Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.stsci.edu/~marel/abstracts/psdir/lauer4.ps Äàòà èçìåíåíèÿ: Sat Jun 15 01:47:14 2002 Äàòà èíäåêñèðîâàíèÿ: Sat Dec 22 10:29:18 2007 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: virgo cluster

Submitted to The Astronomical Journal
Galaxies with a Central Minimum in Stellar Luminosity Density 1
Tod R. Lauer
National Optical Astronomy Observatory 2 , P.O. Box 26732, Tucson, AZ 85726
Karl Gebhardt
Department of Astronomy, University of Texas, Austin, Texas 78712
Douglas Richstone
Department of Astronomy, University of Michigan, Ann Arbor, MI 48109
Scott Tremaine
Princeton University Observatory, Peyton Hall, Princeton, NJ 08544
Ralf Bender
Universit˜ats­Sternwarte, Scheinerstraúe 1, M˜unchen 81679, Germany
Gary Bower
National Optical Astronomy Observatory, P.O. Box 26732, Tucson, AZ 85726
Alan Dressler
The Observatories of the Carnegie Institution of Washington, 813 Santa Barbara St., Pasadena,
CA 91101
S. M. Faber
UCO/Lick Observatory, Board of Studies in Astronomy and Astrophysics, University of
California, Santa Cruz, California 95064
Alexei V. Filippenko
Department of Astronomy, University of California, Berkeley, CA 94720­3411
Richard Green
National Optical Astronomy Observatory, P.O. Box 26732, Tucson, AZ 85726
Carl J. Grillmair
SIRTF Science Center, 770 South Wilson Avenue, Pasadena, CA 91125

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Luis C. Ho
The Observatories of the Carnegie Institution of Washington, 813 Santa Barbara St., Pasadena,
CA 91101
John Kormendy
Department of Astronomy, University of Texas, Austin, Texas 78712
John Magorrian
Department of Physics, University of Durham, Durham, United Kingdom, DH1 3LE
Jason Pinkney
Department of Astronomy, University of Michigan, Ann Arbor, MI 48109
S. Laine, Marc Postman, & Roeland P. van der Marel
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218
ABSTRACT
We used Hubble Space Telescope WFPC2 images to identify six early­type galaxies
with surface­brightness profiles that decrease inward over a limited range of radii near
their centers. The implied luminosity density profiles of these galaxies have local minima
interior to their core break radii. NGC 3706 harbors a high surface brightness ring of
starlight with radius # 20 pc. Its central structure may be related to that in the double­
nucleus galaxies M31 and NGC 4486B. NGC 4406 and NGC 6876 have nearly flat cores
that on close inspection are centrally depressed. Colors for both galaxies imply that this
is not due to dust absorption. The surface brightness distributions of both galaxies are
consistent with stellar tori that are more di#use than the sharply defined system in NGC
3706. The remaining three galaxies are the brightest cluster galaxies in A260, A347, and
A3574. Color information is not available for these objects, but they strongly resemble
NGC 4406 and NGC 6876 in their cores. The thin ring in NGC 3706 may have formed
dissipatively. The five other galaxies resemble the endpoints of some simulations of the
merging of two gas­free stellar systems, each harboring a massive nuclear black hole. In
one version of this scenario, di#use stellar tori are produced when stars initially bound
to one black hole are tidally stripped away by the second black hole. Alternatively,
some inward­decreasing surface­brightness profiles may reflect the ejection of stars from
a core during the hardening of the binary black hole created during the merger.
Subject headings: galaxies: nuclei --- galaxies: photometry --- galaxies: structure

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1. Introduction
Early­type galaxies are brightest in their centers and fade into the background at large radii.
There is no shortage of parametric forms that describe this smooth progression, but all more or less
presume that the density of stars reaches its maximum in the center and decreases monotonically
outwards. Over the last decade, Hubble Space Telescope (HST) imaging has shown that galaxy
centers nearly always have singular surface brightness profiles of the form # # (r) # r -# (Crane et
al. 1993; Kormendy et al. 1994; Ferrarese et al. 1994; Lauer et al. 1995). Low luminosity early­
type galaxies, in general, have brightness profiles that are nearly power laws over several decades in
radius with # # 1 into the HST resolution limit; for galaxies in the Virgo cluster this corresponds to
radii of only a few parsecs. In contrast, the most luminous early­type galaxies have cores, defined by
where the outer power law ``breaks'' or transitions to a shallower inner cusp --- but even there, # > 0.
Lauer et al. (1995) clearly showed that even ``core galaxies'' had central density cusps, #L # r -# ,
with # significantly greater than zero; ``power­law galaxies'' typically had # # 2. Gebhardt et al.
(1996) verified the Lauer et al. (1995) conclusions, showing that non­parametric inversion of the
surface brightness profiles ratified the existence of density cusps in nearly all early­type galaxies
imaged with HST.
Massive nuclear black holes may play a critical role in the origin and survival of core structure
(Faber et al. 1997). This hypothesis is motivated by the dichotomy in the central structure of
elliptical galaxies. The low luminosity but dense power­law galaxies will be cannibalized by the
high luminosity but more di#use core galaxies. The long­term survival of low­density cores in
luminous galaxies appears to demand moderation of any mergers by the black holes; the cores
should have been filled in long ago without a strong tidal field to disrupt the in­spiraling nuclei of
the power­law galaxies. The theoretical work of Milosavljevi’c & Merritt (2001) verifies the Faber
et al. (1997) argument that the initial creation of a core galaxy results from the merger of two
power­law galaxies, each harboring a massive nuclear black hole.
Black holes may also be required to explain the double nuclei of M31 (Lauer et al. 1993) and
NGC 4486B (Lauer et al. 1996), two notable exceptions to the rule that stellar density reaches its
maximum at the geometric galaxy center. The origin of these double nuclei is unknown, but their
equilibrium and stability is most easily understood as a consequence of the massive black holes
believed to reside in their centers (Kormendy & Bender 1999; Kormendy et al. 1997). The two
visible nuclei in each galaxy are probably not distinct stellar systems, but may arise from a torus
of stars bound to the black hole in a Keplerian potential (Tremaine 1995). Again, such tori may
result from a merger in which two massive black holes are brought together by dynamical friction
1 Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope
Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS 5­26555. These observations are associated with GO proposals # 5454, 5512, 6099, 6587, and 8683.
2 The National Optical Astronomy Observatory is operated by AURA, Inc., under cooperative agreement with the
National Science Foundation.

