A&A 479, 355-363 (2008)
DOI: 10.1051/0004-6361:20078570
G. De Francesco1 - A. Capetti1 - A. Marconi2
1 - INAF - Osservatorio Astronomico di Torino, Strada
Osservatorio 20, 10025 Pino Torinese, Italy
2 -
Dipartimento di Astronomia e Scienza dello Spazio, Università di Firenze,
Largo E. Fermi 2, 50125 Firenze, Italy
Received 29 August 2007 / Accepted 26 October 2007
Abstract
We present results from a kinematical study of the gas in the
nucleus of a sample of three LINER galaxies, obtained from archival HST/STIS
long-slit spectra. We found that, while for the elliptical galaxy NGC 5077, the
observed velocity curves are consistent with gas in regular rotation around
the galaxy's center, this is not the case for the two remaining objects.
By modeling the surface brightness distribution and rotation curve from
the emission lines in NGC 5077, we found that the observed
kinematics of the circumnuclear gas can be accurately reproduced by adding to
the stellar mass component a black hole mass of
(uncertainties at a 1
level);
the radius of its sphere of influence (
)
is
well-resolved at the HST resolution. The BH mass estimate in NGC 5077 is in
fairly good agreement with both the
(with an upward
scatter of
0.4 dex) and
correlations (with an upward
scatter of 0.5 dex in the Tremaine et al. form and essentially
no scatter using the Ferrarese et al. form) and provides further support for
the presence of a connection between the residuals from the
correlation and the bulge effective radius. This
indicates the presence of a black hole's ``fundamental plane'' in the
sense that a combination of at least
and
drives the
correlations between
and host bulge properties.
Key words: black hole physics - galaxies: active - galaxies: bulges - galaxies: nuclei - galaxies: kinematics and dynamics
It is now clear that the presence of a supermassive black hole (SMBH)
is a common, if not universal, feature in the center of galaxies. In fact,
since active galactic nuclei (AGNs) are thought to be powered by mass
accretion onto an SMBH, the high incidence of low-luminosity AGN activity in
nearby galaxies (Barth et al. 1998; Maoz et al. 1995; Braatz et al. 1997; Ho et al. 1997b; Heckman 1980; Barth et al. 1999; Nagar et al. 2002; Ho et al. 1997a) has led to the conclusion that a significant fraction of
galaxies in the Local Universe must host SMBH.
This conclusion is now supported by direct measurements of SMBH masses
in the centers of nearby galaxies obtained with different techniques
(see Ferrarese & Ford 2005, for a review).
These measurements indicate that the BH mass
is related to
the properties of the host galaxy, such as bulge luminosity
and mass
(Kormendy & Richstone 1995; Magorrian et al. 1998; Marconi & Hunt 2003), light
concentration (Graham & Driver 2007; Graham et al. 2001), and bulge velocity dispersion
(Tremaine et al. 2002; Ferrarese & Merritt 2000; Gebhardt et al. 2000).
The existence of any correlations between
and host
bulge properties supports the idea that the growth of SMBHs and
the formation of bulges are closely linked (Silk & Rees 1998; Haehnelt & Kauffmann 2000).
This has profound implications for the process of galaxy formation and
evolution. Moreover, SMBH mass estimates inferred via the above correlations,
when more direct methods are not feasible, enter into a variety of important
studies spanning from AGNs physics to the coeval formation and
evolution of the host galaxy and its nuclear black hole.
Table 1: Sample of galaxies and STIS data.
These results need, however, to be further investigated by increasing the
number of accurate BH mass determinations in nearby galactic nuclei
to set these correlations on a stronger statistical basis.
In particular, such a study has the potential of establishing the precise
role of the various host galaxy's parameters in setting the resulting BH mass.
To date, reliable SMBH detections have been obtained for a limited number of
galaxies (30, Ferrarese & Ford 2005), with the bulk of
estimates in the range of
.
To add reliable new points to the
- host galaxy's properties
planes is then a fundamental task for future developments of astronomical
and physical studies.
One widely applicable and relatively simple method of detecting BHs is based on gas kinematics (e.g. Barth et al. 2001; Ferrarese et al. 1996; Macchetto et al. 1997; Harms et al. 1994), through studies of emission lines from circumnuclear gas disks, provided that the gas velocity field is not significantly influenced by non gravitational motions. However, the purely gravitational kinematics of the gas can be established a posteriori from successful modeling of the gas velocity field under the sole influence of the stellar and black hole potential.
