Observational tests of the evolution of spheroidal galaxies and predictions for SIRTFSpitze

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2020年广东省中小学生天文知识竞赛试题(低年组)

2020年广东省中小学生天文知识竞赛试题（低年组）注意事项：1、本卷为闭卷考试，请答卷人按照自己的真实水平独立完成。

2、选择题全部为单项选择，考生直接在试题页面中点选一个最接近正确的答案，答错不扣分。

3、总分100分，每题2分，考试时间100分钟。

4、本场考试允许使用不具编程功能的计算器。

5、考试过程中不得切出考试页面，否则平台将自动收卷。

6、比赛结果将在广东天文学会网站和微信公众号公布。

_______________________________________________________________________________________________ Part 1. 天文热点1. 我国首个自主发射的火星探测器“天问一号”计划于何时入轨火星？ BA. 2020年12月底左右B. 2021年2月底左右C. 2021年5月中左右D. 2022年7月底左右2. 我国嫦娥五号探测器在今年何时发射升空？ CA. 12月24日B. 12月7日C. 11月24日D. 11月28日3. 2020年的诺贝尔物理学奖分别颁发给罗杰·彭罗斯、莱因哈特·根策尔和安德烈娅·盖兹。

其中彭罗斯获奖的理由是“发现黑洞形成是广义相对论的一个预言”，那根策尔和盖兹获奖的理由是？ AA. 发现银河系中心的超大质量致密天体B. 发现第一颗环绕类太阳恒星运动的系外行星C. 验证了引力波的存在D. 发现了一种测量宇宙大尺度结构的探针4. 以下哪所高校在今年正式成立天文系？ DA. 香港科技大学B. 贵州大学C. 中山大学D. 广州大学5. 今年7月，一颗“黑马”彗星亮度达到2等以上，吸引了很多爱好者拍摄。

这颗彗星是？CA. C/2019 Y4 (ATLAS)B. C/2020 F8 (SWAN)C. C/2020 F3（NEOWISE）D. C/2019 U6 (Lemmon)6. 关于今年6月21日的日环食，下列哪个地点位于环食带之外？ BA. 纳木错B. 武汉C. 厦门D. 泸州7. 今年4月24日是我国首个人造卫星“东方红一号”成功发射_______周年。

8星系与宇宙的大尺度结构

~45x109太阳质量
•根据质光关系定M33中发光物质的质量 •太阳的绝对光度：4.8；M33绝对光度：-19.5
•光度差：2.51224.3=~5.2x109
•M33中发光物质的质量： =~5.2x109 太阳质量，只有动力学质量的1/10! •进一步的改正：不发光的气体和尘埃，恒星质光关系的改正，银河系的质光关系：1.5
宽发射线区
Gas clouds moving at several thousand km/sec These appear to be orbital motions (gravity) Gas is photoionized by radiation from the accretion disk and its corona
z
0 0.158 0
活动星系核：高光度

在可见光波段，活动星系核比它的寄主星系要亮几千倍！
活动星系核：宽的发射谱

Comparable power emitted across ~seven orders of magnitude in photon energy
发射区域：尺度小！

Reverberation Mapping
Measure the time lag in response of BLR clouds to changing ionizing flux from the accretion disk Implied sizes range from light weeks in low power AGN to light years in powerful ones Size plus velocity yield black hole mass

天体物理经典公式总结归纳

天体物理经典公式总结归纳天体物理是研究宇宙中天体的性质、演化和相互作用的学科，它所涉及的问题多种多样且复杂。

在天体物理学的发展过程中，科学家们总结出了一些经典公式，这些公式揭示了宇宙中的基本物理规律和天体之间的相互关系，为研究、理解和解释天体现象提供了重要工具。

本文将对一些常见的天体物理公式进行总结归纳。

1. 开普勒第三定律开普勒第三定律描述了行星绕太阳公转的规律，其数学表达式为：T^2 = k * r^3，其中T代表行星公转周期，r代表行星到太阳的平均距离，k是与太阳和行星的质量有关的常数。

这一定律揭示了行星运动周期与其轨道半长轴的立方成正比的关系，为行星运动的研究提供了基本参考。

2. 光谱位移公式光谱位移公式描述了光源在接近或远离观测者时，其光谱发生的位移现象。

对于远离观测者的光源而言，其光谱将发生红移；而接近观测者的光源则产生蓝移。

这一公式的数学表达式为：z = (λ_obs - λ_rest) / λ_rest，其中z是光谱位移，λ_obs代表观测到的光谱波长，λ_rest代表光源的本来波长。

光谱位移公式是测量天体运动速度、判断宇宙膨胀和探索宇宙时空结构的重要工具。

3. 斯蒂芬-玻尔兹曼定律斯蒂芬-玻尔兹曼定律描述了黑体辐射的功率和温度之间的关系。

它通过以下公式进行表达：P = σ * A * T^4，其中P代表黑体辐射的功率，σ是斯蒂芬-玻尔兹曼常数，A代表黑体的表面积，T表示黑体的温度。

斯蒂芬-玻尔兹曼定律提供了研究天体能量平衡、辐射特性和表面温度的依据。

4. 普朗克辐射公式普朗克辐射公式描述了黑体辐射谱线的形状和强度。

该公式的数学表达式为：B(λ, T) = (2h*c^2 / λ^5) * (1 / (e^(hc/λkT) - 1))，其中B(λ, T)代表黑体辐射强度，h是普朗克常数，c是光速，λ代表波长，k是玻尔兹曼常数，T表示黑体的温度。

