Recent Developments

Ho (2008, ARA&A): Nuclear Activity in Nearby Galaxies

Kormendy & Ho (2013, ARA&A): Coevolution of Supermassive Black Holes and Galaxies

Wednesday, February 26, 14

Wednesday, February 26, 14

NGC 4889: M

•

^{= 2 x 1010 M⊙} (McConnell et al. 2011)

Kuo et al. (2011)

7 New

Megamasers!

Wednesday, February 26, 14

Kuo et al. (2011)

7 New

Megamasers!

b lac k ho le

galaxy bulge

velocity dispersion mass

Kormendy & Ho (2013, ARA&A)

Wednesday, February 26, 14

M • ^{– "}

^Relation

Wednesday, February 26, 14

54

If we use individual errors in M_K,bulge (± 0.2) and log ^e and add individual errors in log M_• to the intrinsic scatter in quadrature and iterate the intrinsic scatter until the reduced ² = 1, then

log

✓ M_• 10⁹ M

◆

= (0.253±0.052) (0.484±0.036)(M^K,bulge+24.21); intrinsic scatter = 0.31; (4)

log

✓ M_• 10⁹ M

◆

= (0.501 ±0.049)+(4.414±0.295) log

✓

200 km s ¹

◆

; intrinsic scatter = 0.28. (5) The di↵erence between the two sets of fits is small. Taking account also of fits that use di↵erent combinations of points, we conclude that the intrinsic log M_• scatter in M_•–M_K,bulge is 0.31±0.02, almost the same as the intrinsic scatter 0.29±0.03 in M•– _e. This conclusion has also been reached by other authors who use infrared luminosities (e. g., Marconi & Hunt 2003; Sani et al. 2011).

Rewriting Equations 2 and 3 in physically more transparent forms, M_•

10⁹ M =

✓

0.542^+0.069_0.061

◆ ✓ L_K,bulge 10¹¹ L_K

◆1.21±0.09

(6) M_•

10⁹ M =

✓

0.309^+0.037_0.033

◆ ✓

200 km s ¹

◆4.38±0.29

(7) 6.6.1. The M_• – M_bulge correlation and the ratio of BH mass to bulge mass

Galaxy formation work requires the mass equivalent of Equation 6, the M_• – M_bulge correlation.

This is tricker to derive than it sounds. It is not just a matter of multiplying the bulge luminosity by a mass-to-light ratio that is provided automatically by the stellar dynamical models that give us M_•. Bulge mass is inherently less well defined than bulge luminosity. Mass-to-light ratios of old stellar populations are uncertain; (1) the initial mass function (IMF) of star formation is poorly known; it may vary with radius in an individual galaxy or from galaxy to galaxy; (2) stellar population age and metallicity distributions a↵ect M/L and are famously difficult to disentangle; one consequence is that late stages of stellar evolution – especially asymptotic giant branch stars – a↵ect M/L but but are poorly constrained observationally (e. g., Portinari & Into 2011). Most important of all, (4) dark matter contributes di↵erently at di↵erent radii and probably di↵erently in di↵erent galaxies.

Graves & Faber (2010) provide an up-to-date discussion of these problems. They conclude that all of the above are important, with stellar population e↵ects (age and metallicity) accounting for

⇠ 1/4 of the variations in optical mass-to-light ratios and some combination of IMF and dark matter variations accounting for the rest. However, this field is unsettled; extreme points of view are that even K-band mass-to-light ratios vary by factors of ⇠ 4 from galaxy to galaxy and that all of this range is due to variations in IMF (Conroy & van Dokkum 2012) or contrariwise that IMFs vary little from one place to another (Bastian, Covey, & Meyer 2010).

These problems are background worries that may yet hold unpleasant surprises, but mostly, they are beyond the scope of this paper. The extensive work of the SAURON and ATLAS3D teams (Cappellari et al. 2006, 2013) shows that dynamically determined I- and r-band mass-to-light ratios are very well behaved. For 260 ATLAS3D galaxies, M/L_r / e^0.69±0.04 with an intrinsic scatter of only 22 %. Since M/L_K almost inevitably varies less from galaxy to galaxy than M/L_r, this suggests that we proceed by finding a way to estimate M/L_K. In particular, we want an algorithm that does not involve the use of uncertain e↵ective radii r_e. Here’s why:

Published studies often derive M_bulge dynamically from r_e, _e, and a virial-theorem-like relation M_bulge = k _e²r_e/G, where k is, e. g., 3 (Marconi & Hunt 2003) or 5 (Cappellari et al. 2006, 2010) or 8 (Wolf et al. 2010). This situation is unsatisfactory; di↵erent assumptions about the density profile are one reason why k is uncertain. Also, r_e values are less well measured than we think.

