Spectroastrometry of rotating gas disks for the detection of supermassive black holes in galactic nuclei. II. Application to the galaxy Centaurus A (NGC 5128)

Abstract

We measure the black hole mass in the nearby active galaxy Centaurus A (NGC
5128) using a new method based on spectroastrometry of a rotating gas disk. The
spectroastrometric approach consists in measuring the photocenter position of
emission lines for different velocity channels. In a previous paper we focused
on the basic methodology and the advantages of the spectroastrometric approach
with a detailed set of simulations demonstrating the possibilities for black
hole mass measurements going below the conventional spatial resolution. In this
paper we apply the spectroastrometric method to multiple longslit and integral
field near infrared spectroscopic observations of Centaurus A. We find that the
application of the spectroastrometric method provides results perfectly
consistent with the more complex classical method based on rotation curves: the
measured BH mass is nearly independent of the observational setup and spatial
resolution and the spectroastrometric method allows the gas dynamics to be
probed down to spatial scales of ~0.02", i.e. 1/10 of the spatial resolution
and ~1/50 of BH sphere of influence radius. The best estimate for the BH mass
based on kinematics of the ionized gas is then log(MBH (sin i)^2/M\odot)=7.5
\pm 0.1 which corresponds to MBH = 9.6(+2.5-1.8) \times 10^7 M\odot for an
assumed disk inclination of i = 35deg. The complementarity of this method with
the classic rotation curve method will allow us to put constraints on the disk
inclination which cannot be otherwise derived from spectroastrometry. With the
application to Centaurus A, we have shown that spectroastrometry opens up the
possibility of probing spatial scales smaller than the spatial resolution,
extending the measured MBH range to new domains which are currently not
accessible: smaller BHs in the local universe and similar BHs in more distant
galaxies.

Full text

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arXiv:1110.0936v1 [astro-ph.CO] 5 Oct 2011
Astronomy & Astrophysics manuscript no. specast2˙8
October 6, 2011
c ? ESO 2011
Spectroastrometry of rotating gas disks for the detection of
supermassive black holes in galactic nuclei.
II. Application to the galaxy Centaurus A (NGC 5128).
A. Gnerucci1, A. Marconi1, A. Capetti2, D. J. Axon3,4, A. Robinson3, N. Neumayer5,6
1Dipartimento di Fisica e Astronomia, Universit` a degli Studi di Firenze, Firenze, Italy
e-mail: gnerucci@arcetri.astro.it, marconi@arcetri.astro.it
2INAF - Osservatorio Astronomico di Torino, Strada Osservatorio 20, 10025 Pino Torinese, Italy
e-mail: capetti@oato.inaf.it
3Physics Department, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, NY 14623, USA
e-mail: djasps@rit.edu, axrsps@rit.edu
4School of Mathematical & Physical Sciences, University of Sussex, Falmer, Brighton, BN2 9BH, UK
5Excellence Cluster Universe, Technische Universit¨ at M¨ unchen, Boltzmannstr. 2, 85748, Garching bei M¨ unchen, Germany
e-mail: nadine.neumayer@universe-cluster.de
6European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching bei M¨ unchen, Germany
e-mail: nneumaye@eso.org
Received ; accepted
ABSTRACT
Wemeasure the black hole mass in the nearby active galaxy Centaurus A (NGC 5128) using a new method based on spectroastrometry
of a rotating gas disk. The spectroastrometric approach consists in measuring the photocenter position of emission lines for different
velocity channels. In a previous paper we focused on the basic methodology and the advantages of the spectroastrometric approach
with a detailed set of simulations demonstrating the possibilities for black hole mass measurements going below the conventional spa-
tial resolution. In this paper we apply the spectroastrometric method to multiple longslit and integral field near infrared spectroscopic
observations of Centaurus A. We find that the application of the spectroastrometric method provides results perfectly consistent with
the more complex classical method based on rotation curves: the measured BH mass is nearly independent of the observational setup
and spatial resolution and the spectroastrometric method allows the gas dynamics to be probed down to spatial scales of ∼ 0.02′′,
i.e. 1/10 of the spatial resolution and ∼ 1/50 of BH sphere of influence radius. The best estimate for the BH mass based on kinematics
of the ionised gas is then log(MBHsini2/M⊙) ≃ 7.5 ± 0.1 which corresponds to MBH= 9.6+2.5
nation of i = 35◦. The complementarity of this method with the classic rotation curve method will allow us to put constraints on the
disk inclination which cannot be otherwise derived from spectroastrometry. With the application to Centaurus A, we have shown that
spectroastrometry opens up the possibility of probing spatial scales smaller than the spatial resolution, extending the measured MBH
range to new domains which are currently not accessible: smaller BHs in the local universe and similar BHs in more distant galaxies.
−1.8× 107M⊙for an assumed disk incli-
Key words. Techniques: high angular resolution - Techniques: spectroscopic - Galaxies: active - Galaxies: individual: Centaurus A,
NGC 5128 - Galaxies: kinematics and dynamics - Galaxies:nuclei
1. Introduction
One of the fundamental open questions of modern astrophysics
is understanding the formation and evolution of the complex
structures that characterize the present-day universe such as
galaxies and clusters of galaxies. Understanding how galaxies
formed and how they become the complex systems we observe
today is therefore a major theoretical and observational effort.
There is now strong evidence for the existence of
a connection between supermassive black holes (hereafter
BHs), nuclear activity and galaxy evolution revealing the
so-called co-evolution of black holes and their host galax-
ies. Such evidence is provided by the discovery of “relic”
BHs in the center of most nearby galaxies, and by
the tight scaling relations between BH masses (MBH
106− 1010M⊙) and the structural parameters of the host
spheroids like mass, luminosity and stellar velocity disper-
∼
Send offprint requests to: A. Gnerucci
sion (e.g. Kormendy & Richstone 1995, Gebhardt et al. 2000,
Ferrarese & Merritt 2000, Marconi & Hunt 2003, H¨ aring & Rix
2004, Ferrarese & Ford 2005, Graham 2008). Moreover, while
it has long been widely accepted that Active Galactic Nuclei
(AGN) are powered by accretion of matter on a supermas-
sive BH, it has recently been possible to show that BH
growth is mostly due to accretion of matter during AGN ac-
tivity, and therefore that most galaxies went through a phase
of strong nuclear activity (Soltan 1982, Yu & Tremaine 2002,
Marconi et al. 2004). It is believed that the physical mechanism
responsible for this coevolution of BHs an their host galax-
ies is probably the feedback by the AGN, i.e. the accreting
BH, on the host galaxy (Silk & Rees 1998, Fabian & Iwasawa
1999, Granato et al. 2004, Di Matteo et al. 2005, Menci 2006,
Bower et al. 2006).
The clearest sign of co-evolution, the scaling relations be-
tween BH masses and host galaxy properties should be then se-
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A. Gnerucci et al.: Spectroastrometry of rotating gas disks: II. Application to Centaurus A.
curedbyincreasingnumber,accuracyandmass rangeofexisting
measurements.
Supermassive BHs are detected and their masses measured
by studying the kinematics of gas or stars in galaxy nuclei and,
currently, there are about ∼ 50 BH mass measurements most
of which in the ∼ 107− 109M⊙range (e.g. Sani et al. 2010).