普朗克辐射公式为研究天体的辐射特性和能量分布提供了基本工具。

SrVO3 Hubbard band 和氧空位

PHYSICAL REVIEW B94,241110(R)(2016)Hubbard band versus oxygen vacancy states in the correlated electron metal SrVO3S.Backes,1T.C.R¨o del,2,3F.Fortuna,2E.Frantzeskakis,2P.Le F`e vre,3F.Bertran,3M.Kobayashi,4R.Yukawa,4 T.Mitsuhashi,4M.Kitamura,4K.Horiba,4H.Kumigashira,4R.Saint-Martin,5A.Fouchet,6B.Berini,6Y.Dumont,6A.J.Kim,1F.Lechermann,7,8H.O.Jeschke,1M.J.Rozenberg,9R.Valent´ı,1,*and A.F.Santander-Syro2,†1Institut f¨u r Theoretische Physik,Goethe-Universit¨a t Frankfurt,Max-von-Laue-Strasse1,60438Frankfurt am Main,Germany 2CSNSM,Univ.Paris-Sud,CNRS/IN2P3,Universit´e Paris-Saclay,91405Orsay Cedex,France3Synchrotron SOLEIL,L’Orme des Merisiers,Saint-Aubin-BP48,91192Gif-sur-Yvette,France 4Photon Factory,Institute of Materials Structure Science,High Energy Accelerator Research Organization(KEK),1-1Oho,Tsukuba305-0801,Japan5SP2M-ICMMO-UMR-CNRS8182Universit´e Paris-Sud,Universit´e Paris-Saclay,91405Orsay Cedex,France 6GEMaC,Universit´e de Versailles St.Quentin en Y.-CNRS,Universit´e Paris-Saclay,Versailles,France7Institut f¨u r Theoretische Physik,Universit¨a t Hamburg,Jungiusstrasse9,20355Hamburg,Germany8Institut f¨u r Keramische Hochleistungswerkstoffe,TU Hamburg-Harburg,D-21073Hamburg,Germany 9Laboratoire de Physique des Solides,CNRS,Univ.Paris-Sud,Universit´e Paris-Saclay,91405Orsay Cedex,France(Received22February2016;published19December2016)We study the effect of oxygen vacancies on the electronic structure of the model strongly correlatedmetal SrVO3.By means of angle-resolved photoemission spectroscopy(ARPES)synchrotron experiments,we investigate the systematic effect of the UV dose on the measured spectra.We observe the onset of a spuriousdose-dependent prominent peak at an energy range where the lower Hubbard band has been previously reportedin this compound,raising questions on its previous interpretation.By a careful analysis of the dose-dependenteffects we succeed in disentangling the contributions coming from the oxygen vacancy states and from the lowerHubbard band.We obtain the ARPES spectrum in the limit of a negligible concentration of vacancies,wherea clear signal of a lower Hubbard band remains.We support our study by means of state-of-the-art ab initiocalculations that include correlation effects and the presence of oxygen vacancies.Our results underscore therelevance of potential spurious states affecting ARPES experiments in correlated metals,which are associatedwith the ubiquitous oxygen vacancies as extensively reported in the context of a two-dimensional electron gas atthe surface of insulating d0transition metal oxides.DOI:10.1103/PhysRevB.94.241110Introduction.A major challenge of modern physics is to understand the fascinating phenomena in strongly correlated transition metal oxides(TMOs),which emerge in the neighbor-hood of the Mott insulator state.Some preeminent examples that have gathered interest for almost30years are high temperature superconductivity,colossal magnetoresistance, heavy fermion physics,and,of course,the Mott metal-insulator transition itself[1].Signiﬁcant theoretical progress was made with the introduction of dynamical meanﬁeld theory (DMFT)and its combination with ab initio density functional methods[local density approximation(LDA)+DMFT],which allows treatment of the interactions promoting itinerancy and localization of electrons on equal footing[2–4].Among the most emblematic achievements of DMFT is the prediction of a Hubbard satellite,which separates from the conduction band of a metal.This satellite results from the partial localization of conduction electrons due to their mutual Coulomb repulsion. Early DMFT studies also showed that it is the precursor of the localized electronic states of a Mott insulator[5].Since then,these predictions promoted a large number of studies using photoemission spectroscopy,which is a technique to directly probe the presence of Hubbard bands.In this context, the TMO system SrVO3has emerged as the drosophila model system to test the predictions of strongly correlated electron *valenti@itp.uni-frankfurt.de†andres.santander@csnsm.in2p3.fr theories.In fact,SrVO3is arguably the simplest correlated metal.It is a simple cubic perovskite,with nominally one electron per V site,which occupies a threefold degenerate t2g conduction band.While the presence of a satellite in the photoemission spectra of Ni metal was already well known,in the context of correlated TMOs,the Hubbard band was originally reported in a systematic investigation of Ca1−x Sr x VO3[6],which was followed by many subsequent studies,including angle-resolved photoemission spectroscopy (ARPES)[7–9]and comparisons with theoretical predictions (see,for instance,Refs.[10–20],among others).One of the most salient features in SrVO3is the observation of a broad peak at an energy of about−1.5eV in angle integrated photoemission spectra(upper black curve in Fig.1), which is interpreted as a Hubbard satellite linked to the V t2g electrons.This feature is also seen in a large range of 3d1materials[21,22].The ratio of spectral strength between the quasiparticle(QP)state and the incoherent satellite in SrVO3is an important indicator of the magnitude of electron correlations[1,2].However,photoemission experiments using different photon energies or light brilliance have reported very dissimilar values for such a ratio[11],making the quantitative benchmarking of realistic ab initio theories for correlated electron systems difﬁcult[6,11,18,23,24].Moreover,as shown in Fig.1,a broad peak at about the same energy is also observed in several d0TMO cubic perovskites,such as SrTiO3, KTaO3,or anatase TiO2.Nevertheless,in all these cases the feature has been clearly linked to the presence of oxygenS.BACKES et al.PHYSICAL REVIEW B94,241110(R)(2016)FIG.1.Integrated UV photoemission spectra for various per-ovskite oxides,showing a quasiparticle peak at E F and an in-gap state at energies between1and1.5eV.For SrVO3(upper black curve),a correlated-electron metal,the QP peak corresponds to the bulk conduction band,and as will be shown further,the in-gap state is a superposition of the lower Hubbard band and localized electronic states associated with oxygen vacancies.For the other d0 oxides,such as KTaO3(blue curve),anatase TiO2(green curve), or SrTiO3(red curve),the QP peak and in-gap state correspond respectively to a conﬁned quasi-2D electron gas at the sample surface and to localized states,all formed by oxygen vacancies.The crystal orientation(normal to the samples’surface)is indicated in all cases. defects[25–32].Interestingly,recent ab initio calculations show that the spectral weight at−1.3eV in SrTiO3most likely is not of Ti t2g orbital character,but should be understood as an in-gap defect state with Ti e g character[33–36].Thus,we are confronted with the fact that at about1.5eV below the Fermi level(E F),weﬁnd the lower Hubbard bands of d1systems as well as the in-gap states of oxygen-deﬁcient d0systems.In view of these observations one may unavoidably wonder(and worry),despite the great success of DMFT methods,whether the putative Hubbard satellite of SrVO3might also originate from oxygen vacancy states.Moreover,one should also worry about the possibility of these extrinsic states affecting the features of the conduction band dispersion.In the present Rapid Communication we resolve these issues in a thorough manner.We present a systematic photoemission study of SrVO3,to demonstrate dramatic consequences in the spectra due to the creation of oxygen ing ARPES,we directly show that the UV or x-rays used for measurements can produce a large enhancement, of almost an order of magnitude,of the peak at−1.5eV, similar to the effect observed in d0oxide insulators[25–28,37].Despite these signiﬁcant effects on the energy states around the Mott-Hubbard band,we are able to determine the bulk SrVO3photoemission spectrum in the limit of a negligible concentration of vacancies,where a clear signal of the dispersive correlated Hubbard band remains.We support the interpretation of the experimental data by means of state-of-the-art LDA+DMFT calculations on SrVO3with oxygen vacancies.Consistent with our experimental data,the calculations show that oxygen vacancies produce states(of e g symmetry)at energies near the Hubbard satellite.While our study provides deﬁnite evidence of a correlated Hubbard band in SrVO3as predicted by DMFT,it also underlines the signiﬁcant effects due to oxygen vacancies,which may also affect photoemission data in other TMOs.Methods.The bulk-like relaxed,crystalline(001)oriented SrVO3thinﬁlms were grown by pulsed laser deposition (PLD)either at the GEMaC laboratory,then measured at the CASSIOPEE beamline of Synchrotron SOLEIL,or in a PLD chamber directly connected to the ARPES setup at beamline2A of KEK-Photon Factory(KEK-PF)[9,38,39]. To clean the surfaces in UHV prior to ARPES experiments at SOLEIL,the SrVO3thinﬁlms were annealed at550◦C for t=5–20min at pressures lower than2×10−8Torr.At KEK-PF,the PLD growth was performed under a pressure below10−7Torr,to obtain UHV-clean surfaces,using a Sr2V2O7target,which has excess oxygen with respect to SrVO3,thus minimizing the formation of vacancies during the growth.In all cases,the surface quality was conﬁrmed right before ARPES measurements by low-energy electron diffraction(LEED).The thinﬁlms measured at KEK-PF showed a c(4×4)surface reconstruction,which does not affect the analysis and conclusions of this work.For the ARPES measurements we used linearly polarized photons in the energy range30–110eV and hemispherical electron analyzers with vertical slits at SOLEIL and horizontal slits at KEK-PF.The angular and energy resolutions were0.25◦and 15meV.The mean diameter of the incident photon beam was smaller than100μm.The UV light brilliance,measured using calibrated photodiodes,was≈5×109photons s−1μm−2at SOLEIL,and about100times smaller at KEK-PF.The samples were cooled down to T=20K before measuring.Unless speciﬁed otherwise,all data were taken at that temperature. The results were reproduced on more thanﬁve samples.All through this Rapid Communication,directions and planes are deﬁned in the cubic unit cell of SrVO3.We denote [hkl]the crystallographic directions in real space, hkl the corresponding directions in reciprocal space,and(hkl)the planes orthogonal to those directions.The indices h,k,and l of hkl correspond to the reciprocal lattice vectors of the cubic unit cell of SrVO3.The Supplemental Material[40]presents further details about the sample growth and measurements.Experimental results.Figure2(a)shows the integrated photoemission spectra of SrVO3as a function of the UV dose, measured at CASSIOPEE SOLEIL under the same conditions of light brilliance of any standard ARPES experiment at a third-generation synchrotron.The measurements were done by continuously irradiating the sample with hν=33eV photons while recording the spectra as a function of irradiation time, with an accumulation time of about2min per spectrum.The blue and black curves show spectra for the lowest and highest measured doses,obtained respectively after∼2min and∼2h of irradiation.These data clearly demonstrate that the very UV or x-rays used for photoemission experiments can produce radical changes in the measured spectra of SrVO3.Note in fact that a similar effect has been observed for VO2[41].In particular,from Fig.2(a)we observe that the amplitude ofHUBBARD BAND VERSUS OXYGEN V ACANCY STATES IN THE...PHYSICAL REVIEW B94,241110(R)(2016)FIG.2.(a)Photoemission spectra of SrVO3as a function of UV dose,measured at Synchrotron SOLEIL(hν=33eV).The energy distribution curves(EDCs)were extracted from raw ARPES data around the 002point integrated along the k= 010 direction.(b)Corresponding momentum distribution curves(MDCs)integrated over50meV below E F.Peaks in the MDCs indicate the Fermi momenta.