Herschel-PACS Observations of Far-IR CO Line Emission in NGC 1068: Highly Excited Molecular Gas in the Circumnuclear Disk

Abstract

We report the detection of far-IR CO rotational emission from the
prototypical Seyfert 2 galaxy NGC 1068. Using Herschel-PACS, we have detected
11 transitions in the J_upper=14-30 (E_upper/k_B = 580-2565 K) range, all of
which are consistent with arising from within the central 10" (700 pc). The
detected transitions are modeled as arising from 2 different components: a
moderate excitation (ME) component close to the galaxy systemic velocity, and a
high excitation (HE) component that is blueshifted by ~80 km s^{-1}. We employ
a large velocity gradient (LVG) model and derive n_H2~10^{5.6} cm^{-3},
T_kin~170 K, and M_H2~10^{6.7} M_sun for the ME component, and n_H2~10^{6.4}
cm^{-3}, T_kin~570 K, and M_H2~10^{5.6} M_sun for the HE component, although
for both components the uncertainties in the density and mass are plus/minus
(0.6-0.9) dex. We compare the CO line profiles with those of other molecular
tracers observed at higher spatial and spectral resolution, and find that the
ME transitions are consistent with these lines arising in the ~200 pc diameter
ring of material traced by H_2 1-0 S(1) observations. The blueshift of the HE
lines may also be consistent with the bluest regions of this H_2 ring, but a
better kinematic match is found with a clump of infalling gas ~40 pc north of
the AGN. We discuss the prospects of placing the HE component near the AGN, and
conclude that while the moderate thermal pressure precludes an association with
the ~1 pc radius H_2O maser disk, the HE component could potentially be located
only a few parsecs more distant from the AGN, and might then provide the
N_H~10^{25} cm^{-2} column obscuring the nuclear hard X-rays. Finally, we also
report sensitive upper limits extending up to J_upper=50, which place
constraints on a previous model prediction for the CO emission from the X-ray
obscuring torus. [Abridged]

Full text

Page 1

arXiv:1202.5746v1 [astro-ph.GA] 26 Feb 2012
Submitted to ApJ
Preprint typeset using LATEX style emulateapj v. 5/2/11
HERSCHEL-PACS OBSERVATIONS OF FAR-IR CO LINE EMISSION IN NGC 1068: HIGHLY EXCITED
MOLECULAR GAS IN THE CIRCUMNUCLEAR DISK⋆
S. Hailey-Dunsheath1,2, E. Sturm1, J. Fischer3, A. Sternberg4, J. Graci´ a-Carpio1, R. Davies1, E.
Gonz´ alez-Alfonso5, D. Mark4, A. Poglitsch1, A. Contursi1, R. Genzel1, D. Lutz1, L. Tacconi1, S. Veilleux6,7,
A. Verma8, and J. A. de Jong1
Submitted to ApJ
ABSTRACT
We report the detection of far-IR CO rotational emission from the prototypical Seyfert 2 galaxy NGC
1068. Using Herschel-PACS, we have detected 10 transitions in the Jupper= 14 − 24 (Eupper/kB=
580 − 1656 K) range, all of which are consistent with arising from within the central 10′′(700 pc).
The detected transitions are modeled as arising from 2 different components: a moderate excitation
(ME) component close to the galaxy systemic velocity, and a high excitation (HE) component that is
blueshifted by ∼70 kms−1. We employ a large velocity gradient (LVG) model and derive nH2∼ 105.7
cm−3, Tkin∼ 150 K, and MH2∼ 106.9M⊙for the ME component, and nH2∼ 106.3cm−3, Tkin∼ 440
K, and MH2∼ 105.8M⊙ for the HE component, although for both components the uncertainties
in the density and mass are ∼±1 dex. Both components arise from denser and possibly warmer gas
than traced by low-J CO transitions, and the ME component likely makes a significant contribution
to the mass budget in the nuclear region. We compare the CO line profiles with those of other
molecular tracers observed at higher spatial and spectral resolution, and find that the ME transitions
are consistent with these lines arising in the ∼200 pc diameter ring of material traced by H21-0 S(1)
observations. The blueshift of the HE lines may also be consistent with the bluest regions of this
H2 ring, but a better kinematic match is found with a clump of infalling gas ∼40 pc north of the
AGN. We consider potential heating mechanisms, and conclude that X-ray or shock heating of both
components is viable, while far-UV heating is unlikely. We also report sensitive upper limits extending
up to Jupper= 50, which place constraints on the emission from the X-ray obscuring medium.