The Space Telescope Imaging Spectrograph (STIS) onboard
is still
the most suitable instrument for such studies as it provides a high
angular resolution (
)
in the optical spectral region.
In this band brighter emission lines are found with respect to the infrared,
the only band accessible at high resolution with ground-based adaptive optics
telescopes. The wealth of unpublished data contained in STIS archives
represents an extraordinary and still unexplored resource. With the aim of
finding galaxy candidates to provide a successful SMBH mass measurement,
we performed a systematic search for unpublished data in the
STIS archive.
In this paper we present the results obtained for a sample of three LINER
galaxies. The galaxies were observed with STIS on
during Cycle 7
under Proposal ID 7354 and were part of a larger sample of eight selected
objects. The results on NGC 3998 have already been published
(De Francesco et al. 2006, hereafter Paper I). In a forthcoming paper, we will complete
the proposal targets and discuss the relation between BH mass, host galaxy
properties, and nuclear activity. Table 1 lists the galaxies and
their main physical properties. Basic data are from the Lyon/Meudon
Extragalactic Database (HyperLeda) or NASA/IPAC Extragalactic Database (NED).
Distances are calculated with
km s-1 Mpc-1 and
are corrected for Local Group infall onto Virgo.
The paper is organized as follows. In Sect. 2 we present HST/STIS data and the reduction that lead to the results described in Sect. 3. In Sect. 4 we model the observed emission-line rotation curve for NGC 5077 and show that the dynamics of the circumnuclear gas can be accurately reproduced by circular motions in a thin disk when a point-like dark mass is added to the stellar potential. Our results are discussed in Sect. 5, and summarized in Sect. 6.
The three galaxies considered were observed with STIS on
with the G750M grating and the
slit.
Data were acquired at different slit positions, following a
perpendicular-to-slit pattern with a step of 0
1 and the central slit
centered on the nucleus.
The spectra obtained for each source, NUC for the nuclear slit,
N1-N
(to North), and S1-S
(to South)
for the off-nuclears, were retrieved from the public archive.
Table 1 lists the number of slit positions,
the orientation of the slit (from north to east), the exposure time for each
positioning, and the observation date for the galaxies of the sample.
The data were obtained with a
on-chip binning of the detector pixels
and automatically processed through the standard
pipeline
to perform the steps of bias and dark subtraction, applying the flat field
and combining the two sub-exposures to reject cosmic-ray events.
The data were then wavelength and flux calibrated with conversion to
heliocentric wavelengths and absolute flux units and rectified for the
geometric distortions. The 2-D spectral image obtained for each slit
position has a spatial scale of 0
0507 pixel-1 along the slit,
a dispersion of
Å pixel-1, and a
spectral resolution of
,
covering the rest
frame wavelength range 6480-7050 Å.
For each spectrum we selected the regions containing the lines of interest.
The lines were fitted, row by row, along the dispersion direction, together
with a linear continuum, with Gaussian functions using the task SPECFIT in
STSDAS/IRAF. All emission lines present in the spectra (H,
[N II]
6548, 6583 and [S II]
6716, 6731) were
fitted simultaneously with the same velocity and width and with the relative
flux of the [N II] lines kept fixed to 0.334.
The assumption relative to the sharing of the same kinematics for the emission
lines will result in average kinematical quantities, weighted with the line
surface brightness
.
In the regions where the signal-to-noise ratio (SNR) was insufficient, the
fitting was improved by co-adding two or more pixels along the slit direction.
As an example of the quality of data, Fig. 1 shows the spectrum of
NGC 5077, the only galaxy of the group with a marginal detection of a broad
H
component, at two different positions along NUC slit.
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Figure 1:
Nuclear spectra of NGC 5077: at the slit center position
( upper panels), showing the possible presence of a weak broad H![]() ![]() |
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The results obtained from the fitting procedure for the three galaxies are shown in Figs. 2 through 4, where we plot the kinematical quantities, central velocity, and velocity dispersion, together with the surface brightness of the emission line with the best SNR at each location along the slit. The position-velocity diagram for the off-nuclear with the best quality of data is also reproduced in the upper panels of Figs. 2 and 4 for two sources of the program. In the following we discuss the results obtained for each galaxy of the sample.
The velocity curve on the nuclear slit shows a large-scale rotation with redshift at the negative space values (NE region) and blueshift at the positive (SW region) (Fig. 2). The same trend is observable in the off-nuclear slits, with almost the same values of velocity gradients. However, the velocity gradient is reversed at the very center, suggesting the presence of a counter-rotating nuclear gas disk.