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(Holley­Bockelmann & Richstone 2000).
In this context, we have searched for other galaxies with unusual central structures that may
shed additional light on the formation of the central structure in galaxies, with particular attention
to early­type systems exhibiting a central minimum in surface brightness. We identify six systems
culled from a large sample of galaxies imaged by HST with starlight distributions that do not neatly
fit into the schema that cores always have cusps with # > 0.
2. Observations and Analysis
2.1. The Sample and Observations
The galaxies presented here were identified by searching through a heterogeneous collection of
HST WFPC2 images of early­type galaxies. The goal was to identify systems that had minima in
their stellar volume densities interior to their cores. The search criterion thus was to select galaxies
that did not appear to be a#ected by dust absorption, but that had projected brightness profiles
that decreased inward. This criterion is actually conservative. A core with an essentially flat
profile (# # 0) in projection over an extended radial range can also be consistent with a inwardly
decreasing density profile. Galaxies of this sort that may bear a closer look include NGCs 1600
(Byun et al. 1996; Gebhardt et al. 1996), 4291, 5813, and 5982 (Rest et al. 2001).
Of the galaxy images examined, 51 were observed under HST programs GO­5512, 6099, and
6587; these are our programs to characterize the central structure of nearby early­type galaxies,
with emphasis on spectroscopic searches for massive black holes. We supplemented this sample with
the 15 early­type galaxies with kinematically decoupled cores observed by Carollo et al. (1997) in
program GO­5454. Overall, 66 galaxies were imaged by these four programs.
Although the samples observed in each of these programs were defined with varying criteria,
the observational parameters are fairly uniform. In all cases the nucleus of the galaxy was positioned
at the center of the WFPC2 high­resolution PC1 chip. Images obtained in the F555W (V ­band)
filter were available for all galaxies; F814W (I­band) images were also available in most cases.
The exposures in each filter were generally limited to a single orbit; this was usually su#cient to
obtain a signal­to­noise ratio (S/N) of # 100 per pixel in the galaxy centers. In program GO­6587
we began to use half­pixel dither steps, allowing the construction of Nyquist­sampled images with
double­sampling (Lauer 1999).
All images were deconvolved with 40 iterations of Lucy­Richardson deconvolution (Lucy 1974;
Richardson 1972). This method is well­suited to WFPC2 data; Lauer et al. (1998) show examples of
the deconvolution of simulated observations and compare deconvolved profiles of galaxies observed
with both WFPC1 and WFPC2. The centers of the galaxies discussed in detail below were all
well resolved, and the deconvolution corrections were modest. Further, in all cases, the central
reductions of surface brightness were apparent in the original images; deconvolution improves the

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accuracy of the photometry, but is not required to recognize the morphological features discussed
below.
After we began work on this paper, an additional sample of early­type galaxies became available
through the WFPC2 ``snapshot'' program GO­8683 (van der Marel, PI; Laine et al. 2002) on the
central structure of brightest cluster galaxies (BCGs). The BCG sample consists of the Postman &
Lauer (1995) set of 119 BCGs with z < 0.05; it is the most homogeneous set of galaxies in all five
programs. These galaxies are of special interest, given the likelihood that some galactic cannibalism
is still going on at this epoch, delivering faint cluster galaxies to the centers of the BCGs (Lauer
1988; Faber et al. 1997). The BCG snapshot images were only obtained with the F814W filter and
PC1, and have significantly lower S/N than the more nearby galaxies. Our discussion is based on
the 75 BCG images observed as of December 2001.
We discuss the six candidate galaxies with central minima in their density profiles as follows.
2.2. NGC 3706
NGC 3706 is an S0 galaxy in the Faber et al. (1989) group 242 (2749 km s -1 group veloc­
ity). Its luminosity lies in the transition zone between power­law and core galaxies (Faber et al.
1997). Carollo & Danziger (1994) obtained extensive ground­based photometric and spectroscopic
observations of NGC 3706; they found the galaxy to have strong central rotation and a pronounced
velocity dispersion peak. The WFPC2 images show that NGC 3706 harbors a bright compact
edge­on stellar ring or torus at its center (Figure 1).
A brightness profile (Figure 2) measured along the major axis of the ring shows that its surface
brightness rises from the center by 0.07 mag to a local maxima at 0 ## . 13, or 21 pc from the galaxy
center on both sides. 3 This limb brightening suggests that the structure is not a filled disk. 4 The
image of NGC 3706 was dithered and thus has subpixels with 0 ## . 0228 scale. The profile shows the
intensity at each subpixel along the major axis averaged over the width of a slice four subpixels
(0 ## . 091) thick centered on the ring, with each half of the major axis averaged about the center.
A small inward decrease in surface brightness implies a larger corresponding decrease in the
luminosity density profile, which is shown in Figure 3. This was computed by performing a non­
parametric Abel inversion (see Gebhardt et al. 1996) of the brightness profile along the apparent
ring­plane, assuming that the ring and surrounding galaxy were axisymmetric within this plane.
The luminosity density of the ring has a sharply defined maximum at 0 ## . 18, or 31 pc, falling by a
3 H0 = 80 km s -1 Mpc -1 is adopted throughout the paper.
4 With just one filter, it is not possible to rule out dust absorption as an alternative explanation for the central
dip in the ring brightness. There is no morphological sign of dust outside the ring, however; any dust disk within the
stellar disk would necessarily have a more limited radial extent and a scale height at least as compact as the stellar
system.

