Subclasses: spiral galaxies: Sa/SBa Sb/SBb Sc/SBc (late type galaxies) decreasing bulge size increasing opening angle of spiral windings

Transcription

1 7 Galaxies History 1784: catalogue of Messier 100 nebular object (avoid confusion with comets) 1890: New General Catalogue (NGC): 8000 extended objects around 1925: many extended nebula are galaxies like the Milky Way today: > 10 8 galaxies cataloged SHOW slides: Hubble types and galaxy pictures 7.1 Types of galaxies Hubble sequence: 4 morphological categories S -galaxies (normal spirals): round central bulge and disk with spiral structure SB -galaxies (barred spirals): spiral galaxy, where central bulge has a bar structure E -galaxies (elliptical galaxies): homogeneous spherical or elliptical structure Irr -galaxies (irregular galaxies): other galaxies (later added to the classification) Subclasses: spiral galaxies: Sa/SBa Sb/SBb Sc/SBc (late type galaxies) decreasing bulge size increasing opening angle of spiral windings elliptical galaxies: E0 E7 (early type galaxies) flattening of spheroid Ex (intrinsic ellipticity Ex) x = 10 (a-b)/a (a,b long and short axis) S0: spheroidal galaxies dominant spheroid (perhaps a small disk) Frequency of galaxies in NGC-catalog (nearby, bright galaxies) S/SB: 70 %; E: 20 %; Irr: 7 % Typical luminosity M B : (M B = 20 m is L ) main types [mag] S-galaxies: 17 m to 23 m E-galaxies: ge: 21 m E: 19 m, de: 14 m to 18 m dsph: 10 m to 15 m, cd: 22 m to 25 m (diffuce central cluster elliptical) Irr-galaxies: Irr: 17 m dirr: 10 m to 17 m 46

2 Description of E and S galaxy types: E galaxies very homogeneous appearance no cold gas (no dust lanes, no HI emission, no HII-regions) no star formation integrated spectrum of cool stars (5000 K) stellar orbits with random orientation red and dead spiral galaxies central bulge (like small elliptical) disk contains cold gas (dust lanes, HI and CO emission), and HII-regions spiral arms, more than average young stars and HII-regions gas and stars follow predominant disk rotation trailing spirals integrated spectrum like hot star (HI-absorption) with emission lines (HII-regions) SHOW slides: galaxy spectra and Sersic profiles surface brightness description: (not important for this lecture) Sersic surface brightness fitting functions: k: constant, h: radial scale n Sersic index controls the curvature of the profile A: elliptical galaxies: de Vaucouleurs fit I(r) I 0 exp [ k ( r ) 1/n ] h I(r) = I e exp ( 7.67 [( r/r e ) ]) n = 4, r e : effective radius, I e = I(r e ) : luminosity distribution determined by the distribution of stars in gravitational potential B: disk galaxies: exponential fit I(r) = I 0 e r/r d n = 1, I 0 central (extrapolated) disk surface brightness; r d characteristic radius 47

3 Mass estimates A: for elliptical galaxies observation: widths of strong absorption lines random motions of stars follows from virial theorem (2E kin + E pot = 0) 2 Σ i 1 2 m iv 2 i G Σ i j m i m j x i x j = 0 assumption: Nm = M gal all N stars have mass m mean velocity and velocity dispersion Nm v 2 N 2 2 v 2 GM 2 R B: for disk galaxies: HI-radial velocity measurements, v r = v c cos φ sin i circular velocities (from F centrifug = F grav ) Gm 2 R vc 2 r = GM(r) r 2 for homogeneous mass distribution: M(r) r 3 v c r if mass is inside r: M(r) = M tot vc 2 = GM tot r observed rotation curves are all flat v c const: M(r) r as far out as rotation curves can be determined! strong evidence for the presence of dark matter in all disk galaxies SHOW slides: HI map and rotation curves Velocity-luminosity relations: (empirical relations) A: for elliptical galaxies: Faber-Jackson relation: σ v 220 ( L L ) 0.25 km s 1 L : characteristic galaxy luminosity B: for disk galaxies: Tully-Fisher relation v c 220 ( L ) 0.22 km s 1 L Interpretation: vc 2 M/r d (for given characteristic radius r d ) disk mass scales like M rd 2 luminosity scales like L M vc 2 L/ L or v c L 1/4 48