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Figure 2: Upper panel: velocity curve from the off-nuclear slit with the best quality of data. Lower panels: velocity, surface brightness, and velocity dispersion along NUC slit. Surface brightness is in units of 10-15 erg s-1 cm-2 arcsec-2. Positions along the slit are relative to the continuum peak. |
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For the elliptical galaxy NGC 5077, the observed velocity curves are
apparently consistent with gas in regular rotation around the galaxy's center.
The velocity curve in the central slit, NUC (Fig. 3, central panel),
has a full amplitude of 400
and shows a general reflection
symmetry: starting from the center, the velocity rises rapidly on both sides
by
200
reaching a peak at
from the center.
This trend is followed by a small decrease and a substantially constant value
at larger radii. Line emission and velocity dispersion are strongly peaked and
smoothly decrease from the nucleus outwards.
The behavior seen in the off-nuclear slits is qualitatively similar to what is seen at the NUC location (Fig. 3, left and right panels), but with smaller velocity amplitude and, more important, a less extreme velocity gradient. Both the amplitude and gradient decrease at increasing distance of the slit center from the nucleus, with a behavior characteristic of gas rotating in a circumnuclear disk.
Ground-based photometric and kinematical studies (Demoulin-Ulrich et al. 1984; Bertola et al. 1991)
show that NGC 5077 exhibits a gaseous disk with the major axis roughly
orthogonal to the galaxy photometric major axis (
).
The gas isophotes show twisting and a marked warp on the W side at
(Caon et al. 2000).
The gas has a fairly symmetric and smooth rotation curve at
(
major axis of the ionized gas distribution) with a half amplitude of
270
at
.
At
,
the stellar
rotation curve exhibits a counter-rotating core (
). Along
this axis, the gas rotates in the same direction as the stellar nucleus and
shows a small-scale central velocity plateau.
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Figure 3: Velocity, surface brightness, and velocity dispersion along the off-nuclear slit position N1 ( left panel), NUC ( central panel), and S1 ( right). Positions along the slits are relative to the continuum peak, positive values are NW. |
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The velocity curves for this galaxy are complex (see Fig. 4).
On the nuclear slit, the velocity apparently shows a general rotational trend,
with redshift on the left and blueshift on the right side of the diagram.
The same large-scale rotation is observable on the off-nuclear slit
positions. Smaller scale high-amplitude (200
)
velocity
oscillations are also clearly visible.
In the SW region at
the position-velocity diagrams of
NUC and the adjacent S1 slit show a trend that is inconsistent with gas
in regular rotation around the galaxy's center (see Fig. 4,
second upper panel). In this region the velocity curves diverge, reaching a
separation of
300
at
.
The over-plot of the
position velocity diagrams suggests an expanding bubble of gas.
Summarizing, we find that NGC 5077 shows a line emission consistent with a circumnuclear gas disk in Keplerian rotation around the galaxy's center. For the remaining two objects, the trend of their velocity curves cannot be ascribed to the regular rotation of a nuclear gas disk. The position-velocity diagrams of IC 989 indicate the presence of a counter-rotating gas component. Modeling this configuration would require (at least) a warped geometry for the disk, which cannot be constrained with the present data. By these considerations, only NGC 5077 is a suitable candidate for providing a successful SMBH mass measurement.
Our modeling code, described in detail in Marconi et al. (2003), was used to fit
the observed rotation curves of NGC 5077. The code computes the rotation
curves of the gas assuming that the gas is rotating in circular orbits within
a thin disk in the galaxy potential. The gravitational potential has two
components: the stellar potential (whose mass distribution will be determined
in Sect. 4.1), characterized by its mass-to-light ratio and a dark
mass concentration (the black hole), spatially unresolved at HST+STIS
resolution and characterized by its total mass
.
In computing the rotation curves, we take into account the finite spatial
resolution of the observations, and the intrinsic surface brightness
distribution (ISBD) of the emission lines and we integrate over the slit
and pixel area. The adopted HST+STIS point spread function (PSF) is obtained
by fitting with three Gaussians the Tiny Tim (Krist & Hook 1999) model PSF
calculated at 6700 Å without the Lyot-stop, according to the procedure
suggested by Dressel (2006). The
is minimized to determine the
free parameters using the downhill simplex algorithm by Press et al. (1992).
