The Black Hole Mass Galaxy Bulge Relationship

1
The Black Hole Mass - Galaxy Bulge Relationship
for QSOs in the SDSS DR3
Sarah Salviander1, Greg Shields1, Karl Gebhardt1,
and Erin Bonning2 1. Department of Astronomy,
University of Texas, Austin, Texas, USA 2.
Laboratoire de lUnivers et de ses Théories,
Observatoire de Paris, F-92195 Meudon Cedex,
France
Abstract We investigate the relationship between
black hole mass, MBH, and host galaxy velocity
dispersion, s, for QSOs in Data Release 3 of the
Sloan Digital Sky Survey (www.sdss.org). We
derive MBH from the broad Hb line width and
continuum luminosity, and the bulge stellar
velocity dispersion from the O III narrow line
width (sNL). For higher redshifts, we use Mg II
and O II in place of Hb and O III. For
redshifts z with the MBHs relationship for nearby galaxies.
For 0.5 from the MBHs relationship with redshift such
that bulges are too small for their black holes.
However, some of this apparent trend can be
attributed to observational biases. Accounting
for these biases, we find approximately 0.3 dex
evolution in the MBHs relationship between now
and redshift z 1.
Motivation Method In the nucleus of every
galactic bulge lies a supermassive black hole.
The mass of the black hole, MBH, correlates with
properties of the bulge, especially the stellar
velocity dispersion, s. This relationship has
been established for nearby galaxies with 105-109
M? black holes in the nuclei (Gebhardt et al.
2000a Ferrarese Merritt 2000). Tremaine et al.
(2000) give this relationship as MBH (108.13
M?)(s/200 km s-1)4.02. The cause of this tight
relationship is not well understood, but studying
the comparative evolution of the galactic bulge
and the central black hole may yield clues.
Shields et al. (2003) (S03) use QSO emission
lines to study the MBH - s relationship for
large lookback times. The black hole
photoionization mass is derived from Fig. 6 of
Kaspi et al. (2000) MBH (107.69 M?)v23000
L0.544, where v23000 ? FWHM(Hb)/3000 km s-1 and
L44 ? nLn /1044 erg s-1 , the BLR continuum
luminosity at 5100 Å. Following Nelson (2000)
the stellar velocity dispersion is derived from
the width of O III such that sNL FWHM(O
III)/2.35. We use the Sloan Digital Sky Survey
Data Release 3 (SDSS DR3) (Abazajian et al. 2005)
to extend the MBH - s relationship to redshift z
1 using the UV emission lines Mg II and O II
in place of Hb and O III, respectively. This
material will be presented in more detail in
Salviander et al. (2006).

• Sample Selection and Data Processing
• The QSOs in this study were selected from the
  SDSS DR3, and were chosen on the basis of
  redshift alone in order to include the widest
  possible range of luminosities.
• A lower-redshift sample was created for study of
  the MBH - s relationship using Hb and O III
  only (the HO3 sample). The redshift range is
  0.10 selection for data quality.
• A second data sample was created to study the MBH
  - s relationship in the widest possible range of
  wavelengths using Mg II and O II alone (the
  MO2 sample). The redshift range is 0.44 1.19 with 159 objects in the sample.
• An algorithm originally developed to measure
  stellar absorption features was modified and used
  to process the SDSS emission spectra using
  Gauss-Hermite profiles to model the emission
  lines.
• The O II doublet was modeled as a single line,
  and the intrinsic line width was determined from
  a calibration curve based on modeling the doublet
  using two Gaussians over a wide range of widths,
  using a one-to-one intensity ratio. Modeling of
  O II was tested with simulated spectra.
• Optical Fe II emission was subtracted from ll4300
  - 5700 using a template from Marziani et al.
  (2003) UV Fe II emission was subtracted from
  ll2180 - 3060 using a template based on
  Vestergaard Wilkes (2001) and Sigut Pradhan
  (2003).

