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Astrophysics 2

by: Stephan Kuvalis

Astrophysics 2 ASTR 3830

Stephan Kuvalis

GPA 3.89

Philip Armitage

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Philip Armitage
Class Notes
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This 155 page Class Notes was uploaded by Stephan Kuvalis on Thursday October 29, 2015. The Class Notes belongs to ASTR 3830 at University of Colorado at Boulder taught by Philip Armitage in Fall. Since its upload, it has received 22 views. For similar materials see /class/231956/astr-3830-university-of-colorado-at-boulder in Astronomy at University of Colorado at Boulder.


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Date Created: 10/29/15
Properties of galaxies in galaxy clusters Apart from the high density two striking features of the galaxy population in clusters CD galaxies Many clusters have a single dominant central galaxy I I I l I 20 s A 2l99 NGC 6l66 22 Oemler l976 FV 24 stellar O mag urcsecquot o 26 39 o D O l 28 O o o 30 J l l 1 1 I lX Vll mI39lI39Kl I lpl39IESUJJll lLFllgt 2 rm cistern 4 5 ASTH 3830 Spring 2004 Morpholoqvdensitv relation r rv r quot1 4 1quot 33 Galaxy population is LLH if correlated with the galaxy rtquot quotr Hf M 39 h r denSIty T h spirals 1535 P l Low densntv enVIronments E t 30 Favor spirals E r E i 5 If Cluster envrronments i quot it Favor ellipticals t 39 i 247quot 1 I u Itupn Gl l Fm 4 The fraction ul39 E St and 3 galaxies as 1 function Ifquot lhs log of the funicular density in galaxies Nipzquot The data shown an For ll cluster galaxim in the sample and fur the tint1 Also shown is an estimated scale of true spam density in galaxies Nlpc i The upper histogram shows the number diminution of tile galaxiua over the bins of pruju ed density ASTR 3830 Spring 2004 Gas in galaxy clusters Observe extended emission in Xray observations of clusters of galaxies indicates presence of hot gas distributed throughout the cluster volume Coma in the ogtical Coma in Xrays ASTFl 3830 Spring 2004 If the gas is in virial equilibrium within the cluster expect kT lmpv2 Guess thermal velocity 0 1000 km s1 q T 6 x107 K radiation via bremsstrahlung Formula for the bremsstrahlung emission from a thermal plasma at temperature T is s 68 x10 38ZzneniT1Zehvchrg S 1 cmquot3 HZ 1 lon charge f is Ze Number density of electrons ions ASTR 3830 Spring 2004 From Xray observations easiest quantities to measure are P o o Bremsstrahlung emission o o o o Luminosity LX depends on density temperature and volume of the cluster Xray surface brightness as fradius Mean temperature from the spectrum Bremsstrahlung has a flat spectrum up to hv kT followed by an exponential cutoff Plot shows temperatures of 1073 x 107 K 108 K Most clusters have T between 2X107Kand108K ASTFi 3830 Spring 2004 Harderto measure Temperature gradient Metallicity of the cluster gas Inner 02 amin Kevam2 skaV m Outer 512 arcmin channel Energy kaV 5 Example of an ASCA spectrum of a cluster showing line emission Asm 3930 Spring 2004 Cooling cores Is the gas in galaxy clusters radiating enough to cool significantly Integrated over frequency bremsstrahlung emission is s 14 gtlt10 27T12neniZ2 erg s391 cm393 Roughly estimate t nekT T 12 H 1 3 e G r 108 K 001 cm393 y Gas in most of the cluster will not cool ne lt 10392 cm393 But dense gas in the core is expected to cool significantly ASTR 3830 Spring 2004 Cooling time scales as nquot hence might expect that Cooling starts Pressure drops Gas flows in increased density Increased cooling runaway Some clusters show very bright cores suggesting that this Process is 90mg on ASTB 38305prin92004 But what happens to the cool gas Do not observe o Very high rates of star formation o Lines in the soft Xray spectrum from the cool material Suggests that some source of heating balances the cooling at a lower temperature possibly Conduction from the hotter regions at larger radius Heating due to AGN outflows ASTR 3830 Spring 2004 Chandra observations of clusters High resolution observations with Chandra show that many clusters have substructure in the Xray surface brightness Bow shock FilaAme 1E 065756 A1795 AS TR 3830 Spring 2004 Galactic mergers Most dramatic examples major mergers between galaxies of comparable mass Large morphological changes as a consequence of the interaction Cnluies NCC 1707 and IC 1163 Hubblc Heritage Observationally and theoretically find that major mergers are uncommon perhaps 1 such merger in the lifetime of the Universe for a large galaxy in the field ASTFl 3530 Spring 2004 Minor mergers between galaxies of very different masses are much more common Example the Magellanic clouds Bound satellites orbiting within the extended halo of the Milky Way 50 kpc distance Eventually will spiral in and merge Sagittarius dwarf galaxy is another satellite which is now in process of merging ASTR 3830 Spring 2004 Dynamical Friction Why does the orbit of a satellite galaxy moving within the halo of another galaxy decay Stars in one galaxy are scattered by gravitational perturbation of passing galaxy Stellar distribution around the intruder galaxy becomes asymmetric higher stellar density downstream than upstream Gravitational force from stars produces a frictional force which slows the orbital motion ASTR 3830 Spring 2004 Calculate energy exchange using the impulse approximation assume that we can calculate force along unperturbed path Let galaxy have mass M Move past star of mass m in other galaxy with closest approach distance b the impact parameter at velocity V v Z ASTR 3830 Spring 2004 Total change in perpendicular velocity as a result of the flyby is obtained by integrating over time 1 oo 2Gm AV F tdt t Mf w to 9V Low relative velocities gt larger deflections Star of mass m also receives a transverse impulse By conservation of momentum magnitude is Avim AVLM Total kinetic energy in transverse motions is 2 2 MEL M2Gm 2GM bV 2 bV 2 ASTR 3830 Spring 2004 This energy must come from the change in the forward velocity of the galaxy 2 AKEi MW MW AV 2 AtII 2 2 2 m Neglecting the very small AVH2 terms find 2G2mM m b2V3 Final step is to integrate over all impact parameters Suppose galaxy is passing through region where the stellar density is n stars per cubic pc Then AV bmax 2 2 dV f gymWC Lljmgtnmm dt bmm b V V where A bmax b min ASTR 3830 Spring 2004 How quickly will the LMC merge with the Milky Way Simple estimate dynamical friction time V V3 200 kms I z z dVdt 4 G2Mnm1nA 3 1010 Solar masses Galactic density at LMC for flat rotation curve estimate 3 x 104 Solar masses pc3 With these numbers estimate orbit will decay in 3 Gyr Close satellite galaxies will merge ASTR 3830 Spring 2004 Motion under gravity Motions of the stars and gas in the disk of a spiral galaxy are approximately circular vR and v2 ltlt v Define the circular velocity at radius r in the galaxy as Vr Acceleration of the star moving in a circular orbit must be provided by a net inward gravitational acceleration V2r a r To calculate arr must in principle sum up gravitational force from bulge disk and halo ASTR 3830 Spring 2004 For spherically symmetric mass distributions Gravitational force at radius r due to matter interior to that radius is the same as if all the mass were at the center Gravitational force due to matter outside is zero Thus if the mass enclosed within radius r is Mr gravitational acceleration is GMr V 2 I minus sign reflecting that force is directed inward ASTR 3830 Spring 2004 Bulge and halo components of the Galaxy are at least approximately spherically symmetric assume for now that those dominate the potential Selfgravity due to the disk itself is not spherically symmetric If you are familiar with vector calculus Sparke amp Gallagher 31 derives Poisson s equation needed to calculate force from an arbitrary mass distribution Note no simple form for the force from disks with realistic surface density profiles ASTR 3830 Spring 2004 Rotation curves of simple systems 1 Point mass M Vr iGM Applications 199550 Close to the central black hole rlt 01 pc Suf ficiently far out that r encloses all the Galaxy s mass eg image of the Galactic center Note