The majority of these measurements are made with longslit
spectroscopy, but the development in recent years of Integral
Field Unit (hereafter IFU) spectrographs has allowed some im-
provements. IFUs have proven to be powerful tools to study
galaxy dynamics as they provide two dimensional coverage of
the source without the restrictions of longslit spectrographs,
also plagued by unavoidable light losses. Recent studies have
presented measurements of BH masses in galactic nuclei us-
ing integral field spectroscopy of gas or stellar spectral features
(e.g. Davies et al. 2006, Nowak et al. 2007, Nowak et al. 2010
,Krajnovi´ c et al. 2007, Krajnovi´ c et al. 2009, Cappellari et al.
2009, Neumayer et al. 2010, Rusli et al. 2010). Regardless of
the use of longslit or IFU spectrographs, one crucial issue in
BH mass measurements is spatial resolution: this must be small
enough to spatially resolve the regions where the gravitational
effects of the BH can be disentangled from those of the host
galaxy. Even with the advent of Adaptive Optics (AO) assisted
observations the best spatial resolution achievable are of the or-
der of ∼ 0.1′′which corresponds to ∼ 10 pc at a distance of 20
Mpc.
This paper is the second in a series dealing with gas kine-
matical BH mass measurements based on a new method. This
method, based on spectroastrometry, provides a simple but ac-
curate way to estimate BH masses and partly overcomes the
limitations due to spatial resolution which plague the “classi-
cal” gas (or stellar) kinematical methods, either using longslit or
IFU spectra. In the first paper of the series (Gnerucci et al. 2010,
hereafter Paper I) we illustrated how the technique of spectroas-
trometry can be used to measure black hole masses focusing on
the basis of the spectroastrometric approach and showing with
an extended and detailed set of simulations its capabilities and
limits. While we mostly focussed on the application of spec-
troastrometry to longslit spectra, we also showed the technique
can be extended to integral field spectra.
In this paper we apply the spectroastrometric method devel-
oped in Paper I to estimate the BH mass using real data. As a
benchmark for our spectroastrometric approach to the study of
local BHs, we selected the galaxy Centaurus A (NGC 5128) be-
cause it has been extensively studied with the gas kinematical
method showing that the gas is circularly rotating and that BH
mass and other free parameters are well constrained from the
observed kinematics. Moreover both longslit and IFU data are
available and this allows a direct comparison of the application
of spectroastrometry to different kinds of data.
In Sect. 2 we recap the existing measurements of BH mass
forCentaurusA. InSect. 3 we brieflyresumetheresults of Paper
I on the applicationof spectroastrometryto rotatinggas disks for
the detection of the central BH. In Sect. 4 we apply the method
to the longslit ISAAC spectra of the nucleus of Centaurus A. In
Sect. 5 we applythemethodto integralfield SINFONI spectraof
the nucleus of Centaurus A, both with and without the assistance
of Adaptive Optics. Finally, in Sect. 6 we compare and discuss
the results fromthe differentdatasets, drawingsomeconclusions
on the reliability and accuracy of the method.
2. Previous measurements of the black hole mass
in Centaurus A
Existing measurements of the black hole mass in Centaurus A
are summarized in Fig. 1 where the various measurements are
shown as a function of the spatial resolution of the observations
(Full Width at Half Maximum - FWHM - of the Point Spread
Function - PSF) used for each measurement. In that Figure we
also show the measurement obtained in this paper as a function
of the angular resolution actually obtained with the spectroas-
trometric technique (i.e. a fraction of the PSF FWHM as will be
discussed in detail in the following).
The supermassive black hole in Centaurus A was first de-
tected and its mass measured with a near infrared gas kinemat-
ical study using seeing limited spectra obtained with ISAAC
at the ESO VLT (Marconi et al. 2001). Subsequent higher spa-
tial resolution gas kinematical studies based on longslit spec-
troscopy were performedusing STIS on the HST (Marconi et al.
2006) and AO assisted observations with NAOS-CONICA
at the ESO VLT H¨ aring-Neumayeret al. (2006). More re-
cent studies based on integral field spectroscopy were per-
formed by Krajnovi´ c et al. (2007) using seeing limited obser-
vations with CIRPASS at the Gemini South telescope and by
Neumayer et al. (2007) using AO-assisted observationsobtained
with SINFONIat VLT.On theotherhand,Silge et al. (2005) and
Cappellari et al. (2009)performednearinfraredstellar kinemati-
cal studies based, respectively, on seeing limited longslit spectra
(GNIRS at Gemini South) and AO-assisted integral field spectra
(SINFONI at the ESO VLT).
The top panel of Fig. 1 shows the different MBHvalues ob-
tained by the previous authors, spread over almost an order of
magnitude. To understand the origin of these differences, in the
bottom panel of Fig. 1 we plot the MBHsin2i values, i.e. the val-
ues constrained by the observed velocity fields and not depen-
dent on the inclination of the rotating gas disks. In the case of
the stellar kinematical studies, the authors assumed edge on ax-
isymmetric potentials, therefore no correction is made to obtain
MBHsin2i: Silge et al. (2005) and Cappellari et al. (2009) dis-
cuss the systematic uncertainties associated with their assump-
tions of edgeon models. Afterremovingthe inclinationeffect all
gaskinematicalmeasurementsshowstatistical fluctuationwithin
two times the respective sigma; as noted several times, the incli-
nation of the rotating disk is an important source of uncertainty
in gas kinematical measurements.
3. The spectroastrometric measurement of black
holes masses
In Paper I (Gnerucci et al. 2010) we illustrated how the tech-
nique of spectroastrometry can be used to measure the black
hole masses at the center of galaxies. In that paper we focused
in explainingthe basis of the spectroastrometricapproachand in
showing with an extended and detailed set of simulations how
this method is able to probe the principal dynamical parameters
of a nuclear gas disk.
The spectroastrometrical method (see Bailey 1998) consists
in measuringthephotocenterof emissionlines in differentwave-
length or velocity channels. It has been used by several authors
to study pre-mainsequence binaries and the presence of inflows,
outflowsorthediskstructureofthegassurroundingpre-mainse-
quencestars (Takami et al. 2003; Baines et al. 2004; Porter et al.
2004, 2005, Whelan et al. 2005). We compared this technique
with the standard method for gas kinematical studies based on
the gas rotation curve and showed that the two methods have
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A. Gnerucci et al.: Spectroastrometry of rotating gas disks: II. Application to Centaurus A.
Fig.2. Continuum subtracted ISAAC spectrum (slit PA1) extracted at the position of the continuum peak. Solid red line: simultane-
ous fit of all four lines. Dashed red lines: the deblended Paβ and [FeII] components.
Fig.1. BH mass measurements for Centaurus A from the
works mentioned in the text (top panel) and the correspond-
ing MBHsin2i values (bottom panel) as a function of the spatial
resolution of the observations of each measurement (see text).
Note thatthe uncertaintiesonthe measurementbyMarconi et al.
(2001) are reduced because they were includinguncertainties on
i.
complementary approaches to the analysis of spectral data (i.e.
the former measures mean positions for given spectrum veloc-
ity channels while the latter measures mean velocities for given
slit position channels). The principal limit of the rotation curves
methodresidesintheabilitytospatiallyresolvetheregionwhere
the gravitational potential of the BH dominates with respect to
the contribution of the stars. In Paper I we showed that the fun-
damental advantage of spectroastrometry is its ability to provide
information on the galaxy gravitational potential at scales sig-
nificantly smaller than the spatial resolution of the observations
(∼ 1/10, and better as we will also show in the present work).