(c),(d)Same as(a),(b)for SrTiO3(hν=47eV).Theﬁlling of a2DEG upon UV irradiation is evidenced by the formation of QP peaks in the EDCs and MDCs at E F[inset of(c)and(d),respectively].All data were taken at20K.the in-gap state at−1.5eV,and,more signiﬁcantly,the ratio of in-gap to quasiparticle(QP)amplitudes,strongly increase with increasing UV dose,going from about1:3in a pristine sample to more than2:1in a heavily irradiated sample. Importantly,note that the QP peak position remains basically dose independent,implying that the carriers created by the UV or x irradiation do not signiﬁcantly dope the conduction band,and form dominantly localized states.This is conﬁrmed in Fig.2(b),which shows that the Fermi momenta of the QP band,given by the peak positions in the momentum distribution curves(MDCs)at E F,are also dose independent. Additional data presented in the Supplemental Material further demonstrate that our measurements yield the expected3D bulk Fermi surface of SrVO3.Thus,the observed increase in intensity of the in-gap state upon UV irradiation cannot be ascribed to a change inﬁlling of the conduction band,which could have affected the electron correlations.Instead,this unambiguously shows the light-assisted formation of localized defect states at essentially the same energy as that of the expected intrinsic lower Hubbard band—which should then resemble the in-gap peak observed at the lowest UV doses.In fact,as mentioned previously,it is well established that strong doses of UV or x-rays create a large concentration of oxygen vacancies in several d0perovskites[25–32,42]. As illustrated in Figs.2(c)and2(d)for the case of SrTiO3, the progressive doping of the surface region with oxygen vacancies,due to synchrotron UV irradiation,has two effects: the formation of a very intense in-gap state at about−1.3eV, and,in contrast to SrVO3,the simultaneous creation of a sharp QP peak at E F corresponding to a conﬁned quasi-2D electron gas(2DEG)at the samples’surface.The effective mass of such2DEG,precisely determined by ARPES,matches the mass expected from density functional theory calcula-tions[25,26,43,44].Thus,as in SrVO3,the increase in intensityof the in-gap state observed in SrTiO3upon UV or x irradiationcannot be due to an onset or increase of electron correlations,and should be ascribed to an extrinsic effect.We therefore conclude that,in SrVO3,exposure to syn-chrotron UV or x-rays creates oxygen vacancies,which are inturn responsible for the extrinsic increase in intensity of thein-gap state evidenced by our measurements.This effect canseriously obscure the determination of the spectral function ofthis model system,thus hampering the advancement of validtheories for correlated electron systems.Theﬁndings described above imply that the correct ex-perimental determination of the vacancy-free photoemissionspectrum of SrVO3should(i)use samples that from thebeginning have the lowest possible concentration of oxygenvacancies,and(ii)use doses of UV or x-ray light low enoughto avoid light-induced changes in the measured spectra.Tothis end,we measured SrVO3thinﬁlms grown directly insitu at beamline2A of KEK-PF.As mentioned before,the growth protocol of such thinﬁlms minimizes the formationof vacancies,while the UV light brilliance at KEK-PF is ∼100times smaller than the one in Figs.2(a)and2(b)from measurements at SOLEIL.We checked(see the SupplementalMaterial)that under these conditions the spectra did notchange with time,even after several hours of measurements.The resulting energy-momentum ARPES map,and its secondderivative,are presented in Figs.3(a)and3(b).One clearlyobserves the dispersing QP band along with an also dispersivein-gap state of weaker intensity,corresponding to the intrinsiclower Hubbard band,as reported in previous works[7].Theintrinsic spectral function of SrVO3will then be given by such aphotoemission spectrum,which approaches the vacancy-freelimit,modulo dipole-transition matrix elements,inherent toS.BACKES et al.PHYSICAL REVIEW B94,241110(R)(2016)FIG.3.(a)Energy-momentum ARPES intensity map measured at KEK-PF with a low UV dose on a SrVO3sample prepared in situ,using a well-established protocol to minimize the formation of oxygen vacancies(see the main text and Supplemental Material).Note that due to the choice of light polarization,the heavy bands along(100)are not observed and only the contribution of the light d xy band is detected.The data were acquired at hν=88eV around ¯103.(b)Second derivative(negative values)of the map in(a).The use of second derivatives allows a better visualization of the dispersion of both the quasiparticle and Mott-Hubbard bands on the same color plot.The dispersionless feature at E F is a spurious effect of such a second derivative on the Fermi-Dirac cutoff.(c),(d)Same as(a),(b)after a strong UV irradiation dose,measured at SOLEIL(hν=33eV),typical of modern third-generation synchrotrons.The measurements were done at hν=33eV close to 002.All data were taken at20K.Note that at constant photon energy,ARPES maps out the electronic structure at a spherical surface of three-dimensional (3D)k space,which can be locally approximated to a plane for all our measurements(details in the Supplemental Material).The different choice of photon energies and k-space positions for measurements at KEK-PF[(a)and(b)]and SOLEIL[(c)and(d)]was dictated by the different geometrical conﬁgurations and constraints of the beamlines in both synchrotrons.the photoemission process,which can still modulate the intensity of the QP peak relative to the Hubbard peak.A calculation of such matrix elements requires a full one-step calculation of the photoemission process,which is beyond the scope of this work.By contrast,Figs.3(c)and3(d) show the momentum-resolved electronic structure of a sample, measured at SOLEIL,that was intensively irradiated.There, the peak at−1.5eV becomes broader,more intense,and nondispersive—all characteristic signatures of a high random concentration of oxygen vacancies.Numerical calculations.To rationalize from a microscopic point of view the inﬂuence of oxygen vacancies on the electronic structure of SrVO3,we performed charge self-consistent LDA+DMFT calculations for bulk SrVO3and var-ious relaxed oxygen-deﬁcient SrVO3supercells.The latter are computationally demanding calculations.We shall focus here on the case of a2×2×3supercell with two oxygen vacancies located at opposite apical sites of one vanadium atom,as shown in the inset of Fig.4(b).We use such a vacancy arrangement as it is the prototypical one for d0compounds[43].For our LDA+DMFT calculations we chose values of U= 2.5eV and J=0.6eV for vanadium and included the effects of bandwidth renormalization due to dynamically screened Coulomb interactions by following the prescription suggested in Ref.[45](the LDA+DMFT unrenormalized data are shown in the Supplemental Material).In Figs.4(a)and4(c)we show, respectively,the results of the k-integrated and k-resolved spectral functions for bulk SrVO3without oxygen vacancies. Weﬁnd the expected features of a t2g quasiparticle peak at the Fermi level and a lower Hubbard band at negative energies of the same t2g nature,in agreement with the photoemission spectra in Fig.2(a)and Figs.3(a)and3(b).The light band at E F along k 100 [Fig.4(c)]consists of two degenerate bands of d xy and d xz characters,while the heavy band along the same direction has d yz character.While comparing with the measured k-resolved spectral function[Figs.3(a)and3(b)],HUBBARD BAND VERSUS OXYGEN V ACANCY STATES IN THE...PHYSICAL REVIEW B94,241110(R)(2016)FIG.4.LDA+DMFT results for SrVO3including bandwidth renormalization effects[45].(a)k-integrated spectral function for bulk SrVO3.The V t2g orbitals show a quasiparticle peak at E F and a lower Hubbard band at−1.6eV.(b)Spectral function for the2×2×3supercell of SrVO3with two oxygen vacancies.An additional nondispersive V e g vacancy state originating from the V atom neighboring the oxygen vacancies leads to a sharp peak below the Fermi level at∼−1.0eV.The V t2g orbitals show a quasiparticle peak at E F and a lower Hubbard band at−1.8eV.(c)and(d)show the corresponding spectral functions(multiplied by a Fermi-Dirac function at20K)along the X- -X path.one should bear in mind that along -X(or -Y)the heavy d yz(or d xz)bands are silenced by dipole-transition selection rules in the experiment[25].Inclusion of bandwidth renormalization[45]renders the lower Hubbard band at an energy(−1.6eV)in reasonable agreement with experiment (−1.5eV).We adopted typical values for U and J from the literature.We did not attempt to further optimize the values to get a better quantitative agreement with the experimental data, for two reasons:First is the heavy numerical cost,and second, as we show next in the calculations with oxygen vacancies, the adopted values facilitate the distinct visualization of the contributions from the Hubbard and localized states to the incoherent peak at∼−1.5eV.The removal of oxygen atoms in the system leads to the donation of two electrons per oxygen to its surrounding. Already at the level of density functional theory(DFT)in the local density approximation(LDA)(see the Supplemental Material),weﬁnd that most of the charge coming from the additional electrons is transferred to the3d z2orbitals of the neighboring V atom,developing into a sharp peak of e g symmetry located around−1.0eV,i.e.,at an energy close to the position of the experimentally observed oxygen vacancy states.In analogy to the experimental average over many lattice sites,note that averaging among various supercells with differentoxygen vacancy locations and concentrations(which is beyondthe scope of the present work)would result in a wider in-gape g band,as demonstrated for the case of SrTiO3(see Fig.3ofRef.[34])and for some cases in SrVO3(see the SupplementalMaterial,Fig.S7).By including electronic correlations within(bandwidth renormalized)LDA+DMFT we then see that allthe experimental observations qualitatively emerge.In fact,the conducting t2g orbitals develop a lower Hubbard bandpeaked at energies about−1.8eV[Figs.4(b)and4(d)],similarto the bulk case without oxygen vacancies.Most notably,this lower Hubbard satellite does not increase in amplitudewith the introduction of vacancies,but rather broadens.Inaddition,the oxygen vacancy defect states situated at about −1eV remain qualitatively unchanged by the correlation effects,but experience a broadening with respect to the pureLDA case.This is in agreement with the photoemission data,evidencing that the increase in intensity of the in-gap statein the oxygen-deﬁcient SrVO3is not to be attributed to anincrease in population of the lower Hubbard satellite,butinstead to the manifestation of vacancy states of e g character.Conclusions.In summary,we performed a detailed study of the effects of oxygen vacancies in the spectroscopy of the archetypal strongly correlated electron system SrVO3.We found that oxygen vacancy states,which are created by UV or x-ray irradiation,occur at energies close to the Hubbard satellite.This dramatically affects the measured line shape of the Mott-Hubbard band and the ratio of intensities between the quasiparticle and the Mott-Hubbard peaks.By means of a systematic study under a controlled irradiation dose, using samples directly grown in situ,we were able to obtain the photoemission spectrum of the bulk SrVO3system in the limit of a negligible concentration of oxygen vacancies. Our experimental interpretation is supported by LDA+DMFT calculations,which provided further insight into the likely nature of the oxygen vacancy states.Acknowledgments.We thank Silke Biermann,Ralph Claessen,Marc Gabay,and Michael Sing for discussions. This work was supported by public grants from the French National Research Agency(ANR),project LACUNES No. ANR-13-BS04-0006-01,and the“Laboratoire d’Excellence Physique Atomes Lumi`e re Mati`e re”(LabEx PALM project ELECTROX)overseen by the ANR as part of the“Investisse-ments d’Avenir”program(reference:ANR-10-LABX-0039). 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Globular Clusters in NGC 5128