Subject headings: galaxies: active — galaxies: individual(NGC 1068) — galaxies: ISM — galaxies:
nuclei — galaxies: Seyfert — infrared: galaxies
1. INTRODUCTION
The excited molecular gas in the centers of Seyfert
galaxies offers a sensitive probe of the nature of ac-
tive galactic nucleus (AGN) feedback on the surround-
ing ISM. Observational studies of this material in Seyfert
nuclei have typically used the H2rotational (Lutz et al.
2000; Rigopoulou et al. 2002; Roussel et al. 2007) and
the well-studied ro-vibrational (e.g., Thompson et al.
1978; Mouri 1994; Maloney 1997; Davies et al. 2005;
Rodr´ ıguez-Ardila et al. 2005) transitions. The pure H2
rotational lines (Eupper/kB∼
malized at moderate (nH2∼
⋆Herschel is an ESA space observatory with science instru-
ments provided by European-led Principal Investigator consortia
and with important participation from NASA.
1Max-Planck-Institut f¨ ur extraterrestrische Physik, Postfach
1312, D-85741 Garching, Germany.
2Current Address: California Institute of Technology, Mail
Code 301-17, 1200 E. California Blvd., Pasadena, CA 91125,
USA; shd@astro.caltech.edu.
3Naval Research Laboratory, Remote Sensing Division, 4555
Overlook Ave SW, Washington, DC 20375, USA.
4Tel Aviv University, Sackler School of Physics & Astronomy,
Ramat Aviv 69978, Israel.
5Departamento de Fisica, Universidad de Alcal´ a de Henares,
28871 Alcal´ a de Henares, Madrid, Spain.
6Department of Astronomy, University of Maryland, College
Park, MD 20742, USA.
7Astroparticle Physics Laboratory, NASA Goddard Space
Flight Center, Code 661, Greenbelt, MD 20771 USA
8Department of Astrophysics, Oxford University, Oxford OX1
3RH, UK.
> 500 K) are easily ther-
> 103cm−3) densities, while
the ro-vibrational lines (Eupper/kB∼
excited through collisions in dense (nH2 ∼
gas or through UV fluorescence (Sternberg & Dalgarno
1989).Observations of these tracers in Seyferts have
identified a number of potentially important excitation
mechanisms, including X-rays from the AGN (Maloney
1997; Rodr´ ıguez-Ardila et al. 2005), shocks associated
with supernova remnants, radio jets, and gravitational
instabilities (Roussel et al. 2007), and stellar far-UV
(FUV) radiation (Davies et al. 2005), with no clear con-
sensus on a single dominant excitation source.
far-IR (FIR) CO rotational transitions (CO[Jupper →
Jupper− 1], with Jupper ≈ 13 − 50) arise from states
500 − 7,000 K above ground and have critical densities
of ∼ 106− 108cm−3, and complement the H2 transi-
tions for studies of warm and dense material.
pared with H2, the FIR CO lines trace similar energy
levels, but have higher critical densities, and are less
sensitive to extinction.Additionally, the smaller en-
ergy gaps between levels leads to a finer sampling of
density-temperature phase space. These lines have been
proposed as potential tools for studying the obscuring
medium of type 2 AGN (Krolik & Lepp 1989), deter-
mining the energy budgets of composite starburst/AGN
systems (Meijerink et al. 2007), and identifying accret-
ing black holes in the early universe (Spaans & Meijerink
2008; Schleicher et al. 2010), but previous facilities were
unable to detect this line emission from extragalactic
sources. Here we take advantage of the superb sensitiv-
> 7000 K) may be
> 105cm−3)
The
Com-

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2Hailey-Dunsheath et al.
ity of Herschel-PACS to conduct the first extragalactic
study of FIR CO emission, from the prototypical Seyfert
2 galaxy NGC 1068.
