Hot Molecular Gas in the Circumnuclear Disk

2 MB·

by  E. A. C. Mills

PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
HOT MOLECULAR GAS IN THE CIRCUMNUCLEAR DISK
Elisabeth A.C. Mills
SanJoseStateUniversity,1WashingtonSquare,SanJose,CA95192,USA
Aditya Togi
RitterAstrophysicalResearchCenter,UniversityofToledo,2825WestBancroftStreet,M.S.113,Toledo,OH43606,USA
Michael Kaufman
7 SanJoseStateUniversity,1WashingtonSquare,SanJose,CA95192,USA
1
0
ABSTRACT
2
WepresentananalysisofarchivalISOobservationsofpure-rotationallinesofH2 inthreepointings
n in the central 3 parsecs of the Galaxy: toward the Southwest region and Northeast region of the
a
Galactic center Circumnuclear Disk, and toward the supermassive black hole Sgr A*. We detect pure
J
rotationallinesfrom0-0S(0)toS(13),aswellasanumberofrovibrationallyexcitedtransitions. From
7 the pure rotational lines, we are able to describe the molecular gas with three discrete temperature
1
components: a ‘hot’ component between 500-600 K, a ‘hotter’ component at 1250-1350 K, and a

‘hottest’ component at >2600 K. Toward Sgr A*, likely due to a combination of poorer baselines
]
A and weaker emission, we only detect a single hot component, at 1100 K. The observed excitation is
consistent with heating via C-shocks. We also fit a continuous temperature distribution to the the
G
S(1) through S(7) lines by assuming a power-law distribution of temperatures. We measure power
. lawindicesofn=3.22fortheNortheastregionandn=2.83fortheSouthwestregion, withasmaller
h
indexindicatingahigherfractionofwarmgas. Theseindicesarelowerthanthosemeasuredforother
p
galaxies or other Galactic center clouds, which are measured to have n= 4-6. If we extrapolate this
-
o temperature distribution down to a cutoff temperature of 50 K, then the total molecular gas mass
r that we would measure for the Southwest (Northeast) region is 32 (140) % of the total molecular gas
t
s mass inferred from the dust emission, and 26 (125) % of the total molecular gas mass inferred from
a the CO emission for these regions. Ultimately, we find that the disagreement in the amount of mass
[
recovered for these two regions means that this method cannot yet be verified to yield a reliable and

1 independent estimate of the mass in the local region of the Circumnuclear Disk.
v Subject headings: Galaxy: Center, Infrared: ISM, ISM: Molecules
6
2
8 1. INTRODUCTION the nuclear star cluster (Zhao et al. 1993). Additionally,
4 The center of our Galaxy hosts a supermassive black compared to the cosmic ray ionization rate in the solar
0 hole with a mass of 4 106 M at a distance of 8 kpc neighborhood ( 3 10−16, Indriolo & McCall 2012)
1. (Boehle et al. 2016),×which is(cid:12)currently accretin∼g in an it is likely at lea∼st th×ree times higher ( estimates range
0 extremely quiescent state, having a bolometric luminos- from>10−15 to2 10−14 Gotoetal.2008,2013;Harada
7 itymanyordersofmagnitudebelowtheEddingtonlumi- etal.2015). Allto×gether,itisperhapsthemostextreme
1 nosity at this mass (Narayan et al. 1998; Baganoff et al. environment in our Galaxy for forming stars.
: 2003). Surrounding both the black hole Sgr A* and a Whether or not the CND is currently forming stars is
v
central nuclear star cluster (Lu et al. 2013), with an in- controversial. Measurementsofdensityindicatethatthe
i
X ner radius of 1-1.5 pc, is a molecular gas torus known broad linewidths measured by Christopher et al. (2005)
r asthecircumnucleardisk(CND,e.g.,Genzeletal.1985; andMontero-Castan˜oetal.(2009)arehighlysupervirial,
a Gu¨stenetal.1987). Thisistheclosestreservoirofmolec- and the clumps are therefore not self-gravitating (Smith
ular gas to the black hole, and represents the gas avail- & Wardle 2014). Despite this, there have been sug-
able for its future feeding, activity, and associated star gestions of star formation based on several indicators,
formation. Estimatesofitsmassvary,butrecentstudies including shock-excited methanol masers and suggested
have converged on a value of a few 104 M (Etxaluze outflowstracedbySiO(5-4)(Yusef-Zadehetal.2015),as
(cid:12)
et al. 2011; Requena-Torres et al. 2012). The proper- well as compact, highly-excited SiO emission interior to
ties of this gas are much more extreme than those seen the CND (Yusef-Zadeh et al. 2013b). However, the bulk
in typical molecular clouds: it has broad line widths of these have other plausible explanations: methanol
(σ 10-40 km s−1) on 5(cid:48)(cid:48) (0.2 pc) scales indicative masers can be excited in strong shocks and are in fact
of s∼trong turbulence (Christopher et al. 2005; Montero- are ubiquitous throughout the Galactic center in the ab-
Castan˜o et al. 2009), as well as high average densities of senceofothersignsofstarformation(Yusef-Zadehetal.