-- 6 --
factor of # 2 for r < 0 ## . 1. The small increase in brightness as r # 0 is of marginal significance. A
rough estimate of the total ring luminosity is # 1.3 â 10 8 L# (V -band), measured by integrating
the light within a 0 ## . 68 â 0 ## . 16 slice centered on the ring, crudely corrected for the ``background''
galaxy light, measured in a similar slice slightly o#set along the minor axis.
The thickness of the ring appears to be unresolved by HST. The minor­axis brightness profile
(Figure 2) begins to steepen at r < 0 ## . 1, which is well outside the resolution limit. However,
measuring the thickness of the ring requires an assumed light distribution for the galaxy background.
When simple estimates of the background are considered, it appears that the half­power point of
the ring vertical extent is less than 0 ## . 04, or 6 pc.
The small size and extreme aspect ratio of the ring in NGC 3706 raise the issue of the ring's
lifetime against thickening by two­body relaxation. From the stellar velocity dispersion versus black­
hole mass relationship of Gebhardt et al. (2000) and the velocity­dispersion observations of Carollo
& Danziger (1994), NGC 3706 is expected to have a central black hole of mass M . # 5 â 10 8 M# .
This mass would dominate the stellar mass enclosed within the radius of the ring and implies an
angular rotation rate
of# = 2.8 â 10 -13 s -1 at r = 31 pc. If we assume a Gaussian vertical
luminosity density distribution of the ring, j(R, z) = j 0 (R) exp(-z 2 /2z 2
0 ), then the upper limit on
the ring thickness implies z 0 < 5 pc, which in turn allows calculation of an upper limit to the
vertical velocity dispersion within the ring, # z = z 0
/# < 43 km s -1 . If the shape of the velocity
ellipsoid is similar to that in the solar neighborhood, then the isotropized dispersion is about 1.5
times as large, or # < 64 km s -1 . At the upper limit for the dispersion, the relaxation time (Binney
& Tremaine 1987) within the ring is
t r = 0.34# 3
# G 2 m# ln # # -1 (1)
= 3 â 10 11 yr # 1M#
m
## M
L
# -1
, (2)
where we have adopted a midplane density # 0 = 10 3 M# pc -3 (see Figure 3), the mass­to­light ratio
M/L is in solar units, the stars are assumed to have solar mass, and ln # = ln(1.2z 0 # 2 /(GM# )) =
16. This result for the relaxation time is consistent with the hypothesis that the ring age is compa­
rable to a Hubble time. However, the dependence of t r on # and # 0 implies t r # z -4
0 ; thus t r may be
substantially shorter than the present estimate, and the actual ring thickness could be determined
by two­body relaxation if z 0 were a factor of two or more smaller than the observational upper
limit.
The brightness of the ring falls rapidly from r # 0 ## . 2 to r # 0 ## . 4, where an inflection point in
the major axis luminosity density profile occurs. The ring is actually misaligned with the major
axis of the galaxy at large radii, as can be seen in the contour map (Figure 4) and plot of isophote
position angle (PA; Figure 5). The PA of the ring is 114 # , as compared to the galaxy PA of 78 # for
isophotes with r > 5 ## . Even though the bright portion of the ring is compact, the transition of PA
from the ring to outer­galaxy isophote orientation takes place smoothly over 0 ## . 5 < r < 2 ## . 0; this
is a strong twist, given the high ellipticity of the isophotes over the same radii.

-- 7 --
The existence of this twist raises an interesting dynamical problem. If the isodensity surfaces
in the galaxy are triaxial ellipsoids with aligned principal axes, then isophote twists can arise if
the axis ratios of the isodensity surfaces vary with radius and the line of sight does not lie in one
of the principal planes (e.g., Binney & Merrifield 1998). However, in NGC 3706 we see the ring
edge­on. Therefore the isophote twist between 0. ## 5 and 2. ## 0 implies that the ring plane is not one of
the principal planes of the galaxy at larger radii (> 300 pc). Thus the tidal force from the galaxy
must induce precession of the ring plane; crude estimates suggest that the precession time is a few
times 10 8 yr. Gravitational interactions between the precessing ring plane and passing stars from
the host galaxy can damp or excite the inclination of the ring (Dubinski & Kuijken 1995; Nelson &
Tremaine 1995); the damping timescale is di#cult to estimate accurately but typically is only a few
precession times and hence probably is short compared to a Hubble time. The non­zero inclination
might then indicate either that the ring was young, or that the interactions with the host galaxy
have excited the inclination of a ring that was initially located in or near the equatorial plane of
the galaxy.
We stress that it is essentially impossible to decompose NGC 3706 uniquely into separate
background galaxy and ring components; however, the minor­axis surface brightness profile does
appear to ``break'' at r # 0 ## . 2, which is outside radii associated with the ring itself. The slope of
the minor axis profile for 0 ## . 1 < r < 0 ## . 2 is # # 0.4, suggestive of a transition to a shallow cusp.
NGC 3706 thus appears to be a core galaxy.
2.3. NGC 4406
NGC 4406 is a giant elliptical galaxy in the Virgo cluster. NGC 4406 rotates slowly about its
major axis (Wagner et al. 1988; Franx et al. 1989), but its core interior to r < 5 ## rotates rapidly
about the minor axis (Bender 1988; Franx et al. 1989) and has significantly higher line­strengths
compared to the envelope (Bender & Surma 1992), intriguing results in light of the following
discussion. Carollo et al. (1997) obtained F555W and F814W WFPC2 images of NGC 4406 as part
of their sample of elliptical galaxies with kinematically distinct cores. They found NGC 4406 to
have a well­resolved core with a ``break radius'' r b = 0 ## . 95, with a ring of reduced surface brightness
interior to this radius. Carollo et al. believed that this ``moat'' (our coinage) was due to dust
absorption, but noted that no reddening was seen in a comparison of V and I images. We argue
instead that the moat is a true reflection of the starlight distribution in NGC 4406. One possibility
is that NGC 4406 began with a normal core, and that some of the stars in the region interior to
the core break radius were subsequently ejected; a second is that a di#use stellar torus is encircling
the nucleus at slightly larger radii, creating the appearance of reduced surface brightness interior
to the torus (this could either be a face­on torus or a thick edge­on torus; for reasons given below
we prefer the latter interpretation).
Figure 6 shows the deconvolved WFPC2 F555W and F814W images of NGC 4406, as well as an
STScI HST archive F160W NIC2 image of the same region obtained by Ravindranath et al. (2001).