The general principle of the spectroastrometric method and
its capability in overcoming the spatial resolution limit is illus-
trated by the following simple example: consider two point-like
sourceslocatedat adistancesignificantlysmallerthanthespatial
resolution of the observations; these sources will be seen as spa-
tiallyunresolvedwiththeirrelativedistancenotmeasurablefrom
a conventional image. However, if spectral features, such as ab-
sorptionoremissionlines at differentwavelengths,arepresentin
the spectra of the two sources, the light spatial profiles extracted
at these wavelengths will show the two sources separately. From
the difference in centroid positions at these two wavelengths one
can estimate the separation between the two sources even if this
is much smaller that the spatial resolution. This “overcoming”
of the spatial resolution limit is made possible by the “spectral”
separation of the two sources.
For clarity, we summarize here the principal features and the
main steps of the method presented and discussed extensively in
Paper I.
– From the longslit spectrum of a continuum-subtractedemis-
sion line one constructs the “spectroastrometric curve” by
measuring the line centroid along the slit for all wavelength
channels. The “spectroastrometric curve” of the line is given
by the position centroids as a function of wavelength.
– From the simulations presented in Paper I, we showed that
the information about the BH gravitational field is predom-
inantly encoded in the “high velocity” (hereafter HV) range
of the spectroastrometric curve which comprises the points
in the red and blue wings of the line. The HV part of the
line spectrum originates from the gas moving at high veloc-
ities closer to the BH, in the case of Keplerian rotation and
this emission is spatially unresolved. For this reason the HV
part of the line spectrum is not strongly influenced by the
spatial resolution or other instrumental effects like slit losses
or by the intrinsic line flux distribution. On the other hand
“low velocity” emission (hereafter LV) is usually spatially
resolved (i.e. the gas moving at lower velocities is located
farther away from the BH) and this makes the spectroastro-
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A. Gnerucci et al.: Spectroastrometry of rotating gas disks: II. Application to Centaurus A.
metric curve not useful. The HV range of the curve is iden-
tified by measuring the spatial extent of the line emission as
function of wavelength and discarding the central (i.e. LV
range) bins where the line emission becomes broader than
the instrumental spatial resolution.
– By measuring the spectroastrometric curves of a given line
from at least three spectra taken at different slit position an-
gles,onecanobtaina“spectroastrometricmap”ofthesource
on the plane of the sky by geometricallycombiningthe three
curves. In the case of integral field spectra, this step is obvi-
ously not necessary because the spectroastrometric map is
derived directly from the data cubes. In the case of a ro-
tating disk with a radially symmetric line flux distribution
the points of the spectroastrometric map should lie on the
disk line of nodes. However even for IFU data the effect of
slit losses or a non-symmetric line flux distribution can per-
turb the light centroid positions moving them away from the
disk line of nodes. As shown in Paper I and discussed above,
these effects become negligible for the HV range of the map
where the emission is spatially unresolved. In contrast, the
LV points of the map tend to lie away from the line of nodes
in a typical “loop” shape. The final spectroastrometric map
is then obtained by selecting only the HV points.
– One can then estimate the disk line of nodes by a line fitting
of the HV range of the spectroastrometricmap, project those
points on the estimated disk line of nodesand obtainthe disk
rotation curve. Finally, one can apply a simple model fitting
procedure and obtain the parameters determining the gas ro-
tation curve, and in particular the BH mass.
4. Longslit spectra: observations and data analysis
4.1. The data
We use available near infrared spectra of the nucleus of
Centaurus A obtained with ISAAC at the ESO VLT telescope
(see Marconi et al. 2006, for details). Briefly, the spectra were
obtained with a 0.′′3 wide slit and cover a wavelength range
of 1.24 − 1.30µm with a resolving power of λ/∆λ = 10500,
corresponding to a spectral resolution of ∼ 1.2Å at the cen-
tral wavelength (λ=1.274 µm). The spatial scale of the spec-
tra is 0.147′′/pixel along the slit axis and the dispersion is
0.58Å/pixel. The spatial resolution of the spectra is estimated
as ∼ 0.′′5 (FWHM of the PSF). There are three different spectra
characterized by a different slit position angle: the one we will
referto as “PA1”hasa positionangleof32.5◦,“PA2” has−44.5◦
and “PA3” has 83.5◦(see Marconi et al. 2006, for details).
4.2. Analysis of the spectra
In Fig. 2 we display an example of a typical spectrum of
Centaurus A extracted from one pixel along one of the slits:
in particular, this corresponds to the “PA1” continuum sub-
tracted spectrum, extracted at the position of the continuum
peak. Several gas emission lines can be identified: Paβ at ∼
1.284µm, [FeII] and HeI at ∼ 1.281µm, [FeII] at ∼ 1.259µm
and [SIX] at ∼ 1.255µm. The lines used for the gas kinematics
by Marconi et al. (2006) are the Paβ and the [FeII] lines and we
will also concentrate on these.
As clearly visible in the figure, both the Paβ and [FeII] lines
are blended on the blue sides with [FeII]+HeI and [SIX], re-
spectively. Potentially this constitutes a problem in measuring
the spectroastrometric curve because the blended lines will cer-
tainly affect the position of the light centroid along the slit for a
Fig.3. Position velocity diagram of the observed ISAAC spec-
trumatPA1neartothePaβline.Upperpanel:observedspectrum
of the Paβ and [FeII]+HeI complex. Bottom panel: “synthetic”
reconstruction of the deblended Paβ spectrum. The horizontal
dotted line overplotted on each panel represents the continuum
peakposition.Theisophotesdenotethe same valuesin bothpan-
els.
given blue velocity and the position centroid will not be indica-
tive anymore of the mean position of the gas at a given line of
sight velocity.
In order to solve this problem it is necessary to deblend the
lines under examination and therefore we performed a simulta-
neous fit of the 4 lines, each with a Gauss-Hermite function (the
red solid line), at all slit positions along the PA1, PA2 and PA3
slits. Following Marconi et al. (2006) we assume that all lines,
hence Paβ and [FeII], share the same kinematics: in the simul-
taneous fit all lines are constrained to the same velocity, velocity
dispersion and Hermite parameters (h3and h4), while they can
have different line fluxes. Fig. 2 shows an example of such a fit.
To obtain the spectroastrometric curve we considered all fit-
ted profiles of Paβ and [FeII] and we reconstructed synthetic
longslit spectra of the emission lines, cleaned in terms of noise
and blended lines. In Fig. 3 we show an example of one origi-
nal Paβ longslit spectrum compared with its “synthetic” version
where one can notice that the noise has been smoothed away
and the [FeII]+HeI complex has been removed. It should be no-
ticed that whereas we constrained Paβ and [FeII] to the same
kinematics, their fluxes can be different, therefore, in terms of
the spectroastrometricanalysis,the two lines are distinct andcan
still providedifferentresults.Additionallythe“synthetic”recon-
structed spectrum is noise-free because each row represents the
fitted parametric profile but one has to take into account the er-
rorsonthe freeparametersin orderto estimate theerrorsoneach
synthetic pixel counts. Therefore, for each spectral fit, we simu-
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A. Gnerucci et al.: Spectroastrometry of rotating gas disks: II. Application to Centaurus A.