NGC 1068 is one of the brightest and best stud-
ied Seyfert 2 galaxies.The paradigm of an opti-
cally and geometrically thick molecular torus account-
ing for the Seyfert type 1 and 2 dichotomy followed
the detection of scattered broad line emission from this
source (Miller & Antonucci 1983), and NGC 1068 has
been at the center of subsequent studies of the ISM in
Seyfert nuclei. The molecular gas in the central 1′of
NGC 1068 has been well studied, and here we review
some of the key results. Interferometric observations
of CO(1-0) have identified a pair of ≈15′′(≈1.1 kpc)
radius spiral arms (Planesas et al. 1991; Helfer & Blitz
1995; Schinnerer et al. 2000), which may be modeled as
forming in response to a ≈17 kpc bar (Schinnerer et al.
2000).These arms are bright in Brγ (Davies et al.
1998), PAH emission (Le Floc’h et al. 2001), and sub-
millimeter continuum (Papadopoulos & Seaquist 1999a),
and contain most of the star formation in the cen-
tral region. Centered on the AGN is the ∼5′′
(∼350 pc) circumnuclear disk (CND), which is visi-
ble in CO and H2 1-0 S(1), but becomes particu-
larly prominent in images of HCN (Tacconi et al. 1994)
and other high density tracers (Garc´ ıa-Burillo et al.
2010).Strong emission in CO(4-3) and HCN(1-
0) indicate the gas in the CND is both warm and
dense (Tacconi et al. 1994; Sternberg et al. 1994; Israel
2009) (although see Krips et al. (2011) for a lower
density model).The high abundances of HCN,
CN, H3O+, and other molecules in the CND sug-
gest an X-ray−driven chemistry (Usero et al. 2004;
Garc´ ıa-Burillo et al. 2010; Aalto et al. 2011), and X-ray
heating has also been invoked to explain the strong H21-
0 S(1) and [Fe II] emission (Rotaciuc et al. 1991; Maloney
1997; Galliano & Alloin 2002). At ∼0.3′′resolution the
H2 1-0 S(1) observations resolve the CND into a ∼1′′
ring-like structure (Galliano & Alloin 2002), while the
line spectral profiles show evidence for rotation, expan-
sion, and more complex kinematics (Galliano & Alloin
2002; Galliano et al. 2003; Davies et al. 2008). Shocks
following this non-circular motion, and possibly associ-
ated with jet-ISM interactions, may also be important in
heating the molecular CND (Krips et al. 2011). At ∼0.1′′
resolution the H21-0 S(1) images reveal two clumps of in-
falling molecular material at ∼0.1−0.4′′scales that likely
play an important role in both fueling and obscuring the
AGN, with an estimated infall rate of ∼15 M⊙yr−1to
within a few parsecs of the nucleus (M¨ uller S´ anchez et al.
2009). Finally, milli-arcsec resolution radio observations
identify a series of H2O maser spots that trace out the
inner surface of a ∼0.5 pc radius molecular disk, cen-
tered on the AGN (Gallimore et al. 2004, and references
therein).
Hard X-ray observations of NGC 1068 indicate
large obscuration to the nucleus (Iwasawa et al. 1997;
Matt et al. 1997; Colbert et al. 2002) by an interven-
ing medium with a column density possibly exceeding
NH > 1025cm−2(Matt et al. 1997).
mid-IR observations of NGC 1068 identify a parsec scale
structure of hot dust that, along with the H2O maser
disk, may represent the dusty molecular torus responsible
for the X-ray obscuration (Jaffe et al. 2004; Raban et al.