-- 8 --
A moat of reduced emission is visible in all three images. Figure 7 shows the F555W major axis and
minor­axis surface brightness profiles of NGC 4406. For r > 1 ## . 2, the profiles were derived by the
standard fitting of ellipses to the isophotes; at smaller radii, where the isophotes were poorly fitted
by ellipses, the profiles consist simply of cuts along each axis (of 0. ## 14 width), with the opposite
sides about the nucleus averaged. The moat of reduced emission is visible as a local minimum in
the major axis brightness profile (PA= 127 # ) at 0 ## . 11 from the nucleus. The profile then brightens
outward by 0.07 mag to a maximum at 0 ## . 49 from the nucleus. The minor­axis profile is somewhat
flatter over the same radii, with the surface brightness rising only 0.02 mag outward to a maximum
at 0 ## . 38 (29 pc) from the nucleus. Both profiles show a sharp peak at the smallest radii, which
appears to be a poorly­resolved nuclear point source.
Carollo et al. (1997) noted the somewhat lower maximum brightness along the minor axis and
argued that their ``dust ring'' was elongated in this direction. An equivalent picture, however, is
that we are looking at a di#use, edge­on, thick torus of stars that in projection is elongated along
the major axis; this interpretation is made somewhat more explicit by the contour map presented
in Figure 8. In this case it is natural to assume that both the background galaxy and the torus are
axisymmetric with respect to the projected minor axis of the galaxy, and symmetric with respect to
the plane formed by the line of sight and the projected major axis. We are motivated to consider a
dustless interpretation both by the example of a stellar torus in NGC 3706, and by the lack of any
dust reddening in NGC 4406. Figure 6 shows that the V -I color map made by dividing the F555W
by the F814W image is devoid of any structure or gradients over the extent of the core. NGC 4406
does have a red color gradient as r # 0, with #(V - I)/# log(r) = -0.062 for 1 ## < r < 10 ##
(Figure 9), but this color gradient is completely normal for giant elliptical galaxies (Carollo et al.
1997). The color for r < 1 ## actually appears to be constant with V - I = 1.31 ± 0.01 mag. The
color of the moat, itself, measured from all pixels falling within the annulus 0 ## . 13 < r < 0 ## . 26 is
V - I = 1.309 ± 0.006 mag, as compared to V - I = 1.303 ± 0.006 mag measured in two 0 ## . 32
square patches centered on the points of maximum surface brightness on each side of the nucleus.
From the extinction tables in Holtzman et al. (1995), we infer A V # 2.5#(V - I) for the WFPC2
filter­set. The di#erence #(V - I) = 0.006 ± 0.009 mag is insignificant, and the implied A V is
clearly insu#cient to account for the moat of reduced surface brightness.
The case against dust absorption is made particularly strong by the close similarity of the
F160W NIC2 image to the WFPC2 images (information that was not available to Carollo et al.
1997). Again, the V -H color (Figure 9) is essentially flat over the core interior; if anything, the
V -H may become slightly bluer interior to the radius of maximum brightness in the core.
If the unusual core of NGC 4406 reflects the intrinsic distribution of starlight, then a ring of even
slightly reduced surface brightness implies a stronger corresponding decrease in luminosity density.
Figure 10 shows the implied major axis luminosity density profile obtained from nonparametric
Abel inversions of the profiles shown in Figure 7, again done under the assumption that the galaxy
is axisymmetric in the plane defined by the major axis and line­of­sight. The 0.07 mag inward
decrease in surface brightness on the major axis corresponds to a factor of 2 to 30 decrease in

-- 9 --
luminosity density over the same radii. The exact density profile is clearly sensitive to small
changes in the brightness profile; however, we note that even for a perfectly flat light profile, NGC
4406's core is sharp enough (# = 0 but # > 2 in the parametric form of Lauer et al. 1995) that a
inward decrease in volume density would still be implied.
Is is ambiguous as to whether the NGC 4406 density profile has been created by either adding
stars to or removing them from an originally normal core. Fits to the V ­band profile give I b = 16.03
mag arcsec -2 and r b = 0 ## . 93, corresponding to 72 pc at an assumed distance of 16 Mpc. This implies
that NGC 4406 has a normal core for its luminosity (Faber et al. 1997). There is no unique way to
decompose the density profile into a torus superimposed on a more normal density profile. Under
some assumptions, such an exercise could imply that NGC 4406 had a substantially larger core
prior to some sort of accretion event; scatter in the L - r b and L - I b relationships is too large to
rule this out (Faber et al. 1997). Conversely, NGC 4406 may have had a smaller core prior to the
event --- indeed, it is within the luminosity range of the power­law galaxies, which have no cores at
all. One could thus argue that the present density profile represents an evacuation of a plausibly
more concentrated initial profile.
2.4. NGC 6876
NGC 6876 is a giant elliptical galaxy in the Pavo, or Faber et al. (1989) group 269 (4078 km
s -1 group velocity). Its luminosity is typical for a core galaxy (Faber et al. 1997). Figure 11 shows
the deconvolved WFPC2 F555W and F814W images of NGC 6876. The depression in surface
brightness interior to the core is subtle, but is evident as a reduced band of surface brightness
along the minor axis in both colors. A contour map (Figure 12) of the slightly smoothed F814W
image also highlights the unusual structure. The inner isophotes of NGC 6876 become increasingly
flattened, ultimately developing an indentation on the minor axis; NGC 6876 appears to have a
di#use edge­on torus of starlight added to an otherwise normal core.
Figure 13 shows the F555W major axis and minor­axis surface brightness profiles of NGC
6876. For r > 0 ## . 7, the profiles were derived by the standard fitting of ellipses to the isophotes; at
smaller radii, where the isophotes were poorly fitted by ellipses, the profiles consist simply of cuts
along each axis (of 0. ## 23 width), with the opposite sides about the nucleus averaged. The point
of maximum brightness along the major axis occurs at 0 ## . 24 (60 pc) from the nucleus, where the
surface brightness has brightened by 0.02 mag over its central value. The minor­axis profile actually
has a cusp with # slightly positive over the same radii, again suggestive of a di#use torus that has
its points of maximum projected brightness o#set along the major axis. Looking to larger radii, it
is noteworthy that the major axis brightness profile for 1 ## < r < 3 ## has a steeper power­law index
than that of the envelope at r > 3 ## . NGC 6876 thus has a subtle form of a ``nuclear rise'' exterior
to its nominal core.
The similar appearance of NGC 6876 in both the V and I filters implies that its unusual core