a r X i v :a s t r o -p h /9906247v 1 15 J u n 1999A&A manuscript no.(will be inserted by hand later)ASTRONOMYANDASTROPHY SICS1.IntroductionGlobular star clusters (GCs)are among the oldest stellar systems in the Universe and provide a powerful tracer of2S.Holland et al.:Globular clusters in NGC5128Sharples1988).Recently G.Harris et al.(1998)used HST WFPC2images to construct a color–magnitude diagram for C44,a GC in the halo of NGC5128.They found that this GC was an old,intermediate-metallicity object simi-lar to the GCs in the Milky Way.G.Harris et al.(1992, hereafter referred to as HG92)used Washington CMT1T2 photometry to derive metallicities for62of conﬁrmed GCs in NGC5128and found a mean iron abundance of [Fe/H]=−0.8±0.2,which suggest that the NGC5128 GC system is∼3times more metal rich than the Milky Way GC system.They found no evidence for any GCs having metallicities signiﬁcantly greater than those found in the Milky Way GCs.Such metal-rich GCs might be ex-pected if some of the NGC5128GCs had formed recently in a gas-rich merger event.HG92do,however,suggest that several blue GCs in NGC5128may be analogues of the intermediate-age GCs found in the Magellanic Clouds. On the other hand,Zepf&Ashman(1993)suggest that the metallicity distribution of the NGC5128GCs is bi-modal,with the high-metallicity peak at[Fe/H]=+0.25 due to GCs formed in a merger.Hui et al.(1995)analyzed the kinematics of the NGC5128GC system and found that the metal-rich GCs are part of a dynamically sepa-rate system from the metal-poor GCs.Numerical simula-tions suggest that the merger event occurred between160 (Quillen et al.1993)and500(D/5Mpc)Myr ago,where D is the distance to NGC5128in Mpc(Tubbs1980). This suggests that any GCs that formed in this particular merger should be quite young and,therefore,rather blue (∼0.4<V−I<0.6;see Sect.5).Minniti et al.(1996)and Alonso&Minniti(1997, hereafter referred to as AM97)used HST Wide-Field/Planetary-Camera1(WF/PC-1)images,taken be-fore the corrective optics package was installed in1993, to search for GCs in the inner regions of NGC5128. They identiﬁed125GC candidates,young associations, and open cluster candidates in the inner three kpc of NGC5128.They also used ground-based RK photometry to estimate metallicities for47GC candidates.Schreier et al.(1996)found74compact sources along the northern edge of the NGC5128dust lane using HST WF/PC-1im-ages.They estimate that most of these sources are young stars(spectral class A or earlier)but note that some are resolved and may be GCs.Identifying GC candidates in the inner regions of NGC 5128is diﬃcult since there is nonuniform extinction,con-tamination from foreground stars and background galax-ies,and confusion with open clusters and blue,star-forming knots in NGC5128.GC candidates can not be identiﬁed based solely on their colors since the large amount of uneven reddening makes it very diﬃcult to determine the dereddened color of an object.A better approach is a scheme to identify GC candidates based solely on their structural parameters.All known GCs in the Local Group can be reasonably wellﬁt by Michie–King models(Michie1963;King1966),although∼20%Table1.Log of the observations.Fieldα(J2000)δ(J2000)Filter ExposureS.Holland et al.:Globular clusters in NGC51283cleus of NGC5128.Adjacentﬁelds overlap by∼0.′5givinga total eﬀective area of∼25⊓⊔′for the survey.2.2.Data ReductionsWe combined the exposures for eachﬁeld by taking the average of the three images in eachﬁlter(four images for the F555W exposures of Field2).No re-registration of the images was performed since the shifts between the images were typically less than0.1pixel(0.′′01on the WFC and 0.′′005on the PC).We estimate that combining the images in this way may result in the sizes of the GC candidates be-ing systematically overestimated by no more than∼0.′′02. We prefer to introduce this simple systematic oﬀset than deal with the poorly-understood systematic uncertainties that arise from interpolatingﬂux across fractional-pixel shifts.2.2.1.Identifying Globular Cluster CandidatesAt the distance of NGC5128(d=3.6±0.2Mpc),the mean King core-and tidal-radii of the Milky Way GCs would appear to be r t=2.′′59±0.′′20,respec-tively.Therefore,any GCs in NGC5128will appear to be semi-stellar and be strongly aﬀected by the point spread function(PSF)of the WFPC2.After some experimenta-tion,we adopted the following procedure for identifying GC candidates.We wish to stress that this procedure is quite strict and will probably result in the rejection of some legitimate GC candidates.However,we prefer to re-ject real GCs rather than have our sample contaminated with stars or background galaxies.In order to increase the signal-to-noise ratio(S/N)of the GC candidates–a particularly important point for the faint(V<20)GC candidates–we combined the F555W and F814W images for eachﬁeld to getﬁnding images. The dust lane introduces variations in the background on spatial scales of∼1′′,comparable to the expected sizes of the GC candidates in NGC5128.To reduce the eﬀects of the uneven background light,large-scale spatial varia-tions in the background were removed by running a ring medianﬁlter(Secker1995)over theﬁnding image,sub-tracting the resulting smoothed background,and adding back the mean background value.The medianﬁlter radius was set to1′′,which is∼3.5times the expected full-width at half maximum(FWHM)of a typical GC candidate. This choice ofﬁlter radius ensures that the cores of the GC candidates will not be altered by the medianﬁlter and that any background structure larger than a typical GC candidate will be removed.Since the most extended Milky Way GCs have tidal radii that are signiﬁcantly greater than2.5times their FWHM,and extended halos have been detected around several Galactic and extra-Galactic GCs(Grillmair et al.1995;1996;Holland et al.1997), this approach will alter the distribution of light in the outer regions of most of the GC candidates.However,this is not important since theﬁnding images are used only to construct a preliminary list of GC candidates.A more rigorous set of criteria,based on the structures of the GC candidates as determined from the original images,will be applied to the preliminary list to obtain aﬁnal list of GC candidates in the central regions of NGC5128.Theﬁrst step in our identiﬁcation procedure was to run the daophot ii(Stetson1987;1994)find routine on the background-subtracted images to identify GC can-didates.Theﬁnding thresholds were set to6σsky for the PC images and10σsky for the WFC images.Tests with artiﬁcial GCs suggested that any detections below these thresholds would be rejected at some point in our identiﬁ-cation process.Daophot ii find has an algorithm for re-jecting non-stellar objects based on two parameters called “sharpness”and“round”.This algorithm was turned oﬀsince images of GCs can have diﬀerent shapes and concen-trations from images of stars.Next,the daophot ii photometry routine was used to obtain aperture photometry for each of these detec-tions.The photometry was performed separately on each of the combined F555W and F814W frames,not on the combinedﬁnding frame.An aperture radius of0.′′2was used since most Galactic GCs,if moved to the distance of NGC5128,would appear to have core radii smaller than this.Therefore,the signal within the aperture will be dominated by the light from the object and not from the background.Candidate objects with S/N<5within the photometry aperture were discarded since the signal was not strong enough to determine reliable shape parameters. The sky brightness was determined in an annulus with an inner radius of∼0.′′9and an outer radius of∼1.′′1.This annulus was chosen to be far enough from the center of the GC candidate that the light in the annulus will be dominated by the background,yet near enough to the GC candidate that the light in the annulus will be a reasonable approximation of the mean background at the location of the object.For large GC candidates this annulus will be inside the tidal radius of the object so our estimate of the background will be contaminated.However,the values determined at this stage are only preliminary estimates, which will be improved upon later in the identiﬁcation process when Michie–King models areﬁt to the GC can-didates.The lists of GC candidates in each of the F555W and F814W images were matched using the daomatch and daomaster software.Only objects that appeared in both the F555W and F814W images,and whose centers matched to within0.′′05(∼1.1pixel on the PC images and∼0.5pix on the WFC images),were considered to be real GC candidates.Distinguishing bonaﬁde GCs from stars and back-ground galaxies is challenging.The colors of the objects can not be used since we are interested in studying the color distribution of GCs in NGC5128and do not wish to bias our sample.To make matters worse,the presence of dust in NGC5128will add a signiﬁcant amount of scatter4S.Holland et al.:Globular clusters in NGC5128to the intrinsic color distribution,and may cause legit-imate GCs to be rejected if a color-based identiﬁcationscheme is used.The solution is to identify GC candidatesby their structural parameters,although the best choiceof structural parameters is not obvious.At the distanceof NGC5128a typical Galactic GC would appear to havean intrinsic FWHM of∼0.