Relazioni di scala tra Buchi Neri e Galassie Ospiti Lezione 7
First hints of BH-galaxy relations Kormendy & Richstone (1995) suggest the existence of a correlation between the total blue magnitude of the host spheroid (M B,bulge ) and M BH. bulge (spheroid) = entire galaxy in case of an elliptical Kormendy & Richstone 1995 A. Marconi Fisica delle Galassie (2012/2013) 2
More evidence... Magorrian at al. (1998) find a correlation between M BH and bulge masses ( Magorrian relation) They use mostly low resolution ground based data. Use stellar kinematics with axisimmetric 2-I dynamical models. They find M BH /M bulge ~0.006. Most mass estimates have been shown to be much overestimated (use of 2-I models). Magorrian at al. 1998 A. Marconi Fisica delle Galassie (2012/2013) 3
The M BH -σ correlation Two groups (Ferrarese & Merritt 2000, Gebhardt et al. 2000) independently find a tight relation between M BH and the velocity dispersion of the stars in the galaxy bulge σ (within R e or R c =R e /8) R e and R c much larger than BH sphere of influence, σ should not be affected by BH, only by galaxy grav. potential! Big and hot debate about the slope M BH ~ σ 5 (FM00) and M BH ~ σ 4 (G00) Relation with σ is tighter than relation with B luminosity. MBH-LB MBH-σ MBH-LB MBH-σ Ferrarese & Merritt 2000 Gebhardt et al. 2000 A. Marconi Fisica delle Galassie (2012/2013) 4
What is the meaning of tight? The MBH-σ relation relation is considered the best one because is tighter than the MBH-MB,bulge and MBH-Mbulge correlations. Tightness is related to the intrinsic scatter of MBH-X correlations, i.e. the dispersion in BH masses for given X (eg log σ) beyond measurement errors perfect relation P (M V )= (M a bv) M = log M BH V = log with errors on MBH measurement observed scatter is Z P (M obs V )= P (M obs M)P (M V )dm P (M obs V ) 1 p 2 M exp " 1 2 Mobs a bv M 2 # A. Marconi Fisica delle Galassie (2012/2013) 5
Intrinsic scatter a possible real (non perfect) relation P (M V )= 1 p 2 0 exp " 1 2 M a bv 0 2 # observed distribution for given V (σm error on Mobs) P (M obs V )= observed dispersion (scatter, rms of fit residuals) of relation is therefore obs = q 2 0 + 2 M 1 p 2 ( 2 0 + 2 M )exp apple 1 2 intrinsic scatter of MBH-σ relation is estimated to be ~0.3-0.4 dex (factor 2-2.5 dispersion of MBH for given sigma). (M obs a bv ) 2 ( 2 0 + 2 M ) Beware that intrinsic scatter depends critically on the accuracy on MBH errors! Tremaine et al. 2002
MBH-σ Countless papers in literature, considered two of the most recent ones! Gultekin+2009 [49 MBH, 19 upper lim.] Graham+2010 [64 MBH] log(m BH / M )=(8.12 ± 0.08) + (4.24 ± 0.41) log( /200 km s 1 ) 0 = 0.44 ± 0.06 dex Gultekin+2009 log(m BH / M )=(8.13 ± 0.05) + (5.13 ± 0.34) log( /200 km s 1 ) 0 =0.32 ± 0.05 dex Graham+2010
M BH vs Luminosity in the NIR Marconi & Hunt 2003 Marconi & Hunt 2003 M BH -L K,bul (rms 0.3 in log M BH ) M BH - σ (rms 0.25 in log M BH ) Investigate the M BH -L bul relation in the near-ir and consider only secure BH masses and galaxy structural parameters. MBH-L relation is not worse than MBH-σ relation! A. Marconi Fisica delle Galassie (2012/2013) 8
MBH-L The M BH bulge relations we fit are in the following form: log M /M = α + β (x x 0 ), (2) tained at shorter wavelengths. Finally in Section 3.4 possible M BH correlation with σ and R e separately MH03, Hopkins et al. (2007) and Graham (2008a) Countless papers in literature, considered two of the most recent ones! Sani, AM+2010 [all] Gultekin+2009 [E,S0] L V log(m BH / M )=(8.95 ± Pseudo-bulges 0.11) are+ open red (1.11 squares. ± 0.18) log 10 11 L,V 0 =0.38 ± 0.09 dex Gultekin+2009 L 3.6 µm log(m BH / M )=(8.19 ± 0.06) + (0.93 ± 0.10) log 10 11 L,3.6 µm 0 =0.38 ± 0.05 dex Sani, AM+2010 Figure 2. Scaling relations. The M BH as a function of 3.6 µm luminosity(inequation3).thelinearregressionsareshownasdot da green and red continuous lines, respectively, for the BCES, FITEXY and LINMIX_ERR methods, and are obtained from classical bulges C 2011 The Authors, MNRA Monthly Notices of the Royal Astronomical Soc
MBH-Mbul Marconi & Hunt 2003 Häring & Rix 2004 Tight correlation M BH vs virial bulge mass ( R e σ e2 ) with intrinsic dispersion σ0~0.25. Linear slope (0.96+/-0.07), average ratio M BH /M bul 0.002. Häring & Rix 2004 find σ0 ~ 0.3 in log M BH with M bul from dynamical models.