-- 10 --
morphology is not due to dust. The V - I map in Figure 11 shows no structure. The average
V - I color in two 0 ## . 32 boxes (7 â 7 pixels) centered on the maxima of the presumed torus at
0 ## . 31 on either side of the center is 1.326 ± 0.005 mag, as compared to 1.328 ± 0.007 mag for the
same­sized box about the center, itself; the net di#erence #(V -I) = 0.002±0.009 mag going from
the outer core into the center is clearly insignificant. At the same time, since A V # 2.5#(V - I)
and the central dimming is only 0.02 mag in V, it may be di#cult to rule out an alternative model
consisting of weak dust absorption in a core with an exceedingly weak cusp. As noted above, a
uniformly flat core for r < 0 ## . 24 would still imply a stellar density profile that decreased at smaller
radii. For cusps steeper than even # # 0.02, however, the implied dust absorption and associated
V - I reddening would already be inconsistent with the observations.
It is noteworthy that the PA of the innermost isophotes, PA = 89 # , is twisted by 13 # from the
major axis of the galaxy at r > 2 ## . 9 (PA = 76 # ); given the high ellipticity of the inner isophotes, this
apparently modest twist is actually highly significant. As with NGC 3706, the isophote ellipticity
and PA profiles of NGC 6876 (Figure 14) suggest that its torus is a more extensive system than
might be inferred from the small radius of the major axis brightness profile maximum. The implied
dip in stellar density (Figure 15) is less impressive than those in NGC 3706 and NGC 4406, but
still shows a significant inward decrease.
2.5. Brightest Cluster Galaxies
A search through the HST ``snapshot'' images of BCGs discussed in §2.1 turned up a few
more candidates for galaxies with dips in their core brightness profiles. As the snapshot images
were only obtained in F814W and have relatively low S/N, it is more di#cult to rule out dust
absorption --- already clearly evident in many BCGs --- as an explanation for such galaxies. BCG
candidates for galaxies with true local minima in their stellar density profiles were those that most
closely resembled the three galaxies discussed above. That is, the minima had to be di#use in
appearance, and bracketed by bilaterally symmetric brightness maxima. The first criterion yielded
10 candidates from the sample of 72 observed so far; addition of the second criterion limited the
final candidate list to three BCGs (A260, A347, and A3574). Images of the centers of the three
galaxies are shown in Figure 16 and symmetrized major axis brightness traces are presented in
Figure 17.
A347 is the best candidate for a BCG with a stellar torus. Its isophotes become highly flattened
at small radii, and its central brightness minimum is clearly evident. A3574 and A260 have large
di#use cores that on close examination have subtle (# 2%) surface brightness depressions along the
major axes interior to their break radii. Demonstration that dust is not playing a role in all three
BCGs requires deeper exposures in at least two colors.

-- 11 --
3. Discussion
It is possible that all six galaxies identified in this paper harbor stellar tori superimposed on
normal cores. Certainly, the bright and sharply defined feature in NGC 3706 is di#cult to explain
as anything else. It is tempting to include M31 and NGC 4486B in this class, since the Tremaine
(1995) model for M31 is based on a stellar torus, even though two brightness maxima (``double
nuclei'') in both galaxies are more pronounced and are less symmetric than in the galaxies described
here. The origin of such tori will be discussed further below, as well as the hypothesis that some
of the ``tori'' may really be cores that have been partially evacuated.
In either case, a genuine minimum in the density profile implies significant rotation, triaxiality,
or anisotropy. An inward decrease in density cannot occur in spherical galaxies whose phase­space
distribution functions depend only on the energy. Such functions are guaranteed to be solutions of
the collisionless Boltzmann equation. The density in this case for a spherical system is given by
# = 2 3/2 # # #
0
f(#)(# - #) 1/2 d#, (3)
where f # 0 is the mass per unit volume of phase space, # # -E, and # # -# (the quantities
# (total energy) and # (gravitational potential) are defined so that we work with non­negative
variables: #(r) is positive at all radii, and # is positive for all bound stars). We can use
d#/d# = 2 1/2 # # #
0
f(#)(# - #) -1/2 d# (4)
to evaluate the density gradient anywhere in the galaxy (note that the derivative with respect to
the upper limit of the integral is zero because the integrand goes to zero). Since # is a function
only of radius, the gravitational field and any density gradient are both radial, and the latter is
d#
dr
= d#
dr
d#
d#
. (5)
Since d#/dr = -GM(r)/r 2 is always negative and d#/d# is always positive [f(#) is non­negative for
all #], d#/dr is always negative in any spherical system in which the distribution function depends
only on energy. Thus, the systems observed in this paper are guaranteed to be either nonspherical
or anisotropic, and may be both. All the systems for which we have dynamical observations indeed
appear to have significant central rotation. The rotation amplitude in NGC 4406 is modest, but it
is strong in M31, NGC 3706, and NGC 4486B.
We next discuss two possibilities for the formation of the toroidal stellar systems.
3.1. Star Formation and Nuclear Disks
There are several elliptical galaxies or bulges that harbor central stellar disks. Kormendy et al.
(2002) present a short list of examples and argue that these disks were created in situ by accreted