Fig.4. Spectroastrometric curves of the Paβ (black points) and [FeII] (red points) lines (ISAAC spectra) at the three slit position
angles. Left panel: PA1. Central panel: PA2. Right panel: PA3. The dashed vertical lines on each panel represent the limits of the
HV range.
lated 1000 synthetic spectra from 1000 realization of the set of
the five parameters distributed following a pentavariate distribu-
tion with the fit correlation matrix. The flux and error of each
pixel is then estimated from mean and standard deviation of the
1000 realizations. We note that for each profile along the slit,
the errors on fluxes are uncorrelatedbecause they originate from
independent fits to the line profiles.
Fromthe“synthetic”Paβand[FeII]spectraforthethreeslits
(PA1, PA2 and PA3), following the method outlined above, one
can derivethe spectroastrometriccurveswhichare shown in Fig.
4. Wavelengthsare convertedinvelocityusingas reference(zero
velocity)therestframePaβand[FeII]wavelengths(respectively
1.28216µm and 1.25702µm).
Fig. 4 reveals features which needs further comments. The
extremely large error bars observed in the Paβ curve at PA1
(400km/s ? v ? 550km/s) are due to the fact that the light pro-
file is spatially resolved and in this range our method of measur-
ing the centroid position is not reliable. As observed in section
2.3 this is expected in the LV range, but the relevant informa-
tion are concentrated in the HV range of the curve. Except for
those points, errors on photocenter positions range from ∼ 0.01
to ∼ 0.05′′that is from∼ 1/50to ∼ 1/10of the spatial resolution
of the data and this is the accuracy with which we can measure
centroid positions.
As expected, the spectroastrometric curves for the two lines
are marginallydifferent.Their differencesare due to the intrinsic
flux distribution of the lines on the sky plane but, as observed
in section 2.3.4, these differences tend to disappear in the HV
range.
4.3. The spectroastrometric map of the source
For each emission line we have obtained three spectroastromet-
ric curves, one for each PA of the slit. Each spectroastrometric
curve provides the photocenter position along one slit, i.e. the
position of the photocenter projected along the axis defined by
the slit direction. Combining the spectroastrometric curves we
can thus obtain the map of photocenter positions on the plane of
the sky for each velocity bin. In principle,the spectroastrometric
curves from two non-parallel slits should suffice but we can use
the redundant information from the three slits to recover the 2D
skymap as describedin Section4.1 ofPaperI. We have chosena
reference frame in the plane of the sky centered on the center of
PA1 slit (that correspond to the position of the continuum peak
along the slit) with the X axis along the North direction. For a
given velocity bin we then determined the position of the light
centroid on the sky plane resulting in the 2D spectroastrometric
map shown in Fig. 5.
Note that the coordinates on the plane of the sky of the cen-
ter of the PA2 and PA3 slits must be considered as free parame-
ters. These unknowns are estimated simultaneously with the po-
sition of the photocenterfollowinga χ2minimizationprocedure.
The final spectroastrometric map on the plane of the sky is that
given by the best fitting set of slit centers. The error bars on
the points represent the uncertainties resulting from the fit. The
black points correspond to the HV range (i.e. v ? 380 km/s and
v ? 800 km/s) which were actually used to determine the loca-
tion of slit centers. Indeed, in Paper I we concluded that the HV
range of the spectroastrometric curve is more robust, and less
affected by slit losses which artificially change the photocenter
position in the LV range.
As observed in appendix A of Paper I, we used the width of
the Gaussian fitted to the principal peak of the light profile to se-
lect the HV range: in Fig. 6 we display the FWHMs (Full Width
Half Maxima) of the Gaussian fitted to the principal peak of the
light profile for spectroastrometric curves of Centaurus A. We
can observe that in the LV range the FWHM increases because
the emission peak is spatially resolved. We compare the FWHM
to the spatial resolution(∼ 0.5′′) because the FWHM of the light
profile of an unresolvedsource should be of the order of the spa-
tial resolution. We selected the HV range by imposing that the
FWHM is lower than 1.1 times the spatial resolution (FWHM of
the PSF), resulting in v ? 380km/s and v ? 800km/s for the
spectroastrometric curves of both lines.
The two-dimensional spectroastrometric map just described
(and shown in Fig. 5) can now be used to estimate some geomet-
rical parameters of the nuclear gas disk. If the gas kinematics
are dominated by rotation around a point-like mass (the BH),
the position of the light centroid in the HV range should lie on
a straight line (which identifies the direction of the disk line of
nodes) and should approach, at increasing velocities, the posi-
tion of the BH. These considerations allows us to estimate the
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A. Gnerucci et al.: Spectroastrometry of rotating gas disks: II. Application to Centaurus A.
Fig.5. Spectroastrometric 2D map derived from the Paβ line (ISAAC spectra). Left panel: derived photocenter positions on the sky
plane, the black points are those actually used for the minimization.Right panel: the 3D plot of the map, where the z axis is velocity.
0200 40060080010001200
Velocity (km/s)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
FWHM (arcsec)
0 200 40060080010001200
Velocity (km/s)
0.0
0.5
1.0
1.5
2.0
FWHM (arcsec)
Fig.6. FWHM of the Gaussian fitted to the principal peak of the
light profile for the ISAAC emission line spectra. Upper panel:
Paβ line. Bottom panel: [FeII] line. Solid lines: PA1 curves.
Dotted lines: PA2 curves. Dot-dashed lines: PA3 curves. The
horizontal dashed lines denotes 1.1 times the PSF FWHM.
position angle of the line of nodes (θLON) by fitting a straight
line to the HV points, considering their errors in both X and Y
directions (see Fig. 5). The results of these fits are reported in
Table 1 together with the formal fit uncertainties. We verified
the reliability of these uncertainties using the bootstrap method
(Efron & Tibshirani 1994). In particular, we randomly extracted
100 datasets from the HV points and re-performed the fitting of
the line of nodes. Due to the randomextraction,the new datasets
will have the same number of points as the original one but with
some points replicated a few times and others entirely missing;
we thus randomly assign different weights in the fits of the HV
point. After performing the 100 fits, we estimate the error on
θLONby takingthe standarddeviationof the best fit valueswhich
are usually normallydistributed. This error is consistent with the
formal fit error.
We can also make a first estimate of the BH location by tak-
ing the averagepositionof the HV points in the spectroastromet-
ric map. These positions are then refined with the model fitting
proceduredescribedbelowandarereportedinTable1.Estimates
from different lines are all consistent with each other when tak-
ing into accountthe ∼ 0.01′′uncertainties ( ∼ 1/20 of the spatial
resolution of the data).
In top panels of Fig. 9 we show the derived spectroastromet-
ric maps for the Paβ band [FeII] lines. It should be noticed that
all LV points lie outside of the line of nodes, as expected.
4.4. Estimate of the BH mass from the spectroastrometric
map
Here we recover the BH mass value from the spectroastrometric
map, following the method outlined in Sect. 5 of Paper I.
Briefly, under the assumption that the gas lies in a thin disk
configuration inclined by i with respect to the plane of the sky
(i = 0 face-on) and the disk line of nodes has a position angle
θLON, the circular velocity of a gas particle with distance r from
the BH is given by:
Vrot=
?
G[MBH+ M/L · L(r)]
r
(1)
wherer is thedistancetotheBH, L(r)is theradialluminosity
density distribution in the galactic nucleus and M/L is the mass
to light ratio of the stars (see Paper I for more details).