Interferometric
2009). However, other investigators have found evidence
that at least some of the nuclear obscuration occurs on
few to ten parsec scales from the AGN (Cameron et al.
1993; H¨ onig et al. 2006; M¨ uller S´ anchez et al. 2009).
The organization of this paper is as follows. In sec-
tion 2 we describe the Herschel-PACS observations of
the FIR CO lines in NGC 1068. In section 3 we an-
alyze the gas excitation and estimate physical parame-
ters, and in section 4 we compare the physical parame-
ters and line profiles with those of other molecular gas
tracers. In sections 5 and 6 we discuss potential heat-
ing mechanisms, in section 7 we discuss non-detections,
and in section 8 we summarize our findings. Through-
out this paper we adopt a distance to NGC 1068 of 14.4
Mpc (Bland-Hawthorn et al. 1997), and a systemic ve-
locity VLSR= 1125 kms−1.
2. OBSERVATIONS
The observations were made with the Photode-
tectorArray Cameraand
Poglitsch et al. 2010) on board the Herschel Space Ob-
servatory (Pilbratt et al. 2010), as part of the SHINING
guaranteed time key program. Ten high resolution range
scans were concatenated to cover the 52 − 98 µm and
104 − 196 µm ranges, and we additionally obtained
deeper integrations of CO(17-16),
CO(40-39). These observations amounted to a total of
11.5 hours of integration time. The data reduction was
done using the standard PACS reduction and calibration
pipeline (ipipe) included in HIPE 5.0 975.
for the final calibration we normalized the spectra to
the telescope flux and recalibrated it with a reference
telescope spectrum obtained from dedicated Neptune
observations.
In Figure 1 we show the spectra from the central spa-
tial pixel (spaxel) centered on 11 of the 12 CO transitions
falling in the 104−196 µm range. The CO(25-24) line at
λrest= 104.44 µm lies in a noisy region at the edge of this
range, and is not included. The spatial distribution over
the PACS array of each detected CO line is consistent
with that of an unresolved source. All fluxes and upper
limits presented here were therefore extracted from the
central spaxel, and referenced to a point source by divid-
ing by the recommended beam size correction factors.
The CO line fluxes were measured by fitting a Gaussian
profile to the baseline-subtracted spectra. In most cases
the three free parameters of the Gaussian were allowed
to vary, while baseline uncertainties necessitated fixing
the widths of the CO(15-14) and CO(22-21) lines to typ-
ical values derived from other line fits (corresponding to
a deconvolved FWHM of 250 kms−1; see Figure 2). The
CO(16-15) line is blended with the 163 µm OH doublet,
and CO(17-16) with a pair of flanking OH+lines. In
both cases we estimate the CO flux by simultaneously
fitting all features. CO(23-22) is blended with a strong
H2O line with a rest wavelength 209 kms−1to the red.