noncircular orbits and presence of massive stars Movie Andrea Ghez s group 2 Uniform sphere If the density p is constant then Mr m 3p 47tGp Vr r Rotation curve rises linearly with radius period of the orbit 2m Vr is a constant independent of radius Roughly appropriate for central regions of spiral galaxies ASTR 3830 Spring 2004 3 Power law density profile If the density falls off as a power law r oc pr p0 r0 with or lt 3 a constant then W 1 4quot Gp0r0a r1a2 3 or For many galaxies circular speed curves are approximately flat Vr constant Suggests that mass density in these galaxies may be proportional to r2 ASTR 3830 Spring 2004 4 Simple model for a galaxy with a core Spherical density distribution 2 4JtGpr 2VH 2 aH Density tends to constant at small r Density tends to r392 at large r Corresponding circular velocity curve is Vr VH 1 a HarctanL r aH ASTR 3830 Spring 2004 Resulting rotation curve ASTH 3330 Spring 2004 Evidence for the cosmological constant Evolution of the scale factor in flat universes with matter plus cosmological constant A gt 0 g lt A 0 Unique signature of positive A is an acceleration of the expansion of the Universe Need to measure I L Difficult because we need to measure a second order effect ie must look at distant objects to see curvature in at But not too distant at early times A has little effect on the expansion Turns out that 2 1 is about optimal ASTFl 3830 Spring 2004 Deceleration parameter Expand at the function describing the evolution of the scale factor with time in a power series about t to dd 1 261261 at ato t ma a at to dt2 MO 5100 l 2M at01 t to ato 2t to 61 at01 H0t to qugu to2 which defines the deceleration parameter qO positive q0 means the atoato ato expansion is decelerating 0 61200 ar0H Note as with any truncated power series this description becomes inadequate at large enough ttO ASTR 3830 Spring 2004 Can use the Friedmann equations to evaluate q0 for various universes Matter dominated universes For A 0 models we obtained 4nG ato Tpmfoafo go 39c39lt0 4J1G 0 lpm at0H 3H3 pm 2 p C Flat matterdominated universe has q0 05 Open universes have 0 lt q0 lt 05 Cosmoloqical constant dominated universes a t From Friedmann equations or from solution a aoe 3 find that q0 1 in limit where positive A completely dominates the evolution of the scale factor ASTR 3830 Spring 2004 Observational tests of the deceleration parameter Most useful is the magnitude redshift relation for a population of standard candles in practice supernovae At small 2 this is just the linear Hubble diagram I Higher redshift behavior 3 will vary depending on q0 gr 0 I I m log 2 Suppose the sources emit radiation at time te te lt to Need to know o What redshift corresponds to that time o What flux and therefore apparent magnitude the sources will have when radiation reaches observer ASTR 3830 Spring 2004 Cosmological redshift Suppose that radiation is emitted at time te when the Universe has scale factor ate and received at time to Redshift is E 1 Lie 1 Ag ate observational definition relation to cosmology of the redshift This is quite intuitive wavelength of radiation expands along with expansion of the Universe This allows us to replace ate at0 in the power series expansion of at with the observable quantity 2 ASTR 3830 Spring 2004 Luminosity distance In a static Euclidean universe flux falls off with distance as L f 477D2 This needs to be modified by two factors in an expanding universe since h h E 39 Photons are redshifted E0 C C e lo Ae1z 1z o Time dilation means that the rate at which photons arrive is reduced by a further factor of 1 2 Result is an expression for the flux from a source at comoving distance Re and redshift z L f 4nR a2z01 z2 ASTR 3830 Spring 2004 Observational quantities are the measured flux f and the intrinsic luminosity of the source L assuming that somehow this can be deduced independently Define the luminosity distance 12 d Z 5 L which isjust the ordinary L 471 distance for small 2 The luminosity distance can be expressed as 1 1 2 d z z 1 z L Hi 2 qo If we can measure luminosity distances accurately ie we have a standard candle then plot of dLz vs 2 gives value of the Hubble constant deviations from a straight line fit give q0 ASTR 3830 Spring 2004 Type 1 a supernovae appear to be good enough standard candles to make a direct measurement of qO feasible 20 Key discovery although 3 19 there is some variation in 3quot 39 N absolute magnitude for 17 He Type 1a SN most of the Wl HH H i k dispersion can be removed 9 w v if the rate of decay of the 3 15 39 J luminosity is measured 15 Wmep Peak luminosity vs rate of decline from Phillips 1993 IB N Most luminous SN are also slowest to decline 15 Am no L Duclin rampeak luminosin relation rm Lhc mm bastabscrvcd SN 1539 Absnlul magniludes m B V mm I are plotted vsAm15lHl which m39wni39u l at I am 5 days following maximum ASTR 3830 Spring 2004 Hubble diagram for Type 1a supernovae In 1998 two groups published evidence in favor of a positive A from observations of Type 1a supernovae Calmmm Hamny 2 2 AJ l99 effective m3 002 005 01 02 05 redshift Z ASTB 3830 Spring 2004 Favored flat model 253 has cosmological lt constant dominating the current evolution of the Universe m N Prnjncl m o I A a lie rm Ta44i4iiei4p4ielt as effective mg Calanl39l ululu Hnmuy a mi AJ 1996 a r 157quotquot 77 g 10 w 07 R910 H E1 r1 7 E 3 1 Evidence for an f3 i r 39 0 accelerating w 02 04 06 ova 10 Universe rsdshif l ASTH 3830 Spring 2004 I l llll l No Big Bang 99 35 hawk M u l ni arse 90 1 QM 00 ii ltllllll 2 3 Supernova measurements on their own actually define an allowed region in the plane of 9A vs Qmaner Need additional constraints eg flatness to pin down actual value of 9A Example of degeneracy distinct Universes produce identical results for this cosmological test Need complementary tests to identify which Universe we live in ASTFi 3830 Spring 2004 Classification of AGN Luminous AGN are classified as Seyfert galaxies Type and II Quasars o BL Lacs or Optically Violent Variables Radio galaxies in Broad line and Narrow line variants All powered by accretion onto supermassive black holes But why so many classes are these all physically distinct objects Another class of galaxies are LlNERs lowionization nuclear emissionline region galaxies These are much more common than the other classes but have very low luminosities ASTR 3830 Spring 2004 Se ert galaxies Lowerluminosity AGN normally found in spiral galaxies Two subclasses Type 1 Seyfert galaxies have two sets of emission lines in their spectra Narrow lines with a width measured in velocity units of several hundred kms Broad lines with widths up to 104 kms m nus Szyfzn NGC 554 6 mmwm quot quotquot mum 1 w m um lollnmu FA un39 erg squot cm A H mm elemn Rm wavelengm in A S TR 3830 Spring 2004 Type2 Seyfertgalaxies As Type 1 but with only the narrow line component IIIIIIIIIYT1 Ha N 11 M16548 6583 Seyfert 2 NGC 1667 0111M4959 5007 o m M727 011mm ASTFi 3530 Spring 2004 BL Lacs BL Lacs are named after the prototype BL Lacertae Distinguished by lack of strong emission orabsorption lines in their spectra 400o Suuv Related class of objects are optically violent variables Many AGN are variable but OVVs show larger variations gt 01 mag in optical flux on short timescales eg a day ASTFl 3830 Spring 2004 Collectively OVVs and BL Lacs are called blazars t tt V Am I tangomlltxtau1rll il lt Mural lt51 Can be observed across entire EM spectrum All known blazars are radio sources ASTR 3830 Spring 2004 m Most luminous subclass of AGN Small fraction 510 are the strong radio sources which originally defined the quasar class Nuclear emission normally dominates host galaxy light Spectra very similar to Seyfert galaxies except that Stellar absorption lines are very weak if detectable at all Objects called quasars are all Type 1 in Seyfert jargon ie can see the broad lines ASTR 3830 Spring 2004 Radio galaxies Strong radio sources typically associated with giant elliptical galaxies Two types of radio galaxies have optical spectra that show AGN activity o Broadline radio galaxies like Type 1 Seyferts o Narrowline radio galaxies like Type 2 Seyferts Basically these look