6

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A. Gnerucci et al.: Spectroastrometry of rotating gas disks: II. Application to Centaurus A.
The component of Vrotalong the line of sight (hereafter Vch
for “channel velocity”) is:
¯Vch= Vrotsin(i) + Vsys
(2)
where i is the inclination of the disk and we also added the sys-
temic velocity of the galaxy Vsys(see Marconi et al. 2006, for
details).
As explained in section 4.2 and 4.3 and sections 3 and 5 of
Paper I, we only make use of the HV points of the spectroastro-
metric 2d map to estimate the BH mass.
The first step is to recover the disk line of nodes by fitting a
straight line on the 2d map. We then project the position of the
2d map points (xch,ych) on the line of nodes, calculating their
coordinatewith respect to this referenceaxis (Sch) and then their
distance r from the BH used in Eq. 1 (i.e. r = k|Sch− S0| where
S0is the coordinate along the line of nodes of the BH and k is
a scale factor to transform arcsec in the right distance unit1; see
Paper I for details).
Then from Eqs. 1 and 2 we obtain the model channel veloc-
ity:
¯Vch= ±
?
G(MBH+ M/L · L(k|Sch− S0|)
k|Sch− S0|
sin(i) + Vsys
(3)
and the sign depends on the side of the disk considered. The
unknown parameters of this model are found minimizing the
quantity
χ2=
?
where ∆(Sch; par) is the uncertainty of the numerator. As
previously discussed, we restrict the fit (i.e. the sum over the ve-
locitychannels)totheHV range.As explainedinsect. 5ofPaper
I, the channel velocity Vchanhas no associated uncertainty since
it is not a measured quantity but the central value of the velocity
bin. Finally we add a constant error (∆sys) in quadrature to the
quantity ∆(Sch; par) in order to obtain a reduced χ2close to 1
(see sect. 5 of Paper I for a detailed explanation of this choice).
Finally, using the best fit values of the model parameters we can
compute the (x,y) position of the BH in the sky plane.
We verified that the BH mass value is insensitive to the ac-
tualvalueofthepositionangleofthelineofnodes.Indeed,when
repeating the fit with θLONvalues varying within the uncertain-
ties, MBHchanges by only ∼ 0.02dex, well below the typical 1σ
uncertainties of the fit (see Table 1). We have also checked if the
final BH mass estimate could be biased by incorrect estimates of
both θLONand the BH position. To do this, we repeated the anal-
ysis including only the HV points which deviate by more than
2σ from the linear fit to the line of nodes. The final BH mass
changes by less than 0.1dex.
In the rotation curve model shown in Eq. 3, disk inclination
i and BH mass are coupled since coordinates along the line of
nodes (Sch) do not depend on i and this parameter appears only
as a scaling factor onthe velocity.The reason for this couplingis
that we are effectively measuring velocities of rotating material
located on the line of nodes, thus removing any dependence on
i except for the projection of the velocity along the line of sight.
Therefore our fitting method can only measure MBHsin2i, and
ch
?
Vch−¯Vch
∆(Sch; par)
?2
(4)
1To be consistent with all previous measurements we assume a dis-
tance to Centaurus A of 3.5Mpc. At this distance 1′′corresponds to
∼ 17pc.
we need to assume a value for the inclination to obtain a value
of the mass. In conclusion the free parameters in our fit are:
MBHsin2i mass of the BH;
M/L sin2i mass to light ratio of the nuclear stars;
S0
line of nodes coordinate of the BH;
Vsys
systemic velocity of the galaxy;
in the following we will only report M sin2i values and we will
discuss the inclination values we assume and the relative mass
values we obtain.
We have performed the fit of the spectroastrometric data
from the [FeII] and Paβ lines, both separately and simultane-
ously. Fit results are tabulated in Table 1 and presented graphi-
cally in Fig. 7where we plotthe r = |Sch−S0| vs. V = |Vch−Vsys|
rotationcurveand the line of nodesprojectedrotationcurve(e.g.
Schvs. Vch). The solid red lines represent the curves expected
from the model (r vs. |¯Vch− Vsys| and Schvs.¯Vchrespectively).
Thefirst result is that assuminga disk inclinationof 25◦as in
Marconi et al. (2006) we obtain MBH= 108.14±0.02M⊙, perfectly
consistent with the result presented in that work (Marconi et al.
2006 report MBH = 108.14±0.04M⊙). Since we are actually us-
ing the same ISAAC data of Marconi et al. 2006, we can draw
theimportantconclusionthatthespectroastrometricmethodpro-
vides results perfectlyconsistent with the rotationcurve method,
but with a muchsimpler approachwhich does not requireto take
into account complex instrumental effects.
Furthermore, we note that M/L is not constrained, a re-
sult which has been already found with the classical rotation
curve fitting. Computing the radius of the BH sphere of influ-
ence for Centaurus A and using a stellar velocity dispersion of
σstar≃ 150km/s (G¨ ultekin et al. 2009) one obtains rBH≃ 25pc,
a factor of 20 larger than the distances we are considering here
(at the distance of 3.5Mpc 1′′corresponds to ∼ 17pc and so
the apparent dimension of rBHis ∼ 1.5′′). This implies that at
these small radii the contribution of the stellar mass to the grav-
itational potential is negligible and consequently M/L cannot be
constrained with the fit.
Another important result derived from the application of the
spectroastrometric method is that the minimum distance from
the BH at which there is a velocity estimate is ∼ 0.05′′corre-
sponding to ∼ 0.8 pc, while with the standard rotation curve
method the minimum distance from the BH which can be ob-
served is of the order of half the spatial resolution (0.25′′). This
clearly shows how spectroastrometry can overcome the spatial
resolution limit. In Centaurus A the sphere of influence of the
BH is already well resolved in ground based observations with
good seeing and this enables us to obtain a BH measurement
already from the standard methods. The potential of spectroas-
trometry clearly relies on the possibility of using the extra res-
olution to measure the masses of BHs with smaller spheres of
influence, like those with lower masses, or located in more dis-
tant galaxies.
5. Integral field spectra: observations and data
analysis
5.1. Data and spectra analysis
We use available near infrared spectra of the nucleus of
Centaurus A obtained with SINFONI at the ESO VLT (see
Neumayer et al. 2007 for details). In particular we make use of
H band spectra observed in seeing limited mode and H and K
band spectra obtained with the assistance of the adaptive optics
7

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A. Gnerucci et al.: Spectroastrometry of rotating gas disks: II. Application to Centaurus A.
Fig.8. Example of the FWHM of the fitted 2D gaussian to each
velocity channel map for the H band seeing limited SINFONI
[FeII] data. The horizontal dashed lines denotes 1.1 times the
PSF FWHM.
(AO) system MACAO. The seeing of the observations as mea-
sured by the seeing monitor was FWHMV∼ 0.5′′(transformed
to K band , FWHMK ∼ 0.38′′). Seeing limited spectra use a
pixel scale of 0.125′′×0.250′′and cover a 8′′×8′′field of view.
The SINFONI AO module used as guide star an R ∼ 14 mag
star 36′′southwest of the nucleus providing a spatial resolution
of ∼ 0.12′′(FWHM). AO assisted spectra use a pixel scale of
0.050′′× 0.100′′and cover a 3′′× 3′′field of view. Spectral res-
olution is R ∼ 4000 for the K band and a slightly lower for the
H band, R ∼ 3000. The total on-source exposure for the K band
data cube was 13500s whereas for H band was 3600s. For all
details of observations and data reduction the reader is referred
to Neumayer et al. 2007 and Cappellari et al. 2009.