To assess the contribution of stars to the gravitational potential
in the nuclear region, we derived the stellar luminosity density from the
observed surface brightness distribution. We reconstructed the galaxy light
profile using a WFPC2 F547M (V band) image retrieved from the public
archive (Fig. 5).
Based on WFPC2 F702W (R band) images, Tran et al. (2001) found a filamentary
dust structure in NGC 5077, with position angle of the major axis of the main
dust feature
(at
). Our inspection of
archive images, however, shows that the influence of dust is negligible.
In fact, Tran et al. (2001) derived a mean visual extinction of only
.
We used the IRAF/STSDAS program ELLIPSE to fit elliptical isophotes to the galaxy
(see Fig. 6). Nuclear regions (
)
show the largest
ellipticity variations. At larger radii, ellipticity and position angle show
small variations around the values 0.25 and 10
,
respectively.
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Figure 4: Same as Fig. 2. Second upper panel: over-plot of NUC ( empty squares) and S1 ( filled circles) velocity curves showing the inconsistency of the gas position-velocity diagram with regular rotation of a nuclear gas disk. |
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Figure 5:
Left: V band ( F547M filter) image of
NGC 5077. Right: H![]() ![]() |
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We derived the stars' density profile from the galaxy surface brightness
following the same method described in Paper I when assuming an oblate
spheroid density distribution. Following van der Marel & van den Bosch (1998), the stellar density
distribution was parameterized as
![]() |
Figure 6: Results of the isophotes analysis of the V band image of NGC 5077. Surface brightness is shown in the top panel (in units of erg s-1 cm-2 Å-1 arcsec-2), and the galaxy's ellipticity and position angle are shown in the middle and bottom panels, respectively. |
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The observed kinematical quantities are averages over apertures defined by the slit width and the detector pixel size along the slit. The model fitting to the observed kinematical quantities thus depends on the intrinsic emission-line surface-brightness distribution, which is the weight for the averaging process, and on the following parameters:
A crucial issue for modeling the gas kinematics is the inclination of the
nuclear gas disk, as this is strongly coupled with the black hole mass and
.
In an oblate spheroid, the stable orbits of the gas are
coplanar with the principal plane of the potential, and it is possible to
directly associate the galaxy inclination and line of nodes with those of
the circumnuclear gas. However, the potential shape is not determined well
enough by the isophotal fitting down to the innermost regions of
the galaxy, and it is possible that a change of principal plane might occur
at the smallest radii, in particular within the sphere of influence of a
supermassive black hole. We then performed a
minimization for
different values of i, namely
,
allowing
all other parameters to vary freely, including those describing the
intrinsic line surface brightness distribution. Due to the sensitivity of
the velocity dispersions to the ISBD modeling and to other computational
problems (i.e. a coarse sampling), as shown by Marconi et al. (2006), we
decided to initially restrict the kinematical fitting only to the velocity
curves. We show in Sect. 4.2.1 that including the velocity
dispersions in the fitting procedure only has a marginal effect on our
results.
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Figure 7: Fit to the surface brightness profile obtained from an oblate spheroid stellar density distribution. |
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From the best fits obtained at varying gas disk inclination, we quoted the
goodness of the fits only with respect to the velocity curves, since we are
interested in the kinematical model that reproduces the position-velocity data
best. Excluding the contribution to the
of the ISBD fit is a
conservative choice for our data, as we verified that quoting the global fits
would narrow the ranges of acceptable model parameters. The overall
best-fitting model, presented in Fig. 8, is obtained for
,
,
,
and an angle from the slits to the line of nodes of 34
(i.e. offset by
25
from the ground-based measurements). Table 2 shows the
best kinematical model parameters, together with the corresponding
reduced value (
/d.o.f. with d.o.f. = 16 degrees of
freedom). Apparently, the best fit slightly underpredicts the large-scale
velocity points. We then tested the effect of allowing a higher maximum value
of the mass-to-light ratio, related to a different choice of the IMF. A fit
was performed by adopting the value 13.78 as limit to
,
corresponding to the oldest stellar population and a giant-dominated IMF.
Indeed, the best fit obtained (with
)
reproduces the
observed velocities better at large radii. However, the BH mass does not
change significantly, resulting in log
only 0.02 lower than our
previous result. We therefore preferred to maintain the constraint on
derived by adopting the standard Salpeter IMF.
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Figure 8: Overall best fit to the rotation curves ( left) with the case of null BH mass (dashed line) superposed on the central slit. Corresponding fit to the line surface brightness distribution ( right). From upper to bottom panel: N1, NUC, S1. |
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Table 2: Overall best-fit parameters.