like radio loud Seyferts but they seem to occur in ellipticals rather than spirals ASTR 3830 Spring 2004 Unified models Some order can be imposed on this 200 of AGN subclasses Crucial observational realization is that emission from nuclear regions is not spherically symmetric On observable scales pc in the nearest AGN nucleus often has axial symmetry Radiation is 393 escaping in a conical region NGC 5728 Something blocking the way here ASTFl 3530 Spring 2004 Unified models seek to explain different classes of AGN as being due to different orientations of intrinsically similar systems to the observer s line of sight Seyfert 1 and Seyfert 2 galaxies Most secure unification Basic idea an obscuring torus prevents us seeing the broad line region in Seyfert 2 s Seyfert 1 Broad line x region 1 Torus Seyfert2 Not remotely to scale ASTR 3830 Spring 2004 Why do we still see the continuum in Seyfert 2 galaxies Scattered o f continuum O Continuum radiation comes from the disk at smaller radii than the broad lines why doesn t the torus block that too Assume that a scattering medium eg free electrons scatters some of this radiation into our line of sight Asmaaao prmgzom Support for this picture in some Seyfert 2 galaxies the polarized emission shows broad lines 1 I I l I I I I I I W I I I I I I I I I l I Mrk 348 F Flux 39o ITTIIIIIII IIIlIIIlIIIHIII IIIIIIIIIII I 4500 I I 503900 l I 5500 I 6000 6500 I I 7000 Wavelength Consistent with the unified model since scattering produces polarization Conclude At least some Seyfert 2 galaxies are intrinsically similar to Seyfert 139s If this applies to all Seyferts statistics mean that the torus must block about 34 of the sky as seen from the n ucleus ASTR 3830 Spring 2004 Reasonably secure to also fit quasars and blazars into this unified scheme Obscured Seyfert 2 Type 2 quasar Unobscured Seyfert 1 Type 1 quasar Viewed directly Blazars down the jet Accretion rate a Type 2 quasars aren t seen in the optical but highly obscured luminous AGN are needed to make up the Xray background Giant elliptical galaxies have higher mass black holes so reasonable to expect quasars to favor these galaxies ASTR 3830 Spring 2004 Radio loud vs radio quiet More ambitious unification schemes aim to explain why some AGN are radio loud others radio quiet Possible physical difference spin of the hole Radio loud Radio guiet High spin holes a 1 Low spin holes a ltlt 1 Produce jets which are No jets origin of radio emission cf blazars are radio loud Je ES powered by Spin energy Spectrum produced by extracted from black hole accretion disk blackbody plus nonthermal coronal emission ASTFl 3830 Spring 2004 Different lensing regimes Conceptually simplest situation for gravitational lensing is when the lens is massive enough to produce a large angle of deflection Case where we can resolve multiple images of the background source is called strong lensing Near perfect Einstein ring Weslphal et all 1995 AS TR 3830 Spring 2004 Strong lensing normally requires galaxy mass lenses which are extended objects ie slightly more complicated than the point mass case we considered Consider instead a Solar mass star half way between us and the Galactic Bulge d5 8 kpc dL dLS 4 kpc E g GM dLS 5 gtlt10399 radians 10quot3 arcscc c deS Warning lots of possibilities for getting the units wrong here Need M in g distances in cm 0 in cm 5quot Answer is in radians Can t resolve the multiple images the separation is only 1 milliarcsecond ASTR 3830 Spring 2004 All is not lost if there is relative motion between the lens and the background source Brightness of the unresolved source changes as the lens passes in front of the source Star in the Galactic disk Sun Line of sight to a star in the Galactic Bulge Lensing event occurs as the disk star passes within an angular distance SE of the bulge star bulge star initially brightens eventually fades as the alignment is lost This unresolved lensing regime microlensing ASTR 3830 Spring 2004 Physics lensing canserves surface brightness Lensed images are bigger so seurce appears magnified 0 Strong effect for impact parameters 8 lt 8E seurce can be magnified by a factor of 10 25 magnitudes er more 8 But very rare probability pf a given star in the ulge being lensed at any instant is few x 10395 MOA ZOOI BLGB 2 ngb1 3 3868 NOW rounnely Qbserveds example light curve at a lensed star 5 2 a as o a a a 2000 JD 2450000 ASTR 3830 Spring 2004 Final regime is weak lensing o no multiple images deflection causes only a distortion in the shape of extended sources eg a distant spherical galaxy may appear as an ellipse rather than a circle due to weak lensing by all the matter along the line of sight Intervening matter both luminous and dark True projected shape of source Observed image after lensing along line of sight Subtle and hard to measure effect distortion is only a few at most But an important probe of the dark matter distribution on very large scales ASTR 3830 Spring 2004 Cosmic Microwave Background Following recombination photons that were coupled to the matter have had very little subsequent interaction with matter Now observed as the cosmic microwave background Arguably the most important cosmological probe because it originates at a time when the Universe was very nearly uniform Fluctuations were small easy to calculate accurately linear rather than nonlinear Numerous complications associated with galaxy and star formation cooling magnetic fields feedback that influence other observables not yet important Basic properties isotropy thermal spectrum Anisotropies pattern of fluctuations ASTR 3830 Spring 2004 Basic properties of the CMB Excellent first approximation CMB has a thermal spectrum with a uniform temperature of T 27 K in all directions Wavelength cm l0 to l x DMR 39 o LBLr ltaly Whue Mm 3e South Pole Princeton ground chzlloon m y o UBC soundrng rocket 0 quot Cyanogen optical I f 2 726 K blackbody Brightness A erg cm 2 rec er Hz l l o l l Frequency GHz Thermal spectrum support for the hot big bang model lsotropy evidence that the Universe is homogenous on the largest observable scales Asmma SWHQZW Can show that thermal radiation filling the Universe maintains a thermal spectrum as the Universe expands Suppose that at recombination the radiation has a thermal spectrum with a temperature T 3000 K Spectrum is given by the Planck function B 2hv3 1 2 hkT V 0 eV 1 At time t number of photons in volume Vt with frequencies between v and v dv is Sam2 1 c e 1 since each photon has energy hv and the energy density of thermal radiation is vadv C ASTR 3830 Spring 2004 Now consider some later time t gt t If there have been no interactions the number of photons in the volume remains the same dNt dNt However the volume has increased with the expansion of the Universe and each photon has been redshifted Vt39 Vt 0 a t v39 v at dv39 dv a at39 Substitute for Vt v and dv in formula for dNt and use fact that dNt dNt ASTR 3830 Spring 2004 Obtain 717le 1 C3 ehv kTgtltat at dNt 8 1Vt39dv39 which is a thermal spectrum with a new temperature at at39 Conclude radiation preserves its blackbody spectrum as the Universe expands but the temperature of the blackbody decreases Toca loc1z T39T Recombination happened when T 3000 K at a redshift z 1090 ASTR 3830 Spring 2004 CMB anisotropies Universe at the time of recombination was not completely uniform small over underdensities were present which eventually grew to form clusters voids etc In the microwave background sky fluctuations appear as o A dipole pattern with amplitude A T z 10393 T Origin Milky Way s velocity relative the CMB frame Reflects the presence of local mass concentrations clusters superclusters etc Smaller angular scale anisotropies with AT T 105 originate mostly from the epoch of recombination greatest cosmological interest ASTR 3830 Spring 2004 Experiments detect any cosmic source of microwave radiation not just cosmic microwave background Low frequencies freefree synchrotron emission High frequencies dust KaO V W Antenna Temperature uK rms i i i i i i i i 20 40 60 80 100 200 Frequencv GHzi CMB dominates at around 60 GHz Also different spectra can be separated given measurements