105 106 cm−3(Requena-Torres et al. 2012; Mills et al. 2013a; Mills et al. 2015), and in fact many of the masers
2013−). Someofthemoleculargasisalsobeingionizedby highlightedbyYusef-Zadehetal.(2015),areatvelocities
not associated with CND gas. Linewidths in the CND,
[email protected] as noted above, are generally broad with complex pro-
2
filesthatcanbeattributedtoextremeturbulenceinthis tral parsecs are critical for advancing our understanding
source. Finally, in the vicinity of the strong radiation oftheCNDonseveralfronts. First,improvedconstraints
field from a nuclear star cluster, the detection of highly- on the temperature are needed for better constraints on
excitedSiOmayindicateradiativeexcitation(Godard& the density. Without strong constraints on the gas tem-
Cernicharo 2013) rather than denser gas that could be perature, the degeneracy between high temperature/low
associated with a protostar. At present then, conclusive density and low temperature/high density solutions to
evidence for active star formation in the CND is lack- radiativetransfermodelscanlimitdensitymeasurements
ing,andthisstructureappears,likemanyotherGalactic up to 2 orders of magnitude uncertainty (e.g, Requena-
centerclouds(e.g.,Longmoreetal.2013)toberelatively Torres et al. 2012; Mills et al. 2013; Smith & Wardle
quiescent. 2014). More precise measurements of the gas density
Although observations motivated by constraining star structure are needed in order to better assess the evolu-
formation have led to estimates of the gas density, we tion, longevity, and star-forming potential of this struc-
arestilllackingthefullpictureofthephysicalconditions ture. Improved constraints on the temperature are also
thatdominateinthisregion. Inparticular,newobserva- needed to determine the dominant heating mechanism
tions have failed to yield improved estimates of the gas for the dense molecular gas in the CND. Cosmic rays
temperature in this region. The temperature is uncon- (Gotoetal.2008;Haradaetal.2015),UVradiation(Lau
strained in the analysis of Mills et al. (2013) using HCN etal.2013;Ciurloetal.2016),X-rays(Gotoetal.2013),
and HCO+ over a range from 50 to 300 K. While Brad- and turbulent dissipation (Lugten et al. 1987) have all
ford et al. (2005) report a temperature of 200-300 K been suggested to contribute to the heating in this en-
using CO, they acknowledge that there are ∼no stringent vironment. Isolating the dominant heating source is rel-
upperlimitsonthisvalue. Thisisconsistentwithearlier evant for determining the extent to which the CND gas
observations of Lugten et al. (1987), as well as observa- may be taken to be an analog for gas in the centers of
tions of a larger number of CO transitions by Requena- more extreme galaxies like ULIRGs, nuclear starbursts,
Torres et al. (2012) that constrain the temperature only or even AGN.
to be (cid:38)150 K, over a range of considered temperatures In clouds in the central 300 pc of the Galactic cen-
thatextendsupto600K.WhileHerrnstein&Ho(2002) ter,mostgastemperaturemeasurementshavebeenmade
detect the highly-excited NH (6,6) line (E 400 with NH (Gu¨sten et al. 1985; Hu¨ttemeister et al. 1993;
3 upper 3
K), they do not calculate a gas temperature from∼their Mills & Morris 2013), other symmetric tops like CH CN
3
observations. In comparison, many more observational and CH CCH (Gu¨sten et al. 1985), CO (Martin et al.
3
constraintsonthedusttemperatureexist: dusttempera- 2004), and more recently H CO (Ao et al. 2013; Gins-
2
turesaswarmas90Khavebeenmeasured,thoughthese burg et al. 2016). However, in the CND these tracers
are only suggested to apply to a small fraction (<10%) havenotyieldedwell-definedtemperatures. H COisex-
2
of the CND mass (Etxaluze et al. 2011; Lau et al. 2013). tremelyweakintheCND,likelyduetophotodissociation
However, this may not give any constraint on the dust (Mart´ın et al. 2012), and the same is true of CH CN
3
temperature, as the gas and dust temperatures are ob- and CH CCH (Riquelme, private communication). As
3
served to be decoupled in Galactic center clouds (e.g., already noted, analysis of CO and NH have also failed
3
Ginsburg et al. 2016), and the gas densities present may toyieldwell-definedconstraintsontemperature(Lugten
not be high enough that the gas and dust would be ex- et al. 1987; Requena-Torres et al. 2012; Herrnstein &
pectedtobethermalizedhere, giventhehighcosmicray Ho 2002). In this paper, we undertake an alternative
ionization rate (Clark et al. 2013; Goto et al. 2013). approach by directly measuring the temperature of the
Inside the central cavity of the CND, the gas is pre- gas using H . Typically, due to a combination of the
2
dominately atomic (Jackson et al. 1993), with an esti- weakness of the dipole moment of H and the energy
2
mated mass of 300 M , and its temperature is also not of the lowest rotational transition (510 K), H is not
(cid:12) 2
constrainedHowever, thereisalsoanionizedcomponent a detectable tracer of the cool molecular ISM, and one
(the ‘minispiral’ Lo & Claussen 1983; Ekers et al. 1983) must rely on the previously-listed indirect tracers of gas
with about 10% of the mass of the atomic component, temperature. However, clouds in the Galactic center are
forwhichthetemperatureoftheintermixeddustismea- muchwarmer,andsotheselinescanbedetectedinasig-
sured to be as high as 220 K (Cotera et al. 1999). There nificant fraction of the gas. As an example, Rodr´ıguez-
is also suggested to be a hot molecular component, as Fern´andezetal.(2001)detectpure-rotationallinesofH
2
highly-excited CO is detected toward Sgr A* with Her- inasampleof16Galacticcenterclouds,andmeasuregas
schel(Goicoecheaetal.2013)thatisconsistentwithtem- with temperatures from 150-600 K that comprises 30%
peraturesof 1300K.However,giventhelowspatialand of the total H column.
