________ (休息).14.The process of chromatography separates mixtures based on _____.15.W hen it’s cold, I wear ______ (毛衣).16.The __________ helps to maintain earth's climate.17.We should protect __________ (濒危) plant species.18.What do we call the study of living organisms?A. BiologyB. ChemistryC. PhysicsD. Astronomy答案:A19.What is the past tense of "go"?A. GoesB. GoneC. WentD. Going答案:C20.What is the main gas found in the air we breathe?A. OxygenB. HeliumC. NitrogenD. Hydrogen答案:C21. A wild boar has sharp ______ (牙齿).22.The __________ can reveal the history of the Earth's geological formations.23.My friends and I had a toy ____ party! (玩具名称)24.What is the name of the famous British author known for "Harry Potter"?A. J.K. RowlingB. Philip PullmanC. C.S. LewisD. Roald Dahl答案:A25.I like _____ (to eat/to drink).26.I have a special ________ that tells jokes.27.I like to ________ (experiment) with ideas.28.The _______ (小狼) plays with its siblings in the den.29.I like to _____ at the park. (play)30.Which of these is a type of tree?A. FernB. MapleC. GrassD. Flower答案:B31.The __________ (历史遗址) help preserve past cultures.32.The _____ (thyme) plant is aromatic and useful.33.I hope to make a positive impact on my _______ (社区). Every little effort counts.34.What do we call the person who plays the violin?A. ViolinistB. PianistC. MusicianD. Conductor35.What is the capital of Iraq?A. BaghdadB. BasraC. ErbilD. Mosul36.The first Olympic Games took place in _______.37.I enjoy _____ (reading/watching) movies.38.The stars are _____ (twinkling/shining) in the sky.39.What is the name of the famous American singer known for her powerful voice?A. Aretha FranklinB. Mariah CareyC. Whitney HoustonD. Adele答案:C Whitney Houston40. A substance that conducts electricity in solution is called an ______.41.We are learning about ______ (historical) events.42. A __________ (温室) is a good place for plants.43.The doctor, ______ (医生), takes care of sick people.44.I have a ___ (big) dream.45.Which animal says "moo"?A. DogB. CatC. CowD. Duck答案:C Cow46.She is ___ (reading/writing) a letter.47.In a chemical reaction, the total number of atoms of each element must be the same on both _____.48.The chemical formula for cobalt(II) sulfate is _____.49.The ________ was a notable treaty that settled numerous disputes.50.What is the name of the famous bear in "The Jungle Book"?A. BalooB. MowgliC. Shere KhanD. Bagheera答案:A51. A ______ (园艺) hobby can be rewarding.52.Metals tend to lose electrons and form ______ ions.53.The boy is ___ a ball. (catching)54.I like to _____ my friends at school. (see)55.I made a puppet show with my ____. (玩具名称)56.They are _____ (skipping) rope.57.The stars are _____ (twinkling/shining) in the sky.58. A _____ (野生植物) grows naturally without human care.59.My friend is very __________ (有耐心).60.What do we call the outer layer of the Earth?A. CrustB. MantleC. CoreD. Lithosphere答案:A Crust61. A ____(public-private partnership) leverages resources for community benefit.62.What is the opposite of soft?A. HardB. SmoothC. GentleD. Tender63.Which month is known for April Fools’ Day?A. MarchB. AprilC. MayD. June64. A _____ (生态旅游) can focus on plant life.65.The birds sing in the ______.66.What is the capital of Iceland?A. OsloB. ReykjavikC. HelsinkiD. Copenhagen答案:B67. A ball falls down because of ______ (gravity).68.My cousin is a ______. She loves to help out at school.69.The _______ (Chernobyl disaster) was a catastrophic nuclear accident in 1986.70.What do you call the person who takes care of animals?A. VeterinarianB. FarmerC. ZookeeperD. All of the above71.What do we call an animal that eats both plants and meat?A. HerbivoreB. CarnivoreC. OmnivoreD. Insectivore72.What is the term for a collection of stars, gas, and dust bound together by gravity?A. GalaxyB. NebulaC. Star ClusterD. Solar System答案:A73.The _______ produces beautiful blooms throughout the year.74.Which instrument has keys and is played by pressing them?A. GuitarB. PianoC. ViolinD. Drum答案:B75.What is the freezing point of water in Celsius?A. 0B. 32C. 100D. -1答案:A76.The _______ (蜥蜴) is a quick mover.77.What do you call the story of someone's life?A. BiographyB. NovelC. FictionD. Poem78.What is the largest mammal in the ocean?A. SharkB. DolphinC. WhaleD. Octopus答案:C Whale79.What do you call the study of weather?A. GeographyB. MeteorologyC. EcologyD. Climatology答案:B80.I see _____ (猴子) at the zoo.81. A ____ is a friendly pet that often wags its tail.82.What is the opposite of "happy"?A. SadB. AngryC. ExcitedD. Tired答案:A83.My sister's favorite color is ______ (粉红色). She has many ______ (玩具).84.of Mexico is located ________ (在美国南部). The Gupt85.The _______ can be used for decoration.86.How many months are in a year?A. TenB. ElevenC. TwelveD. Thirteen答案:C87.What do we call the person who studies stars?A. BiologistB. AstronomerC. GeologistD. Chemist88.The Andromeda Galaxy is on a collision course with the _______.89.The _______ provides shelter and food for