All data cubes were continuum subtracted by fitting a power
law function to the spectrum of each spatial pixel (with emis-
sion and absorption lines masked) which was then subtracted.
As observed in sections 3 and 4.1 of Paper I, for this applica-
tion of spectroastrometry it is mandatory to use continuum sub-
tracted spectra. The focus is exclusively on gas kinematics and
the presence of an underlying continuum can significantly alter
the spectroastrometric measurement of the emission line gas by
modifying the spatial light distribution in each velocity channel.
In the following spectroastrometric analysis we will use [FeII]
observed in the H band (1.6468µm) and the H2line observed in
K band (2.1259µm). Wavelengths are then converted in velocity
using as reference (zero velocity) the rest frame [FeII] and H2
wavelengths (respectively 1.6435µm and 2.1213µm).
5.2. The spectroastrometric map of the source
As observed in section 6 of Paper I, the extension of the spec-
troastrometric technique to integral field spectra is straightfor-
ward, and deriving a 2d spectroastrometric map becomes triv-
ial due to the 2d spatial coverage of integral field spectra. The
analysis of data now reduces to fitting a 2d Gaussian to each
channel map in turn, yielding the X, Y positions of the photo-
centers as a function of velocity, i.e. the spectroastrometric map.
Therefore, we can directly derive the 2d spectroastrometric map
from the continuum subtracted SINFONI data cubes, overcom-
ing the problems related to the uncertainties in slit positioning
with respect to the galaxy nucleus.
To select the HV range in the case of integral field data we
also make use of the widths of the 2d Gaussians fitted to each
velocity channel map. As explained in sect. 3 and appendix B
of Paper I we search for unresolved spatial emission. In Fig. 8
we show as an example the FWHMs of the fitted 2d Gaussian2
for the seeing limited [FeII] data in the H band where the esti-
mated seeing is ∼ 0.4′′. We can observe an evident peak in the
FWHM in the LV range due to the presence of spatially resolved
emission. As previously, we identify the HV range by consider-
ing FWHMs lower than 1.1 times the spatial resolution(∼ 0.4′′).
The resulting range in this particular case is v ? 250km/s and
v ? 950km/s.
In the lower panels of Fig. 9 we show the derived spectroas-
trometric maps for the H band [FeII] data (both AO assisted and
not) and for the K band H2AO assisted data. Typical uncertain-
ties in the light centroid positions are of the order of ∼ 0.01′′for
the seeing limited data (spatial resolution ∼ 0.4′′and pixel scale
0.125′′× 0.250′′), and a factor ∼ 2.5 lower for the AO assisted
data (∼ 0.004′′with spatial resolution of ∼ 0.12′′and pixel scale
of 0.05′′×0.10′′). It should also be noticed that all LV points lie
outside the line of nodes, as expected.
As previously explained, these 2d spectroastrometric maps
can now be used to obtain the direction of the disk line of nodes
and a first estimate of the BH position on the plane of the sky
(see Table 1). The derived BH positions are consistent within
∼ 0.02′′. The origin of the sky plane corresponds to the contin-
uumpeakposition measureddirectlyon the SINFONI datacubes
with uncertainties of ∼ 0.006′′for the seeing limited data and
∼ 0.002′′for the AO data. Taking into account these system-
atic errors in setting the origin of the map and the typical uncer-
tainties of the BH position estimate, BH positions are consistent
among each other.
We also note that the derived θLONvalues for the [FeII] line
observed with or without the AO are consistent within ∼ 8◦. The
differences between AO and seeing limited observations might
also originate because of a warping in the gas disk which results
in different orientations of the line of nodes at different spatial
scales (see also Neumayer et al. 2007).
FromFig.9 we canalso observethat the BH positionderived
from ISAAC J band spectra are shifted by ∼ 0.08′′with respect
to that derived from SINFONI H band spectra. This effect can
be accounted from the fact that the continuum peak positions
measured in J and H band (i.e. the maps coordinates origin) can
be different due to the different effect of dust reddening on the
two bands.
5.3. Estimate of the BH mass from the spectroastrometric
map
Here we estimate the BH mass using the spectroastrometricmap
as described in Sect. 5 of Paper I. The application is exactly the
same as in the case of the longslit spectra presented in section
4.4, because in both cases we use as input the 2d spectroastro-
metricmap(i.e.thepositionsofthelightcentroidsintheplaneof
sky xch,ychas a function of the corresponding channel velocity
Vch).
We have performed the fit of the data from the three spec-
troastrometric maps of Fig. 9. Fit results are tabulated in Table
1 and presented graphically in Fig. 10 where we plot either the
r = |Sch− S0| vs. V = |Vch− Vsys| rotation curve and the line of
nodes projected rotation curve (e.g. Schvs. Vch). The solid red
2Actually we fit a non circularly symmetric 2D Gaussian function.
In Fig. 8 we show the minimum of the two FWHM values along the
proper axis.
8

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A. Gnerucci et al.: Spectroastrometry of rotating gas disks: II. Application to Centaurus A.
Table 1. Fit Results.
Parameter Best fit value±error
ISAAC data
Paβline fit
SINFONI data
[FeII] line fit both lines fitNO AO [FeII] line fit AO [FeII] line fit
θLON [◦](1)
−20.3 ± 1.2
−18.3 ± 1.8
−19.8 ± 1.0
−47 ± 2
−39.2 ± 0.8
log10(MBHsin2i/M⊙)
log10(M/L sin2i/M⊙)
S0 [′′]
Vsys [km/s]
∆sys [km/s]
7.39 ± 0.02
−10.1 ± 0.0(2)
0.105 ± 0.008
593.5 ± 15.6
11
7.39 ± 0.03
−9.6 ± 0.0(2)
0.103 ± 0.009
584.8 ± 17.4
0
7.39 ± 0.02
−7.9 ± 0.0(2)
0.104 ± 0.006
591.4 ± 9.7
0
7.51 ± 0.06
−14.5 ± 0.0(2)
0.054 ± 0.006
599 ± 33
0
7.53 ± 0.01
−9.1 ± 0.0(2)
0.018 ± 0.003
592 ± 19
19
χ2
red(χ2/D.O.F.)
xBH [′′]
yBH [′′]
1.01 (9.11/9)0.82 (8.20/10)0.93 (21.49/23)0.55 (6.59/12)1.02 (12.2/12)
0.012 ± 0.006
0.099 ± 0.008
−0.003 ± 0.007
0.098 ± 0.008
0.007 ± 0.005
0.098 ± 0.005
−0.001 ± 0.007
0.037 ± 0.005
−0.002 ± 0.002
0.014 ± 0.002
Notes.(1)Best fit parameter estimated in the fit of the line of nodes.(2)Parameter not constrained from the fit.
lines represent the model rotation curves (r vs. |¯Vch− Vsys| and
Schvs.¯Vch).
From the [FeII] data we estimate a value of the BH mass of
log10(MBHsin2i/M⊙) = 7.5, perfectly consistent between AO-
assisted and seeing limited (tab. 1) whereas from the H2line we
obtainavalue(∼ 0.2dex)larger.Notethatthehigheraccuracyof
the light centroid positions of the spectroastrometric map for the
AO assisted [FeII] data with respect to the seeing limited ones
results in a lower uncertainty on the MBHsin2i best fit value.