2
spectral reso∼lution of Herschel, the detected gas may be Inthispaper,weundertakeananalysisofarchivalISO
associated in part or full with the CND or other Galac- spectraofpure-rotationalandrovibrationallinesofH in
2
tic center clouds on the same line of sight (e.g, the 50 threepositionstowardtheCNDandcentralparsectaken
and 20 km s−1 clouds Herrnstein & Ho 2005). Resolved withtheSWSatwavelengthsgreaterthan3.4µm. There
observations of the inner edge and cavity of the CND in are a number of prior observations of rovibrational lines
rovibrationallinesofH havebeenmadebyCiurloetal. in the near-infrared (Yusef-Zadeh et al. 2001; Lee et al.
2
(2016), and indicate temperatures up to a few thousand 2008; Feldmeier et al. 2014; Ciurlo et al. 2016), however
K,withthetotalmassofgasatthesetemperaturebeing to our knowledge this is the first analysis of the pure-
<10−2 M . However, muchofthecavitygasalsoshows rotationallinesinthissource. Wepresentatemperature
(cid:12)
strong deviations from thermal equilibrium. analysisoftheselinethatincludesbothafittoadiscrete
Accurate gas temperature measurements in the cen- number of temperature components, as well as a power-
law analysis assuming a continuous distribution of tem-
3
peratures. WethendiscussthefractionofwarmH that emissionisdetectedfromtheNorth,withslightlyweaker
2
is detected in the CND, the implications of this temper- emission in the Southwest and toward Sgr A*. Toward
ature distribution for identifying a heating source, and the Southwest region we detect 12 pure-rotational lines,
theuniquenessoftheCNDcomparedtoothersourcesin upto0-0S(13),and7rovibrationallines,upto1-0Q(5)
which H temperatures have been measured. and1-0O(6). TowardtheNortheastregionwedetect13
2
pure-rotationallinesupto0-0S(13),and10rovibrational
2. DATA
lines up to 1-0 Q(7) and 1-0 O(6). Toward Sgr A* we
The data used in the analysis in this paper were ob- detectonly5pure-rotationallinesfromS(4)toS(8),and
tained from the NASA/IPAC Infrared Science Archive. we only detect two rovibrational lines: O(4) and O(5).
We analyzed spectra from three positions observed with The continuum is significantly stronger toward Sgr A*,
the Infrared Space Observatory (ISO) toward the cen- and the baseline structures are more complicated, hin-
traltwoparsecsoftheMilkyWay. Allobservationswere dering the detection of a similarly large number of lines
made in May 1996 using the Short Wavelength Spectro- in this source. Typical baseline uncertainties are 0.3 Jy
graph (SWS) in low-resolution, full-grating scan mode. for N and S, and 0.7 Jy for Sgr A*.
SpectraofthecentralpointingtowardtheblackholeSgr We fit Gaussian profiles to all of the detected lines
A*(RA=17h45m39.97s,Dec= 29◦00(cid:48)28.7(cid:48)(cid:48))werepub- (shown in Figures 3, 4, and 5), and report the line pa-
lishedinLutzetal.(1996),howe−vertheH lineswerenot rametersforeachsourceinTables1, 2,and3. Thespec-
2
analyzed. The other two pointings, toward the North- tral resolution of these SWS observations is 15 km s−1,
east region (RA=17h45m41.76s, Dec= 28◦59(cid:48)50.7(cid:48)(cid:48)) so with typical measured linewidths of 140 40 km s−1
and the Southwest region (RA= 17h45m−38.58s, Dec= thelinesaretypicallywellresolved. How∼ever±,thecentral
29◦01(cid:48)05.8(cid:48)(cid:48)) have not been published. velocitiesshowvariationwithineachsource,ontheorder
−The spectra were obtained with an aperture of 14(cid:48)(cid:48) of 30-40 km s−1, which we attribute to the low spectral
20(cid:48)(cid:48) for wavelengths of2.38-12.0 µm, 14(cid:48)(cid:48) 27(cid:48)(cid:48) for wav×e- resolution and uncertainty in the wavelength calibration
lengthsof12.0-27.5µm,and20(cid:48)(cid:48) 27(cid:48)(cid:48) for×wavelengthsof of these observations. We measure a mean central ve-
27.5-29.0 µm. Only the 0-0 S(0)×H line at a wavelength locity of -34 38 km s−1 toward the Southwest region,
2
of 28.221 µm is observed with an aperture of 20(cid:48)(cid:48) 27(cid:48)(cid:48). 57 38 km s−±1 toward the Northeast region, and 28 25
