ASTROPHYSICS I: lecture notes, ETH Zurich 2019

8 covers Sections 9 in Choudhuri, except 9.3 and 9.6 which are treated in “cosmology” not covered at all: sections 9.4.2 and 9.7 additional topics: the local group, detailed model of steady accretion disks, and a few points on gravitational lensing

History – 1784: catalogue of Messier ≈ 100 nebular object (avoid confusion with comets) – 1890: (NGC): ≈ 8000 extended objects – around 1925: many extended nebula are galaxies like the Milky Way – today: > 108 galaxies cataloged

SLIDES: Hubble types and pictures

8.1 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 %

m 10 Typical luminosity MB:(MB = −20 is ≈ 10 L ) main types [mag] – S-galaxies: −17m to −23m – E-galaxies: gE: ≈ −21m E: ≈ −19m, dE: −14m to −18m dSph: −10m to −15m, cD: −22m to −25m (diffuce central cluster elliptical) – Irr-galaxies: Irr: −17m dIrr: −10m to −17m

61 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 formation – integrated spectrum of cool (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)

SLIDES: galaxy spectra and Sersic profiles surface brightness description: (not important for this lecture)

Sersic surface brightness fitting functions: k: constant, h: radial scale – Sersic index n controls the curvature of the profile

h  r 1/ni I(r) ∝ I exp −k 0 h A: elliptical galaxies: de Vaucouleurs fit

 h 0.25 i I(r) = Ieexp −7.67 r/re − 1

– n = 4, re: effective radius, Ie = I(re) →: luminosity distribution determined by the distribution of stars in gravitational potential

B: disk galaxies: exponential fit

−r/rd I(r) = I0e

– n = 1, I0 central (extrapolated) disk surface brightness; rd characteristic radius

62 Mass estimates

A: for elliptical galaxies – observation: widths of strong absorption lines – random motions of stars follows from virial theorem (2Ekin + Epot = 0)

1 2 mimj 2 Σi mivi − G Σi6=j = 0 2 |xi − xj| assumption: Nm = Mgal all N stars have mass m N 2 Gm2 Nmhv2i ≈ 2 hRi mean velocity and velocity dispersion GM hv2i ≈ 2hRi B: for disk galaxies: – HI-radial velocity measurements, vr = vc cos φ sin i – circular velocities (from FZ = FG) as for the Milky Way v2 GM(r) c = r r2 observed rotation curves are all flat vc ≈ 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

SLIDES: HI map and rotation curves

Velocity-luminosity relations: (empirical relations)

A: for elliptical galaxies: Faber-Jackson relation:

 L 0.25 −1 σv ≈ 220 km s L∗

L∗: characteristic galaxy luminosity

B: for disk galaxies: Tully-Fisher relation

 L 0.22 −1 vc ≈ 220 km s L∗ Interpretation: 2 – vc ∝ M/rd (for given characteristic radius rd) 2 – disk mass scales like M ∝ rd – luminosity√ scales like L ∝ M 2 1/4 → vc ∝ L/ L or vc ∝ L

63 8.2 The local group SLIDES: 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, interactions are 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 MB [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) dE6 −16.1 M32 E2 −16.0 IC10 dIrr −15.6 NGC 147 dE5 −14.9 Triangulum galaxy (M33) Sb −18.9

64 8.3 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 galaxy – 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 (star-star collisions are very rare) – 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 > 106 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

SLIDES and video: colliding galaxies

65 8.4 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: 37 11 – Seyfert galaxies: L ≈ 10 W ≈ 10 L 39 13 – Quasars: L ≈ 10 W ≈ 10 L Size of source: – e.g. for NGC 4151 (20 Mpc): source not spatially resolved (e.g. < 100) → rSource < 50 pc – e.g. for 3C273: luminosity variability ∆L/L ≈ 30 % on time scales ∆t ≈ days 5 5 11 → rSource < c · ∆t = 3 · 10 km/s · 3 · 10 s = 10 km = 0.003pc