4 7.2 The local group SHOW slide: M31 and Magellanic Clouds Galaxies of the local group: dominated by three disk galaxies (MW, M31, M33) MW and M31 have > 5 faint satellite galaxies, type dirr, de, or dsph local group contains > 50 galaxies most are low luminosity objects with low metallicity [Fe/H] < 1 (only few previous stellar generations) Many satellites are in interaction with MW or M31 LMC and SMC show strong loss of HI-gas because of interaction M32 and NGC 205 are so close to M31 that interaction is unavoidable Sgr dwarf galaxy collides just now with MW interaction of dwarf galaxy with large spiral has only little effect because mass ratio is < 1 : 100 possible giant collision in the future between M31 and MW: separation: 0.74 Mpc relative velocity: 110 km/s tangential velocity: < 10 km/s (HST-data from 2012) expected collision in 4 Gyr The 3 brightest galaxies of the local group and their brightest satellite galaxies galaxy type M B [mag] Milky Way SBb 20.8 Large Magellanic Cloud Irr 17.9 Small Magellanic Cloud Irr 16.3 CMa dwarf galaxy dirr 14.5 Sgr dwarf galaxy dsph 12.7 Andromeda galaxy (M31) Sb 21.6 NGC 205 (M110) de M32 E IC10 dirr 15.6 NGC 147 de Triangulum galaxy (M33) Sb

5 7.3 Galaxy interactions (only few qualitative points are given) Galaxy interactions are very frequent: between spirals and small satellite galaxy (small + big) collisions between two large spiral galaxies (big + big) interactions in galaxy clusters and groups (one + many) interactions are important for galaxy evolution A: Collision between small galaxy and large spiral galaxy: impact on spiral galaxy relatively small tidal distortion: disk is warped vertically to disk plane tidal distortion: deviation of axisymmetry of disk (loopsided disks) spiral structure can be enhanced by corotating disturbance (M51) density wave produces disk with ring structure instead of spirals (e.g. M31) star formation may be triggered locally impact on the smaller galaxy are strong motion of stars is disturbed by potential of spiral many stars leave potential of dwarf gas of small galaxy collides with gas of spiral and is lost only the more compact bulge remains formation of de and dsph galaxies alternative: small galaxy is totally disrupted B: Collision between two large spiral galaxies: stars move through potential of other galaxy (no star-star collisions expected) stellar motions strongly disturbed systematic disk rotation is reduced, central bulge size increases (more stars with random orbit orientation) merged galaxy (E-type), possibly with diffuse halo (cd-galaxy) gas collides, shock heating to T > 10 6 K, gas expands into intergalactic space gas is removed from one or both galaxies (gas stripping) E-galaxy without cold gas alternative: gas is compressed, burst of star formation very prominent, peculiear galaxies (ultra)-luminous IR-galaxies C: Interaction in galaxy clusters: main processes: gas stripping by hot intercluster gas S-galaxies are distroyed infalling galaxies merge with central galaxies formation of (diffuse) giant galaxies SHOW slides and video: colliding galaxies 50

6 7.4 Active galactic nuclei (AGN) History: Karl Seyfert 1947: describes spiral galaxies with very bright central regions Seyfert galaxies around 1955: detection of extended radio emission which can be associated with galaxies Radio galaxies: e.g. Vir A, Her A, Cen A, Cyg A etc. M. Schmidt (1963): radio source 3C273 is 13 mag point-like object at d 1 Gpc Quasars (quasi-stellar radio sources) estimaged energy output: Seyfert galaxies: L W L Quasars: L W L Size of source: e.g. for NGC 4151 (20 Mpc): source not spatially resolved (e.g. < 1 ) r Source < 50 pc e.g. for 3C273: luminosity variability L/L 30 % on time scales t days r Source < c t = km/s s = km = 0.003pc Big question: How to produce L within pc (3 light-days) Minimum mass from Eddington luminosity limit assumptions: source is stable: radiation pressure force F r < F G gravitational force object is made of ordinary matter: σ e electron scattering dominates opacity m H is the corresponding gas mass per electron F r = L/(4πr 2 ) σ e /c per electron (photon-flux photon-momentum cross section: N γ /4πr 2 hν/c σ e ) F G = GMm p /r 2 per proton Eddington limit F r = F G L E = 4πGMm pc σ e source is only stable, if mass M > M for a L -Seyfert galaxy M > M for a L -quasar (M/M )L 51