at several different frequenCIes Asmaaamsp ngzom Full sky map from WMA Dipole subtracted recall dipole is much larger than the smaller scale features Galactic foreground emission subtracted as far as possible ASTR 3830 Spring 2004 Characterizinq the microwave background skv First approximation actual positions of hot and cold spots in the CMB is random does not contain useful information Cosmological information is encoded in the statistical properties of the maps o What is the characteristic size of hot cold spots one degree angular scale o How much anisotropy is there on different spatial scales CMB is a map of temperature fluctuations on a sphere conventionally described in terms of spherical harmonics Earth s gravitational field is similarly described ASTR 3830 Spring 2004 Spherical harmonics Any quantity which varies with position on the surface on a sphere can be written as the sum of spherical harmonics AT 7094 SalliMew 1quot spherical measured anisotro harmonic map as function of W Weight 39 h0W mUCh funCt39On spherical polar angles 0f the Signal iS E and q accounted for by this particular mode The spherical harmonic functions themselves are just increasingly complicated trignometric functions eg 1226l13sin2 66m ASTR 3830 Spring 2004 Having decomposed the observed map into spherical harmonics result is a large set of coefficients alm Next compute the average magnitude of these coefficients as a function of l Cl E ltlalm2gt Plot of CI as a function of l is described as the angular power spectrum of the microwave background Each CI measures how much anisotropy there is on a particular angular scale given by 180 9N l ASTR 3830 Spring 2004 Examples Z 2 E 1 6 Map With Cl nonzero Map with Cl nonzero only f0 2 only for l 16 In currently popular cosmological models based on the theory of inflation the primary CMB anisotropies are truly random in the sense that a plot of C vs I describes completely the cosmological information contained in the original map Astonishing result means that angular power spectrum is basic measurement to compare r with theo y AS TH 3530 Spring 2004 Evidence for black holes in galactic nuclei Strongest evidence from our own Galactic center Observe individual stars orbiting an unseen companion with a mass of around 3 x 106 Solar masses 199550 Closest approach of this star to the focus of the ellipse the black hole position is 130 AU 080716 0302 39 507 0 301 Derived position of the black 0719 hole coincides with a radio and Xray source which varies on short timescales ASTH 3830 Spring 2004 Can we prove the unseen mass is a black hole No but can demonstrate that if it s not a black hole it must be something even weirder A very dense cluster of stars Suppose we packed 3 x 106 Solar masses of stars into a sphere of radius rlt 130 AU Is this stable First assume they are Solar mass stars moving at velocity v Average time for a given star to collide with another star is 1 collision z nZv where 2 m 22 is the crosssection for a physical collision and n is the number density of stars ASTR 3830 Spring 2004 t Estimate these quantities 6 n Nquot 3X10 9x10 4lcm393 Em 3 4nlt130 x 15 gtlt101301rngt3 3 3 2 M21202 z 6 x10220m v z M z 45 gtlt1080ms391 1 Using these numbers find tcollision 10 years A superdense cluster of ordinary stars would collide almost instantaneously of course we could also see such a cluster ASTR 3830 Spring 2004 NGC4258 Next best evidence for a black hole in the galaxy NGC 4258 Observe the positions and velocities of water masers in a thin gas disk orbiting the black hole Thin disk L I ROtation A Mummwfw ff m g 4w w i it 39 i Wool f k g 45 Wis tineoistgm Velocity km 5quot ASTH 3830 Spring 2004 Rotation curve of the maser spots is accurately Keplerian ie consistent with a single central point mass of MBH 39 i 01 x107Mm most accurately measured black hole mass Maser emission extends from 016 pc to 028 pc close enough that nonblack hole explanations are difficult Also NGC 4258 is an AGN Unfortunately only a small fraction of AGN have observable water masers in their disks and of those that do this example is much the best ASTR 3830 Spring 2004 Most black hole masses are derived from less accurate methods Gas disk kinematics Measure the velocity of gas disks in the nucleus correct for inclination and assume Keplerian motion Then use 2 W M G to estimate mass from observed radius and velocity Works well but less accurate because Measurements are made much further from the black hole 1OO pc Gas disk may have more complex motions eccentricity pressure support ASTR 3830 Spring 2004 Stellar kinematics If the velocity dispersion in the galaxy is 0 black hole will dominate motion of stars with a radius rBH the black hole s sphere of influence given by GjW BPIO39 a rBHGLZBPI V VBH O Subtler effects on stellar orbits outside this radius If we can measure the velocities of stars within the sphere of influence from spatially resolved spectra expect to see increase in stellar velocities due to presence of black hole use detailed galaxy models to derive mass ASTR 3830 Spring 2004 This is very difficult in practice eg consider a black hole of mass 108 Msun at the center of a galaxy with velocity dispersion o 200 kms Sphere of influence is rBH 11 pc For a galaxy in the Virgo cluster distance 16 Mpc the angular size of the sphere of influence is 014 arcseconds Feasible for nearby galaxies and requires HST resolution ASTR 3830 Spring 2004 quot39quot lquot quot39quot39iquot39 El tj lon 200 El i g mm m a 100 Y ft j g Reasonably easy E o jg 5 galaxy close 10 Mpc f 5 5i 3 with evidence for a 100 j 533 E massive black hole 200 of 109 Solar masses IlIIIIIIIIIIIIIIIIIIIII Velocity Hww39Ivul Clear rise in thevelocity dispersion 300 1 dispersion but only A within central arcsecond lm aw 100 39 I l I l I l I I r I 5 4 6 z u 2 x arcsec ASTB 3830 Spring 2004 The Mo relation 1 l l l l 60 70 50 90100 l l l 200 300 400 dispersion km 3quot Plot the derived black hole mass against the velocity dispersion of the galaxy Find that MBH 2 CO4 where C is a constant Recall FaberJackson law L 04 lmplies black hole mass roughy proportional to luminosity of the bulge This relationship has apparently very little scatter A S TR 3830 Spring 2004 Morphological classification of galaxies Edwin Hubble devised a scheme for classifying galaxies based on their appearance in his 1936 book The Realm of the Nebulae Wis Jar mr normal 5p u y f f r 1 k f if K 1 9quot I A y 9 M e ellpIca nebulae RM 3 0 50 0 3 E 7 SM 531 a fax W 47 K 39 w gt r it 7 I a uquotlt0 I a 4 EEE a WM5 Elliptical galaxies Spiral galaxies ASTR 3830 Spring 2004 Elliptical galaxies are smooth usually round and almost featureless No spiral arms or dust lanes Generally lacking in cool gas and hence few young blue stars b Ellipticity is defined as 8 1 a b n Elliptical galaxies are denoted En where 1 a 10 A round elliptical is E0 the most elongated ellipticals are of type E7 ASTR 3830 Spring 2004 Spiral galaxies are named for their bright spiral arms which are prominent due either to bright O and B stars evidence for recent star formation or to dust lanes Define two sequences of spiral galaxies Sa Sb Sc Sd Central bulge becomes less important Disk becomes more important Spiral arms become more open and ragged Sba 83b 83c 83d As above except that these galaxies also have a central linear bar while the Sa Sb are unbarred ASTR 3830 Spring 2004 Transition class between ellipticals and spirals are the SO galaxies also called Ienticulars SO galaxies have a rotating disk in addition to a central elliptical bulge but the disk lacks spiral arms or prominent dust lanes Lenticulars can also have a central bar in which case they are labeled SBO ASTR 3830 Spring 2004 Classification of real galaxies on Hubble s tuning fork diagram Obviously easiest to classify taceon spirals Hubble interpreted this diagram as an evolutionary sequence this is not supported by more modern work ASTFt 3830 Spring 2004 Other galaxy types Hubble dubbed galaxies that didn t fit into his scheme irregular Today irregular galaxies are defined as small blue galaxies lacking any organized spiral structure Other types of galaxy Hubble