The value of minimum
The case of no black hole mass is also shown in Fig. 8 for the
central slit. This model (obtained by constraining
and
to the same value of the best fit) predicts a velocity gradient
that is too shallow with respect to the data, particularly in the central
region
,
with a correspondingly unacceptable value of
(properly rescaled to the overall best fit).
To evaluate the uncertainty associated to the black hole mass estimate, we
explored its variation with respect to the parameter that is more strongly
coupled to it, i.e. the mass-to-light ratio
(having already
considered the dependence on orientation). The uncertainty on
associated to changes in
has been estimated by building a
grid in the
vs.
parameter
space. At each point of the grid, described by a fixed pair of
and
values, we obtained the best fit model allowing all
other parameters to vary freely and derived the corresponding
value (properly rescaled). The result of this analysis at
is
presented in Fig. 10. The 1
range of the black hole mass at
this disk inclination is
,
reported in the error bar in Fig. 9.
If we conservatively adopt the same fractional uncertainties on
,
associated to variations in
,
for the allowed disk
inclinations, we obtain a global range of acceptable black hole mass of
at a 1
level.
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Figure 9:
Upper panel: best fit values of
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 10:
![]() ![]() ![]() ![]() ![]() |
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At this point in our analysis we tested the influence on the above
results of including the velocity dispersions in the fitting procedure.
The observed ionised-gas velocity dispersions are fairly large in
NGC 5077, reaching almost 400
in the nuclear slit.
Velocity dispersions larger than expected from unresolved rotation
could be an indication of non circular motions that could invalidate
the BH mass estimate (Cappellari et al. 2002; Barth et al. 2001; Verdoes Kleijn et al. 2002,2000).
However, in the case of NGC 5077, rotational and instrumental broadening
is sufficient to reproduce the behaviour of velocity dispersions.
First of all, by adopting the best fit parameter set (Table 2), we obtained the velocity dispersion distribution shown in Fig. 11. The observed velocity dispersions are reproduced acceptably well by the model, with only a small mismatch of observed and model peak positions. Thus the nuclear rise of the velocity dispersion is accounted for as unresolved rotation by the fitting model.
Furthermore, we repeated the
minimization at
,
this
time by including the observed velocity dispersions in the fitting procedure
(with no free parameters added). The best fit obtained is shown in
Fig. 11. An improvement of the match with observed values
is obtained, while there is a slight worsening of the fit to the velocity
curves, with
(scaled to the overall best fit) = 1.08.
The effect of including the line widths in the analysis results in
increasing the BH mass by only
24% to
.
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Figure 11:
Velocity dispersion distribution expected from the
overall best fit model (solid line) at
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The model fitting performed for NGC 5077 indicates that the kinematics
of gas in its innermost regions is described correctly as circular motions
in a thin disk when a point-like dark mass of
is added to the galaxy potential.
We can now explore how BH mass relates to the properties of the host
galaxy, including spheroid (bulge) mass (Marconi & Hunt 2003), stellar velocity
dispersion (Tremaine et al. 2002; Ferrarese & Ford 2005), and light concentration
(Graham & Driver 2007).
Following Marconi & Hunt (2003), we used the virial mass
,
with k = 5 (Cappellari et al. 2006) to determine the
bulge mass of NGC 5077. We found discrepant values for the effective radius
of the bulge,
,
in the literature. The values were derived through
different methods (i.e. isophotal fitting, photometric aperture growth curves)
and are 15
4 (Bender et al. 1989), 15
9 (Sánchez-Portal et al. 2004), 17
3
(Poulain & Nieto 1994), 19
(Bertola et al. 1991), 22
1 (Trujillo et al. 2004),
22
8 (de Vaucouleurs et al. 1991, RC3), and 25
(Burstein et al. 1987).
We decided to adopt the average of the above values,
as the effective bulge radius of NGC 5077.
At the adopted distance of the galaxy, this value corresponds to
kpc.
The stellar velocity dispersion determinations we found in the literature
are
(Davies et al. 1987,
aperture),
(Carollo et al. 1993,
and
apertures), and
(Caon et al. 2000,
aperture). All the above values refer to the very central
regions of the galaxy, corresponding to equivalent circular apertures
(see Cappellari et al. 2006) from
1
to 1
5. We then
normalized the values of the central velocity dispersion to a circular
aperture of radius equal to the adopted
,
following the formula
for aperture corrections by Cappellari et al. (2006). The average of these
normalized values leads to
.