The 0-0 S(1) and S(2) lines are observed with an×aper- km±s−1 toward Sgr A*. ±
ture of 14(cid:48)(cid:48) 27(cid:48)(cid:48) and the remainder of the lines are ob- There are several lines for which it appears there is a
servedwith×aconsistentapertureof14(cid:48)(cid:48) 20(cid:48)(cid:48). However, contaminating line at nearly the same wavelength. The
the SWS spectra we use are highly-proce×ssed data prod- 1-0 O(2) line at 2.4066 µm shows two signatures indica-
ucts that have had their continuum level normalized to tive of contamination with a species tracing the ionized
a consistent value (Sloan et al. 2003). Based on mapped gas: it is anomalously strong compared to other nearby
observations of the 1-0 Q(1) line (Feldmeier et al. 2014), H lines, and the emission toward Sgr A* is stronger
2
we assume that the H emission can be taken to fill the than the emission toward the two pointings in the CND,
2
aperturewithafillingfractionof1forthisrangeofaper- which is not observed in other H lines. In addition, the
2
ture sizes, and so in subsequent calculations we take the 1-0 O(2) line appears offset from the velocity inferred
effective aperture size to be 14(cid:48)(cid:48) 20(cid:48)(cid:48), and apply no from the H lines. Based on the strength and velocity of
2
additional correction for variations×in the aperture size thefeaturenearthe1-0O(2)line,wesuggestthatthisis
between lines. For all aperture sizes, the long axis of the the [Ti II] 7/2-7/2 line at 2.6244 µm (an offset velocity
slit is oriented with a position angle of -1◦.4 in an eclip- of 284 km s−1). In addition, the wavelengths of the 1-0
tic coordinate frame. The position of these pointings is Q(7) line at µm and the 3-2 S(0) line at µm are nearly
shown in Figure 1, superposed on the map of the 1-0 overlapping (having an offset velocity of 183 km s−1). If
Q(1) line from Feldmeier et al. (2014) we assume the feature detected at this wavelength is 3-
The full spectra toward each position from 2.5 to 40 2 S(0), then the measured velocity is significantly offset
µm are shown in Figure 2. Integration times for these from that measured for the other H lines. We thus in-
2
observations were 6528 s, resulting in per-channel noise fer that the emission here is dominated by the 1-0 Q(7)
levels of 0.5-1 Jy for all lines except the 0-0 S(0) line, line, and do not report a detection of the 3-2 S(0) line.
whichha∼sanoiseof 10Jy. Additionalbaselinefluctua- There are also several lines for which there are features
tionswithamplitude∼s0.5-1Jyarepresentinthespectra at nearby wavelengths that appear as emission at offset
that can become as high as 5-40 Jy toward Sgr A*. The velocities (e.g., in the 1-0 O(8) and 1-0 Q(2) lines, and
spectral resolution of the observations is 15 km s−1. the 2-1 O(6) line) that are likely due to other species.
We fit a first-order polynomial to the cont∼inuum in the From the Gaussian fits to the flux of each line, we
2000kms−1 surroundingtheline. Thecontinuumlev- can calculate a column density for each level using the
±elsrangefrom10to3000Jyandtheshapesaregenerally relation
well-fit by this approach. For the S(0) line, the contin-
uumislarger,withasteeperslopeandgreatervariation.
4πλ I (v,J v(cid:48),J(cid:48))
For this line, we fit a first-order polynomial to a more N(v,J)= obs − eA(λ) (1)
limited range. The baseline-subtracted spectra of the 0- hc Aobs(v,J v(cid:48),J(cid:48))
−
0 S, 1-0 Q, and 1-0 O lines are shown in Figure 3, 4, and
5. where Iobs(v,J v(cid:48),J(cid:48)) is the observed line flux from
the transition fro−m level (v,J) to (v(cid:48),J(cid:48)), A (v,J
obs
3. RESULTSANDANALYSIS v(cid:48),J(cid:48)) is the Einstein A radiative transition probabilit−y
We detect multiple pure-rotational and rovibrational fromlevel(v,J)to(v(cid:48),J(cid:48)), andA(λ)istheextinctionat
lines of H toward all three positions. The strongest H the wavelength of that transition.