If the combined feature were attributed solely to H2O it
would be both broader and more blueshifted than any
of the other 6 H2O lines detected in the PACS scans,
and we interpret this as evidence for significant contam-
ination by CO(23-22). A comparison with the average
of the CO(22-21) and CO(24-23) profiles suggests the
CO(23-22) line is weaker and/or more redshifted than
these lines (Figure 2). However, due to the uncertain-
Spectrometer(PACS;
CO(24-23),and
However,

Page 3

FIR CO in NGC 10683
TABLE 1
PACS CO Line Observations
Lineλrest
[µm]
186.00
173.63
162.81
153.27
144.78
137.20
130.37
124.19
118.58
113.46
108.76
104.44
100.46
96.77
93.35
90.16
87.19
84.41
81.81
79.36
77.06
74.89
72.84
70.91
69.07
67.34
65.69
64.12
62.62
61.20
59.84
58.55
57.31
56.12
54.99
53.90
52.85
Fluxa
V0b
FWHM
[kms−1]
305 ± 32
329c
369 ± 28
359 ± 27
379 ± 31
324 ± 55
297 ± 55
407 ± 87
387c
[10−17Wm−2]
7.2 ± 2.3
6.8 ± 2.1
8.1 ± 2.5
5.8 ± 1.8
5.1 ± 1.6
2.6 ± 0.9
2.5 ± 0.9
2.4 ± 0.9
4.0 ± 1.4
blended
2.6 ± 1.0
< 11.2
n/a
< 5.8
< 6.0
< 9.3
< 6.2
blended
< 7.4
< 9.5
< 5.8
< 6.2
< 8.3
< 7.9
< 10.1
< 19.2
< 22.3
< 13.3
< 21.7
< 16.9
< 10.8
< 14.9
blended
< 14.8
< 28.4
< 31.9
< 45.4
[kms−1]
19 ± 23
2 ± 25
49 ± 25
0 ± 26
−15 ± 28
−31 ± 35
−62 ± 36
−17 ± 46
−44 ± 43
CO(14-13)
CO(15-14)
CO(16-15)
CO(17-16)
CO(18-17)
CO(19-18)
CO(20-19)
CO(21-20)
CO(22-21)
CO(23-22)
CO(24-23)
CO(25-24)
CO(26-25)
CO(27-26)
CO(28-27)
CO(29-28)
CO(30-29)
CO(31-30)
CO(32-31)
CO(33-32)
CO(34-33)
CO(35-34)
CO(36-35)
CO(37-36)
CO(38-37)
CO(39-38)
CO(40-39)
CO(41-40)
CO(42-41)
CO(43-42)
CO(44-43)
CO(45-44)
CO(46-45)
CO(47-46)
CO(48-47)
CO(49-48)
CO(50-49)
−94 ± 49385 ± 95
aTotal uncertainties combine a 30% calibration error with statis-
tical errors in line fits. Upper limits are 3σ, and refer to the flux
density integrated over a 600 kms−1bin. Some lines are blended
with a strong feature, and it is not possible to obtain a flux mea-
surement or useful upper limit. CO(26-25) was not covered in the
PACS scans.
bRelative to VLSR= 1125 kms−1. Total uncertainties combine
a spectral calibration accuracy of 10% of the spectral resolution
(20 − 30 kms−1) with statistical errors in line fits.
cFixed to an intrinsic FWHM of 250 kms−1(see text).
ties involved in deconvolving the CO and H2O lines, we
simply exclude CO(23-22) from our analysis. All other
transitions from CO(14-13) through CO(24-23) are well
detected (Table 1).
The 52−98 µm range includes the CO(27-26) through
CO(50-49) transitions, and none of these lines are de-
tected. We estimate upper limits by first binning the
data to 600 kms−1bins, and then estimating the 3σ
noise levels (Table 1). We also detect no emission from
13CO. The13CO(14-13) transition at λrest= 194.55 µm
lies at the noisy edge of a scan, while the Jupper∼
transitions at λ ≥ 104 µm are blended with12CO lines.
For13CO(15-14) through13CO(20-19) we estimate 3σ
upper limits of (2 − 4) × 10−17Wm−2, also for a 600
kms−1bin size.
> 21
3. EXCITATION ANALYSIS
3.1. Evidence for Two Components
Fig. 1.— Continuum-subtracted spectra of the Jupper= 14 − 24
CO lines. The blue curves show the line fits, and features other
than CO are labeled in red. For CO(16-15) and CO(17-16) the
green and red curves show the decomposition of the fit into CO and
other lines, respectively. All lines are detected with the exception
of CO(23-22), which is blended with a strong H2O line 209 kms−1
to the red. Here the overplotted green curve is an average of the
CO(22-21) and CO(24-23) profiles as a reference.

Page 4

4Hailey-Dunsheath et al.