Using this value of
as an approximation for
,
we obtained the value
for the bulge mass. From the correlation of Marconi & Hunt (2003),
the expected
for NGC 5077 is
,
in agreement within a factor
2.3, with our determination
(see Fig. 12).
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Figure 12:
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For the correlations between BH mass and central stellar velocity
dispersion, one obtains
for NGC 5077 adopting
the form by Tremaine et al. (2002) (see Fig. 13, upper panel), a
factor 3.4 lower than our estimate. We also compared our measurement with
the expected value from the
relation derived by
Ferrarese & Ford (2005)
,
,
in full agreement with
our estimate (see Fig. 13, bottom panel).
Conversely, the BH mass expected for NGC 5077 on the basis of its correlation
with the Sérsic concentration index (from Trujillo et al. 2004) is a
factor lower than our estimate when using
the linear
Sérsic index correlation (Graham & Driver 2007)
and a factor 3 lower when using the quadratic form they proposed.
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Figure 13:
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Marconi & Hunt (2003) noticed that
is separately correlated with
both
and
.
This is shown by the weak correlation between
the residuals of the
correlation with
reproduced here in Fig. 14 for the Tremaine at al.
form
. Our determinations of the black hole mass in
NGC 5077 and in NGC 3998 (Paper I) support this idea. Unlike NGC 3998,
which has one of the lowest values of
among galaxies with
measured
(0.85 kpc) and shows a negative residual from the
correlation, NGC 5077 has an intermediate
value (3.6 kpc) and show a small but positive residual
(see Fig. 14). In the same sense, but with a larger positive
residual, there is the result found by Capetti et al. (2005) for NGC 5252, a
galaxy with quite a large effective radius (9.7 kpc). This indicates the
presence of a black hole's ``fundamental plane'' in the sense that a
combination of at least
and
drives the correlations
between
and the bulge properties. The physical implications
of these results will be discussed in a forthcoming paper, when new direct
BH mass measurements are presented, in order to base our discussion on a
statistically more significative sample of
determinations.
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Figure 14:
Residuals from the
![]() ![]() ![]() |
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We have presented results from a gas kinematics study in the nucleus of three nearby LINER galaxies: IC 989, NGC 5077, and NGC 6500 using archival HST/STIS spectra. Only in the case of NGC 5077 does the nuclear velocity curves appear to be associated with gas in regular rotation. For IC 989 our results indicate an inner counter-rotating gas system, while for NGC 6500 the complex trend in the velocity curves suggests a nuclear expanding bubble.
We used our modeling code to fit the observed [N II]6583
surface brightness distribution and velocity curve of NGC 5077.
The dynamics of the rotating gas can be accurately reproduced by motions
in a thin disk when a compact dark mass of
is added to the stellar mass
component. Furthermore, the black hole in NGC 5077 has a sphere of
influence radius,
,
of
62 pc (
), well-resolved at the HST
resolution (2
).
For what concerns the connections of this BH mass estimate with the
properties of the host galaxy, the
value for NGC 5077 is
in good agreement (within a factor of 2.3) with the
correlation between BH and host bulge mass. The black hole mass predicted by
the
correlation is a factor of 3.4 lower than our measure,
adopting the relation found by Tremaine et al. (2002) and in excellent agreement
using the parameterization by Ferrarese & Ford (2005).
This result, in conjunction with the previous results for NGC 3998 (Paper I),
strengthens the possibility of a connection between the residuals from the
relation and the bulge effective radius. While NGC 3998,
indeed, has one of the lowest values of
among galaxies with
measured
and shows a negative residual, NGC 5077 has a larger
effective radius and shows a small positive residual. We also recently showed
that the same result was found for the Seyfert galaxy NGC 5252: a larger
effective radius corresponds in this galaxy to a still larger positive
residual.
Apparently, only with a combination of at least
and
is
it possible to account for the correlations between
and other
bulge properties, indicating the presence of a black hole's ``fundamental
plane''. Clearly, the number of direct black-hole mass measurements must be
further increased, together with precise determinations of
and
,
to test these conclusions on astronger statistical basis. In a
forthcoming paper we will present new BH mass determinations and discuss the
physical implications of our results.
Acknowledgements
This publication makes use of the HyperLeda database, available at http://leda.univ-lyon1.fr, and of the NASA/IPAC Extragalactic Database (NED) operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.