′′25,or approximately twicethe FWHM of the WFPC2PSFs.Therefore,the observedFWHM,concentration,and ellipticity of a GC candidatecan be heavily inﬂuenced by the PSF.Since the PSF variesstrongly with position on the WFPC2CCDs,the poten-tial for confusion between stellar images and concentratedGC candidates is great if the PSF is not removed,in someway,from the data.Therefore,the observed shape of anobject can not be directly used to classify it as a star,GCcandidate,or galaxy.After some experimentation with adding and recover-ing artiﬁcial GCs and artiﬁcial stars,we found that thefollowing procedure was reasonably reliable for identify-ing GC candidates.For each GC candidate we took allthe pixel values within1′′of the center of the object andsubtracted an estimate of the local background(the centerand background were determined by the daophot ii pho-tometry algorithm).A one-dimensional Moﬀatian(Mof-fat1969),M(r eﬀ)=M(0) 1+ r eﬀ1Image Reduction and Analysis Facility(IRAF),a softwaresystem distributed by the National Optical Astronomy Obser-vatories(NOAO).S.Holland et al.:Globular clusters in NGC51285Fig.2.Thisﬁgure shows the best-ﬁtting Moﬀatianαand βparameters for each object(small circles)on the F555W images.Simulated data(see Fig.1)suggest that objects that lie inside the wedge formed by the solid lines are ex-tended objects.Therefore we consider any objects that lie inside the wedge to to be GC candidates.The solid squares show the locations of the GC candidates from Table2. 2.2.2.Fitting Michie–King ModelsWeﬁt a two-dimensional,PSF-convolved,single-mass Michie–King model to each of the403GC candidate us-ing software developed by Holland(1997).This software assumes that the surface brightness proﬁle along the ef-fective radius axis of a GC candidate with an ellipticity ofǫand a position angle ofθ0has a King proﬁle with a concentration of c and a core radius of r c.It then builds a two-dimensional model based on this surface brightness proﬁle,ǫ,andθ0.The two-dimensional model is convolved with the appropriate PSF for the location on the CCD and a chi-square minimization is performed between the PSF-convolved model and the original data image.The soft-ware uses CERN’s minuit function minimization package toﬁt simultaneously the concentration,core radius,to-talﬂux in the object,ellipticity,position angle,and mean background.Objects located within32pixels of the edge of a CCD(=3.′′2for the WFC and1.′′6for the PC)were notﬁt to avoid the edges of the CCD biasing theﬁts.Once a bestﬁt had been determined,the King tidal radius,r t, and the half-mass radius,r h,of the model were computed.Separateﬁts were made to the F555W images and the F814W images and an object was considered to be GC Fig.3.Thisﬁgure shows the best-ﬁtting Moﬀatianαand βparameters for each object(small circles)on the F814W images.Simulated data(see Fig.1)suggest that objects that lie inside the wedge formed by the solid lines are ex-tended objects.Therefore we consider any objects that lie inside the wedge to to be GC candidates.The solid squares show the locations of the GC candidates from Table2. candidate only if a Michie–King model could beﬁt in both colors.We were able toﬁt Michie–King models to98of the 403potential GC candidates.Mean structural parameters were calculated for these object by taking the mean of the values found in eachﬁlter.Four objects(#8,#113, #128,and#129)(see Tables2,3,and4)were identiﬁed on multipleﬁelds.In these cases we computed the mean of the structural parameters measured in eachﬁeld.We elected to separate GC candidates from back-ground galaxies based on theirﬁtted ellipticities and half-mass radii(see Fig.4).Half-mass radii are preferred to tidal radii or core radii because Fokker–Planck models of spherical stellar systems show that half-mass radii re-main reasonably constant over periods of several Gyr (e.g.Cohn1979;Takahashi1997),making it a unique length scale for GCs.The mass interior to the half-mass radius tends to undergo a gravo-thermal collapse and become concentrated at the center of the GC over time(i.e.core-collapse),which results in the core radius shrinking.Meanwhile,the mass exterior to the half-mass radius tends to expand outwards,causing the tidal ra-dius to grow.Since we are interested inﬁnding young, intermediate-age,and old GCs in NGC5128,it is useful to have a selection criterion that does not depend on the age6S.Holland et al.:Globular clusters in NGC5128Fig.4.The ellipticity vs.half-mass radius of the best-ﬁtting single-mass Michie–King model for each object where a Michie–King model was successfully ﬁt.Objects with r h >10′′(∼175pc)have not been plotted.The solid box in the lower left of the plot shows the region occupied by Galactic GCs.Based on this plot we have assumed that any object with r h <2′′(∼35pc)and ǫ<0.4(the dashed box)is a GC candidate in the NGC 5128system.of the GC candidate.Galactic GCs have half-mass radii of approximately 1.3<r h <31.9pc (W.Harris 1996),which corresponds to 0.′′07<r h <1.′′83at the distance of NGC 5128.There is no evidence that the radius of a Galactic GC depends on its mass (van den Bergh et al.1991).There-fore,we have assumed that only objects with r h ≤2′′(∼35pc at the distance of NGC 5128)were GC candi-dates.It is possible that some of the objects in Fig.4that have high ellipticities and low half-mass radii are double clusters.However,Innanen et al.1983have shown that a binary GC could not survive a single Galactic orbit in the Milky Way so it is unlikely that there are any old,or intermediate-age double GCs in NGC 5128.It is possi-ble that very young multiple GCs that formed within the last ∼100−200Gyr could have survived to the present day,but we are unable to diﬀerentiate between them and background galaxies.The most elliptical Galactic GC is M19with ǫ=0.27(White &Shawl 1987)and the most elliptical GC known is NGC 2193in the Large Magellanic Cloud (LMC)which has ǫ=0.33(Geisler &Hodge 1980).Geisler &Hodge (1980)modelled the distribution of observed el-lipticities for 25GCs in the LMC and found that it was unlikely that the largest true ellipticity exceeded ǫ=0.4.The LMC contains both dynamically young and dynami-Fig.5.A ﬁnding chart for Field 1.The GC candidates are circled with their identiﬁcation numbers (see Table 2)printed near each object.Fig.6.A ﬁnding chart for Field 2.Fig.7.A ﬁnding chart for Field 3.Fig.8.A ﬁnding chart for Field 4.cally old GCs,so the largest ellipticity seen in the LMC is a reasonable estimate of the largest ellipticity that we can expect to see in NGC 5128.Therefore,only objects with ǫ≤0.4were considered to be GC candidates.The ﬁnal step was to examine visually the WFPC2images of each GC candidate to ensure that the Michie–King model ﬁts looked realistic.We found that ∼20%of the objects were either located on diﬀraction spikes from saturated stars,or exhibited unusually large resid-uals when the best-ﬁtting Michie–King models were sub-tracted.These spurious identiﬁcations were discarded.Fig.4shows the measured half-mass radii and ellip-ticities for the surviving objects in NGC 5128and Ta-ble 2shows the ﬁnal list of GC candidates that we ﬁnd in the central regions of NGC 5128.The second and third columns show the J2000coordinates of the objects as determined using the IRAF/STSDAS (v2.0.1)task sts-das.toolbox.imgtools.xy2rd .Column 4is the ob-served (projected)distance of the GC candidate from the center of NGC 5128in arcminutes.The center of NGC 5128was taken to be αJ2000=13h 25m 27.s 3,δJ2000=−43◦01′09′′(Johnston et al.1995).Columns 5and 6give the ﬁeld (from Table 1)and CCD that the object was found on.Columns 7and 8give the X and Y coordinates (in pixels)on the CCD.Column 9lists the identiﬁcation number of the object in Table 1of Minniti et al.(1996).Tables 3and 4lists the coordinates for the 61extended objects with r h >2′and ǫ>0.4.Some of these objects may be GCs in NGC 5128while others may be background galaxies with structures similar to those of Michie–King models.Six of these objects have been previously identi-ﬁed as GCs by Minniti et al.(1996)and Sharples (1988).Figs.5through 10show the locations of the 21GC can-didates on the F814W-band WFPC2images.Only objects that pass all of the criteria described above are marked on these ﬁgures.Objects (such as #15)were only marked on the ﬁelds that they were identiﬁed as GC candidates in.In most of the cases where a GC candidate is present in multiple ﬁelds,but only identiﬁed in one ﬁeld,the GC candidate was located very near the edge of one of the CCDs.Spatial variations in the PSF are largest near the edges of the CCDs so the Michie-King model ﬁts are less reliable near the edges of the CCDs.S.Holland et al.:Globular clusters in NGC51287 Table2.The GC candidates in the central regions of NGC5128.IDαJ2000δJ2000D Field CCD X Y Other8S.Holland et al.:Globular clusters in NGC5128Table3.Extended objects with r h>2′′andǫ>0.4in the central regions of NGC5128IDαJ2000δJ2000D Field CCD X Y OtherS.Holland et al.:Globular clusters in NGC51289 Table4.Extended objects with r h>2′′andǫ>0.4in the central regions of NGC5128,continued.IDαJ2000δJ2000D Field CCD X Y Other∆W0)and standard error in the mean oftheseﬁve values for each GC candidate.This gave us anestimate of the systematic uncertainty in the value of W0that we derived for each GC candidate.Finally,we com-puted the mean,standard error in the mean,and medianof the individual10S.Holland et al.:Globular clusters in NGC5128Table5.The best-ﬁtting structural parameters for the NGC5128GC candidates.The values are the means of the structural parameters derived from the F555W and F814W images.ID W0±σr c±σr h±σr t±σc±σǫ±σθ0±σχ2ν∆r c0.