-- 12 --
gas funneled into the center. Scorza & van den Bosch (1998) emphasize that the disks can be
radially compact and of high surface brightness. One might then ask if the tori in the present
systems result from in situ star formation as well. Of the six galaxies, the relatively cold and dense
ring in NGC 3706 comes closest to resembling a stellar disk formed directly from a gas disk. One
possible scenario is that the overall core structure was formed by the cannibalization of a low­mass
stellar system, which contained some amount of gas, by NGC 3706. As is discussed in §2.2, the ring
in NGC 3706 is embedded in a larger stellar system that itself rises above and is twisted from the
envelope brightness profile. This system would contain the pre­existing stars in the denser portions
of the cannibalized object, while the abrupt transition to the bright ring, itself, would reflect stars
formed by gas delivered to the center of NGC 3706 in the same merger event. The issues remain:
(1) Why has the ring not been filled in? (2) Why has the ring and surrounding stellar system not
settled to the midplane defined by the envelope? Presently, the maximum ring density falls well
inside the Roche radius of the estimated nuclear black hole mass. Thus, star formation in the ring
requires either that the black hole was initially less massive, or that the pre­existing gas was in
the form of dense molecular clouds, or that the gas layer in the disk was thinner than the current
stellar disk.
The tori in the five remaining galaxies, however, appear to be considerably more di#use and
are less suggestive of thin stellar disks than the ring in NGC 3706. Further, the transition from
the outer cores to the radii of the tori appears to be smooth and gradual --- there is no abrupt
transition to a high surface brightness ring, as is seen on the minor axis of NGC 3706. While it
may be likely that these remaining tori were created in a merger event, as well (as we argue below),
there is presently no compelling evidence that suggests that gas infall, followed by star formation
within the cores, played a role in their formation.
3.2. Mergers of Galactic Nuclei Containing Black Holes
It is now believed that the orbital decay of the massive black holes added to a galaxy by
mergers with other galaxies may largely determine the inner distribution of starlight in the merger
remnant. We speculate that the unusual structures seen in the present sample (with the possible
exception of NGC 3706) may be evidence of this process. As it happens, both the ``stellar torus
added'' and ``evacuated core'' interpretations of the observations may be supported by this scenario.
Begelman et al. (1980) argued that galaxies harboring massive black holes should occasionally
merge and sketched out the orbital decay of the binary black hole that would be created in such an
event. Among other predictions, they suggested that in the later stages of the binary's life, the two
black holes would eject stars from the newly merged core as the binary hardened, creating a local
minimum in stellar density at the few parsec scale. Ebisuzaki et al. (1991) studied this problem
numerically and showed that the binary black hole would generate a core with a shallow cusp in the
merger remnant. Intriguingly, Makino (1997) showed that local minima in stellar density occurred
within the core in some simulations.

-- 13 --
The preservation of cores during mergers essentially demands that the final stages of such
events are dominated by nuclear black holes (Faber et al. 1997). The central density contrast
between core and power­law galaxies is strong enough that even modest cannibalism of the latter
by the former should have filled in the di#use cores long ago. The ``core within a core'' merger
endpoint hypothesized by Kormendy (1984) prior to HST observations, however, has never been
found. The tidal field of the nuclear black hole solves this problem by shredding the incoming
nucleus prior to its final delivery to the center. That cores exist only in the more luminous non­
rotating elliptical galaxies, where gaseous dissipation may be less important during the merging of
their progenitors, bolsters this picture (Faber et al. 1997).
All six galaxies discussed here appear to be core galaxies. The strong central isophote twist in
NGC 3706 and the kinematically decoupled core in NGC 4406 suggests that mergers have influenced
the inner structure of both galaxies. The increase in isophote ellipticity in NGC 6876 and A347
with decreasing radius, but at radii larger than at of the putative stellar tori, may also suggest
cannibalization of a pre­existing stellar system. The cannibalized system would be less luminous,
but denser and dynamically colder --- the ellipticity increase would reflect stars from such a galaxy
being preferentially deposited in the core of the more luminous galaxy.
One immediate concern is why evacuated cores are so rare if they are a natural consequence
of the process (decaying binary binary holes) that is supposed to make all cores. It is noteworthy
that the recent simulations of Milosavljevi’c & Merritt (2001) only produced the # > 0 cusps seen
in ``normal'' core galaxies. The nearly constant density cores generated by Makino (1997), let
alone cores with dips in density, were not seen. Significantly, Milosavljevi’c & Merritt (2001) always
merged two power­law galaxies to test the initial formation of a core as advocated by Faber et
al. (1997), while Makino (1997) started with cores already present in the merging galaxies. In
a merging hierarchy, the more luminous galaxies may experience multiple episodes of merging or
cannibalism. If a merger product is used as the input for subsequent mergers, then there is a variety
of possible initial structural forms. Two core galaxies may merge, a core galaxy may cannibalize
a power­law galaxy, and so on; allowing for the concentration of the pre­merger cores provides an
additional variable. If the Milosavljevi’c & Merritt (2001) simulations are correct for the original
formation of a core galaxy, but the Makino (1997) simulations are correct that central evacuation
can occur with appropriate initial conditions, then perhaps the rarity of observational examples of
evacuated cores merely reflects the likelihood of these conditions.
As the black hole binary hardens, it will eject stars from the merged core to increasingly large
distances. Early in its life, however, when the separation of the two black holes is similar to the core
break radius, tidally stripped stars originally bound to either hole may still linger within the core.
Holley­Bockelmann & Richstone (2000) emphasize that under some circumstances, such as when
one galaxy has a relatively high nuclear stellar density and arrives at the center of the other galaxy
with a high impact parameter, stars stripped from the incoming galaxy may form a di#use torus.
Zier & Biermann (2001) have also discussed the formation of a stellar torus as one black hole strips
stars from the other. In this picture, we really are seeing di#use stellar tori superimposed against