13 Big question: How to produce 10 L within 0.003 pc?

Minimum mass from Eddington luminosity limit assumptions: – source is stable: radiation pressure force Fr < FG gravitational force – object is made of ordinary matter: – σe scattering dominates opacity – mH is the corresponding gas mass per electron 2 – Fr = L/(4πr ) · σe/c per electron 2 (photon-flux · photon-momentum · cross section: Nγ/4πr · hν/c · σe) 2 – FG = GMmp/r per proton

Eddington limit Fr = FG

4πGMmpc 4.5 LE = ≈ 10 (M/M )L σe source is only stable, if mass 6.5 11 – M > 10 M for a 10 L - 8.5 13 – M > 10 M for a 10 L -quasar

66 Energy source: disk accretion onto

Schwarzschild-radius for black hole 2GM  M  RS = 2 = 3000m c M

8 – for M8 = 10 M → rS(M8) = 2AU

Accretion onto black hole from infinity to RS: – change in potential energy ∆Epot per mass unit m: GMm mc2 ∆Epot = − = RS 2

→ ∆Epot is half of the rest mass!

Energy production in an : – 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 < 107 K energy production for a given mass accretion rate M˙ – last stable orbit at 3 RS (typically)

dE GMM˙ Mc˙ 2 pot = = dt 3RS 6 Assumption: Virial theorem is valid for quasi-Keplerian accretion disk – Ekin = −Epot/2 – ∆Epot/2 goes into orbital energy of the gas – ∆Epot/2 is dissipated and heats disk gas 7 – disk radiates L ≈ ∆Epot/2 and stays cool (< 10 K) – other energy loss mechanism may be important (gas jet)

Result for the equilibrium disk luminosity:

L < η Mc˙ 2 – η ∼< 0.1 is the energy efficiency parameter

Eddington accretion rate: Eddington (= maximum) accretion rate for given black hole mass M

˙ LE 4πGMmp 8 ME = 2 = = 2.2 (M/10 M ) M /yr η(= 0.1)c ησec 8 Result for a black hole of 10 M ˙ – Eddington (maximum) accretion rate ME ≈ 2M 12.5 – corresponding Eddington luminosity: LE ≈ 10 L – larger luminosity → more massive black hole

67 8.5 Steady accretion disks Assumptions: R +∞ – axissymmetry, surface density Σ(r) = −∞ ρ(r, z)dz 1/2 – quasi-Keplerain motion of the gas vφ = rΩ = (GM/r) – radial velocity component vr mass conservation – mass transfer rate [kg m−1 s−1] for each annulus r dΣ d 2πr + (2πr · Σ · vr) = 0 dt dr | {z } | {z } ˙ =0 =M – first term: temporal change of mass in an annulus = 0 for steady disk – second term: radial mass flow M˙ (accretion rate kg/s) constant through disk – Example A: vr = const → Σ ∝ 1/r and 2πrΣ = const. conservation of angular momentum: 2 – angular momentum of an annulus: Lr = 2πrΣ · r Ω(r × v = r · rΩ) 2 2 3 1/2 1/2 – Example A: Lr ∝ r Ωr (GM/r ) ∝ r –(L per kg decreases for mass moving toward the center) → angular momentum must be transported outwards

Equation for the angular momentum d d 2πr (Σ · r2Ω) + (2πr · Σv · r2Ω) = G(r) dt dr r | {z } =0 – first term zero for a steady disk – radial change of angular momentum connected to mass inflow vr 1/2 – specific angular momentum, e.g. per gramm, in Keplerian disk is Ls ∝ r – G is the required momentum transfer to allow the accretion

→ disk viscosity because of differential rotation – A = shear due to differential rotation dΩ A = r dr 2 friction force Ff with ν [m /s] as dynamical viscosity dΩ F = νΣA = νΣr f dr Transport of angular momentum by viscosity d G = (2πr · νΣ A ·r) dr |{z} =r(dΩ/dr) change of angular momentum for “inspiraling” gas in a Keplerain disk = angular momentum transport by dynamic viscosity d d dΩ (2πr · Σv · r2Ω) = (2πr · νΣr · r) dr r dr dr

