Mon. Not. R. Astron. Soc. 000, 000–000 (0000)

Printed 20 March 2011

(MN LATEX style file v2.2)

Effects of Biases in Virial Mass Estimation on Cosmic
Synchronization of Quasar Accretion
Charles L. Steinhardt
IPMU, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba-ken, Japan 277-8583

20 March 2011

ABSTRACT

Recent work using virial mass estimates and the quasar mass-luminosity plane has
yielded several new puzzles regarding quasar accretion, including a sub-Eddington
boundary on most quasar accretion, near-independence of the accretion rate fromproperties of the host galaxy, and a cosmic synchronization of accretion among black
holes of a common mass. We consider how these puzzles might change if virial massestimation turns out to have a systematic bias. As examples, we consider two recent
claims of mass-dependent biases in MgII masses. Under any such correction, the surprising cosmic synchronization of quasar accretion rates and independence from thehost galaxy remain. The slope and location of the sub-Eddington boundary are very
sensitive to biases in virial mass estimation, and various mass calibrations appear tofavor different possible physical explanations for feedback between the central blackhole and its environment. The alternative mass estimators considered do not simply
remove puzzling quasar behavior, but rather replace it with new puzzles that may be
more difficult to solve than those using current virial mass estimators and the Shenet al. (2008) catalogs.
Key words: black hole physics — galaxies: evolution — galaxies: nuclei — quasars:
general — accretion, accretion discs

1

INTRODUCTION

Recent work developing the quasar mass-luminosity planefrom a combination of large quasar catalogs (Schneider et al.
2010) and virial mass estimators (Vestergaard & Peterson
2006; McLure & Dunlop 2004) has provided a new picture ofquasar accretion seemingly inconsistent with existing models(Steinhardt & Elvis 2010b, 2011), including:
1. Characteristic Accretion Rate at Fixed M and z:
At any fixed combination of mass and redshift, quasar accretion is apparently only possible within a narrow (< 1dex) luminosity range around a central, characteristic, subEddington accretion rate. Therefore, ephemeral propertiesof host galaxies such as star formation rate and recent
merger activity appear to have a minimal effect upon theaccretion rate of the central supermassive black hole.
2. Accretion is Time-Dependent: The characteristic accretion rate is time-dependent at fixed mass, decreasing towards lower redshift. Even though galaxies of the same stellar mass may virialize at different times and have different
morphologies at the same redshift, the accretion rates of
their central supermassive black holes are well synchronized.
3. Sub-Eddington Accretion: The characteristic accretion rate is near the Eddington luminosity for the lowestc 0000 RAS

mass quasars at every redshift, but at higher masses falls
increasingly short of Eddington. Quasars at most combinations of mass and redshift are constrained to lie below
Eddington, with the highest mass quasars (and most of themass growth) taking place closer to L/LEdd ∼ 0.1.
There appears to be a universality to quasar accretion
implying that only a few, simple physical processes may play
important roles. If correct, these results may be incompatible with our current understanding of not just quasar accretion and turnoff but perhaps also structure formation.
These analyses were performed using virial masses provided by Shen et al. (2008) in an extension to the Sloan
Digital Sky Survey (SDSS) quasar catalog (Schneider 2007).
Since the publication of these masses, there have been several investigations into whether virial masses might systematically mis-measure black hole masses, particularly for
Mgii-based masses. Perhaps the existing virial mass scaling
relationships must be corrected to account for quasar wind,thermal effects, or other non-virial motion in the quasar
broad-line region (BLR) (Onken & Kollmeier 2008; Risaliti
et al. 2009; Marconi et al. 2009). Alternatively, at least thestatistical uncertainty in virial mass estimation appears tobe better than previously believed, and might even be better
than that of more difficult reverberation mapping techniques(Steinhardt & Elvis 2010c). Rafiee & Hall (2010) claim that