wildlife.90.The __________ (古罗马) used aqueducts to transport water.91.What do we call the lines of latitude and longitude on a map?A. GridsB. CoordinatesC. ScalesD. Borders92.What do you call the layer of gases surrounding Earth?A. AtmosphereB. HydrosphereC. LithosphereD. Biosphere答案:A93.The process of fermentation converts sugars into ______.94.I saw a fox in the ______.95. A ______ reaction releases energy, often as heat or light.96.What do we call a person who writes books?A. AuthorB. PainterC. MusicianD. Director97.What is the name of the famous ancient city in Italy?A. PompeiiB. RomeC. HerculaneumD. All of the above98.What is 7 + 6?A. 12B. 13C. 14D. 1599.The kitten is ______ in a sunny spot. (sleeping)100.What is the capital of China?A. TokyoB. BeijingC. SeoulD. Bangkok。

tpo50阅读-3 Star Death原文 (1)译文 (2)题目 (3)答案 (7)背景知识 (8)原文Star Death①Until the early- to mid-twentieth century, scientists believed that stars generate energy by shrinking. As stars contracted, it was thought, they would get hotter and hotter, giving off light in the process. This could not be the primary way that stars shine, however. If it were, they would scarcely last a million years, rather than the billions of years in age that we know they are. We now know that stars are fueled by nuclear fusion. Each time fusion takes place, energy is released as a by-product. This energy, expelled into space, is what we see as starlight. The fusion process begins when two hydrogen nuclei smash together to form a particle called the deuteron (a combination of a positive proton and a neutral neutron). Deuterons readily combine with additional protons to form helium. Helium, in turn, can fuse together to form heavier elements, such as carbon. In a typical star, merger after merger takes place until significant quantities of heavy elements are built up.②We must distinguish, at this point, between two different stellar types: Population I and Population ll, the latter being much older than the former. These groups can also be distinguished by their locations. Our galaxy, the Milky Way, is shaped like a flat disk surrounding a central bulge. Whereas Population I stars are found mainly in the galactic disk, Population II stars mostly reside in the central bulge of the galaxy and in the halo surrounding this bulge.③Population II stars date to the early stages of the universe. Formed when the cosmos was filled with hydrogen and helium gases, they initially contained virtually no heavy elements. They shine until their fusible material is exhausted. When Population II stars die, their material is spread out into space. Some of this dust is eventually incorporated into newly formed Population I stars. Though Population I stars consist mostly of hydrogen and helium gas, they also contain heavy elements (heavier than helium), which comprise about 1 or 2 percent of their mass. These heavier materials are fused from the lighter elements that the stars have collected. Thus, Population I stars contain material that once belonged to stars from previous generations. The Sun is a good example of a Population I star.④What will happen when the Sun dies? In several billion years, our mother starwill burn much brighter. It will expend more and more of its nuclear fuel, until little is left of its original hydrogen. Then, at some point in the far future, all nuclear reactions in the Sun’s center will cease.⑤Once the Sun passes into its "postnuclear" phase, it will separate effectively into two different regions: an inner zone and an outer zone. While no more hydrogen fuel will remain in the inner zone, there will be a small amount left in the outer zone. Rapidly, changes will begin to take place that will serve to tear the Sun apart. The inner zone, its nuclear fires no longer burning, will begin to collapse under the influence of its own weight and will contract into a tiny hot core, dense and dim. An opposite fate will await the outer region, a loosely held-together ball of gas. A shock wave caused by the inner zone's contraction will send ripples through the dying star, pushing the stellar exterior's material farther and farther outward. The outer envelope will then grow rapidly, increasing, in a short interval, hundreds of times in size. As it expands, it will cool down by thousands of degrees. Eventually, the Sun will become a red giant star, cool and bright. It will be so large that it will occupy the whole space that used to be the Earth's orbit and so brilliant that it would be able to be seen with the naked eye thousands of light-years away. It will exist that way for millions of years, gradually releasing the material of its outer envelope into space. Finally, nothing will be left of the gaseous exterior of the Sun; all that will remain will be the hot, white core. The Sun will have become a white dwarf star. The core will shrink, giving off the last of its energy, and the Sun will finally die.译文恒星的消亡①直到二十世纪中叶之前，科学家们一直认为恒星通过收缩来产生能量。