68 Integration dΩ 2πr · Σv · r2Ω = 2πr · νΣr · r + C (∗) r dr Determination of the integration variable C: – boundary condition at inner disk radius ri: – 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) q 2 ˙ C = 2πri · Σivri · ri Ωi = M GMri q √ ˙ 2 2 3 (using: 2πri · Σv = M and ri Ωi = ri GM/ri = GMri)

Equation (*) with inserted boundary condition √ √ ˙ ˙ q M GMr = 2πνΣ(−3/2) GMr + M GMri q √ (using for second term: r3 · dΩ/dr = r3 · (−3/2) GM/r5 = (−3/2) GMr) yields product of viscosity and surface brightness after rearrangement:

M˙  rr  νΣ = 1 − i 3π r q – f(r) = 1 − r/ri = 0 for r = ri, 0.5 for r = 4ri, ≈ 1 for r  ri hydrodynamics: relation between dynamic friction (drag ∝ v2) and dissipation 1 D = νΣA2 2 produced thermal energy D(r) as function of radius (A2 = (9/4)(GM/r3)

3GMM˙  rr  D(r) = 1 − i 4πr3 r −3 → D(r) ∝ r for r  ri

Z ∞ 1 GMM˙ Ldisk = D(r)2πrdr = · ri 2 ri

– Ldisk corresponds to ∆Epot from ∞ to ri

Temperature structure follows from D(r) = D+(r) + D−(r) (upper and lower disk surface)

D(r)1/4 3GMM˙  rr 1/4 T (r) = = 1 − i disk 2σ 8σπr3 r −3/4 → Tdisk ∝ r for r  ri – peak temperature near inner rim ri (see excercise) – a disk annulus emits the following luminosity L(r) ∝ 2πrσT 4 ∝ 1/r2

69 spectral energy distribution of accretion disk: – peak emission for λ ≈ 2.9mm K/T (ri) (Wien’s displacement law) – exponential cut-off for shorter wavelengths 1/3 – Iν ∝ ν for disk (superposition of Planck-curves from the annuli at different r) 2 – Iν ∝ ν 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

8.6 General structure of AGNs SLIDE: disk/torus image, unification scheme

6 10 – accreting black hole M ≈ 10 − 10 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 → pole-on view – NLRG: narrow-line radio galaxy → edge-on view

13 Quasars and QSO (high luminosity > 10 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)

70 8.7 Clusters of galaxies Properties of cluster of galaxies: – 100 - 10000 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: σv ≈ GM/R – typical velocity dispersion: σv ≈ 1000 km/s – typical radius: R ≈ 1 Mpc 15 → M ≈ 10 M 13 – observed brightness (stars) → L ≈ 10 L

Mass to light ratio for clusters of galaxies M M ≈ 100 L 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)

71 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−

n n Z2 −51 e i −hν/kB T ν = 6.8 · 10 g(ν, T ) √ e T 17 – X-ray emission requires T ≈ hν/kB for hν = keV (ν = 2.4 · 10 Hz, λ = 1.2 nm) → typical value T ≈ 108 K, – typical volume ≈ 1Mpc3 37 10 – observed luminosity ≈ 10 W (= 2.5 · 10 L ) → very low density (see Exercise) → very long cooling time (see Exercise)

Origin of the gas: 14 – Mgas > Mstars or Mgas ≈ 10 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: 1 GM ∆E ≈ m = k T pot 2 R p B – yields about T ≈ 108 K as observed

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: Mstars ≈ 0.03Mcl – based on X-ray data of hot gas: Mgas ≈ 0.1Mcl → all visible mass only ≈ 0.1 − 0.3× the mass derived from the virial theorem

72 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 4GM ∆φ = c2R – proven to exist for background stars during solar eclipse of 1919 00 – ∆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: Dd, obs.-source Ds, lens-source: Dds – replace: R = Ddθ

4GM 1 Dds θ = 2 c Dd∆φ Ds

– for Ds  Dd, then Dds/Ds → 1 – for given Ds, θ maximal for lens in the middle (Dd = Dds)

Mass estimates: – for given lens configuration (Dd,Ds)

– θ ∝ M for a point mass – θ ∝ MtotfM (r), where fM (r) is mass distribution of the lens Problem: fM (r) is often not well defined

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