7 Energy source: disk accretion onto black hole Schwarzschild-radius for black hole R S = 2GM c 2 = 3000m ( M M ) for M 8 = 10 8 M r S (M 8 ) = 2AU Accretion onto black hole from infinity to R S : change in potential energy E pot per mass unit m: E pot is half of the rest mass! E pot = GMm R S = mc2 2 Energy production in an accretion disk: steady flow of matter towards black hole angular momentum must be transported away energy in the disk must be radiated away to keep disk cool < 10 7 K energy production for a given mass accretion rate Ṁ last stable orbit at 3 R S (typically) de pot dt = GMṀ = Ṁc2 3R S 6 Assumption: Virial theorem is valid for quasi-keplerian accretion disk E kin = E pot /2 E pot /2 goes into orbital energy of the gas E pot /2 is dissipated and heats disk gas disk radiates L E pot /2 and stays cool (< 10 7 K) other energy loss mechanism may be important (gas jet) Result for the equilibrium disk luminosity: η < 0.1 is the energy efficiency parameter L < η Ṁc2 Eddington accretion rate: Eddington (= maximum) accretion rate for given black hole mass M Ṁ E = L E η(= 0.1)c = 4πGMm p 2 ησ e c Result for a black hole of 10 8 M Eddington (maximum) accretion rate ṀE 2M corresponding Eddington luminosity: L E L larger luminosity more massive black hole = 2.2 (M/10 8 M ) M /yr 52

8 7.5 Steady accretion disks Assumptions: axissymmetry, surface mass Σ(r) = + ρ(r, z)dz quasi-keplerain motion of the gas v φ = rω = (GM/r) 1/2 radial velocity component v r mass conservation mass transfer rate [kg m 1 s 1 ] for each annulus r 2πr dσ dt } {{ } =0 + d dr (2πr Σ v r) = 0 }{{} =Ṁ first term: temporal change of mass in an annulus = 0 for steady disk second term: radial mass flow Ṁ (accretion rate kg/s) constrant through disk Example A: v r = const Σ 1/r and 2πrΣ = const. conservation of angular momentum: angular momentum of an annulus: L r = 2πrΣ r 2 Ω (r v = r rω) Example A: L r r 2 Ωr 2 (GM/r 3 ) 1/2 r 1/2 (L per kg decreases for mass moving toward the center) angular momentum must be transported outwards Equation for the angular momentum 2πr d dt (Σ r2 Ω) + d }{{} dr (2πr Σv r r 2 Ω) = G(r) =0 first term zero for a steady disk radial change of angular momentum connected to mass inflow v r G is the required momentum transfer to allow the accretion disk viscosity because of differential rotation A = shear due to differential rotation A = r dω dr friction force F f with ν [m 2 /s] as dynamical viscosity Transport of angular momentum by viscosity F f = νσa = νσr dω dr G = d (2πr νσ dr A }{{} =r(dω/dr) change of angular momentum for inspiraling gas in a Keplerain disk = angular momentum transport by dynamic viscosity r) d dr (2πr Σv r r 2 Ω) = d dω (2πr νσr dr dr r) 53

9 Integration 2πr Σv r r 2 Ω = 2πr νσr dω dr r + C Determination of the integration variable C: boundary condition at inner disk radius r i : the differential rotation goes to zero: dω/dr = 0 last stable orbit around black hole before gas falls into it gas rotation is braked by surface (for accreting star) C = 2πr i Σ i v ri ri 2 Ω i = Ṁ GMr i (using: 2πr i Σv = Ṁ and r2 i Ω i = ri 2 GM/ri 3 = GMr i ) ( ) Equation (*) with inserted boundary condition Ṁ GMr = 2πνΣ( 3/2) GMr + Ṁ GMr i (using for second term: r 3 dω/dr = r 3 ( 3/2) GM/r 5 = ( 3/2) GMr) yields product of viscosity and surface brightness after rearrangement: f(r) = 1 νσ = Ṁ 3π ( ri ) 1 r r/r i = 0 for r = r i, 0.5 for r = 4r i, 1 for r r i hydrodynamics: relation between dynamic friction (drag v 2 ) and dissipation D = 1 2 νσa2 produced thermal energy D(r) as function of radius (A 2 = (9/4)(GM/r 3 ) D(r) r 3 for r r i L disk = D(r) = 3GMṀ 4πr 3 L disk corresponds to E pot from to r i r i ( ri ) 1 r D(r)2πrdr = 1 2 GMṀ r i Temperature structure follows from D(r) D + (r) = D (r) = D(r)/2 are the energies radiated from the upper and lower surfaces T disk (r) = ( D + (r) 2σ ) 1/4 = ( 3GMṀ T disk r 3/4 for r r i peak temperature near inner rim r i (see excercise) 8σπr 3 ( ri )) 1/4 1 r 54