2Charles L. Steinhardt

different methods of determining the velocity of gas in thequasar BLR show evidence of a mass-dependent, systematic
error. They also claim that correcting for this error returns
all quasars to lying at their Eddington luminosity.
These reports of possible biases in virial mass estimation must also lead us to re-examine the conclusions drawn
from the quasar mass-luminosity plane. Virial mass estimation is inherently a difficult proposition, and estimators arecalibrated against only 35 low-redshift quasars with reverberation mapping-based mass estimates (Vestergaard & Peterson 2006; Wang et al. 2009; Peterson et al. 2004). It istherefore essential to understand how sensitive each of theconclusions drawn using the Shen et al. (2008) mass catalog
are to biases in virial mass estimation.
In general, potential biases can be divided into four categories:(i) Affine Biases: Biases that affinely translate virial
mass estimate, shifting, stretching, or contracting the distribution in the M − L plane. While this may seem a restrictive definition, because the velocity of broad-line gas is notstrongly correlated with its radius, most currently-proposedcorrections to virial masses are affine.
(ii) Correctable Biases: Biases that do not affect virial
mass estimates uniformly across a large catalog, but for
which each spectrum contains enough information to correct them. For example, a hypothetical bias might only affect quasars with strong HeII lines, but could be correctedby properly subtracting HeII before fitting the Hβ-OIII complex.
(iii) Uncorrectable Biases: Biases that affect different
objects in different ways and cannot be corrected from theindividual spectra, but can be understood well enough to
be modeled in a probabilistic way for large catalogs. For
example, a hypothetical bias might arise from a time delay between variability in the quasar continuum and response of the broad-line region, leading to errors when using
monochromatic continuum luminosity to estimate the BLR
radius in some objects.
(iv) Byzantine Biases: Along the lines of Pease et al.
(1980), biases maliciously chosen as a worst-case scenario;
one might use these to determine what we have learned withabsolute certainty.
In this work, we will consider the effects of affine biases, a category that includes most currently-proposed corrections. Both Risaliti et al. (2009) and Rafiee & Hall (2010)
propose systematic, linear corrections for MgII-based estimators relating the true black hole mass MBH and theShen08 mass MShen as MBH = AMShen + B. A compressive correction with A > 1 will act to narrow the quasar
mass distribution from its appearance in the Shen08 catalog, while an expansive correction with A < 1 will broaden it.
It is instructive to consider the effects of both types of corrections, biasing the Shen08 masses in different directions,on the key puzzles emanating from the M − L plane analysisof the SDSS catalog. In § 2, we consider the proposed correction from Rafiee & Hall (2010), a compressive correction
with A < 1. In § 3, the implications of an expansive correction with A > 1, from Risaliti et al. (2009), are discussed.
Finally, § 4 considers the lessons learned from this analysis.

2

A COMPRESSIVE CORRECTION (RAFIEE& HALL 2010)

Rafiee & Hall (2010) (RH10) consider the possibility thatthe the full-width half-maximum (FWHM) of quasar broad
emission lines might not directly indicate the velocity of gas
in the broad-line region, i.e., that motion in the broad line
region may not be predominantly virial. They instead fit
MBH ∝ FWHM1.27±0.40 using the MLIN-IX ERR fitting
method of Kelly (2007). Although this work may suffer fromseveral flaws discussed elsewhere (Steinhardt & Elvis 2010a),
we use it as an example of a possible mass-dependent biasthat produces a compressive correction, narrowing the mass
distribution at fixed redshift.
Applying the Rafiee & Hall (RH) formula produces approximately log MRH = 0.67 log MShen + 3.0. Although the
RH10 correction itself is only calibrated for MgII, since virial
mass estimators using different broad emission lines are calibrated against each other, we will consider the effects ofthis adjustment at all redshifts, not just 0.4 < z < 2.0 where
MgII is available. A compressive correction such as this does
not remove all of the puzzling behavior in the quasar massluminosity plane, but does recast some puzzles in a different
light.
2.1