2 2
4
3.1. Extinction Correction fit to a curve representing the sum of the three single-
temperaturecomponents(eachofwhichisastraightline
Wefindthatthe0-0S(3)lineisanomalouslyweak,ly-
in the Boltzmann plot).
ingbelowtheother0-0SlinesinaBoltzmannplot(Fig-
Weperformaminimizationoftheresidualsofthefitto
ure6),aresultthatcanbeattributedtoextinctionfrom
simultaneously determine the best-fit temperature (the
the8µmsilicatefeature(e.g.,Rodr´ıguez-Fern´andezetal.
inverseoftheslopeoftheline)foreachofthethreetem-
2001; Lutz et al. 1996). In order to correct the observed
perature components, as well as the optimal extinction
H lines for the extinction at mid-infrared wavelengths
2 value. The total column density of each component (the
we adopt the Fritz et al. (2011) extinction law derived
y-intercepts) are free parameters that are also optimized
from the ISO continuum toward Sgr A*. As extinction
to determine the best fit.
is a complicated function of the wavelength, we describe
TheresultsofthisminimizationareshowninFigure9.
this law by taking the values of 100 data points on their
The extinction, and the two lowest-temperature compo-
derivedcurvefrom0.43µmto25µmandinterpolatingto
nents(the‘hot’and‘hotter’gas)arewell-constrainedby
obtaintheextinctionvaluesattheobservedwavelengths.
ourdata. Thebest-fitextinctionis0.98 theextinction
The extinction values from Fritz et al. (2011) are then
towardSgrA*(orA =1.07)fortheSo×uthwestregion,
scaled in order to minimize the scatter in a linear fit to L(cid:48)
and slightly higher for the Northeast region: 1.17 the
theS(1), S(2), S(3)andS(4)lines. Wenotethattheisa
extinction toward Sgr A* (or A = 1.28). How×ever,
significant improvement over the Lutz et al. (1996) law L(cid:48)
the highest-temperature or ‘hottest’ component is not
adopted by Rodr´ıguez-Fern´andez et al. (2001). As can
strongly constrained, and is effectively a lower limit on
be seen in Figure 6, interpolating a fit to using the same
the highest temperatures present( (cid:38) 2600 K, which is is
method is unable to bring the S(3) line into alignment
alsoapproximatelythetemperatureofthedetectedrovi-
with the S(2) and S(4) lines without assuming a much
brational Q(1) and O(1) lines of H at these positions.).
larger extinction as well as overcorrecting the S(2) line 2
However, we will use the best-fit values for the very hot
to be brighter than the S(1). We note however that the
component in our estimates of the total column density
extinction correction does not significantly change the
which follow. We find best-fit temperatures of 580 K,
measured temperatures.
1350 K, and 3630 K toward the Southwest region, and
TheappliedextinctioncorrectionusingtheFritzetal.
520K,1260K,and2840KtowardtheNortheastregion.
(2011) law significantly raises the flux of the S(3) line,
Toward Sgr A*, we separately fit a single temperature
making it consistent with the flux observed in the other
component and find the best-fit temperature to be 1100
0-0 S pure rotational lines. It indicates that the extinc-
K.WefindthatthetemperaturesintheNortheastregion
tion in N and S is only slightly larger than that derived
are 100-200 K cooler than in the Southwest region. One
by Fritz et al. (2011) toward Sgr A* (Note that as the
possibleexplanationisthatthisisbecausetheSouthwest
extinction law is determined using the same ISO obser-
region is closer to a source of heat provided by the cen-
vations of Sgr A* that are analyzed here, we adopt the
tral nuclear cluster. After all, only the Southwest edge
unscaled Fritz et al. (2011) extinction values for this lat-
of the CND appears to be ionized, while the Northeast
ter source). However, minimizing the scatter in a linear
edgedoesnot(Zhaoetal.1993). Wediscussotheralter-
fit to the first four detected rotational lines of H does
2 natives in Section 4.2.2.
not account for the slight curvature seen in the Boltz-
The extremes of temperature that we find are higher
mann plots of the H lines. This method thus actually
2 thantemperaturesthathavebeenmeasuredintheCND
slightly overestimates the extinction, yielding a slightly
orinnercavitywithothertracers. Thehottestmeasured
overlarge flux for the S(3) line. We thus find it is better
dust temperatures are 220 K (Cotera et al. 1999), and
to perform a simultaneous optimization of the fit to ex-
measurements of highly-excited CO using Herschel by
tinction and temperature, as described in the following
Goicoecheaetal.(2013)findtemperaturesofjust 1300
section.
K. The only measurements of comparably-hot gas∼are of
T 1700-2500KgasmeasuredbyCiurloetal.(2016)for
3.2. Discrete Temperature Fitting ot∼her near-infrared rovibrational lines of H in the inner
2
We next plot the column densities N(v,J) divided by edge and central cavity of the CND. However, there is a
the level degeneracy g against the upper level energy large uncertainty on the highest temperature they mea-
J
gEe(nve,rJa)c/ykisingJa=‘Bgoslt(z2mJa+nn1)pwloht’e.reFgosr=H23 tfohreolervthelo-dHe2- tshuerey(aTn∼aly2z5e0s0h+−o39w00000s)ig,nainfidcatnhtedmevaijaotrioitnysoffrotmheaptohseitrimonasl
(odd J) and gs=1 for para-H2 (odd J). With the ex- distributionthattheyattributetorecentformationofH2
ception of the pointing toward Sgr A* (for which only in the central cavity. In contrast, we find that the 0-0 S
5 pure-rotational lines are detected), the pure-rotational linesintheNortheastandSouthwestregionsoftheCND
lines measured toward the CND follow a convex curve appear to be consistent with a thermal distribution up
that is indicative of the presence of multiple tempera- to temperatures of at least 2600 K.