-- 14 --
the cores of the merger remnants. Ironically, Holley­Bockelmann & Richstone (2000) attempted to
explain the thin nuclear disks (as discussed in the context of NGC 3706) as being created by this
process, but noted that they could only generate di#use tori, not the high aspect­ratio disks seen
in systems like NGC 3115 or NGC 4594. Some of the present systems may be the realizations of
the toroidal structures seen in the Holley­Bockelmann & Richstone (2000) simulations.
4. Summary
We have discussed six early­type galaxies in which the luminosity density distribution in the
core cannot be represented as a simple power law. The surface brightness profiles of all six systems
decrease over limited radii interior to their cores. This implies that there are correspondingly more
pronounced dips in their luminosity density profiles. In the systems for which we have multi­color
imaging (NGC 4406 and NGC 6876), it is unlikely that we are being confused by some low level
of di#use dust absorption. The three BCG strongly resemble these two systems, and they show no
compact dust clouds anywhere around their cores. We have therefore included them within this
discussion, although additional multicolor imaging of the BCG should be obtained to verify this
conclusion. The final system, NGC 3706, harbors a bright, apparently edge­on stellar ring.
There are two literally complementary interpretations of the core structures seen in the six
galaxies. The first picture is that we are seeing stellar tori superimposed on otherwise normal
cores. The narrow ring in NGC 3706 stands in such strong contrast with its surrounding core that
it is di#cult to accept any alternative interpretation. NGC 3706, and perhaps some of the five
remaining systems, may be related to the double­nucleus galaxies M31 and NGC 4496B. The six
galaxies discussed here did not present themselves as double nuclei; however, as they all do have
subtle local maxima in surface brightness that bracket their apparent nuclear centers, it would take
only a modest brightness enhancement at these locations to have them appear as doubles. Instead,
perhaps the more suggestive presence of stellar tori in the present galaxies bolsters the plausibility
of this interpretation for M31 and NGC 4486B, as well.
The thinness of the NGC 3706 torus probably requires it to have formed dissipatively. The core
structure of NGC 3706 suggests that it and the inner ring were formed in a merger or cannibalism
of a stellar system that contained some amount of gas. In the ``torus­added'' picture the tori in the
remaining systems may have formed from the cannibalization of gas­free stellar systems. In this
case, the tori would have been generated by the tidal disruption of the cores or central cusps of the
original systems by a massive black­hole binary formed from the nuclear black holes contained in
the original systems.
In the second picture we are seeing a true depletion of stars within the cores of the galaxies.
As in the picture above, a black hole binary would be formed in a merger. As the binary hardens,
it ejects stars from the core. The di#erence between this picture and the ``torus­added'' scenario
may be one of initial conditions, in which ejection of stars at later stages in the binary's evolution

-- 15 --
competes against deposition of relatively colder stars around the core at an earlier stage in the
binary's life for domination of the final integrated structure of the core.
The ``core­evacuated'' scenario is suggested by theoretical results that are only weakly evident
in some merger simulations. If core evacuation does occur, it may require rare initial conditions.
The Milosavljevi’c & Merritt (2001) simulations argue that evacuation is not likely to be seen in
the merger of two power­law galaxies that would create a core galaxy initially. It may be that
evacuated cores can occur in subsequent mergers in which at least one of the two galaxies already
contains a core.
Regardless of which scenario is correct, we present the six galaxies as interesting probes on the
formation of cores. Theoretical and observational work both point to a strong role for nuclear black
holes for establishing the core structure of merger remnants. Rare and unusual core structures may
o#er a unique narrative in this story not otherwise voiced by more normal galaxies.
We thank Joseph Jensen for providing the reduced NIC2 images of NGC 4406. Support for
GO proposals 5512, 6099, 6587, and 8683 was provided by NASA through grants from the Space
Telescope Science Institute, which is operated by the Association of Universities for Research in
Astronomy, Inc., under NASA contract NAS 5­26555.

-- 16 --
Table 1. Observational Summary
Galaxy D (Mpc) MB (mag) AB (mag) Images
NGC 3706 35 -21.24 0.36 500 s F555W (2 â 2 subsampled)
NGC 4406 16 -21.26 0.11 500 s F555W, 500 s F814W, 140 s F160W
NGC 6876 51 -22.43 0.16 4100 s F555W, 4100 s F814W
Note. --- H 0 = 80 km s -1 Mpc -1 is assumed. Group velocities were used for distance
estimation.

-- 17 --
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This preprint was prepared with the AAS L A T E X macros v5.0.

-- 19 --
Fig. 1.--- The F555W image of NGC 3706. The panel on the left shows the central 5 ## â 5 ##
of the WFPC2 F555W image of NGC 3706. The galaxy was centered on the PC1 chip. The
image is double­sampled, deconvolved, and displayed with a logarithmic stretch. The right panel
is magnified by a factor of 5 to show the ring itself; the stretch is linear in this image. North is at
219.0 # measured counterclockwise from the vertical axis.