Puzzling Behavior

Specifically, this adjustment produces the mass-luminosity
plane shown in Figure 1 in 12 redshift bins ranging from0.2 < z < 4.1. These distributions exhibit the following
substantial puzzles:
1. Characteristic Accretion Rate at Fixed M, z: At
any fixed combination of mass and redshift, the quasar luminosity range spans a range of less than 0.8−1 dex. Because
SDSS views objects across nearly half the sky, these quasars
should lie in host galaxies with very different ephemeral
properties such as star formation rate and recent merger
activity. Thus, these ephemeral properties can only be important at the . 1 dex level to the quasar accretion rate.
This puzzle also appears when using Shen08 masses.
2. Linear Mass Dependence: At fixed redshift, the characteristic accretion rate increases nearly linearly with mass.
In the Shen08 picture, the characteristic accretion rate in0.4−0.7
creased between L ∝ MShen, and thus for log MRH =0.67 log MShen + 3.0, the characteristic accretion rate will
be closer to L ∝ M . This is best demonstrated by the behavior of the sub-Eddington boundary using different massestimation techniques (Fig. 2. The sub-Eddington boundary
should run parallel to the characteristic accretion rate, but
is easier to measure precisely because it is determined using the brightest and best-measured quasar spectra at eachmass and redshift. Because the slope appears to vary with
redshift, the accretion rate cannot be exactly linear in M
(or at any other constant value) at all redshifts under any
time-independent adjustment to the Shen08 masses. Nevertheless, the accretion rate remains nearly linear. Since the
Eddington luminosity is also LEdd ∝ M , this means quasars
at fixed redshift all lie at nearly the same Eddington ratio
L/LEdd .
3. Accretion is Time-Dependent: The characteristic accretion rate at fixed mass, or chararacteristic Eddington rac 0000 RAS, MNRAS 000, 000–000

Effects of Biases in Virial Mass Estimation on Cosmic Synchronization of Quasar Accretion
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Figure 1. A contour plot of the mass-luminosity distribution in 12 different redshift ranges using the Rafiee & Hall (2010) massestimators. Quasars at decreasing redshift lie increasingly below their Eddington luminosity (black, dashed).

tio across all masses in the RH10 picture, increases withincreasing redshift (Fig. 1). Near z ∼ 2, quasars are typically able to reach but not exceed their Eddington luminosity. However, at lower redshift, quasars all miss Eddington by increasingly large margins, and at z > 3.0, CIVbased masses correspond to super-Eddington accretion. Although CIV masses have a substantially higher statisticaluncertainty than MgIV (Steinhardt & Elvis 2010c), sufferfrom quasar wind and radiation pressure-induced broadening (Marconi et al. 2009), and have a large scatter whencompared against MgII masses (Shen et al. 2008), there isno systematic disagreement between MgII and CIV masses in
the Shen08 sample. Therefore, corrections inducing a massdependent shift in Shen08 MgII masses should also apply
to CIV masses, and this super-Eddington accretion is either
evidence against such a mass correction or yet another puzzle.
4. Narrow Active Mass Range: At fixed redshift, theobserved range in quasar luminosities spans ∼ 1 − 1.5 dex,
while Shen08 masses span 2 − 2.5 dex. A correction narrowing the mass range to the point that quasars all lie near ac 0000 RAS, MNRAS 000, 000–000

fixed Eddington ratio must also result in a mass range spanning 1 − 1.5 dex at fixed redshift. There are three major
contributions to the width of this mass distribution:• Mass Growth: From when they first enter the SDSS
catalog, quasars grow in mass via luminous accretion.
Quasars must enter the catalog at least as the lowest-mass
objects at the redshift they are observed, and must ceasethat luminous accretion at a mass no higher than the maximum mass observed at some later redshift. Since the maximum mass is decreasing with redshift, the turnoff mass fora quasar in the SDSS catalog must actually be lower thanthe maximum mass at the redshift it is observed. The Soltan
argument (Soltan 1982; Yu & Tremaine 2002) demonstrates
that most supermassive black hole mass is accreted as aquasar; the mass growth in this phase must be at least ∼ 1dex.
• Different Timing: The evolution of quasar host galaxies of a common halo mass is not well synchronized (cf.
(Springel et al. 2005)), yet they will eventually produce postturnoff supermassive black holes of the same mass (Ferrarese& Merritt 2000; Gebhardt et al. 2000). The lowest-mass