Fig. 2.— Top: FIR CO line fluxes and upper limits measured
here, along with lower-J lines from the literature.
est set of Jupper = 1 − 4 line fluxes are measured in 11′′− 21′′
beams that contain a mixture of the CND and the more extended
emission (Israel 2009). The second set of Jupper = 1 − 3 points
are interferometric measurements integrated over the central 4′′
from Krips et al. (2011), and the fainter CO(1-0) flux is the same
from Schinnerer et al. (2000). The shaded region shows the range
of good-fitting LVG models (χ2≤ 3/2; section 3.2.3), and the
solid black curve is the single best fitting model, with the red and
blue curves showing the individual contributions from the ME and
HE components. Middle: Central velocities of the FIR CO lines,
with average values of the ME and HE line centers indicated with
horizontal red and blue lines. Bottom: Measured FWHM of the
FIR CO lines, with tracks indicating the expected line widths for
sources with intrinsic widths of 0, 100, 200, and 400 kms−1.
The bright-
In the top panel of Figure 2 we show the line fluxes
and upper limits measured here, along with lower-J mea-
surements obtained from the literature. The middle and
bottom panels show the central velocities and widths ob-
tained from the Gaussian fitting. The inflection point
seen in the FIR CO line SED at Jupper ≈ 19 suggests
the presence of multiple components, as does the shift
in central velocities between the lowest- and highest-J
transitions. For simplicity we assume the FIR CO lines
are produced by 2 discrete components: a moderate ex-
citation (ME) component near the systematic velocity,
and a blueshifted high excitation (HE) component. Our
excitation analysis described below indicates that the
Jupper≤ 17 and Jupper≥ 20 transitions are dominated
by the ME and HE components, respectively. Separately
averaging the central velocities of these two sets of lines
gives VME= 17±12 kms−1and VHE= −54±21 kms−1
(Figure 2), with a difference of VME− VHE = 71 ± 25
kms−1.
3.2. LVG Modeling
To quantitatively analyze the FIR CO line SED we em-
ploy a large velocity gradient (LVG) model. We use the
LVG calculation described in Hailey-Dunsheath et al.
(2008), with updated CO-H2 collisional coefficients
from Yang et al. (2010), and a thermalized H2 or-
tho/para ratio. In this model the shape of the CO line
SED is determined by the gas density (nH2), kinetic tem-
perature (Tkin), and CO abundance per velocity gradient
([CO/H2]/(dv/dr)). The source is assumed to consist of
a number of unresolved clouds, and the absolute line lu-
minosities scale with the total CO mass (MCO). In the
following analysis we use a CO abundance of [CO/H2]
= 10−4to reparameterize [CO/H2]/(dv/dr) as dv/dr,
and MCO as the H2 mass (MH2). This results in an 8
parameter model, with 4 parameters for each of the ME
and HE components.
3.2.1. Background Radiation
The CO excitation may be affected by the background
radiation, and we must therefore estimate the local ra-
diation density.At millimeter wavelengths the back-
ground is dominated by the cosmic microwave back-
ground (CMB) (Kamenetzky et al. 2011), but the FIR
background arises from within the galaxy. The PACS
integral field spectra provide a continuum map of the
central 47′′×47′′with 9.4′′pixels, and demonstrate that
the continuum emission in the central pixel is dominated
by sources within the central ≈10′′. The flux density
in the central pixel may be modeled as an optically thin
modified blackbody with β = 1.5, Tdust= 48 K, and nor-
malized to Fν(λ = 100 µm) = 49 Jy, and we adopt this
as an estimate of the continuum brightness of the ∼5′′
CND. If the flux in the central spaxel is indeed due solely
to the CND than this is a moderate (by a factor of ? 2)
underestimate, while emission from within the central
≈10′′but outside of the CND may also be contributing.