called irregular are now identified as starburst or interacting galaxies These have a disturbed appearance due to recent episodes of violent star formation or close encounters with other galaxies The Mice ASTR 3830 Spring 2004 Problems with traditional galaxy classification Subiective especially for spiral galaxies In practice experienced observers can almost always provide a consistent classification at least for well resolved galaxies so this is not a major problem Very large surveys such as the Sloan Digital Sky Survey currently in progress will image 108 galaxies to classify galaxies Some based on the Development of several automated schemes Hubble system others use different criteria ASTR 3830 Spring 2004 Problems with traditional galaxy classification Appearance of galaxies is strongly dependent on which wavelength the observations are made in eq the nearby qalaxv M81 X39ray UV Visible NearIR FarIR Note large change in appearance between the UV and the near infrared images Galaxies look clumpier in the UV and increasingly smooth as we go to the visible and longer wavelengths ASTR 3830 Spring 2004 Cosmology Cosmology study of the origin structure and evolution of the Universe What would we like a theory of cosmology to explain o Origin of the Universe what was the Universe like at much earlier epochs Fate of the Universe How did the structure seen in today s Universe form How did the elements form 39 We will discuss the hot big bang model for understanding some of these problems ASTR 3830 Spring 2004 Elements of the hot big bang model Model rests on a number of fundamental assumptions and observations 1 Universe is homogenous and isotropic When averaged over sufficiently large volumes the Universe is isotropic same in all directions and homogenous other observers at different locations see the same general picture of the Universe at the same time Described as the cosmological principle evidently makes the mathematical description much easier as there are no special places or directions ASTR 3830 Spring 2004 Nearby galaxies are strongly clustered Angular distribution of the most distant sources is much closer to isotropic Radio sources Texas survey at 365 MHz 65000 sources I Gamma ray bursts i5 E 2 Z BATS E catalog of I firSt 1000 bursts l LM It hi V a7 i l 39I 7 l L 1 1 r7 i v 39 39 i I I 39 5 1 in 3quot 39 I quot quotm In g 115 C I 39 39 Z u a M I In 939 LI Ly 1 LquotILf 5 H ASTR 3830 Spring 2004 Xray background and especially the cosmic microwave background are very close to isotropic once the dipole has been subtracted CMB isotropic at 10395 level once the dipole and Galactic emission have been accounted for ASTR 3830 Spring 2004 2 Universe is expanding The mean distance between conserved particles is increasing with time at the rate dl H01 dt Constant of proportionality is timedependent the present value is Hubble s constant HO Best observational estimates of HO are H0 71 i 4 kms391 Mpc 1 this is value quoted by the WMAP team from observations of the microwave background HST Key Project result from measurements of Cepheids in external galaxies is identical within the errors ASTR 3830 Spring 2004 Can define a Hubble length c H0 4000 Mpc at which this expression for the recession velocity extrapolates to the speed of light more detailed relativistic treatment is needed for distances of this order Can also define a Hubble time 1 HO 1010 years this is to order of magnitude the age of the Universe ASTR 3830 Spring 2004 3 Universe expanded from a hot dense state Implied by a naive extrapolation of the expansion back to much earlier times Direct evidence from the existence and spectrum of the microwave background which is very well fit by a blackbody spectrum Wavelength cm m i W i i i TN a I goquot 70 Jquot 39 3 u 0 VC 7 E o E n FIRAS COBE satellite amp it y x DMR COBEsatelhte 39 N no o LBLr italy Vxhite Mm amp South Pole w vquot Princeton ground ampballoon w m o UBC sounding rock o 5 C Cyanogen op 21 a r g f 2726 Kblackbody m it i i i m Frequency GHz ASTB 3830 Spring 2004 4 Dynamics of the Universe are described by Einstein s theory of General Relativity Need a theory of gravity in order to make quantitative predictions eg for how the expansion will evolve with time Newtonian gravity is not quite sufficient mathematical description relies instead on General Relativity Conservative view validity of General Relativity on scales of the Universe not proven from cosmological measurements though certainly consistent with available observations Belief in validity of relativistic description rests on other measurements experiments which are fully consistent with predictions of General Relativity ASTR 3830 Spring 2004 Measuring galaxy luminosities Galaxies unlike stars are not point sources The Hubble Space Telescope can resolve ie detect the extended nature of essentially all galaxies Even from the ground most galaxies can easily be distinguished from stars morphologically Define the surface brightness of a galaxy l as the amount of light from the galaxy per square arcsecond on the sky Consider a small square patch of side D in a galaxy at distance d Angle patch subtends on sky or Dd ASTR 3830 Spring 2004 If the luminosity of all the stars within the patch is L total flux is L F 2 4er Define surface brightness as Units of l are mag arcseC392 ie if a galaxy has a surface brightness of 20 mag arcseC392 then we receive as many photons from one square arcsecond of the galaxy s image as from a star of 20th magnitude Centers of galaxies have lB 18 mag arcseC392 ASTR 3830 Spring 2004 To measure the total amount of light coming from a galaxy need to integrate the surface brightness across the galaxy image This leads to a related problem galaxies do not often have sharp edges Typically integrate out to some limiting isophote eg sum up all the light coming from regions with surface brightness IB lt 25 mag arcseC392 This measure of the total galaxy brightness is called an isophotal magnitude numerous variations are possible ASTR 3830 Spring 2004 Salpeter Mass Function The Initial Mass Function for stars in the Solar neighborhood was determined by Salpeter in 1955 He obtained M SUM 2 35 Salpeter IMF constant which sets the local stellar density Using the definition of the IMF the number of stars that form with masses between M and M AM is MAM To determine the total number of stars formed with masses between M1 and M2 integrate the IMF between these limits M2 M2 N f MdM 50 f M3923935dM M1 M1 M 135 M2 g 135 135 0 135 wl M2 M1 ASTR 3830 Spring 2004 Can similarly work out the total mass in stars born with mass M1 lt M lt M2 M AM MdM M1 Properties of the Salpeter IMF most of the stars by number are low mass stars most of the mass in stars resides in low mass stars o following a burst of star formation most of the luminosity comes from high mass stars Salpeter IMF must fail at low masses since if we extrapolate to arbitrarily low masses the total mass in stars tends to infinity Observations suggest that the Salpeter form is valid for roughly M gt 05 Msun and that the IMF flattens at lower masses The exact form of the low mass IMF remains uncertain ASTR 3830 Spring 2004 Comments on the Salpeter IMF What is the origin of the IMF Most important unsolved problem in star formation Many theories but no consensus Observationally known that dense cores in molecular clouds have a powerlaw mass function rather similar to the IMF So the IMF may be determined in part by how such cores form from turbulent molecular gas Is the IMF universal ie is M the same function everywhere Most theorists say no Predict that fragmentation is easier if the gas can cool so primordial gas without any metals should form more massive stars Observationally little or no evidence for variations in the IMF in our galaxy or nearby galaxies Asm 3830 Spring 2004 Accretion Disks Luminosity of AGN derives from gravitational potential energy of gas spiraling inward through an accretion disk Derive structure of the disk and characteristic temperatures of the gas First consider vertical structure F Gas at radius R x e 2 cylindrical and r Z height 2 above the disk midplane central 212 mass