10 spectral energy distribution of accretion disk: peak emission for λ 2.9mm K/T (r i ) (Wien s displacement law) exponential cut-off for shorter wavelengths I ν nu 1/3 for disk (superposition of Planck-curves from the annuli at different r) I ν ν 2 at lower energy end (Rayleigh-Jeans part of outermost disk region) Problem: description of viscosity is unclear mangetic turbulence jet acceleration by magnetic field lines fixed in rotation disk accretion happens, therefore there must be some kind of disk viscosity 7.6 General structure of AGNs SHOW slide: disk/torus image, unification scheme accreting black hole M M an accretion disk emitting far/extreme UV radiation a relativistic particle jet perpendicular to the disk (weak or strong) broad line region BLR: high density, high velocity clouds near BH < 1pc narrow line region (NLR): low density clouds on scales of kpc a dust torus outside the accretion disk BLR and NLR are photoionized by UV radiation from disk the dust torus is heated by disk radiation dust torus hides central region (disk and BLR) for edge-on systems strong jets produce extended radio emission jets aligned with line of sight produce strong variability, and superluminal motion Different types of AGNs are caused by the viewing angle: Seyfert galaxies - AGN in spiral galaxies: Seyfert I: pole-on view BLR and disk visible Seyfert II: edge-on view S-galaxy with strong emission lines from the center Radio galaxies - AGN with strong jet in elliptical galaxies: BLRG: broad-line radio galaxy pole-on view NLRG: narrow-line radio galaxy edge-on view Quasars and QSO (high luminosity > L AGNs) Quasars: radio-loud object (with jet) QSO: quasi-stellar object without strong radio emission blasars: high luminosity AGN where we look into the jet (strongly variable brightness prototype object BL Lac blasar) 55

11 7.7 Clusters of galaxies Properties of cluster of galaxies: members gravitationally bound dominated by giant elliptical galaxies (cd) in the center the result of many merged galaxies disk galaxies are rare and often show gas stipping processes they do not survive long in clusters Two types of galaxy clusters regular clusters: well defined structure, central big ellipticals regularly distributed smaller galaxies around it virialized (or dynamically relaxed) example: Coma cluster: d=100 Mpc, R 3 Mpc, > 1000 galaxies irregular clusters: center often not well defined galaxies irregularly distributed not virialized yet (large fraction of galaxies still falling in ) example: Virgo cluster: d=16.5 Mpc, R 2.2 Mpc, 1300 galaxies M/L-ratio for galaxy clusters Virial theorem yields mass: σ v GM/R typical velocity dispersion: σ v 1000 km/s typical radius: R 1 Mpc M M observed brightness (stars) L L Mass to light ratio for clusters of galaxies M L 100M L low mass star have M/L 3M /L individual galaxies M/L 3 10M /L (Tully-Fisher and Faber-Jackson relations) cluster of galaxies contain a lot of dark matter (Zwicky 1933) 56

12 Hot X-ray emitting gas in galaxy clusters X-rays telescopes detected hot gas in all clusters of galaxies: emission process is bremsstrahlung acceleration of charged particles electromagnetic radiation mainly e in the Coulomb field of nucleons and e ɛ ν = g(ν, T ) n en i Z 2 T e hν/k BT X-ray emission requires T hν/k B for hν = kev (ν = Hz, λ =) typical value T 10 8 K, typical volume 1Mpc 3 observed luminosity W (= L ) very low density (see Exercise) very long cooling time (see Exercise) Origin of the gas: M gas > M stars or M gas M X-ray spectrum shows Fe 7 kev line (Lyα line of FeXXVI) metallicity half solar [Fe/H] 0.3 all this processed gas comes most likely from infalling spirals which lost their gas they were converted or merged with elliptical galaxies gas falling into a potential gets virialized Potential energy per proton available for gas heating: yields about T 10 8 K as observed E pot 1 2 GM R m p = k B T Dark matter and gravitational lensing individual galaxies point to the presence of dark matter (flat rotation curves) problem is particularly clear in galaxy clusters based on the stellar (visual) luminosity: M stars 0.03M cl based on X-ray data of hot gas: M gas 0.1M cl all visible mass only the mass derived from the virial theorem 57

13 Gravitational lensing is an independent method to derive the mass of an object apparent bending of light beams by gravitational potentials (predicted by Einstein s theory of general relativity) formula for the deflection angle φ for a beam passing at distance R from point mass M φ = 4GM c 2 R proven to exist for background stars during solar eclipse of 1919 φ 1.7 at the limb of the sun (M, R ) angular separation of an image from the lens θ assuming a point mass distances: obs.-lens: D d, obs.-source D s, lens-source: D ds replace: R = D d θ θ = 4GM 1 D ds c 2 D d φ D s for D s D d, then D ds /D s 1 for given D s, θ maximal for lens in the middle (D d = D ds ) Mass estimates: for given lens configuration (D d,d s ) θ M for a point mass θ M tot f M (r), where f M (r) is mass distribution of the lens Problem: f M (r) is often not well defined 58