-- 20 --
0.01 0.1 1 10
18
17
16
15
14
Fig. 2.--- Surface brightness profiles for NGC 3706. The solid line is the major axis brightness
profile. For r < 0 ## . 5 the profile is measured from a cut (0 ## . 09 in width) along the disk, with the
opposite sides of the nucleus averaged. At larger radii, standard isophote fitting is used (connected
dots). The dotted line is a cut perpendicular to the ring, again with both sides averaged.

-- 21 --
0.01 0.1 1 10
10
100
1000
Fig. 3.--- V ­band luminosity density profile for the major axis of NGC 3706. Dashed lines give the
±1# error envelopes. The profile has been corrected for foreground extinction.

-- 22 --
-2
0
2
-2
0
2
Arcsec
Arcsec
Fig. 4.--- A contour map of NGC 3706 in the deconvolved F555W image. Contours are spaced
by 0.5 mag in surface brightness; the outermost contour corresponds to µ V = 18.0 mag arcsec -2 .
North is at 219.0 # measured counterclockwise from the vertical axis.

-- 23 --
0.1 1 10
70
80
90
100
110
120
0.1 1 10
0
0.1
0.2
0.3
0.4
0.5
Fig. 5.--- Isophote ellipticity and position angle profiles for NGC 3706. No points are shown for
isophotes with semimajor axes < 0 ## . 5, as these isophotes are poorly fitted by ellipses.

-- 24 --
Fig. 6.--- Images of NGC 4406 are shown in three di#erent filters. The upper left and upper
right panels are the deconvolved WFPC2 F555W and F814W images. The lower right panel is the
deconvolved NIC2 F160W image resampled and rotated to match the WFPC2 images. The area
of the panels is 4 ## â 4 ## . An arbitrary linear stretch (the same in all three panels) has been used
to enhance contrast in the core. The lower left panel is a slightly smoothed F555W/F814W ratio
image; the full range of its gray scale is ±10%. North is 8.9 # measured counterclockwise from the
vertical axis. The nuclear point­source is most evident in the V ­band image.

-- 25 --
0.01 0.1 1 10
18
17.5
17
16.5
16
15.5
Fig. 7.--- Major axis (solid) and minor axis (dotted) deconvolved F555W brightness profile for
NGC 4406. The profile at r > 1 ## . 2 was measured by isophote fitting (connected dots). At smaller
radii the profile for each axis was measured from a cut along the axis (of width 0. ## 14), with the
opposite sides across the nucleus averaged.

-- 26 --
-1 0 1
-1
0
1
Arcsec
Arcsec
Fig. 8.--- A contour map of NGC 4406 in the deconvolved F555W image. Contours are spaced by
0.05 mag in surface brightness; the outermost contour corresponds to µ V = 16.42 mag arcsec -2 .
North is 8.9 # measured counterclockwise from the vertical axis.

-- 27 --
0.01 0.1 1 10
1.1
1.2
1.3
1.4
0.01 0.1 1 10
3.2
3.3
3.4
3.5
3.6
Fig. 9.--- Major axis V -H and V - I color profiles of NGC 4406.

-- 28 --
0.01 0.1 1 10
1
10
100
1000
Fig. 10.--- V ­band luminosity density profile for the major axis of NGC 4406. Dashed lines give
the ±1# error envelopes. The profile has been corrected for foreground extinction.

-- 29 --
Fig. 11.--- Images of the NGC 6876 core are shown in two filters. The left and middle panels
are the deconvolved WFPC2 F555W and F814W images. The area of the panels is 4 ## â 4 ## . An
arbitrary linear stretch has been used to enhance contrast in the core. The right panel is a slightly
smoothed F555W/F814W ratio image; the full range of its gray scale is ±10%. North is 24.1 #
measured counterclockwise from the vertical axis.

-- 30 --
-1
0
1
-1
0
1
Arcsec
Arcsec
Fig. 12.--- A contour map of NGC 6876 in the deconvolved F814W image. Contours are spaced
by 0.05 mag in surface brightness; the outermost contour corresponds to µ I = 16.71 mag arcsec -2 .
North is 24.1 # measured counterclockwise from the vertical axis.

-- 31 --
0.01 0.1 1 10
19
18.5
18
17.5
17
16.5
Fig. 13.--- Major axis (solid) and minor axis (dotted) deconvolved F555W brightness profile for
NGC 6876. The profile at r > 0 ## . 7 was measured by isophote fitting (connected dots). At smaller
radii the profile for each axis was measured from a cut along the axis (of width 0. ## 14), with the
opposite sides across the nucleus averaged.

-- 32 --
0.1 1 10
70
75
80
85
90
0.1 1 10
0
0.1
0.2
0.3
0.4
0.5
Fig. 14.--- Isophote ellipticity and position angle profiles for NGC 6876. No points are shown for
isophotes with semimajor axes < 0 ## . 6, as these isophotes are poorly fitted by ellipses.

-- 33 --
0.01 0.1 1 10
0.1
1
10
Fig. 15.--- V ­band luminosity density profiles for the major axis of NGC 6876. Dashed lines give
the ±1# error envelopes. The profile has been corrected for extinction.

-- 34 --
Fig. 16.--- Three BCG candidates with centrally depressed stellar density profiles. Left to right, the
galaxies are the BCG in A260, A347, and A3574. Each panel is a 4 ## â 4 ## subset of the deconvolved
F814W PC snapshot image. The intensity stretch is arbitrary. North is 98.6 # measured clockwise
from the vertical axis for A260, 175.1 # measured counterclockwise from the vertical axis for A347,
and 42.4 # measured clockwise from the vertical axis for A3574. A faint point­source is visible in
the A3574 core.

-- 35 --
A0260 PA=59
A0347 PA=50
A3574 PA=67
Fig. 17.--- Surface brightness profiles are shown for the three BCG candidates with centrally
depressed stellar density profiles. The profiles were measured from cuts along the major axis of
width 0. ## 23, with the opposite sides averaged. The position angles of the cuts are noted in each
panel.