A measure of the evolution of the MBH - s
relationship with lookback time is shown in Fig.
4. We compare MBH calculated with eqn. 2 to the
O III mass of S03that is, MBH calculated
with eqn. 1 using sNL in place of s. Fig. 4
shows the results for D log MBH as a function of
redshift for the HO3 and MO2 samples. The mean D
log MBH is 0.14 for the HO3 sample, with a
dispersion of 0.62 dex (1 s), comparable to the
findings of S03. The positive mean indicates that
our O III masses slightly under-predict MBH
compared to the photoionization masses. The MO2
sample shows a dispersion of 0.65 dex and a mean
D log MBH of 0.65 dex, a significantly higher
offset than for the HO3 sample. Fig. 4 shows an
upward trend in D log MBH, with an increase of
0.5 dex from low redshift to z 1. Fig. 3 shows
that this rise is due to an increase in MBH that
is not accompanied by a commensurate increase in
sNL. It is possible that this trend is influenced
by observational biases and selection effects. In
fact, we find two significant sources of bias.
(1) Due to increasingly noisy spectra with
redshift our sample favors narrower sNL for a
given MBH. Modeling of this effect indicates that
this bias can account for 0.1 dex of the trend
in Fig. 4. (2) The limiting magnitude of the
sample survey introduces a Malmquist-like bias in
which the brightest QSOs are overrepresented in
our sample. Tremaine et al. (2002) find an r.m.s.
dispersion of 0.3 dex in the local MBH - s
relationshipif, for a given galaxy mass, the
biggest black holes tend to have the highest
luminosities, this will lead to an effect in
which, increasingly with redshift, our sample
favors galaxies with higher MBH for a given s.
Monte Carlo trials show that such a bias can
account for 0.1 dex of the trend in Fig. 4.
Adding the two biases linearly, we estimate a
cumulative effect of 0.2 dex on D log MBH,
leaving a residual 0.3 dex of trend in D log MBH
that possibly represents real evolution in the
MBH - s relationship.

• Conclusions
• The widths of O III and deblended O II show
  overall agreement, with a mean log sOIII - log
  sOII of 0.00 dex there is good agreement
  between the widths of Hb and Mg II, with a mean
  difference in width of log FWHM(Hb) - log FWHM
  (Mg II) 0.05 dex
• For z with the MBH - s relationship for nearby
  galaxies, with a dispersion of 0.62 dex for the
  HO3 sample and 0.65 dex for the MO2 sample. Mg II
  and O II can be used to extend the
  relationship to redshifts up to z ? 1.
• For z 0.5 there is apparent evolution in D log
  MBH in the sense that bulges are too small for
  their black holes. The overall trend is 0.5 dex
  from low redshift to z 1, corresponding to when
  the universe was approximately six billion years
  old. We find that approximately half of this
  trend can be attributed to observational biases,
  with the remaining 0.3 dex in D log MBH possibly
  representing real evolution in the MBH - s
  relationship. This is also consistent, within a
  factor of two in MBH, with contemporaneous growth
  of black holes and bulges or with black holes and
  bulges completing their growth by z 1.

Results and Discussion
Acknowledgements We thank Todd Boroson, Sandy
Faber, Gary Hill, Eliot Quataert, and Bev Wills
for helpful discussions, and Ashley Davis, Pamela
Jean, and Michael Shields for assistance. Funding
for the creation and distribution of the SDSS
Archive has been provided by the Alfred P. Sloan
Foundation, the Participating Institutions, the
National Aeronautics and Space Administration,
the National Science Foundation, the U.S.
Department of Energy, the Japanese
Monbukagakusho, and the Max Planck Society. The
SDSS Web site is http//www.sdss.org/. This
work is supported by the Texas Advanced Research
Program under grant 003658-0177-2001 and by NSF
grant AST-0098594.
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A strong correlation is evident in Fig. 1 and is
generally consistent with the findings of McLure
Jarvis (2002). Hb tends to be wider than Mg II
for FWHM 4000 Å, but this could be due to the
tendency of the broad base of Mg II to blend with
Fe II emission and the continuum for larger Mg
II widths, this broad base can be especially
affected by Fe II removal. Fig. 2 shows the
correlation between the widths of O III and O
II. In the mean there is good agreement between
the widths of O II and O III, with a
dispersion in the relationship of 0.13 dex. The
MBH - s relationship for both the HO3 and MO2
samples is shown in Fig. 3. Results for z are consistent with the findings of S03, with the
data points tending to scatter evenly about the
MBHs correlation. For z 0.5, there is a mean
departure from this correlation in the sense that
MBH is larger than predicted for a given s.