4Charles L. Steinhardt
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Figure 3. The quasar mass-luminosity distribution for all quasars
at 0.4 < z < 2.0, using MgII masses as described by Rafiee & Hall(2010). Quasars at log M/M⊙ < 8.5 lie below Eddington, with theshortfall increasing towards lower mass.
Figure 2. Slope of the sub-Eddington boundary as a function ofmass for masses estimated using four virial mass calibrators: Hβ(green) and Mgsmall II (blue) masses from Shen et al. (2008) arecompared with MgII masses from Rafiee & Hall (2010) (red) and
Risaliti, Young, & Elvis (2009) (magenta). Only the Rafiee & Hall
masses yield L ∝ M (black, dashed) at any redshift, although nomass estimate is consistent with this dependency at z ∼ 1.9.

quasars in the SDSS catalog decrease with decreasing redshift. Thus, if quasars in these host galaxies all turn on at acommon mass but at different times, some must not be thelowest-mass quasars when they enter the SDSS catalog. Differences in the timing of quasar phases will lead to a mass
distribution broader than one due to mass growth alone.
• Mass Errors: Uncertainties in quasar masses will artificially broaden the quasar distribution; the observed mass
distribution is the physical mass distribution convolved withthe mass error function. Statistical errors alone in virial
masses have been estimated at ∼ 0.4 dex (Vestergaard &Peterson 2006).
Since mass growth cannot span . 1 dex according to
the Soltan argument, the timing of quasar phases in different host galaxies of the same halo mass must be very wellsynchronized and mass uncertainty must have substantiallysmaller than an ∼ 0.4 dex scatter in order to produce a mass
distribution spanning 1 − 1.5 dex. Each of these is a puzzle
in its own right.
5. Some Masses Never Reach Eddington: In the
Shen08 catalog, at every redshift there is some mass which
quasars reach but do not exceed their Eddington luminosity,and at every mass there is some redshift at which quasars
lie at Eddington. With this compressive correction, quasars
below z ∼ 1.7 do not reach Eddington. Since only a narrow
mass range is active at each redshift, quasars with lower
masses are never seen at Eddington (Fig. 3). If, as we areassuming in this section, this is not a calibration problem,
then it is a new puzzle requiring a physical explanation.

2.2

Physical Interpretation

Like previous mass estimators, the compressive correction
proposed by Rafiee & Hall (2010) produces a quasar massluminosity plane exhibiting several puzzling behaviors. However, some of these features are unique, particularly thenear-linear dependence of the characteristic accretion rateon black hole mass. It is natural to believe that the characteristic accretion rate is due to feedback between the central
black hole and its environment. A linear dependence of accretion rate on black hole mass is typical of a model in which
gravity is dominant. Further, black hole binaries, anotheraccretion disk system, are capable of radiatively-efficient accretion only in a Eddington ratio range spanning ∼ 1 dex;
accretion is radiatively inefficient both above and below that
range. Using these mass estimators, quasars, too, can only
accrete in an Eddington ratio range spanning ∼ 1 dex, although the Soltan argument precludes radiatively inefficientaccretion at a higher Eddington ratio being common.
If the mass-dependence appears easy to understand,though, the time-dependence is quite difficult. The laws ofgeneral relativity are time-independent, while a black hole
has no memory; just mass, charge, and spin. So, if the accretion rate is set purely by gravity, and feedback from thehost galaxy is not important, novel high-energy astrophysics
or physics will be needed to explain this time-dependence.
Another puzzling feature using Shen08 masses is thesynchronization of quasar accretion in host galaxies of thesame halo mass. A compressive correction appears to require
even stronger, near-perfect synchronization in order to remain consistent with the Soltan argument. This picture requires either very well synchronization of the first epoch ofstar formation in each of these host galaxies or, more likely,
some sort of primordial black hole seeding mechanism.