54

If we use individual errors in M_K,bulge (± 0.2) and log ^e and add individual errors in log M_• to the intrinsic scatter in quadrature and iterate the intrinsic scatter until the reduced ² = 1, then

log

✓ M_• 10⁹ M

◆

= (0.253±0.052) (0.484±0.036)(M^K,bulge+24.21); intrinsic scatter = 0.31; (4)

log

✓ M_• 10⁹ M

◆

= (0.501 ±0.049)+(4.414±0.295) log

✓

200 km s ¹

◆

; intrinsic scatter = 0.28. (5) The di↵erence between the two sets of fits is small. Taking account also of fits that use di↵erent combinations of points, we conclude that the intrinsic log M_• scatter in M_•–M_K,bulge is 0.31±0.02, almost the same as the intrinsic scatter 0.29±0.03 in M•– _e. This conclusion has also been reached by other authors who use infrared luminosities (e. g., Marconi & Hunt 2003; Sani et al. 2011).

Rewriting Equations 2 and 3 in physically more transparent forms, M_•

10⁹ M =

✓

0.542^+0.069_0.061

◆ ✓ L_K,bulge 10¹¹ L_K

◆1.21±0.09

(6) M_•

10⁹ M =

✓

0.309^+0.037_0.033

◆ ✓

200 km s ¹

◆4.38±0.29

(7) 6.6.1. The M_• – M_bulge correlation and the ratio of BH mass to bulge mass

Galaxy formation work requires the mass equivalent of Equation 6, the M_• – M_bulge correlation.

This is tricker to derive than it sounds. It is not just a matter of multiplying the bulge luminosity by a mass-to-light ratio that is provided automatically by the stellar dynamical models that give us M_•. Bulge mass is inherently less well defined than bulge luminosity. Mass-to-light ratios of old stellar populations are uncertain; (1) the initial mass function (IMF) of star formation is poorly known; it may vary with radius in an individual galaxy or from galaxy to galaxy; (2) stellar population age and metallicity distributions a↵ect M/L and are famously difficult to disentangle; one consequence is that late stages of stellar evolution – especially asymptotic giant branch stars – a↵ect M/L but but are poorly constrained observationally (e. g., Portinari & Into 2011). Most important of all, (4) dark matter contributes di↵erently at di↵erent radii and probably di↵erently in di↵erent galaxies.

Graves & Faber (2010) provide an up-to-date discussion of these problems. They conclude that all of the above are important, with stellar population e↵ects (age and metallicity) accounting for

⇠ 1/4 of the variations in optical mass-to-light ratios and some combination of IMF and dark matter variations accounting for the rest. However, this field is unsettled; extreme points of view are that even K-band mass-to-light ratios vary by factors of ⇠ 4 from galaxy to galaxy and that all of this range is due to variations in IMF (Conroy & van Dokkum 2012) or contrariwise that IMFs vary little from one place to another (Bastian, Covey, & Meyer 2010).

These problems are background worries that may yet hold unpleasant surprises, but mostly, they are beyond the scope of this paper. The extensive work of the SAURON and ATLAS3D teams (Cappellari et al. 2006, 2013) shows that dynamically determined I- and r-band mass-to-light ratios are very well behaved. For 260 ATLAS3D galaxies, M/L_r / e^0.69±0.04 with an intrinsic scatter of only 22 %. Since M/L_K almost inevitably varies less from galaxy to galaxy than M/L_r, this suggests that we proceed by finding a way to estimate M/L_K. In particular, we want an algorithm that does not involve the use of uncertain e↵ective radii r_e. Here’s why:

Published studies often derive M_bulge dynamically from r_e, _e, and a virial-theorem-like relation M_bulge = k _e²r_e/G, where k is, e. g., 3 (Marconi & Hunt 2003) or 5 (Cappellari et al. 2006, 2010)

M • ^{– "}

^Relation

Wednesday, February 26, 14

M • ^{– M bulge Relation}

Wednesday, February 26, 14

M • ^{– M bulge Relation}

57

Presumably these galaxies contain larger contributions of dark matter that we choose not to include.