MBH-Mbul Sani, a) AM+2010 [all] Countless papers in literature, considered the most recent one! Mvir from virial theorem M vir =5 R e 2 G Similar dispersion as other relations. This is really a relation of MBH with a combination of bulge parameters. Does Mvir really represents bulge mass? Yes, within 0.1 dex ( Lecture 3) log(m BH / M )=(8.20 ± 0.06) + (0.79 ± 0.09) log 0 =0.37 ± 0.05 dex Mvir 10 11 M
Are these relations independent? Assume the basic correlation is M BH ~M bulge Combine with galaxy scaling relations: M BH ~L bulge 1.1 consistent with M BH ~M bulge if (M/L) bulge ~L bulge 0.1 (consistent with fundamental plane) Faber-Jackson L~σ 4 implies M BH ~(σ 4 ) 1.1 ~ σ 4.4 All M BH -galaxy correlations can be explained as the result of a fundamental relation (e.g. M BH ~M bulge ) combined with galaxy scaling relations. Big Black Holes are in big galaxies! This argument is too simple, does not take into account intrinsic scatters but indicate that one must take into account the intrinsic relations among the various parameters (eg. Fundamental Plane of elliptical galaxies). A. Marconi Fisica delle Galassie (2012/2013) 12
Observational biases Recall the RBH=Δθ for BH detection, then maximum distance at which a BH can be detected is 2 1 MBH? D = 22 Mpc 10 8 M 200 km/s 0.1 00 Δθ=0.1 (HST) NO detection areas on MBH-σ diagram for given Δθ, D: D = 250 Mpc Direct MBH measures are limited to the local universe (D~250 Mpc) D = 25 Mpc D = 2.5 Mpc There are definitely no BHs above the correlation (big BHs in small galaxies) The area below the correlation is biased and cannot be explored (small BHs in big galaxies?)
Problems and open issues Problems and open issues (beyond those on MBH): 64 galaxies with MBH (Graham+2010) difficult to assess the reliability and accuracy of all points; few points at low/high mass ends #9 10 6 < MBH < 10 7 M Graham+2010 #7 10 9 < MBH < 5 10 9 M Small BHs mostly E/S0, few spirals in big bulges here! #48 E+S0 #16 Spirals is there really a BH fundamental plane? do all galaxies follow the same correlation? are there small BHs in massive galaxies (e.g. MBH-galaxy relations an upper envelope)?
What is the physical origin? How does the BH know about its host galaxy and galaxy about its BH? Radius of BH sphere of gravitational influence: R BH = GM BH 2? Observed correlation: Spheroid virial mass: M BH ' 10 3 M sph M sph ' 5 R BH 5 10 3 R sph R BH = GM BH ' 5 10 3 R 2 sph BH 1.3 10 V sph BH ' 1.3 10 7 V sph 2?RR sph The volume under the BH influence is only ~10-7 of the total volume. No gravitational exchange of information! G
BH-galaxy coevolution If BH grown by accretion, the energy released during growth is The gravitational binding energy of the virialized spheroid is L = "Ṁaccc 2 Ṁ BH = =(1 ")Ṁacc c E grow = " 1 " M BHc 2 2 E grav ' M sph? E grow ' " E grav 1 " MBH M sph? c 2 2? = 250 200 km s 1 Energy released by accreting BH (i.e. AGN) can affect galaxy structure and can unbind, eg, gas in the galaxy. AGN feedback can let the galaxy know about the BH! By regulating the feeding to the BH the galaxy can let the BH know about it!