M/L is notconstrainedfromthe fit even with SINFONI data.
As observed in section 4.4, the radius of the BH sphere of in-
fluence for Centaurus A is rBH ≃ 14.9pc corresponding to an
apparent dimension of ∼ 0.9′′; here we are studying the rota-
tion curve at ∼ 1/20 smaller scales where the contribution of the
stellar mass to the gravitational potential is negligible.
An impressiveresult of the spectroastrometricmethodis that
the minimum radii at which we can probe the rotation curve are
∼ 25mas for seeing limited data and ∼ 20mas for AO assisted
data. The latter are only slightly smaller but have a much bet-
ter positional accuracy, as shown in Fig. 10. These values are
∼ 1/16 and ∼ 1/6, respectively, of the spatial resolution (∼ 0.4′′
for the seeing limited and ∼ 0.12′′for the AO assisted observa-
tions) and correspond to distances from the BH of ∼ 0.42pc and
∼ 0.35pc, respectively, ∼ 1/40 of the radius of the BH sphere of
influence. This is a clear demonstrationof the great potentials of
spectroastrometry in overcoming the spatial resolution limit.
5.4. SINFONI H2line spectra
As described above, we also have available AO assisted
SINFONI spectra in K band where the molecular hydrogen line
(H2) is observed. Neumayer et al. (2007) used this emission line
to study the nucleargas kinematicsand to estimate the BH mass.
They find that this line spectrum has a good S/N and spatial res-
olution and that the derived gas kinematics are well explained
by a rotating disk. In contrast the kinematics from the [FeII] H
band spectra clearly show disturbances from the presence of the
jet.
However, H2proved to be of lower quality for the purpose
of spectroastrometric analysis. In particular, the line emission
is spatially well extended and the S/N in the HV line wings is
much lower with respect to the [FeII] line. At first sight this
mightseem surprisinggiventhe highqualityofthe dataobtained
by Neumayer et al. 2007, but this is due to the different features
of the spectroastrometric method. In the spectroastrometric ap-
plication, as extensively discussed in Paper I, we search for a
spatially unresolved emission in the HV wings of the line as a
“signature” of the gas kinematics of the BH gravitational po-
tential and discard all the spatially resolved emission in the LV
range. On the contrary, in standard gas dynamical studies, it is
important to concentrate on the spatially resolved LV range of
the line spectrum, and particular gas kinematics features like the
presence of inflows, outflows or jets can be detected in this con-
ditions.
In Fig. 11 we show the comparison between the line profiles
of the [FeII] and H2lines. Both spectra extracted from the re-
spective SINFONI datacubes (AO assisted observations) from a
circular aperture of ∼ 0.75′′centered on the continuum peak.
Clearly the H2line spectrum has almost no signal in the HV
rangecomparedto the[FeII]line. Forthis reasontheapplication
of our method results in a poor quality spectroastrometric map.
On the other hand in the present work we find the SINFONI
[FeII] spectra very useful and it seems our results are not dom-
inated by the contamination of the jet as observed for the [FeII]
kinematicsbyNeumayer et al. 2007. This is becausewe are con-
centrating on the unresolved HV gas emission that comes from
the inner region of the nuclear disk and that seems not to be
strongly influenced by the presence of the jet.
Summarizing, [FeII] is detected both on large spatial scales
(those probed with the classical kinematical analysis) and on
small spatial scales (those probed with the spectroastrometric
analysis). On large spatial scales and low velocities, the [FeII]
kinematics is likely affected by the presence of the jet, while
this is not the case for H2(see Neumayer et al. 2007 for more
details). On small spatial scales and high velocities, the [FeII]
kinematics is little affected by the presence of the jet, if any,
while H2emission is absent and therefore cannot be used for
spectroastrometry. This different behavior of [FeII] emitting gas
is might be related to the warping of the disk, which at small
spatial scales tends to be perpendicular to the jet axis.
6. Discussion and conclusions
We have obtained new mass measurements for the nuclear BH
of the Centaurus A galaxy by applying the spectroastrometric
method to longslit and both seeing limited and AO corrected
IFU spectra.Comparedto the standardmethodbased on rotation
curves analysis, the spectroastrometric method is much simpler
9

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A. Gnerucci et al.: Spectroastrometry of rotating gas disks: II. Application to Centaurus A.
Table 2. Mass estimates for Centaurus A
“Classical” method applications
log10(MBHsin2i/M⊙)
ISAAC J band [FeII] and Paβlines (Marconi et al. 2006) (i = 25◦)
NACO H band AO [FeII] line (H¨ aring-Neumayer et al. 2006) (i = 45◦)
CIRPASS J band Paβline (Krajnovi´ c et al. 2007) (i = 25◦)
SINFONI K band AO H2line (Neumayer et al. 2007) (i = 34◦)
7.39 ± 0.04
7.48+0.04
7.2+0.1
−0.3
7.1 ± 0.1
−0.06
Spectroastrometric method applications
ISAAC J band [FeII] line
ISAAC J band Paβline
ISAAC J band [FeII] and Paβsimultaneous fit
SINFONI H band no AO [FeII] line
SINFONI H band AO [FeII] line
7.39 ± 0.02
7.39 ± 0.03
7.39 ± 0.02
7.51 ± 0.06
7.52 ± 0.01
Fig.11. Comparison between the [FeII] and H2line spectra ex-
tracted from a circular aperture of ∼ 0.75′′centered on the
continuum peak (from SINFONI AO assisted observations).
OverplottedtheHVrangelimitsusedforthe[FeII]analysis.The
0km/s velocity correspond to the respective central line wave-
lengths and the counts are rescaled to approximately match the
two line peaks.
from the modeling point of view; it only requires the determina-
tion of the “spectroastrometric map” and is relatively insensitive
by the problems that plague the standard approach based on ro-
tation curves like, e.g., the effect of beam smearing, the intrinsic
flux distribution of the line, and the biases due to the slit posi-
tioning in longslit observations.
With our proposed spectroastrometric approach we can de-
rive two-dimensional plane-of-the-sky spectroastrometric maps
of the source characterized by accuracies of position measure-
mentsmuchlowerthanthespatial resolutionoftheobservations.
The mean accuracies of our light centroid position estimates are
∼ 0.01′′for the ISAAC data and seeing limited SINFONI data
(∼ 1/40 of the spatial resolution) and ∼ 0.004′′for AO assisted
SINFONI data (∼ 1/30 of the spatial resolution). The position
angles of the disk line of nodes estimated from those maps are
∼ −19◦for the two ISAAC maps (consistent within ∼ 2◦). The
estimates from SINFONI maps are ∼ 20◦offset from the previ-
ous. However the SINFONI [FeII] observations (seeing limited
and AO assisted) provides line of nodes PA estimates consistent
within ∼ 8◦.
Thedifferencesbetweenthevariousestimatesofthediskline
of nodes PA might be due to the different ways in which the
spectroastrometric maps are constructed, i.e. combining three
long-slit spectroastrometric curves for ISAAC data and directly
from the datacube for SINFONI data. Moreover there are many
clear indications that the Centaurus A nuclear disk is warped
(see Neumayer et al. 2007) and thereforethe different spectroas-
trometric maps might probe the average disk line of nodes at
different spatial scales. In any case, the derived rotation curves
and hence the BH mass estimates are consistent and not affected
by the differences in PA.