The remaining 22 galaxies satisfy log (M/L_K) = 0.287 log σ_e − 0.637 with an RMS scatter of 0.088.

As expected, the relation is shallower than the one in r band (above). It has essentially the same scatter of ∼ 23 %. Dynamically, M/L^K = 1 at σ_e = 166 km s⁻¹, where the Into & Portinari (2013) calibration gives M/L_K # 0.76. Cappellari et al. (2006) argue that the difference may be due to the inclusion of some dark matter in the dynamical models. We use the dynamical zeropoint.

To shift the Into & Portinari log M/L_K values to the above, dynamical zeropoint, we first use their Table 3 relation log M/L_K = 1.055(B − V )⁰ − 1.066 to predict an initial, uncorrected M/L^K. This correlates tightly with σ_e: log M/L_K = 0.239 log σ_e−0.649 with an RMS scatter of only 0.030.

We then apply the shift ∆ log M/L_K = 0.1258 or a factor of 1.34 that makes the corrected Into &

Portinari mass-to-light ratio agree with the dynamic one, M/L_K = 1.124, at σ_e = 250 km s⁻¹. We then have two ways to predict M/L_K that are independent except for the above shift,

log M/L_K = 0.2871 log σ_e − 0.6375; RMS = 0.088; (8) log M/L_K = 1.055(B − V )⁰ − 0.9402; RMS = 0.030, (9) where we use the RMS scatter of the correlation with σ_e to estimate errors for the latter equation.

We adopt the mean of the mass-to-light ratios given by Equations 8 and 9. For the error estimate, we use 0.5!0.088² + 0.030² + (half of the difference between the two log M/L_K values)². We use the resulting M/LK together with MK,bulge to determine bulge masses. For the log Mbulge error estimate, we add the above in quadrature to (0.2/2.5)². The results are listed in Tables 2 and 3.

Figure 18 shows the correlation of M_• with bulge mass M_bulge. A symmetric, least-squares fit to the classical bulges and ellipticals omitting the monsters and (for consistency with M_• – σ_e), the emission-lime M_• values for NGC 4459 and NGC 4596 plus NGC 3842 and NGC 4889 gives the mass equivalent of Equation 6,

M_•

10⁹ M_" =

"

0.49^+0.06_−0.05

# "

M_bulge 10¹¹ M_"

#1.16±0.08

; intrinsic scatter = 0.29 dex. (10) Thus the canonical BH-to-bulge mass ratio is M_•/M_bulge = 0.49^+0.06_−0.05 % at M_bulge = 10¹¹ M_".

This BH mass ratio at M_bulge = 10¹¹ M_" is 2–4 times larger than previous values, which range from ∼ 0.1 % (Sani et al. 2011), 0.12 % (McLure & Dunlop 2002), and 0.13^+0.23−0.08 % (Merritt &

Ferrarese 2001; Kormendy & Gebhardt 2001) to 0.23^+0.20_−0.11 % (Marconi & Hunt 2003). The reasons are clear: (1) we omit pseudobulges; these do not satisfy the tight correlations in Equations 2 – 7;

(2) we omit galaxies with M_• measurements based on ionized gas dynamics that do not take broad emission-line widths into account; (3) we omit mergers in progress. All three of these tend to have smaller BH masses than the objects that define the above correlations. Also, the highest BH masses occur in core ellipticals (more on these below), and these have been revised upward, sometimes by factors of ∼ 2, by the addition of dark matter to dynamical models. Moreover, thanks to papers like Schulze & Gebhardt (2011) and Rusli et al. (2013), we have many such objects.

The exponent in Equation 10 is slightly larger than 1, in reasonable agreement with H¨aring &

Rix (2004), who got M_• ∝ M_bulge^1.12±0.06 and again a lower normalization, BH mass fraction # 15 %

M • ^{– M bulge Relation}

old value

57

Presumably these galaxies contain larger contributions of dark matter that we choose not to include.

The remaining 22 galaxies satisfy log (M/L_K) = 0.287 log σ_e − 0.637 with an RMS scatter of 0.088.

As expected, the relation is shallower than the one in r band (above). It has essentially the same scatter of ∼ 23 %. Dynamically, M/L^K = 1 at σ_e = 166 km s⁻¹, where the Into & Portinari (2013) calibration gives M/L_K # 0.76. Cappellari et al. (2006) argue that the difference may be due to the inclusion of some dark matter in the dynamical models. We use the dynamical zeropoint.