ture components. The resulting Boltzmann diagrams of the extinction-
In order to constrain the temperatures present in the corrected column density for each position are shown
CNDgas,wefirstfollowtheapproachofRosenbergetal. in Figure 7. Each individual temperature component is
(2013) and perform a simultaneous fit to three temper- plottedintheBoltzmanndiagramasadashedline, with
ature components in the pure-rotational lines observed thesumofallthreecomponentsplottedasasolidcurve.
in the Southwest and Northeast regions (note that with In addition to the 0-0 S lines which are used in the tem-
the smaller number of lines detected toward Sgr A*, we perature fit, we also plot the v =1 0 O and Q rovibra-
can only justify fitting a single temperature component tional lines. We find that they follo−w a roughly straight
in this source). The measured column densities are then
5
line on these plots, lying below the pure-rotational lines a power law function with respect to temperature, dN
with similar upper level energies. The temperature of T−n dT, where dN is the number of molecules in th∝e
theselinesisroughlyconsistentwiththatofthehighest- temperature range T—T+dT. The model then consists
temperature gas component measured in the 0-0 S lines of just three adjustable parameters: an upper and lower
( 3000 K). These two distinct distributions are in con- temperature cutoff (T and T ) and a power law index
u (cid:96)
tr∼ast to what is observed in the Orion-KL outflow in (n).
which the rotational and vibrational lines are thermal- As our primary goals in adopting this model are to
ized and follow a single distribution in the Boltzmann comparethepowerlawindicesbetweenthetwoobserved
diagram (Rosenberg et al. 2013, although the high-J CO regions, and to make an estimate of the total amount of
linesobservedinOrionKLdoshowacurveddistribution H which could be present if this power law extends to
2
similartothe0-0SH linesintheCND,e.g.,Goicoechea lower temperatures (T< 500 K), we focus only on the
2
et al. 2015). Although we do not detect the S(0) (J=2– S(1) to the S(7) lines. We also keep the upper temper-
0)line,wecanalsoestimateaT temperaturefromour ature, T , fixed at 2000 K, as hotter gas is a negligible
32 u
measured upper limit on the strength of this line and contributor to the total column. The only two parame-
ourmeasurementoftheS(1)(J=3–1)line. Weconstrain ters which then vary in the model fitting are the lower
T >110 K in the Southwest region and >130 K in the cutoff temperature T and the power law index n. We
32 (cid:96)
Northeast region. then use this model to fit the observed column densi-
Usingthetemperaturefits,wecanextrapolatethecon- ties for the Northeast and Southwest lobes (corrected
tribution of each component to lower J and determine for the best-fit extinction value that was determined in
thetotalcolumndensityofeachtemperaturecomponent. our discrete temperature fits). We report results for two
The fraction of the (warm) H column in each compo- adoptedvaluesofalowercutofftemperature: T=50K,
2
nent is given in Table 4. We find that for the Northeast roughly consistent with the coolest molecular gas typi-
andSouthwestregions, thevastmajorityofthedetected callymeasuredinothercloudsintheGalacticcenter(Ao
warm H is in the ‘hot’ 500-600 K component: more etal.2013;Ginsburgetal.2016), andT=100K,which
2
than 95% for both sources. Both sources have 3-4% of isroughlythecoolestgasallowedbyournondetectionof
the H column in the ‘hotter’ 1200-1300 K component, the S(0) line (though given the large upper level energy
2
andlessthan0.1%oftheH columninthe‘hottest’T of this line, cooler gas may be present that would not
2
3000 K component. While this makes both sources ap∼- contribute emission to this line).
pear quite similar, the best-fit temperature components Figure8showstheresultingmodelfitstotheobserved
in the Northeast region are somewhat cooler than those H columns for the Southwest and Northeast regions.
2
in the Southwest region. We find that a fit to a continuous temperature distribu-
Summingoverallthecomponentswecanalsoestimate tion shows that the Southwest region (n = 2.83) is sys-
the total column of hot (T>500 K) H in each source. tematically warmer than the Northeast region (n=3.22),
2
For the Southwest region we measure a total column of whereashallowerorsmallerpowerlawindexindicatesa
1.12 1021 cm−2. For the Northeast region we measure greaterfractionofwarm/hotgas. Thisisconsistentwith
a to×tal column of 2.38 1021 cm−2. We thus find that the trend seen in our discrete temperature fits, that the
there is around a facto×r of 2 times more hot H in the Northeast region appears systematically cooler than the
2
Northeast region than in the Southern region. This is Southwest region. The power law indices measured for
consistent with our observations that the H lines are both regions of the CND are much shallower than typi-
2
stronger in the Northeast than in the Southwest. cal values measured in the centers of other star-forming
galaxies,indicatingthattheCNDgasishotterthantyp-
3.3. Continuous Temperature Fitting
ical gas in the nuclei of other galaxies (Togi & Smith
As we do not detect the S(0) line in the ISO data, 2016). We will discuss this further in Section 4.1.