3

AN EXPANSIVE CORRECTION (RISALITI,YOUNG, & ELVIS 2009)

Risaliti et al. (2009) (RYE09) calibrate MgII-based masses
against Hβ, finding that the MgII masses systematically disc 0000 RAS, MNRAS 000, 000–000

Effects of Biases in Virial Mass Estimation on Cosmic Synchronization of Quasar Accretion
agree with Hβ masses as log MHβ = 1.8 log MM gII − 6.8. As
discussed in Steinhardt & Elvis (2010c), this may be due todifficulties in separating the MgII line and continuum fromnearby Fe lines, and as such, the correction may be substantially smaller or unnecessary for the brightest quasars
with the highest signal-to-noise spectra at each redshift. Evidence for this includes good agreement in the sub-Eddington
boundary slope calculated using unadjusted Hβ and MgII
masses at a common redshift, but poor agreement between
Hβ and adjusted MgII masses (Fig. 2). The best agreementin sub-Eddington boundary slopes comes from a substantially smaller, yet also expansive, correction to MgII massestimates (Steinhardt & Elvis 2010c). We will use the RYE09
calibration as an example of a possible mass-dependent biasthat produces an expansive correction, widening the mass
distribution at fixed redshift.
3.1

5

estimated at 1.8 × 1010 M⊙ (Valtonen et al. 2008). Applying
the RYE09 adjustment to MgII masses produces a more massive population at z > 1.6, with the number of more massive
objects increasing towards higher redshift. Although some ofthese masses use higher-uncertainty CIV-based estimates, at
1.6 < z < 2., these extraordinarily massive black holes arefound using MgII masses, which are directly calibrated by
Risaliti et al. (2009).
5. No Eddington Accretion at z ∼ 1: At z ∼ 2 andz < 0.8, the least massive quasars reach their Eddington luminosity, while more massive quasars fall increasingly short.
This is an adjusted version of the sub-Eddington boundary
described in Steinhardt & Elvis (2010b). However, between
these redshifts, all quasars, including those with the lowest black hole masses, fall short of Eddington. Because thelowest-mass quasars also lie at luminosities near the SDSS
detection limit, this may merely be a selection effect.

Puzzling Behavior

Specifically, this adjustment produces the mass-luminosity
plane shown in Figure 4 in 12 redshift bins ranging from0.2 < z < 4.1. As with the compressive correction consideredin § 2, this does not remove all of the puzzling behavior in
the quasar mass-luminosity plane, but rather includes thefollowing surprises:
1. Characteristic Accretion Rate at Fixed M, z: At
any fixed combination of mass and redshift, the quasar luminosity range spans a range of less than 0.8−1 dex. Because
SDSS views objects across nearly half the sky, these quasars
should lie in host galaxies with very different ephemeral
properties such as star formation rate and recent merger activity. Thus, these ephemeral properties can only be important at the . 1 dex level to the quasar accretion rate. This
puzzle also appears when using Shen08 and RH10 masses,
and can only be removed by a correction that interprets
quasars with different Shen08 masses as having identical
black hole masses.
2. Sub-linear Mass Dependence: At fixed redshift, thecharacteristic accretion rate increases with mass as L ∝0.2−0.4
MRY, with the slope closer to 0.4 at most redshifts (Fig.
E2). This dependence is very sensitive to mass-dependent
biases, pushing towards a linear mass dependence for extremely compressive corrections and towards only slightmass dependence for extremely expansive corrections.
3. Accretion is Time-Dependent: The characteristic
accretion rate at fixed mass, or chararacteristic Eddington ratio across all masses in the RYE09 picture, increases
with increasing redshift (Fig. 4). For example, quasars withlog MRY E /M⊙ = 108.5 reach Eddington at z ∼ 2, but lie increasingly sub-Eddington at lower redshifts. Even the mostluminous quasars at log MRY E /M⊙ = 108.5 and z ∼ 0.2 lie
nearly 1 dex below their Eddington luminosities. As withthe existence of a characteristic accretion rate, this puzzle
also appears using Shen08 and RH10 masses; it can only beremoved with a time-dependent mass adjustment. This may
be the least surprising puzzle, as it could be described asquasar downsizing analogous to galactic and star formation
Madau et al. (1998) downsizing.
4. Extraordinarily Massive Black Holes: The most
massive known supermassive black hole, OJ 287, has a massc 0000 RAS, MNRAS 000, 000–000