To shift the Into & Portinari log M/L_K values to the above, dynamical zeropoint, we first use their Table 3 relation log M/L_K = 1.055(B − V )⁰ − 1.066 to predict an initial, uncorrected M/L^K. This correlates tightly with σ_e: log M/L_K = 0.239 log σ_e−0.649 with an RMS scatter of only 0.030.

We then apply the shift ∆ log M/L_K = 0.1258 or a factor of 1.34 that makes the corrected Into &

Portinari mass-to-light ratio agree with the dynamic one, M/L_K = 1.124, at σ_e = 250 km s⁻¹. We then have two ways to predict M/L_K that are independent except for the above shift,

log M/L_K = 0.2871 log σ_e − 0.6375; RMS = 0.088; (8) log M/L_K = 1.055(B − V )⁰ − 0.9402; RMS = 0.030, (9) where we use the RMS scatter of the correlation with σ_e to estimate errors for the latter equation.

We adopt the mean of the mass-to-light ratios given by Equations 8 and 9. For the error estimate, we use 0.5!0.088² + 0.030² + (half of the difference between the two log M/L_K values)². We use the resulting M/LK together with MK,bulge to determine bulge masses. For the log Mbulge error estimate, we add the above in quadrature to (0.2/2.5)². The results are listed in Tables 2 and 3.

Figure 18 shows the correlation of M_• with bulge mass M_bulge. A symmetric, least-squares fit to the classical bulges and ellipticals omitting the monsters and (for consistency with M_• – σ_e), the emission-lime M_• values for NGC 4459 and NGC 4596 plus NGC 3842 and NGC 4889 gives the mass equivalent of Equation 6,

M_•

10⁹ M_" =

"

0.49^+0.06_−0.05

# "

M_bulge 10¹¹ M_"

#1.16±0.08

; intrinsic scatter = 0.29 dex. (10) Thus the canonical BH-to-bulge mass ratio is M_•/M_bulge = 0.49^+0.06_−0.05 % at M_bulge = 10¹¹ M_".

This BH mass ratio at M_bulge = 10¹¹ M_" is 2–4 times larger than previous values, which range from ∼ 0.1 % (Sani et al. 2011), 0.12 % (McLure & Dunlop 2002), and 0.13^+0.23−0.08 % (Merritt &

Ferrarese 2001; Kormendy & Gebhardt 2001) to 0.23^+0.20_−0.11 % (Marconi & Hunt 2003). The reasons are clear: (1) we omit pseudobulges; these do not satisfy the tight correlations in Equations 2 – 7;

(2) we omit galaxies with M_• measurements based on ionized gas dynamics that do not take broad emission-line widths into account; (3) we omit mergers in progress. All three of these tend to have smaller BH masses than the objects that define the above correlations. Also, the highest BH masses occur in core ellipticals (more on these below), and these have been revised upward, sometimes by factors of ∼ 2, by the addition of dark matter to dynamical models. Moreover, thanks to papers like Schulze & Gebhardt (2011) and Rusli et al. (2013), we have many such objects.

The exponent in Equation 10 is slightly larger than 1, in reasonable agreement with H¨aring &

Rix (2004), who got M_• ∝ M_bulge^1.12±0.06 and again a lower normalization, BH mass fraction # 15 % at M_bulge = 10¹¹ M_". McConnell & Ma (2013) get a similar range of exponents from 1.05 ± 0.11 to 1.23 ± 0.16 depending on how the bulge mass is calculated (dynamics versus stellar populations).

Wednesday, February 26, 14

? ? ^?

Wednesday, February 26, 14

Wednesday, February 26, 14

M33: M • < 1500 M

^⊙

Wednesday, February 26, 14

M33: M • < 1500 M

^⊙

Wednesday, February 26, 14

Wednesday, February 26, 14

G1: M • ^{= 2 × 10}

⁴

^M

^⊙

Gebhardt, Ho & Rich (2005)

Wednesday, February 26, 14

Fan et al.

J. Wise & T. Abel

Wednesday, February 26, 14

Wednesday, February 26, 14

Wednesday, February 26, 14

Are there mini-quasars in

these ‟simpler” galaxies?

Filippenko & Ho (2003); Barth, Ho et al. (2004)

Wednesday, February 26, 14

Fast-moving gas

Filippenko & Ho (2003); Barth, Ho et al. (2004)

在文檔中 Luis C. Ho (何子山) (頁 42-77)