′′0100.′′0030.′′004∆r t0.′′1540.′′0510.′′060∆ǫ0.0240.0040.022n n.(3) The mean core radius for the21NGC5128GC candidates isr c=0.′′11±0.′′01(se).A Kolmogorov–Smirnov(KS)test shows that we can reject the hypothesis that the two samples are drawn from the same distribution at the46%conﬁdence level.Therefore, there is no evidence that the core radii of the GC can-didates in NGC5128are distributed diﬀerently from the core radii of the Milky Way GCs.The most noticeable diﬀerence between the core radii of the NGC5128GCcandidates and the core radii of the Milky Way GCs in Fig.11is the lack of a tail extend-ing to large core radii in the NGC5128data.This may be an artifact of the small number(21)of NGC5128GC candidates in our sample.The mean of a distribution is sensitive to the presence of tails and outliers,but the me-dian is much more robust against outliers.Therefore we computed the median core radius for each data set.Both the NGC5128GC candidates and the Milky Way GCs have median core radii of[r c]=0.′′07(=1.22pc,or∼0.7 pixels on the WF CCDs and1.4pixels on the PC CCD). The similarity in the median core radii suggests that theFig.11.Thisﬁgure compares the distribution of core radii for GC candidates in NGC5128with the distribution of core radii for selected GCs(see Sect.3.1)in the Milky Way.The vertical axis is the fraction of the total number of GCs and the error bars show the Poisson uncertainties in each bin.“typical”core radius of a GC candidate in NGC5128is similar to that of the Milky Way GCs.There may be systematic biases in the core radii that we have derived for the GC candidates in NGC5128.Fit-ting Michie–King models to objects with core radii that are similar to the pixel scales of the images requires that the centers of the objects be accurately known.Small er-rors in determining the center of a candidate GC,and small systematic errors introduced by integrating Michie–King model proﬁles over the area of a pixel,may be suf-ﬁcient to bias theﬁtted core radii towards smaller values. In addition to pixelation eﬀects,the similarity between the core radii and the FWHMs of the PSFs may also be biasing ourﬁts toward smaller core radii.3.2.Tidal RadiiThe tidal radius of a GC is aﬀected by the gravitational potential of its parent galaxy(e.g.,Innanen et al.1983; Heggie&Ramamani1995).In order to compare the tidal radii of GC candidates in NGC5128with those of GCs in the Milky Way it is necessary to correct for the tidal ﬁelds of both galaxies.Theﬁrst step is to normalize the tidal radius of each GC candidate by its mass,M cl,to getr t/M1/3cl .If we assume that the gravitational potentials ofthe Milky Way and NGC5128can be approximated by aspherical logarithmic potential of the formΦ=V2rot ln(R2+R2s)+ln(C),(4)where R is the galactocentric distance,R s is a scale length,and C is a constant,then we can compare the mean valueof the normalized tidal radii of the GC candidates usingr tV rot 2/3GM1/3cl= V rot,MW g(e) 1/3 R2/3pM1/3cl MW,(6)where the subscript MW denotes the value for the MilkyWay.Eq.6assumes that the shape of the galactic potentialis the same in both galaxies,but allows the total mass,as parameterized by V rot,of each galaxy to vary.It alsorequires a knowledge of the distribution of GC orbits ineach galaxy,as parameterized by g(e)and R p.We as-sumed a rotation velocity of V rot,MW=220km s−1for theMilky Way and V rot=245km s−1for NGC5128(Huiet al.1995).The only information available on the distri-bution of orbits for GC candidates in NGC5128is theprojected radial distances of the GC candidates from thecenter of NGC5128,so we have assumed that the NGC5128GC system is dynamically similar to the Milky WayGC system.This involves two assumptions about the na-ture of the GC orbits.First,we assume that the mean ec-centricity of the NGC5128GC orbits is the same as thatfor the Milky Way GCs(Fig.12.Thisﬁgurecompares the distribution of normal-ized tidal radii(see Sect.3.2)for GC candidates in NGC 5128with the distribution of normalized tidal radii(af-ter correcting for the diﬀerence in mass between the two galaxies)for GCs in the Milky Way.The vertical axis is the fraction of the total number of GCs and the error bars show the Poisson uncertainties in each bin.5128GC candidates from the observed distance from the center of NGC5128usingR p=1−e8D.(7)Fig.12shows the distribution of the normalized tidal radii for the NGC5128GC candidates and the Milky Way GCs.The cluster masses were computed from their total V-band luminosities assuming a mass-to-light ratio of two.Our sample of GC candidates has r t/M1/3cl=0.36±0.05(se)pc/M1/3⊙(N=21).The mean normalized tidalradius for73selected Milky Way GCs is r t/M1/3clMW=0.69±0.08(se)pc/M1/3⊙.The multiplicative factor in Eq.6is0.703,which yields a corrected r t/M1/3clMW of0.49±0.06(se)pc/M1/3⊙.A KS test says that we can reject the hypothesis that the two samples are drawn from the same distribution at the74%conﬁdence level.Therefore,there is insuﬃcient evidence to state that the distribution of the tidal radii of the NGC5128GC candidates diﬀers from that of the Galactic GCs if the diﬀerence in the masses of the two galaxies is taken into account.However,we wish to stress that this calculation assumes that the distribution of GC orbits are statistically similar for both galaxies.Fig.13.Thisﬁgure compares the distribution of half-mass radii for GC candidates in NGC5128with the distribution of half-mass radii for a subset of GCs in the Milky Way. The vertical axis is the fraction of the total number of GCs and the error bars show the Poisson uncertainties in each bin.3.3.Half-Mass RadiiThe distribution of half-mass radii for the NGC5128GC candidates is shown in Fig.13along with the same dis-tribution for our subsample of73Milky Way GCs.The half-mass radii for the Milky Way GCs were determined by computing a Michie–King model(with concentrations and core radii taken from W.Harris1996)for each Milky Way GC.This allowed us to make a direct comparison between the half-mass radii of the best-ﬁtting single-mass Michie–King models for the NGC5128GC candidates and the half-mass radii of the best-ﬁtting single-mass Michie–King models for the Milky Way GCs.The mean half-mass radius for the21NGC5128GC candidates isr h=0.′′67±0.′′05(se).However, a KS test says that we can reject the hypothesis that the two samples are drawn from the same distribution at only the74%conﬁdence level,so there is no evidence that the distribution of half-mass radii in our sample of NGC5128 GC candidates is diﬀerent from that of the GCs in the Milky Way.3.4.EllipticitiesThe distribution of ellipticities for the NGC5128GC can-didates is shown in Fig.14.The21NGC5128objects haveFig.14.The upper panel shows the distribution of ellip-ticities for the GC candidates in NGC5128.The lower panel shows the distribution of ellipticities for the Milky Way’s GCs(from White&Shawl1987).ǫ=0.07±0.01(se)for the 73Milky Way GCs.A KS test says that we can reject the hypothesis that the two samples are drawn from the same distribution at the99.7%conﬁdence level.Therefore,we conclude that the NGC5128GC candidates may have a diﬀerent distribution of ellipticities from the Milky Way GCs.The NGC5128GC candidates appear to be system-atically more elliptical than the Milky Way GCs.There appears to be a lack of objects with low ellipticities and an excess of GC candidates withǫ∼0.3.The lack of GC can-didates withǫ≤0.05is probably due to the elliptical PSF not being fully removed from the data.Another possible source of ellipticity is the stochastic distribution of bright stars near the center of the object.Geisler&Hodge(1980) found that the random placement of stars with respect to the adopted center of a GC can introduce a systematic error in the observed ellipticity of+0.045±0.015for GCs which are intrinsically spherical.This eﬀect acts to make nearly spherical GCs appear to be more elliptical than they actually are.They also found that this systematic error decreases as the intrinsic ellipticity of the GCs in-creases.This would explain the lack of nearly circular GC candidates in NGC5128,relative to the Milky Way.AM97identiﬁed125GC candidates in the inner2.′8×2.′8of NGC5128.Table7lists the ellipticities from those GC candidates in common between the two studies.The Table7.A comparison of our ellipticities with those of AM97.ID AM97Ourǫ±σAM97ǫ。