our discrete temperature fits are not very sensitive to The best-fit power law for each region can then be
the presence of ‘warm’ gas with T < 500 K. Further, as extended to lower temperatures in order to estimate the
the discrete fitting approach seeks to optimize a fit to totalcolumnofwarmH withtemperaturesgreaterthan
2
three temperature components that are not consistent theassumedcutoffvalue(50or100K).Adoptingacutoff
between the Northeast and Southwest regions, it is diffi- value of 100 K for the coolest gas present, we measure a
cult to objectively compare the hot gas properties (such totalcolumnofwarmH of1.2 1022cm−2fortheNorth-
2
asthefractionofgasateachtemperature)betweenthese eastregion,and4.4 1021cm−2×fortheSouthwestregion.
two sources. We thus also employ a second approach Inthiscase,thereis× 3.5timesmorewarm(T>100K)
for quantifying the temperature differences between the H present in the N∼ortheast region than in the South-
2
Northeast and Southwest regions. west region, compared to twice as much hot (T>500 K)
Here, we first assume that a fixed number of dis- H intheNortheast,asmeasuredfromthediscretetem-
2
crete temperature components is not a physically well- perature fits. The warm H column would also be 4-5
2
motivated model for this gas, and that a more realis- timeslargerthanthehotcolumnthatwemeasured∼with
tic description would be gas in which the temperature ourdiscretetemperaturefits. Ifwegofurtherandadopt
varies smoothly or continuously from cool to hot values. a lower cutoff temperature of 50 K, the total column of
We then follow the approach of Togi & Smith (2016) by H presentwouldbe5.6 1022cm−2fortheNortheastre-
2
adopting a continuous power-law temperature distribu- gion, and 1.6 1022 cm−×2 for the Southwest region. This
tion for the H , which extrapolates the temperature dis- is again 3.5×times more warm (T> 100 K)H present
2 2
tribution down to lower values than those we were able in the N∼ortheast region than in the Southwest region.
to measure. In this model, the measured column densi- TheoverallincreaseinH columnwouldalsomeanthat
2
tiesofH moleculesaremodeledasthedistributionfrom if this power-law extrapolation holds, and if there is gas
2
6
as cool as 50 K in the CND, 70-80% of the H would twice the ISO aperture, we also scale the masses to the
2
have temperatures in the range of 50-100 K. We discuss ISO aperture, assuming uniform emission. The resulting
this further in Section 4.4. masses for the Southwest (557 M .) and Northeast (413
(cid:12)
M .) regions are also reported in Table 5. We can also
(cid:12)
3.4. The warm/hot gas mass of the CND and the measure a molecular mass from the H columns deter-
2
central cavity mined from Herschel dust measurements (Battersby et
al., in prep. and private communication). These H col-
WecanalsotranslatethesetotalcolumndensitiesofH 2
2 umn densities were derived by fitting a modified black-
intototalmasseswithintheobservedISO-SWSaperture
body to each positing in the Galactic center, with the
for the extrapolated amount of warm (T>50 or 100 K)
dusttemperatureandopacityallowedtovaryasfreepa-
gas and the measured amount of hot (T> 500 K) gas.
rameters, and assuming a constant gas to dust ratio of
The total H mass M is given by:
2 H2 100 and dust with a β of 1.75 over the entire Galactic
M =N Ωd2µ m (2) center (the method is described in more detail in Bat-
H2 H2 H2 H tersby et al. 2011). Toward the Southwest region, we
whereNH2 isthetotalmeasuredcolumndensityofH2, measure an H2 column of 4.9 1022 cm−2 in the ISO
Ω is the solid angle of the ISO-SWS aperture, d is the aperture, and toward the North×east region, we measure
distancetotheGalacticcenter(8kpcBoehleetal.2016), an H column of 4.0 1022 cm−2, both consistent with
2
µH2 is the mean molecular weight of the gas, which we thevaluesshowninth×ecolumndensitymapsofEtxaluze
take to be 2.8, assuming abundances of 71% H, 27% He, etal.(2011). Thesecolumndensitiescorrespondtototal
and 2% metals (e.g., Kauffmann et al. 2008), and mH is moleculargasmassesof456M(cid:12) intheSouthwestregion
the mass of a Hydrogen atom. Taking an aperture size and 370 M in the northeast region.
(cid:12)
of 14(cid:48)(cid:48) 20(cid:48)(cid:48) (0.54 by 0.78 pc on the sky, at the assumed If our power-law extrapolation is valid, and if 50 K
distanc×e of 8 kpc), the measured total column densities is a correct cutoff temperature for the CND, then the
fromourdiscretetemperaturefitswouldcorrespondtoa total molecular mass we infer from this method for the
totalmassofhotmoleculargasof10.6M(cid:12) intheSouth- Northeast(Southwest)regionwouldthenaccountfor140
west region, and 22.7 M(cid:12) in the Northeast region. (32)%ofthetotalmolecularmassinferredfromthedust
Additionally, wecandeterminethe massofhotmolec- emission, or 125 (26)% of the total molecular mass in-
ulargasinthecentralcavityfromtheobservationtoward ferred from the CO observations. In contrast, the col-
Sgr A* (for just the measured 1100 K temperature com- umn of hot (T>500 K) H measured from our discrete
2
ponent). Here, we find a total mass of 0.5 M(cid:12) within temperature fits toward the Northeast (Southwest) re-
theISO-SWSaperture. Incomparison,t∼hereismeasured gion only accounts for 6 (2)% of the total H column
2
to be roughly 30 solar masses of ionized gas in the min- inferred from the dust emission, and 5 (2)% of the total
ispiral,and300solarmassesofneutralgasinthecentral molecular mass inferred from the CO observations.