A simple model for AGN feedback Assume AGN emit (close) to the Eddington ratio and that there is a radiation driven outflow from the AGN: can explain MBH-σ The wind creates a bubble which expands and sweeps the gas in the ISM of the host galaxy. At the interface between outflow and swept material there is a shock propagating outward. The shocked material either cools: the wind transfer to the gas only its momentum (ram pressure) and thermal pressure is negligible momentum driven outflow does not cool: the wind transfer its energy to the swept up gas (thermal pressure is larger than ram pressure) energy driven outflow ISM gas outer shock driven into ISM gas AGN wind strongly shocked ISM gas swept up ISM gas (mildly shocked) A. Marconi Fisica delle Galassie (2012/2013) 17
A simple model for AGN feedback Assume galaxy is described by a singular isothermal sphere with maximum radius R. Its temperature is parameterized with velocity dispersion σ, therefore (recall Lecture 2): (r) = 2 2 Gr 2 M(r) = 2r 2 (r) = G GM(R) r r apple R = 2 2 R r v esc (R) = p 2 (R) =2 r R also the gas mass is a fraction fgas of galaxy mass M gas (r) =f gas M(r) A. Marconi Fisica delle Galassie (2012/2013) 18
AGN feedback: momentum driven For L/LEDD~1 wind is optically tick (Thomson scattering) to AGN photons, all photon momentum is transmitted to wind; Compton cooling (Compton scattering of AGN photons) is effective up to galactic scales; Momentum driven case; the momentum of swept ISM gas is equal to the total momentum of the AGN photons. M g v g = L Edd c t M g v g = L Edd c M g =4 r 2 g (r)v g =4 r 2 2 f gas 2 G r 2 v g L Edd = 4 Gm pcm BH T v 2 g = 2 G2 M BH m p T f gas 2 = v 2 esc =4 2 M BH = 2f gas T 4 G 2 m p outflow velocity equal (or larger) than escape velocity at R otherwise swept material recollapses in galaxy
AGN feedback: energy driven In case cooling time is much larger than expansion time scale or if gas does not cool effectively (L/LEDD >>1), energy injected by AGN is conserved Energy driven case: the energy of swept ISM gas must be equal to the total energy of the radiation 1 2 M gv 2 g = L Edd t 1 2 M g v 2 g = L Edd M g =4 r 2 g (r)v g =4 r 2 2 f gas 2 G r 2 v g v 3 g = 4 G2 m p cm BH f gas T 2 = v 3 esc =8 3 M BH = 2f gas T G 2 m p c 5 outflow velocity equal (or larger) than escape velocity at R otherwise swept material recollapses in galaxy M BH = M BH (momentum) c
The need for AGN feedback (eg King 2010) Assume AGN emit (close) to the Eddington ratio and that there is a radiation driven outflow from the AGN: can explain MBH-σ Two relevant cases for ṁ 1 momentum driven outflow which sweeps ISM in a shell. This shell recollapses unless MBH has reached critical value ṁ 1 M BH = 2f g T m p G 2 M BH = 2f g T m p G 2 c ṁ = Ṁ/ṀEdd 4 =4.6 10 8 M ~OK 5 =3.0 10 5 M 200 km energy driven outflow which sweeps ISM gas in a shell; imposing expansion work equal to E injection rate (Silk & Rees 1998) too small! Slope and normalization different in the two cases 200 km No free parameters, the energy driven case does not seem to appear in nature (bubble blown in energy driven case should break up for Rayleigh-Taylor instability due to large density contrast in shock) 4 5 f g =0.1 f g =0.1
The need for AGN feedback AGN feedback (i.e. BH growth) can affect galaxy growth and explain MBHgalaxy relation Lectures on galaxy formation But AGN feedback is also needed to explain observed galaxy properties (e.g. apparent anti-hierarchical behaviour of galaxy evolution, red colors of ellipticals, steepness of optical luminosity function). AGN phases are fundamental in the evolution of galaxies. No AGN feedback! Croton +06 A. Marconi Fisica delle Galassie (2012/2013) 22