国家天文台复试笔试物理类试题 (2)

国家天文台复试笔试物理类试题引言概述：国家天文台是我国最高级别的天文研究机构，其复试笔试物理类试题是评估考生物理学知识和能力的重要手段。

本文将从五个大点出发，详细阐述国家天文台复试笔试物理类试题的内容和要求。

正文内容：1. 理论基础知识1.1 牛顿力学1.1.1 万有引力定律1.1.2 运动方程和动量守恒1.1.3 刚体力学1.2 电磁学1.2.1 静电学和电场1.2.2 磁场和电磁感应1.2.3 电磁波和光学1.3 热力学1.3.1 热力学基本定律1.3.2 热传导和热辐射1.3.3 热力学循环和热力学平衡2. 实验技能与数据处理2.1 实验设计和仪器使用2.1.1 实验目的和步骤2.1.2 仪器使用和调试2.1.3 数据采集和处理2.2 误差分析和不确定度2.2.1 误差来源和类型2.2.2 不确定度计算和处理2.2.3 实验结果的可靠性评估2.3 统计学方法2.3.1 数据分布和概率论2.3.2 参数估计和假设检验2.3.3 相关性和回归分析3. 天体物理学基础3.1 星体结构和演化3.1.1 恒星的内部结构3.1.2 恒星演化的主要阶段3.1.3 恒星的死亡和残骸3.2 宇宙学3.2.1 宇宙的起源和演化3.2.2 宇宙的膨胀和背景辐射3.2.3 宇宙的结构和暗物质3.3 天体测量和观测技术3.3.1 天体坐标和时间系统3.3.2 天体测量方法和仪器3.3.3 数据处理和观测误差分析4. 数学工具与计算方法4.1 微积分4.1.1 极限和连续性4.1.2 导数和微分4.1.3 积分和微分方程4.2 线性代数4.2.1 矩阵和向量4.2.2 线性方程组和矩阵运算4.2.3 特征值和特征向量4.3 计算方法4.3.1 数值计算和误差分析4.3.2 插值和拟合4.3.3 常微分方程的数值解法5. 科学研究与学术素养5.1 科学研究方法5.1.1 科学假设和实证研究5.1.2 实验设计和数据分析5.1.3 科学论文写作和学术道德5.2 学术素养与科学文化5.2.1 学术交流和合作5.2.2 科学与社会的关系5.2.3 天文学史和科学哲学总结：国家天文台复试笔试物理类试题内容丰富，涵盖了物理学的各个领域，并要求考生具备扎实的理论基础知识、实验技能和数据处理能力。

第三章恒星的演化

2．较高质量 (M > ~2M⊙) 恒星的演化 (20.4, 21.221.3) (1) 与低质量恒星演化的主要区别恒星内部的H燃烧通过CNO循环进行，内部温度更高，辐射压对维持恒星的力学平衡起更大的作用，主序寿命更短。 He核不再是简并的，C和更重元素的燃烧可以进行。核心区核反应产生的能量主要以对流的方式向外传递。
第三章恒星的演化
§3.1 主序星的演化 §3.2 恒星主序后的演化 §3.3 恒星演化的观测证据 §3.4 密近双星的演化
§3.1 主序星的演化
(20.1)
1. 恒星演化的基本原理
恒星在一生的演化中总是试图处于稳定状态（流体静力学平衡和热平衡）。当恒星无法产生足够多的能量时，它们就无法维持热平衡和流体静力学平衡，于是开始演化。
L ~ M 2.5-4, R ~ M 0.5-1
主序星的演化
(1) 零龄主序 (zero age main-sequence star, ZAMS) 刚刚开始核心H燃烧的恒星，在H-R图上占据主序带的最左侧。 (2) 演化时标 ——核反应 (4 1H→4He +γ) 时标 tn＝η△Mc2/L ≈(1010 yr) (M/M⊙) (L/L⊙)-1 ≈(1010 yr) (M/M⊙)-2.5 for M > M⊙ or (1010 yr) (M/M⊙)-2 for M < M⊙
(4) 特大质量恒星的演化
星风引起的质量损失和恒星演化。高光度恒星通常有很强的星风～10-6-10-4 M⊙yr-1 如沃尔夫-拉叶(WR)星。演化过程 O型星→蓝超巨星→（红超巨星）→WR星→Ib/Ic型超新星 + 中子星/黑洞
小结：
不同质量恒星的演化结局
恒星初始质量 (M⊙) < 0.01 0.01 < M < 0.08 0.08 < M < 0.25 0.25 < M < 8 8 < M < 12 12 < M < 40 M > 40 演化结局行星褐矮星 He白矮星 CO白矮星? ONeMg白矮星? 超新星→中子星? 超新星→黑洞?

AGN

绝大部分星系是正常星系,但也有部分星系的中心表现出强烈的活动(show up strong activities),称为活动星系(active galaxies) 或活动星系核（Active Galactic Nuclei,即AGN）活动星系核种类繁多(a great varities)，并且互相交叉(overlap)。

观测上主要分为4种类型(types)：Radio galaxies 射电星系Seyfert galaxies 赛弗特星系Quasars 类星体BL Lac objects 蝎虎（座）BL Lac天体（致密densify，高能high energy，多波段multiband，强宽发射线strong and broad lines of emissions）达到（reach）3C 273 类星体Hydra A 长蛇座Centaurus A 半人马座Hercules A 武仙座Cygnus A 天鹅座A射电源Pictor A 绘架座Fornax A 天炉星座Brightness光变时标Brightness varies on timescale非热连续谱non-thermal continuous spectrum高偏振辐射high polarized radiation 偏振（polarization）黑体辐射blackbody radiation系内恒星star within galaxy红外（infrared）远红外（far infrared）主要类型main types种类的分析双瓣的bivalve单瓣的unibalve视线方向direction of visual line漩涡星系swirl galaxy明亮的核类似于恒星的bright nucleus are similar with stellar 行星planet。

5 星系天文学-第四章-银河系结构和演化

(4-2)
式中 K 为单位长度的消光系数，与介质的组成、密度、物理条件以及辐射波段有关。 r 引入光学厚度 (r, l , b) 0 K (r, l, b)dr 则式(4-2)变为
E E0e ( r ,l ,b )
2. 单位长度消光值 a 与总消光 A 总消光 A A(r, l , b) m m0
星际物质从成份来说可以分为气体和尘埃两种，但它们往往是混杂在一起的，在密度高的地方构成星际弥漫云，又有亮星云和暗星云之分。除了云之外就是分布在星际云之间的连续介质。亮星云从发光机制来说包括发射星云和反射星云两种。发射星云因附近高光度恒星的辐射激发而发光，星云中间通常有一个或一群光谱型早于B1的高温恒星。这些恒星有着丰富的紫外辐射，使星云气体激发，从而产生光致电离而形成星云发射光谱，所以称为发射星云。除大量的炽热气体外还包含有少量的尘埃物质。光能量主要集中于一些发射线，如H、H 和H 。
a (r , l , b) a 1.086 K A (r , l , b) ar
这种情况下有时引入透明系数 P e K 于是可以得到 E E0e Kr E0 P r 当 K = 0 时，P = 1，介质完全透明； K = ∞ 时，P = 0，介质完全不透明。
m M 5 lg r A(r ) 5
计算的距离不同，r' 称为视距离，r 称为真距离，它们间的关系是 5 lg r ' 5 lg r A(r ) 或 r ' r 10 0.2 A( r ) 当消光物质为均匀分布时有
5 lg r ' 5 lg r ar r ' r 10 0.2 ar
1. 星光吸收。星际尘埃会吸收和散射星光，且对蓝光比对红光更厉害。星际气体则不同，它会在恒星光谱中形成明显的吸收线，因此可以借助某些原子或离子造成的特征吸收线来探测星际气体的存在。特征吸收谱线的强度用等值宽度W 来表征。W 与视线方向致吸收原子数密度 N 间的对数关系 lgN－lgW 称为生长曲线，可用来确定 N。 2. X射线观测。所有星系中都包含大量炽热 (T>105K) 气体,其中H和He完全被电离, 称为等离子体，主要在极端紫外 (EUV)和X射线波段发出辐射，能量范围为13.6 －100eV (EUV) 、0.1－1KeV（软X）、1－10KeV（中 X）、>10KeV（硬X）。