M R Gravitational acceleration in vertical direction GM GM z GM 8 2 COS 2 3z zltltR r r r R ASTR 3830 Spring 2004 If the gas is supported against gravity by a pressure gradient force balance in the vertical direction gives dP dz Assume the disk is isothermal in the vertical direction with sound speed cs The pressure is then P pcs2 Pg Solve for the vertical structure 207 10 GM 92 S2 is angular CS dz p R3 z Z velocity in disk 039 S22 f p 2fzdz p Cs 522 p20 is density in 2 26S a p pzOe dISk mldplane ASTR 3830 Spring 2004 Rewrite this equation as P hoe Z M where h is the vertical scale height of the disk Since 9 v r can write h as 22632 ZCSZR2 h 92 V2 P E s R v The thickness of the disk as a fraction of the radius is given by the ratio of the sound speed to the orbital velocity A disk for which h R ltlt 1 is described as a geometrically thin disk Structure of thin disks is relatively simple because radial pressure forces can be neglected ie v for the gas is the same as a particle orbiting at the same radius ASTR 3830 Spring 2004 Angular momentum transport If the disk is thin then orbital velocity of the gas is Keplerian GM 12 1 R Specific angular momentum v R is I wGMR ie increasing outwards Gas at large R has too much angular momentum to be accreted by the black hole To flow inwards gas must lose angular momentum either o By redistributing the angular momentum within the disk gas at small R loses angular momentum to gas further out and flows inward o By loss of angular momentum from the entire system eg a wind from the disk could take away angular momentum allowing inflow ASTR 3830 Spring 2004 Redistribution of angular momentum within a thin disk is a diffusive process a narrow ring of gas spreads out under the action of the disk viscosity gas surface density an m u 12 5 21 With increasing time radius R Mass a flows inward to small R and is accreted Angular momentum is carried out to very large R by a vanishingly small fraction of the mass ASTH 3830 Spring 2004 Radiation from thin disk accretion Consider gas flowing inward through a thin disk Easy to estimate the radial distribution of temperature Potential energy per unit mass at radius R in the disk is E GM a dE GM R dR R2 Suppose mass dM flows inward distance RdR dR Change In potential energy Is AE GAE deR R Half of this energy goes into increased kinetic energy of the gas If the other half is radiated luminosity is GMM 2 dR 2R ASTR 3830 Spring 2004 L Divide by the radiating area 2 x 2nR x dB to get luminosity per unit area Equate this to the rate of energy loss via blackbody radiation GMM 4 ois StefanBoltzmann 831R3 constant Gives the radial temperature distribution as GMM 14 SawR3 Correct dependence on mass accretion rate and radius but wrong prefactor Need to account for o Radial energy flux through the disk transport of angular momentum also means transport of energy Boundary conditions at the inner edge of the disk ASTR 3830 Spring 2004 Correcting for this radial distribution of temperature is 3GMM 1 8710R3 R where Flin is the radius of the disk inner edge For large 14 TR radii R gtgt Rm we can simplify the expression to 3GMM 1 4 R 34 TR z 3 SJ39EO39RS RS with FlS 2GM c2 the Schwarzschild radius as before For a hole accreting at the Eddington limit Accretion rate scales linearly with mass Schwarzschild radius also increases linearly with mass Temperature at fixed number of RS decreases as M39 4 disks around more massive black holes are cooler ASTR 3830 Spring 2004 For a supermassive black hole rewrite the temperature as M 14 M 14 R TR 63x105 8 ME 10 R S 34 K Accretion rate at the Eddington limiting luminosity assuming n01 A thermal spectrum at temperature T peaks at a frequency hvmX z 28kT An inner disk temperature of 105 K corresponds to strong emission at frequencies of 1016 Hz Wavelength 50 nm Expect disk emission in AGN accreting at close to the Eddington limit to be strong in the ultraviolet origin of the broad peak in quasar SEDs in the blue and UV ASTR 3830 Spring 2004 Disk has annuli at many different temperatures spectrum is weighted sum of many blackbody spectra flat v1 3 region 39 39 39 exponential sv cut off at 10L high v flux 4 m IT in 1 1a 13 1 1 frequency Consistent with the broad spectral energy distribution of AGN in the optical and UV regions of the spectrum ASTH 3830 Spring 2004 Measuring the spin of black holes Important but difficult task try to measure the spin of black holes Only affects local spacetime around the hole 323373 Physics last stable orbit Rms varies depending upon spin parameter a 6GM c2fora0 Rapidlyrotating gt C2 as a gt 1 black hole Suggests several possible routes to measuring spin Luminosity for the same accretion rate rapidly spinning hole will be more luminous than nonrotating hole n 006 Schwarzschild 7 03 near maXimal Kerr ASTFl 3830 Spring 2004 Variability shortest orbital period for a Kerr black hole is less than for a Schwarzschild black hole Rotation also introduces new effects eg frame dragging that may show up in variability Problem details of variability poorly understood Velocity highest velocities in the disk are greater for a Kerr black hole than a Schwarzschild one Observable if we can see a spectral line produced in the inner disk Note gravitational radiation from a close black hole binary is probably a better ie easier to interpret probe Possible with LISA ASTR 3830 Spring 2004 Spectral lines from the inner disk Redshi ed emission Elugshi Newtonian case Consider an annulus in the disk with orbital velocity v Projected velocity is vobs V sin i where i is the inclination Leads to a Doppler shift iv Lab V C Doublehorned profile Doppler shift only effect for a Newtonian disk frequency energy AS TH 3530 Spring 2004 N ewto n is In Special relativity lEieneral relativity Line pro le Relativistic disk several new effects lel 05 Newtonian profile from single annulus Transverse doppler effect moving clocks appear to run slow Observed frequency is reduced compared to rest frame value by factor Y 1 V2 C212 Beaming Boosts blue wing of the line attenuates red wing Gravitational redshift Further shifts profile to lower energies Finally integrate overall disk radii Predict broad asymmetric line profile with a sharp cutoff at high E ASTR 3830 Spring 2004 For disks viewed almost edgeon light bending around the black hole also affects the line profile Prediction assuming a smooth distribution of disk emissivity Prediction for a turbulent disk Note Beaming Light bending Redshift is not visualized A STE 3830 Spring 2004 Iron lines Inner disk is too hot to produce spectral lines in the optical In some Seyfert galaxies detect fluorescent iron line in the Xray spectrum Physics assume cold not fully ionized disk is illuminated by high energy Xray photons C39 I r J Incident J Dec to o4 keV Photoquot g rounjlgtate P hamquot K shell N 39 n1 o Eject electron from ground state o Electron from n2 level drops down into ground state energy emitted as photon at 64 keV ASTR 3830 Spring 2004 counts per unit energy arb Detailed calculation shows the predicted spectrum from a cold slab of gas illuminated by Xrays o O uI 1o5 104 1000 100 5 10 Energy keV Range of photon energies can eject an electron but emitted photon is always at single energy Strong line emission Fluorescent yield scales as Z4 so iron line is the strongest Low energy photons are mostly absorbed high energy photons scatter back out of slab A S TR 3830 Spring 2004 Iron line profile for the Seyfert qalaxv MCG63015 J I I tn 3quot T I39 l quot th II it 39 It ng 2511 I 461 L 1 I I T I H I 3 I I I I l I I I I I I I I I I I I I 1 I L I I I L I r 4 Observation with XMMNewton observatory ASTFI 3830 Spring 2004 lron line profile is found to be Often extremely broad Favors a rapidly spinning hole o Variable high and low states of the source have significantly different lines Best proof to date of presence of black holes in AGN Relativistically broad iron lines also detected in Galactic black hole candidate sources ASTR 3830 Spring 2004 Observational determinations of OMB anisotropy 7000 5000 U C c c 4000 3000 ll1C 21r MKZ h c c c 1000 Angular scale deg 90 2 05 02 2003 data 10 40 100 200 Multipole