One possible cause of concerncould be the supportprovided
against gravity by turbulent motions. However Marconi et al.
(2006) showed that the line widths of ionized lines and Paβ
are consistent with unresolved rotation and therefore there is
no indication for turbulent pressure. Moreover the BH mass de-
termination based on H2by Neumayer et al. (2007) which in-
cludes turbulent support is similarly consistent with the result
by Marconi et al. (2006) (once the different disk inclinations are
taken into account, see Fig. 1) indicating that its effect is small.
The most important result in this work is the demonstration
of the capability of spectroastrometry to overcome the spatial
resolution limit and estimate BH masses in a simple and neat
way. The minimum distance from the BH at which we can probe
the gas rotation curve is ∼ 50mas for the ISAAC data (∼ 1/10
of the spatial resolution) and ∼ 20mas for the SINFONI data
(∼ 1/15 of the spatial resolution for the seeing limited data and
∼ 1/6fortheAO assisted data).Inthecase ofCentaurusA,these
corresponds to ∼ 1/30 and ∼ 1/50, respectively, of the radius of
the BH sphere of influence indicating that is is possible to probe
deep in the BH potential well, where the contribution from the
mass in stars is negligible.
In table 2 we compare MBHsin2i values resulting from re-
cent applications of the classical rotation curve method to var-
ious data sets of Centaurus A (including those analyzed here)
with our results from the application of the spectroastrometric
method. From Table 2 several conclusion can be reached.
– Our new simple method based on spectroastrometryis in ex-
cellent agreement with the classical method based on the ro-
tation curves, at least when comparing the results obtained
from the same dataset (cf. the ISAAC Marconi et al. 2006
data). This is a fundamental indication for the robustness of
our new method: using the same dataset we can apply in-
differently the classical and the spectroastrometrical method
obtaining perfectly consistent results.
– Whenapplyingthetwomethodstodifferentdatasetsbutwith
the same target line we obtain consistent estimates (cf. the
MBHestimate by H¨ aring-Neumayer et al. 2006 targeting the
H band [FeII] line and the one presented in this paper, and
that by Krajnovi´ c et al. 2007 based on the J band Paβ, with
our own which is within ∼ 0.2 dex).
– In general all the measurements reported in Table 2 are con-
sistent within ±0.2 dex and these differences are mainly due
10

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A. Gnerucci et al.: Spectroastrometry of rotating gas disks: II. Application to Centaurus A.
to the different data sets and target lines and not from the
application of a particular method.
– The application of the spectroastrometric method to differ-
ent data type (IFU andlongslit) give consistent result (within
only ∼ 0.1 dex) and this demonstrates the versatility of our
method. The application to IFU data is obviously much sim-
pler but this agreement also show that our method of “recon-
struction” of the 2d map from multiple longslit spectroas-
trometry is correct.
– The application of the method to IFU data with and with-
out AO also produces consistent results at similar spatial
scales. This clearly demonstrates how spectroastrometry is
much less sensitive to spatial resolution than the classical
method. As expected, the accuracy of measurement posi-
tions without AO is worse. This is due to the fact that for
each velocity channel we recover the centroid position by
fitting a two dimensional Gaussian function and the width of
this functionclearlydecreases with increasingspatial resolu-
tion of the data. Since this function is centro-symmetric we
can always recoverthecorrectcenterposition.Increasingthe
width of the function only makes the center position uncer-
tainty larger but does not alter its position.
A typical feature of spectroastrometry is its insensitivity to
disk inclination. In our fit, in fact, mass and disk inclination
are coupled. This is because coordinates along the line of nodes
(Sch) do not depend on i, which only appears as an unavoid-
able projecting factor on the velocity. Therefore our method can
return only a MBHsin2i value with the need of assuming an in-
clination value to derive the value of the mass. In this paper we
decided to present only the MBHsin2i values and to move the
discussion on the MBH values to a discussion on the i values
estimated or assumed by the various authors. For completeness
we report in Table 2 the inclinations estimated or assumed in
those previous works. Summarizing, we have applied the spec-
troastrometric method presented in Paper I to several datasets of
the nucleus of the Centaurus A galaxy obtaining MBHestimates
which are consistent with the classical method based on rotation
curves.
In conclusion,the application to Centaurus A has shown that
the spectroastrometric method is much simpler and straightfor-
ward than the classical rotation curves method and provides the
major advantage of enabling spatial scale much smaller than the
spatial resolution to be probed. It is thus possible to obtain more
robust and accurate BH mass measurements where the classi-
cal method fails. Therefore the spectroastrometric method can
be used to extend the measured MBHrange to smaller BHs in the
local universeandto similar BHs in moredistant galaxiesthan is
currently possible. Moreover this method can be applied to any
type of long-slit or integral field spectra without any particular
regard for instrument or wavelength range. A very interesting
and promising application, for example, could be in the sub-mm
high spatial resolution data provided by ALMA.
So far the spectroastrometric method has been applied inde-
pendently from the classical method. However as discussed in
Paper I, it is clear that the spectroastrometric and “classical” ro-
tation curves are complementary and orthogonal descriptions of
the position velocity diagram. Therefore, a future development
of this method will be its application in combination to the clas-
sical method based on rotation curves. This will also allow us to
constrain the disk inclination and thus remove mass-inclination
degeneracy.
Acknowledgements. We would like to thank the anonymous referee for a useful
and constructive report on this paper. We also acknowledge financial support
from the Italian National Institute for Astrophysics by INAF CRAM 1.06.09.10
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A. Gnerucci et al.: Spectroastrometry of rotating gas disks: II. Application to Centaurus A.
Fig.7. Results of the spectroastrometric modeling of the ISAAC [Fe II] data (upper panels), ISAAC Paβ data (central panels) and
simultaneous fit of the [FeII] and Paβ data (lower panels). The left panels show the line of nodes projected rotation curve Schvs.
Vchan. The right panels show the r = |Sch− S0| vs. V = |Vch− Vsys| rotation curve. The solid red lines represent the curves expected
from the model
12

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A. Gnerucci et al.: Spectroastrometry of rotating gas disks: II. Application to Centaurus A.
Fig.9. 2D spectroastrometric map for the ISAAC longslit J band data (upper panels): Paβ line (upper left panel) and [FeII] line (up-
per right panel). Spectroastrometricmap for the SINFONI H band data (lower panels): [FeII] line for the seeing limited observation
(lower left panel) and AO assisted [FeII] line (lower right panel). The red point marks the inferred BH position. The red solid line
represents the line of nodes of the disk obtained with a linear fit of the HV points, as described in the text. The dotted red lines
represent the 1σ uncertainties on the line of nodes position angle. All boxes have the same angular dimension on the plane of sky
(∼ 0.3′′× 0.3′′).
13

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A. Gnerucci et al.: Spectroastrometry of rotating gas disks: II. Application to Centaurus A.
Fig.10. Results of the fit for the SINFONI seeing limited [FeII] data (upper panels) and SINFONI AO assisted [FeII] data (lower
panels). The left panels show the line of nodes projected rotation curve Schvs. Vch. The horizontal and vertical dotted lines denote
respectively the BH line of nodes coordinate S0and the systemic velocity Vsys. The right panels show the r = |Sch− S0| vs.
V = |Vch− Vsys| rotation curve. The solid red lines represent the curves expected from the model.
14