3.2

Physical Interpretation

Like other mass estimators, the expansive correction proposed by Risaliti et al. (2009) produces a quasar massluminosity plane exhibiting several puzzling behaviors. Someof these behaviors, including the narrow luminosity range atfixed mass and redshift and the time-dependence of thatcharacteristic accretion rate, are common to all virial massestimators. A unique feature of this correction is an accre0.2−0.4
tion rate L ∝ MRY.
E
The accretion rate is likely due to interaction between
the central black hole and its environment, and a sub-linear
mass-dependence likely indicates a balance between gravitational and non-gravitational effects. One model with approximately the right mass dependence considers a competition for infalling gas between accretion and star formation(Thompson et al. 2005), yielding L ∝ M 1/3 .
As before, although model may exist for the massdependence, the time-dependence is more difficult. The lawsof general relativity are time-independent, while a black hole
has no memory; just mass, charge, and spin. We might expect the feedback mechanism to be sensitive to properties of
the host galaxy, but because accretion is well-synchronized
between host galaxies containing supermassive black holes ofa common mass, ephemeral properties of the galaxy cannot
be critical. As in the Shen08 and RH10 pictures of quasar
accretion, the time-dependence continues to defy explanation.

4

DISCUSSION

We have considered the effects of affine biases in virial massestimation by examining two recent reports of biases in different directions (Risaliti et al. 2009; Rafiee & Hall 2010).
Correcting for one would expand the mass distribution at
fixed redshift, while the other would compress it. Common
to all of these virial mass estimators are two major puzzles:(1) that quasars at a common black hole mass and redshift
have the same, characteristic luminosity and (2) that thecharacteristic luminosity is time-dependent.
It should be immediately apparent that a purely massdependent error cannot be responsible for these two results.

6Charles L. Steinhardt
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Figure 4. A contour plot of the mass-luminosity distribution in 12 different redshift ranges using the Risaliti, Young, & Elvis massestimators for MgII masses and a corresponding adjustment for Hβ and CIV masses. Higher-mass quasars at fixed redshift lie increasingly
below their Eddington luminosity (black, dashed).

Any linear (or more complex) correction to black hole masses
in which objects at a common Shen08 mass have a common
black hole mass while objects at different Shen08 masses
have different black hole masses will yield this same pair ofpuzzles. A related puzzle is that using Shen08 masses, thelowest-mass quasars at each redshift are found near their
Eddington luminosities, while the highest-mass quasars all
fall short of Eddington. Rafiee & Hall (2010) claim to haveremoved this “sub-Eddington boundary” (SEB) with theirsystematic correction, but because the characteristic luminosity is time-dependent, it is, again, impossible for a purely
mass-dependent correction to MgII masses to remove thisboundary at all choices of redshift.
Another puzzling feature of the quasar M − L distribution is the mass-dependence of the characteristic luminosity at fixed redshift. Using the Shen et al. (2008) extensionof the SDSS catalog based upon previous mass calibrations(McLure & Jarvis 2002; McLure & Dunlop 2004; Vestergaard & Peterson 2006) produces Lc ∝ M 0.4−0.7 , which
thusfar is unmatched by physical modeling. Unlike the previous two puzzles, the slope of the mass-dependence is highly
sensitive to mass correction. The Rafiee & Hall (2010) correction produces a nearly linear dependence, implying thatthe characteristic accretion rate might be explained due
purely to gravity from the central black hole. Such an explanation would help us to understand why the characteristic
accretion rate is universal, and does not depend upon properties of the host galaxy such as star formation rate, merger
activity, and age since virialization. The Risaliti et al. (2009)
correction, on the other hand, is a good match for a feedback
model describing competition between gravitational attrac-