moment 1 Results from the WMAP satellite 1st year data ASTFl 3830 Spring 2004 Compilation of all available data by Max Tegmark includes WMAP and some ground based balloon experiments sensitive to smaller angular scales Angular scale in degrees 5 02 01 20 5 2 l V WWW Wt l l Peak at g1 80 e degree F gt Scales E Decline E toward 3 to x very small Plateau at g h scales large scales g 207 l 7 E l l l 10 40100200 m 600 600 1000 120014001500 Mu ipole 1 Want to understand physical origin of each of these features ASTFt 3830 Spring 2004 Most of the anisotropy power spectrum reflects fluctuations in the density at the time of recombination Photons escape from the overdense region Recombination Consider a slight overdensity collapsing during the radiation dominated phase Photons escaping at recombination Escape from a hotter denser region Are redshifted escaping from a deeper potential well Have a Doppler shift due to relative velocity ASTR 3830 Spring 2004 How this works in detail depends upon the scale of the fluctuations Largest scales low I On the largest scales perturbations have not had time to collapse significantly prior to recombination At low I directly see the fluctuations generated at an earlier epoch Intermediate scales degree Overdensities start to collapse but increased pressure causes them to bounce leading to oscillations ASTR 3830 Spring 2004 Maxima and minima of these oscillations lead to the strongest signals in the microwave background o Doppler peaks o First peak compression occurs at degree scales Small scales Start En Q Recombination is not instantaneous Photons will leak out of small over underdensities during the process damping very small scale fluctuations Exponential suppression of anisotropy at the smallest scales ASTR 3830 Spring 2004 Dependence on cosmology 1 Is the Universe flat open or closed 10 1ca Power Doppler peaks define a physical scale at recombination Angular scale this corresponds to depends upon the geometry of the Universe 01 1111111 0010 1111 1 11111111 1 11111111 1 1111111 1 Blue curve effect of changing the geometry Open universe position of the peaks is shifted to smaller angular scales ie larger multipole l llllllll l lllllll l llllllll l 10 100 1000 l Animations from Wayne Hu ASTR 3830 Spring 2004 Observed position of the first peak is at l 220 92W 102 i 002 ie the Universe is flat or very close to being flat What does this imply about the cosmological constant Directly almost nothing CMB anisotropy is mainly sensitive to the totalenergy density not to the individual contributions from matter and cosmological constant Indirectly estimate by other means that the total matter density is perhaps 9m 2 03 mostly dark matter Need something else to make up the inferred value of Qtotal 1 A cosmological constant with 9A 07 as deduced from SN is consistent with this ASTR 3830 Spring 2004 2 Baryon content of the Universe I I I l I I I I I I I I I I I I I I I I 030005 8 d1C Power ohllllllk 11111 500 1000 1500 2000 Increasing the fraction of baryons Increases the amplitude of the Doppler peaks Changes the relative strength of the peaks odd peaks due to compressions become stronger relative to the even peaks due to rareiactions ASTR 3830 Spring 2004 WMAP results give Qbmomhz 0024 i 0001 Hubble constant in units of 100 km s1 Mpc1 Estimates based on nucleosynthesis and the measured abundance of deuterium give a range 52 112 0021 a 0025 baryons Good consistency between two independent measurements of the baryon abundance ASTR 3830 Spring 2004 Full power spectrum from WMAP and other experiments is consistent with the predictions of ACDM ie the tamin ot cosmological models that include dark matter plus a cosmological constant Angular Scale 2t IlhllClZn luK Simplest such models have 6 tree parameters Being able to tit the data is a genuine success Parameters are mostly well constrained by the data ASTFt 3830 Spring 2004 Adding in other cosmological information eg from the supernovae measurements further constrains the model lOD i00VI I I I I I 090 WMAPexISN 070 060 LA 050 040 s2 om Important information provided by Microwave background WMAP eventually Planck Type 1a Supernovae Nucleosynthesis Lymana forest galaxy clustering 2dF Sloan Digital Sky Survey weak gravitational lensing ASTH 3830 Spring 2004 Summary The Universe is flat and will expand forever 39 Ordinary matter stars gas dark baryons is negligible 39 Cold dark matter and dark energy dominate the evolution of the Universe and currently make roughly equal contributions to the total energy density Suggests that the Universe at the time of recombination is now very well understood we know the initial conditions that eventually gave rise to galaxies stars quasars etc Discuss on Wednesday where the initial conditions may have come from ASTR 3830 Spring 2004 Active Galactic Nuclei Basic picture of Active Galactic Nuclei AGN Most galaxies have supermassive black holes at their centers Masses range from 106 Solar masses to 109 Solar masses Gas accreting onto the black hole releases a large amount of gravitational potential energy L Mlle2 Efficiency Accretion rate Both the efficiency and the accretion rate vary across orders of magnitude between different galaxies ASTR 3830 Spring 2004 Accretion process produces a host of observational phenomena Important examples o Very high luminosity from a point source in the nucleus Small physical size of the emission region allows rapid variability Broad spectral lines due to Doppler shift of gas orbiting the black hole o Xray emission from high temperature plasma close to the black hole o Mechanical power in the form of outflows and jets from the central regions In the most powerful AGN these phenomena dominate over starlight What we see in a particular system reflects both the accretion rate and the viewing angle to the central engine ASTR 3830 Spring 2004 Classes of AGN AGN are classified into numerous types depending mostly upon their luminosity in different wavebands especially the optical and radio Seyfert Galaxies First class of AGN to be identified Carl Seyfert obtained spectra of several nearby galaxies with very bright cores and found emission lines that were unusually broad up to 8500 kms These AGN are reasonably common around 1 of spirals Thus numerous nearby examples ASTR 3830 Spring 2004 Modern spectra of Seyfert qalaxies Seyfert 1 NGC 4151 Jawwt NGC 491 J wannaLa meWwImJmdwj LIL mvm w gt u Wavelength Angstroms Ht ASTR 3830 Spring 2004 Quasars First radio surveys of the sky were completed in the late 1950 s Many prominent radio sources at high galactic latitudes were found to coincide with starlike objects on photographic plates Named quasistellar radio sources quasars Spectra did not initially seem to match those of known galaxies or other sources ASTR 3830 Spring 2004 Mystery was solved with the realization that most quasars are distant luminous objects with highly redshifted spectra Define the redshift 2 via z 1 Brightest known quasar mB131 mag has zO158 Convert this redshift into distance using Hubble s law valid for small 2 only dC Z670Mpc H 0 Distance implies a luminosity absolute magnitude 1OO times greater than galaxies such as the Milky Way Proposal that black holes were involved was made by Zeldovich amp Novikov within year of the identification ASTR 3830 Spring 2004 Properties of quasars Characteristic of quasars include Pointlike sources originally associated with radio sources though these radio loud quasars are actually small fraction of the total Broad spectral energy distribution with large UV flux Time variable continuum o Broad emission lines Typically high redshift record now 264 High redshift is mainly because quasars are rare and luminous Other properties more useful for understanding the physics ASTR 3830 Spring 2004 Quasar images Even with HST imaging difficult to detect the light of the host galaxy due to the high luminosity of the nucleus Spiral host unusual Elliptical host more common case Imagine how difficult using only photographic plates A STR 3830 Spring 2004 Spectral energy distributions Quasars have a very broad spectral energy distribution SED Spectra cannot be described