The measured continuum is in reasonable agreement with
previous calculations and observations. For comparison,
this measured Fν is a factor of 1 → 4 times larger in
the λ = 50 → 200 µm range than obtained from the ra-
diative transfer modeling in Spinoglio et al. (2005). Ad-
ditionally, extrapolating our modeled SED to λ = 450
µm yields Fν(λ = 450 µm) = 1.2 Jy, comparable to the
peak value of ∼1.5 Jybeam−1measured in a ∼9′′beam
by Papadopoulos & Seaquist (1999a). The 60 µm/100
µm ratio in this model is 1.27, and the FIR flux10is
2.7×10−12Wm−2, giving LFIR= 4πd2FFIR= 1.7×1010
L⊙.
We include the effects of background radiation
on the equations of statistical equilibrium follow-
ing Poelman & Spaans (2005). The important param-
eter in this approach is the mean specific intensity of the
external radiation field at the cloud surface, which we
define as Jν,ext. We estimate Jν,ext using a simple ge-
ometrical model in which the gas clouds are uniformly
distributed in a sphere with an observed angular size Ω,
and are evenly mixed with the FIR-emitting dust grains.
For optically thin continuum, the mean value of Jν,ext
is then related to the observed continuum flux density
Fν,obsas
Jν,ext= Iν,CB+
9
16
Fν,obs
Ω
,(1)
where Iν,CBis the sum of the CMB and cosmic IR back-
ground (CIB), and we take Ω to correspond to a circular
diameter of 4′′. We have run calculations both including
and ignoring the local contributions to the background,
and see negligible difference in the results. In part this
10FFIR= 1.26 × 10−14[2.58f60/Jy + f100/Jy] Wm−2

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FIR CO in NGC 10685
is due to the fact that the background radiation tem-
peratures are only Trad= 13 − 21 K at the wavelengths
of the detected FIR lines, while the typical excitation
temperatures achieved through collisions alone for the
best-fitting models are Tex≈ 100 K and Tex≈ 400 K for
the ME and HE transitions, respectively. In addition,
most of the lines are optically thick for the best-fitting
models, and hence the CO is insulated from the external
radiation field.
3.2.2. Parameter Limits
We explore two component fits to the FIR CO emis-
sion over a large volume of 8-dimensional parameter
space, applying physical limits to the model parame-
ters. The most important prior restrictions are placed
on the velocity gradient.
in virial equilibrium, we can approximate (dv/dr)vir ≈
10 kms−1pc−1(nH2/105cm−3)1/2(Goldsmith 2001).
The actual velocity gradient may be larger due to
additional sources of gravitational potential, a high
pressure inter-cloud medium, or non-virialized mo-
tion (Bryant & Scoville 1996), but smaller values are un-
likely.Defining Kvir as the ratio between dv/dr and
(dv/dr)vir(Papadopoulos et al. 2007):
For self-gravitating clouds
Kvir=
dv/dr
10 kms−1pc−1
?
nH2
105cm−3
?−1/2
,(2)
we restrict parameter space to Kvir ≥ 1. The largest
measured velocity gradient in NGC 1068 is in the H2O
maser disk associated with the AGN. The line of sight
velocities of the maser spots shift by ∼600 kms−1over a
∼2 pc linear range (Gallimore et al. 2001), correspond-
ing to an effective dv/dr ∼ 300 kms−1pc−1.
commodate the maser disk and other high dispersion
regions in our models, we extend our calculations up
to dv/dr = 1000 kms−1pc−1. We note that restrict-
ing Kvir≥ 1 and dv/dr ≤ 1000 kms−1pc−1combine to
limit the density to nH2≤ 109cm−3, but as we discuss
below, such high densities are ruled out by other consid-
erations. We calculate the total gas mass in our models
as Mgas= 1.36 × MH2, including the contribution from
helium. Schinnerer et al. (2000) estimate a dynamical
mass of Mdyn= 9 × 108M⊙for the CND, and we dis-
card any of our models in which the total Mgas of the
two components exceeds Mdyn.