c 0000 RAS, MNRAS 000, 000–000

Effects of Biases in Virial Mass Estimation on Cosmic Synchronization of Quasar Accretion
tion and star formation for infalling gas, which again might
be independent of ephemeral properties of the host.
However, neither mechanism can explain the M − L
plane obtained using Shen et al. (2008) masses. Moreover,both of these mass corrections introduce new, puzzling features in the M − L plane. Using the Rafiee & Hall correction, all quasars will fall short of Eddington at some redshifts, all quasars at some mass will never reach Eddington, and the quasar distribution may be so narrow that the
Soltan argument requires perfect synchronization and tiny
mass errors. Using the Risaliti, Young, & Elvis correction,
again all quasars fall short of Eddington at some reshifts,
and many quasars contain black holes more massive than
any currently known. The Shen et al. masses, on the other
hand, provide some quasars reaching but not exceeding Eddington at all masses, provide some quasars reaching but notexceeding Eddington at all redshifts, and produce masses
lying within the bounds of observed post-turnoff supermassive black holes near redshift zero. The uncorrected masses
appear to be the best of the three options considered, although a smaller correction such as that found in Steinhardt & Elvis (2010c) by comparing the Hβ and MgII viewsof sub-Eddington boundaries may also be plausible.
4.1

Further Remarks

One of the reasons for skepticism about virial masses has
been that if taken at face value, the interpretation of the
mass-luminosity plane appears inconsistent with what would
seem to be obvious properties of supermassive black hole
growth. In particular, supermassive black holes are composed of gas and dust from their host galaxy, live in their
host galaxy, and the mass-stellar velocity dispersion (M −σ)relation (Ferrarese & Merritt 2000; Gebhardt et al. 2000)
and black hole mass-galactic luminosity relation (Ferrarese& Ford 2005) require that SMBH cease their accretion at a
final mass dynamically linked to their host galaxy. It also
seems natural that episodes of stronger accretion might belinked to galactic processes such as star formation and mergers that might drive gas and dust into their central regions.
It should be noted that although these puzzles regarding SMBH accretion are new, several other evolutionary
phases remain poorly understood. There are a wide variety
of proposed quasar seeding mechanisms (Volonteri 2010),
none of which has yet been supported by direct observational evidence. The black hole mass-stellar velocity dispersion (M − σ) relation (Ferrarese & Merritt 2000; Gebhardt
et al. 2000) and black hole mass-galactic luminosity relation (Ferrarese & Ford 2005) require that SMBH cease theiraccretion at a final mass dynamically linked to their hostgalaxy, but this link is not understood theoretically. In short,including these new results, we must conclude that we do notunderstand how SMBH are born, we do not understand how
they grow, and we do not understand how they die.
An inability to understand observational results within
the framework of a physical model should indeed be worrying, but in this case, the alternative is no better. The Sloan
Digital Sky Survey quasar catalog appears complete whencompared against other quasar catalogs (Jester et al. 2005;
Steinhardt & Elvis 2010b), and while the interpretation ofvirial masses as indicative of the central black hole mass
may be in question, our ability to measure the component
c 0000 RAS, MNRAS 000, 000–000

7continuum flux and emission line FWHM is not. Thus, inorder to explain these observations, one of two things mustbe true:• Virial masses are not indicative of the central
black hole mass. Therefore, to explain the observed quasar
distribution in M , L, and z, a physical model for accretion isneeded in which the BLR velocity is very tightly correlatedwith the bolometric luminosity, but that correlation is also
sharply redshift-dependent.
• Virial masses do measure the central black holemass. Therefore, to explain the observed quasar distribution in M , L, and z, a physical model is needed in which
quasars at fixed mass and redshift truly lie in a narrow
range in luminosity, and that narrow range is both massand redshift-dependent.
It is unclear which interpretation, if correct, would be
more intriguing. If the BLR velocity is a sufficiently good indicator of bolometric luminosity, a predictive physical model
might allow the use of quasars as a bright, high-redshift standard candle. If virial masses indeed measure central blackhole masses, the observed synchroniation of quasar evolution continues until turnoff, at which point the SMBH mustlie on the M − σ and M − L relations. Thus, quasars lying in two galaxies of the same mass and same redshift, butwith different star formation rates, different morphologies,
different merger histories, and different virialization times
have the same accretion rate. So, we are forced to choose
between two difficult model-making problems, both requiring a new understanding of quasar accretion, and neither
accommodated by existing models.
The author would like to thank Forrest Collman, Martin Elvis and John Silverman for valuable comments. This
work was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan.

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