高中物理竞赛习题天体运动

2 3
解：【分析】最小周期出现在轨道半长轴最小时【解答】（1）设地月半径分别为 R 和 r，质量分别为 M 和 m，密度分别为 ρE , ρM ，则当表面卫星运动时引力提供向心力，地球表面： 4π 2 GM R= 2 T2 R 月球表面： Gm 4π 2 r= 2 T2 r 因此得到： R3 M = r3 m (39) (38) (37)
第 2 页 (共 37 页)
解：【分析】本题要分析清楚需要几个同步卫星，利用对称性将问题集中在一个几何参量上，再判断单调性即可. 【解答】设同步卫星轨道半径为 r，有动力学方程 mω 2 r = 其中 GM = gR2 , ω = 2π /T 得 r= ( R2 gT 2 4π 2 )1/3 = 4.23 × 107 m (16) GM m r2 (15)
解：【分析】分析受力，合成两个引力，即可由动力学方程求解【解答】质点 B 对质点 A 的引力为 FBA = G 万有引力为 FCA = G m2 ，方向由 A 指向 B . 质点 C 对质点 A 的 a2
m2 ，方向由 A 指向 C . 质点 A 受到的合力为 a2 FA = FBA cos 30◦ + FCA cos 30◦ =
2 2
2
解：【分析】考查万有引力定律的基本使用【解答】近似认为由引力提供全部的重力 mg = 得 g= 改变至 R′ = (1 − 0.0150)R g′ = g GM R2 (22) GM m R2 (21)
R2 = 10.1ms−2 R ′2
(23)
8. 用不同的方法估算银河系的质量，所得结果也不相同. 以下是诸多估算方法中的一种：根据观测结果估计，从银河系中心到距离为 R = 3 × 109 R0 （R0 表示地球绕日轨道半径）的范围内集中了质量 M1 = 1.5 × 1011 M0 （M0 表示太阳质量） . 在上面所指的范围内星体运转周期为 T = 3.75 × 108 年. 求银河系“隐藏”的质量是太阳质量的多少倍，即在半径为 R 的球体内未被观察到的物质质量. 计算中可以认为银河系的质量都集中在其中心.

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arXiv:astro-ph/0403166v1 6 Mar 2004Astronomy&Astrophysicsmanuscriptno.lsilvaFebruary2,2008

(DOI:willbeinsertedbyhandlater)

ObservationaltestsoftheevolutionofspheroidalgalaxiesandpredictionsforSIRTF/Spitzercosmologicalsurveys

L.Silva1,G.DeZotti2,G.L.Granato2,R.Maiolino3,andL.Danese41INAF-Trieste,ViaTiepolo11,I-34131Trieste,Italy

2INAF-Padova,VicoloOsservatorio5,I-35122Padova,Italy

3INAF-Arcetri,LargoE.Fermi5,I-50125Firenze,Italy

4SISSA,ViaBeirut4,I-34014Trieste,Italy

Received/AcceptedAbstract.Granatoetal.(2004)haveelaboratedaphysicallygroundedmodelexploitingthemutualfeedbackbetweenstar-formingspheroidalgalaxiesandtheactivenucleigrowingintheircorestoovercome,intheframeworkofthehierarchicalclusteringscenarioforgalaxyformation,oneofthemainchallengesfacingsuchscenario,i.e.thefactthatmassivespheroidalgalaxiesappeartohaveformedmuchearlierandfasterthanpredictedbyprevioushierarchicalmodels,whiletheformationprocesswasslowerforlessmassiveobjects.AdoptingthechoicebyGranatoetal.(2004)fortheparametersgoverningthehistoryofthestarformation,ofchemicalabundancesandofthegasanddustcontentofgalaxies,weareleftwithonlytwo,ratherconstrained,butstilladjustable,parameters,aﬀectingthetime-andmass-dependentSEDsofspheroidalgalaxies.Afterhavingcomplementedthemodelwithasimplephenomenologicaldescriptionofevolutionarypropertiesofstarburst,normallate–typegalaxies,andofAGNs,wehavesuccessfullycomparedthemodelwithabroadvarietyofobservationaldata,includingdeepK-band,ISOCAM,ISOPHOT,IRAS,SCUBA,radiocounts,andthecorrespondingredshiftdistributions,aswellasthe1–1000µmbackgroundspectrum.SpecialpredictionshavebeenmadefortheespeciallychallengingcountsandredshiftdistributionsofEROs.WealsopresentdetailedpredictionsfortheGOODSandSWIREsurveyswiththeSpitzerSpaceTelescope.WeﬁndthattheGOODSdeepsurveyat24µmandtheSWIREsurveysat70and160µmarelikelytobeseverelyconfusionlimited.TheGOODSsurveysintheIRACchannels(3.6to8µm),reachingﬂuxlimitsofafewmJy,areexpectedtoresolvemostofthebackgroundatthesewavelengths,toexplorethefullpassiveevolutionphaseofspheroidalgalaxiesandmostoftheiractivestar-formingphase,detectinggalaxiesuptoz≃4andbeyond.Asubstantialnumberofhighzstar-formingspheroidalgalaxiesshouldalsobedetectedbythe24µmSWIREandGOODSsurveys,whilethe70and160µmwillbeparticularlyusefultostudytheevolutionofsuchgalaxiesintherange1∼populationinMIPSchannels,except,perhaps,at160µm.

Keywords.galaxies:ellipticalandlenticular,cD—galaxies:evolution—galaxies:formation—QSOs:formation

1.IntroductionThestandardLambdaColdDarkMatter(ΛCDM)cosmologyisawellestablishedframeworktounderstandthehierarchi-calassemblyofdarkmatter(DM)halos.Indeed,ithasbeenremarkablysuccessfulinmatchingtheobservedlarge-scalestructure.Howeverthecomplexevolutionofthebaryonicmat-terwithinthepotentialwellsdeterminedbyDMhalosisstillanopenissue,bothontheoreticalandonobservationalgrounds.Fullsimulationsofgalaxyformationinacosmologicalset-tingarefarbeyondpresentdaycomputationalpossibilities.Thus,itisnecessarytointroduceatsomelevelroughpara-metricprescriptionstodealwiththephysicsofbaryons,basedonsometimesdebatableassumptions(e.g.Binney2004).Aclassofsuchmodels,knownassemi-analyticmodels,hasbeenextensivelycomparedwiththeavailableinformationon2L.Silvaetal.:Evolutionofspheroidalgalaxies2003;Pozzettietal.2003;Somervilleetal.2004;seeCimatti2003forareview).However,thegeneralagreementofabroadvarietyofob-servationaldatawiththehierarchicalscenarioandthefactthattheobservednumberofluminoushigh-redshiftgalaxies,whilesubstantiallyhigherthanpredictedbysemi-analyticmodels,isneverthelessconsistentwiththenumberofsuﬃcientlymassivedarkmatterhalos,indicatesthatwemaynotneedalternativescenarios,butjustsomenewingredients.Previousworkbyourgroup(Granatoetal.2001;Romanoetal.2002;Granatoetal.2004)suggeststhatacrucialingre-dientisthemutualfeedbackbetweenspheroidalgalaxiesandactivenucleiattheircenters.Granatoetal.(2004,henceforthGDS04)presentedade-tailedphysicallymotivatedmodelfortheearlyco-evolutionofthetwocomponents,intheframeworkoftheΛCDMcosmol-ogy.Inthispaper,wepresentacomprehensivecomparisonofthemodelwiththeavailabledata(numbercountsandred-shiftdistributions)innear-IR(NIR)tosub-mmbandsandex-tensivepredictionsrelevantforsurveyssuchasGOODSandSWIRE,whicharebeingcarriedoutwithNASASpitzer(for-merlySIRTF)Observatory.InSect.2wegiveashortoverviewoftheGDS04modelforspheroidalgalaxies,adescriptionofthephenomenologicalapproachadoptedtomodeltheevolutionofstarburstandnormallate-typegalaxies,andofactivegalacticnuclei(AGNs).InSect.3wediscussthedeterminationofthetwomainparameterscontrollingthetime-dependentspectralenergydistributions(SEDs)ofspheroidalgalaxies.InSect.4,themodelcountsandredshiftdistributionsarecomparedwithdatafromtheISOsurveysandfollow-up,fromtheIRAS60µmsurvey,fromtheSCUBA850µmsurveysandfollow-up,fromtheradio1.4GHzsurveysdowntosub-mJyﬂuxdensities,andfromdeepK-bandsurveysandfollow-up.InSect.5,wepresentourpredictionsforSpitzerGOODSandSWIREsurveys.ThemainconclusionsaresummarizedinSect.6.Weadoptthefollowingcosmologicalparameters:Ωm=0.3,ΩΛ=0.7,H0=70kms−1.