as blackbodies Characterize crudely as a powerlaw Fv Cv o or is the powerlaw index C is a constant FV is the specific flux ie per frequency interval units of erg s1 cm392 Hzi Integrate to get power between frequency v1 and v2 P Tdev ASTR 3830 Spring 2004 V Flat spectrum source equal energy output per unit frequency interval VF log y Equal energy per unit logarithmic frequency interval most useful way of plotting AGN spectra ASTR 3830 Spring 2004 Observed SED of radio loud and radio quiet quasars m m i m m mu u m u 1 14 man A 1an m m I i i i i i 45 7 5 3 7 m a a Maya gag 4 2944 uv HardX u Bump Gap component A a m 342 3 an 2 4D 7 4c 3447 mam loud 7 i i i i i i i i i mmrbreak A45 iw maaii EM 5044 7 r w xuv v T Inflectmn excess 42 3 El 2 40 J H m Mkn 555 radio quiet i 1 4 39 39 iogu Hz fat from farIR through to hard Xrays ASTH 3830 Spring 2004 Optical spectra show strong broad emission lines 4 39 LynNV 39 gr 1216 amp 1240 Balmer lines of hydrogen m i MgH on 3727 H o m Nev 3426 Flux FO arbitrary uniis N I 5007 Nenn 3869 4959 01n i O i i I 1000 2000 3000 4000 5000 Quos R stiframe Wavelength Prominent lines of abundant Ions ASTR 3830 Spring 2004 Microlensing experiments 39 Several experiments have searched for microlensing events toward the Galactic Bulge lenses are disk or bulge stars toward the Magellanic Clouds lenses could be stars in the LMC SMC or halo objects MACHO Massive Compact Halo Object observed 119 million stars in the Large Magellanic Cloud tor a total of 57 years OGLE Optical Gravitational Lensing Experiment ongoing experiment presently monitor 33 millions stars in the LMC plus 170 million stars in the Galactic Bulge ASTH 3830 Spring 2004 Microlensing observables Suppose that between us and the Magellanic Clouds there are a large number of dark compact objects Source stars in the LMC Unseen lenses in the Galactic halo At any one time we will see a clear lensing event ie the background star will be magnified if the line of sight passes through the Einstein ring of one of the lenses Previously derived the angular radius of the Einstein ring on the sky 8E Area is nGEZ ASTR 3830 Spring 2004 2 GMdLS Single lens of mass M at distance dL W Observer source distance IS d3 lens C L S source distance is dLS dsdL 6E Probability that this lens will magnify a given source is d d39 tl t39 t 2 LS Irec y propor Iona o P 0c 6E 0C a d X M the mass of the lens L 3 Same is obviously true for a population of lenses with total mass MIDOID just add up the individual probabilities Conclude o measuring the fraction of stars that are being lensed at any one time measures the total mass in lenses independent of their individual masses geometric factors remain we need to know where the lenses are to get the right mass estimate ASTR 3830 Spring 2004 No way to determine from a single image whether a given star is being magnified by lensing Need a series of images to see star brighten then fade as the alignment changes Position of Einstein ring when event stars Line of sight when event ends 1 Motion of lens Lensing time scale equals the physical distance across the Einstein ring divided by the relative velocity of the lens I ZdLHE VL ASTR 3830 Spring 2004 4 M Time scale is proportional to the square vLC d5 root of the individual lens masses Put in numbers appropriate for disk stars lensing stars in the Galactic bulge dS8kpc dLdLS4kpc 39 M 03 Msun o vL 200 km s1 t40 M 03 sun days Weak dependence on mass is very convenient observationally if we observe every night can detect o events with 1 1 day M lt Jupiter mass 10393 Msun o events with 1 1 year M 25 Solar masses eg stellar mass black holes everything in between ASTR 3830 Spring 2004 MACHO project detected 1317 microlensing events toward the LMC in just under 6 years of operation compared to only 2 4 expected on the basis of known stellar populations Ablue Arzd Lensing events are expected to be achromatic same light curve in different wavebands which helps distinguish them from variable stars ASTR 3830 Spring 2004 For each event there are only two observables o duration 1 if we know the location of the lens along the line of sight this gives the lens mass directly peak amplification A this is related to how close the line of sight passes to the center of the Einstein ring b q gt Deflnc u dLth we won t try to A 2 2 prove this formula Lulu2 4 Note amplification tells us nothing useful about the lens Additionally observing many events gives an estimate of the probability that a given source star will be lenses at any one time often called the optical depth to microensing This measures the total mass of all the lenses if their location is known ASTR 3830 Spring 2004 Based on the number and duration of MACHO events If the lenses are obiects in the Galactic Halo 20 of the mass of the Galactic halo inferred from the Galactic rotation curve is in the form of compact objects Typical mass is between 015 M and 09 Msun sun Idea that all the mass in the halo is MACHOs is definitely ruled out One interpretation of these results is that the halo contains a much larger population of white dwarf stars than suspected Other authors suggest the lenses may not be our halo at all but rather reside in the Magellanic Clouds If correct implies that none of the halo is in the form of planetary mass to 10 Msun compact objects ASTR 3830 Spring 2004 Ambiguity in the distance to the lenses is the main problem Can be resolved in a few special cases a If distortions to the light curve caused by the motion of the Earth around the Sun can be detected parallax events b If the lens is part of a binary system Light curves produced by binary lenses are much more complicated but often contain sharp spikes caustic crossings and multiple maxima Provide more information about the event One event seen toward the Small Magellanic Cloud was a binary event and it is known to lie close to the SMC My guess is therefore that the majority of the lenses are not in the Galactic halo which is probably made up of elementary particle dark matter instead ASTR 3830 Spring 2004 25 logmagnificatl0n I w l llll o flit Tilquot iiililii39ji39il V39T iii if l l l l t y dq 054050 ill llll 1000 1050 l l l l I l l l 850 900 HJD 2450000 Observed binary lensing event Note a star with an orbiting planet is just a special case of a binary system with a large difference in masses Much more numerous events toward the Bulge are being monitored for signs of any planets so far without any definite detections ASTR 3830 Spring 2004 The Galaxy luminosity function The luminosities of galaxies span a very wide range most luminous ellipticals are 107 more luminous than faintest dwarfs Luminosity function cIgtL describes the relative number of galaxies of different luminosities Definition If we count galaxies in a representative volume of the Universe ltIgtLdL is the number of galaxies with luminosities between L and L dL Identical to the definition of the stellar luminosity function Luminosity functions are easiest to measure in clusters of galaxies where all the galaxies have the same distance ASTR 3830 Spring 2004 The Schecter luminosity function A convenient approximation to the luminosity function was suggested by Paul Schecter in 1976 ILdL exp L dL L L In this expression n is a normalization factor which defines the overall density of galaxies number per cubic Mpc o L is a characteristic galaxy luminosity An L galaxy is a bright galaxy roughly comparable in luminosity to the Milky Way A galaxy with L lt 01 L is a dwarf o or defines the faintend slope of the luminosity function or is typically negative implying large numbers of galaxies with low luminosities ASTR 3830 Spring 2004 The Schecter luminosity function The Schecter function is o a fitting formula that does not distinguish between galaxy types as with the stellar mass function parameters must be determined observationally Illustrative m 8 x 103 Mpc393 related to mean galaxy numbers density L 14 x 1010 Lsun luminosity of galaxies that dominate light output or 07 lots of faint galaxies where Lsun 39 x 1033 erg s1 is the Solar luminosity ASTR 3830 Spring 2004


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