The range of parameter space allowed by the CO data
can be further reduced by considering the H2pure rota-
tional lines, which arise from states with similar upper
energy levels as the FIR CO transitions. We calculate
the H2 rotational spectrum for each model, under the
simplifying assumption that the lines are optically thin
and thermalized, and the H2ortho/para ratio is thermal-
ized. We then rule out any model that overpredicts the
flux in any of the lines measured in the large (14′′−27′′)
ISO-SWS apertures (Lutz et al. 2000). These prior con-
straints on the LVG model parameters are summarized
in Table 2.
To ac-
3.2.3. General Features of Good-Fitting Models
We proceed by generating model SEDs over a regular
8-dimensional grid, and for each model calculating χ2in
TABLE 2
LVG Model Restrictions
1) Kvir≥ 1
2) dv/dr ≤ 1000 kms−1pc−1
3) 1.36 × [MH2(ME) + MH2(HE)] ≤ 9 × 108M⊙
4) H2 rotational lines not overproduced
the normal manner. With 10 data points and 8 free pa-
rameters, our modeling has 2 degrees of freedom (dof),
and here we discuss the general properties of the set of
solutions satisfying χ2/dof ≤ 3/2. In Figure 2 we show
the range of SEDs covered by this set of good solutions,
and for the single best fit model we show the decompo-
sition into the ME and HE components. The CO(18-17)
and CO(19-18) lines typically receive comparable con-
tributions from the ME and HE components, while the
lower- and higher-J transitions are dominated by the
ME and HE components, respectively. The shape of the
ME SED is relatively well constrained, and peaks in the
Jupper= 13 − 16 range. The single dish measurements
of CO(1-0), CO(2-1), CO(3-2), and CO(4-3) we show in
Figure 2 were obtained with 11′′− 21′′beams, in some
cases comparable to the Herschel-PACS resolution (Israel
2009). However, these low-J lines receive strong contri-
butions from the lower excitation gas in the ≈15′′radius
starburst ring, and do not constrain our models. The
interferometric measurements of the CO(1-0) flux in the
CND range from 20 − 120 Jykms−1(Schinnerer et al.
2000; Krips et al. 2011), larger than the median ME
model flux of 8 Jykms−1, suggesting the ME compo-
nent contributes no more than a minor fraction of the
observed low-J emission. The HE component is much
less well constrained, with the best fitting SEDs that
peak at Jupper ≈ 23 only providing a marginally lower
χ2than those that turn over at Jupper∼
latter models, our upper limits to CO(30-29) and CO(34-
33) become useful constraints.
The FIR CO emission is an important coolant of the
nuclear molecular ISM, but does not dominate.
total luminosity emitted in the 10 transitions detected
here is LCO,FIR= 3.1 × 106L⊙, and summing the mod-
eled ME and HE emission over all transitions yields
LCO,ME+ LCO,HE = (4.3 − 10.5) × 106L⊙.
highest excitation models some additional cooling may
arise from the Jupper> 40 transitions not included in our
LVG calculation, and significant emission is also expected
in the Jupper≤ 13 submillimeter transitions. The total
emission in the H2 0-0 S(1), S(3), S(4), S(5), and S(7)
rotational lines detected by ISO-SWS is LH2= 1.7×107
L⊙(Lutz et al. 2000). Treating the upper limits to S(0),
S(2), and S(9) as detections increases this by a factor of
1.5, while at the same time some fraction of the lowest-J
emission measured with the largest apertures may arise
from the starburst ring. Our PACS scans have also de-
tected a number of OH and H2O transitions. The bulk
of the emission in these molecules detected in the cen-
tral spaxel likely arises from the unresolved CND, and
with this assumption we estimate nuclear luminosities of
LOH,FIR≈ 1.5 × 107L⊙and LH2O,FIR≈ 3.0 × 106L⊙.
The FIR range includes the strongest OH lines at 79 µm,
119 µm, and 163 µm, while for H2O (as with CO) the
longer wavelength emission should be strong. In the FIR
> 30. For these
The
For the