cavity(Jackson et al. 1993). This is a larger mass of hot We find that dust and CO yield relatively consistent
H2 in the central cavity than measured by Ciurlo et al. estimatesofthetotalmoleculargaswithintheISOaper-
(2016), who estimate a total H2 mass of 7 10−3 M(cid:12) ture, however, the molecular gas masses extrapolated
if the emission they observe is representat∼ive×of emission from our continuous temperature fits to H deviate sig-
2
along a narrow inner edge of the CND that abuts the nificantly. In the Southwest region, our mass estimate
central cavity. However, unlike the high-resolution ob- from H is only one quarter to one third of the total
2
servations of Ciurlo et al. (2016) and as we discuss in molecular gas measured from CO and dust. In contrast,
Section 4.3, it is not clear that all of the gas we detect intheNortheastregion,themassestimatefromH issig-
2
toward Sgr A* is actually confined to the central cavity. nificantly larger than the total molecular gas measured
There is then no requirement that this hot gas be asso- fromCOanddust. Thisextremevariationislargelydue
ciated (solely) with the inner edge of the CND or the tothefactthattheSouthwestregionhasfainterH and
2
central cavity. a correspondingly lower column density than the North-
The total molecular mass of gas inferred to be present east region, but yet is significantly brighter in CO and
from our extrapolated continuous temperature fits is dust(andthushasahigherinferredtotalcolumnofH .)
2
muchlargerthanthemassofjustthehotgasdetermined We further discuss the assumptions underlying the indi-
fromthediscretetemperaturefits. Foracutofftempera- rectandextrapolatedmeasurementsofanH columnin
2
tureof100K,thetotalmoleculargasmassinSouthwest Section 4.4.
region would be 41 M , and for the Northeast region it
(cid:12)
would be 111 M . For a lower cutoff temperature of 50
(cid:12) 4. DISCUSSION
K, the total molecular gas mass in the Southwest region
4.1. The CND compared to other sources
would be 146 54 M , and for the Northeast region it
(cid:12)
would be 518±243 M . To understand how the temperature of the warm H
(cid:12) 2
Wecancom±parethesemassestootherindependentes- andthefractionofgasatthesetemperaturesintheCND
timates of the total molecular gas mass in these regions. match up with the properties of other sources, we first
CO observations Requena-Torres et al. (2012) inferred compare the CND to observations of other Galactic cen-
masses of 795 M and 590 M toward nearly identical termolecularclouds. Thepure-rotational0-0S(0), S(1),
(cid:12) (cid:12)
positions in the Southwest and Northeast respectively, S(3), S(4) and S(5) lines of H were observed in a sam-
2
for a beam with FWHM = 22(cid:48)(cid:48).5. As these are just ple of 16 clouds in the central 500 pc of the Galaxy by
masses of H (Requena Torres, private communication) Rodr´ıguez-Fern´andez et al. (2001). As they used the
2
wefirstscalethesemassesfortheadoptedmeanmolecu- Lutz et al. (1996) law to correct for the extinction of
lar weight. As solid angle of this beam is approximately their sample, we have taken their reported line fluxes
7
andredonetheextinctioncorrectionusingtheFritzetal. or electrons in energetic shocks (e.g., Shull & Beckwith
(2011) law in order to be more consistent with our CND 1982), and fluorescent excitation, in which the observed
analysis. We select a subset of 5 clouds from their sam- levels are populated by decay into lower states after the
ple, all of which have detections of the 0-0 S(4) and S(5) resonant absorption of ultraviolet photons in the Lyman
lines. Fitting a power law temperature distribution to and Werner bands (e.g., Gould & Harwit 1963; Black &
these clouds as we did for the CND, we find power law Dalgarno 1976). Collisional excitation can be thought
indicesthatrangefrom4.7to5.0,withfitsshowninFig- of as a “bottom-up” population of the levels of H , as
2
ure 10. These are steeper than the power law indices we persistentcollisionsinshockswithtemperaturesofthou-
measure in the Northeast (n = 3.22) and Southwest (n sands of K thermally excite H out of its ground state
2
= 2.83) regions of the CND, and indicate that the H in and into the observed rotationally- and vibrationally-
2
typicalGalacticcentercloudsiscoolerthanintheCND. excited states. In contrast, fluorescent excitation can
This is consistent with a comparison of the mean T be thought of as a “top-down” population of the lev-
76
for the 5 of these clouds for which the S(5) line could be els of H , as the molecules are directly excited into high
2
detected (700 K; Rodr´ıguez-Fern´andez et al. 2001) with vibrational levels by the resonant absorption of ultravio-
whatwewouldmeasureforT fromourCNDdata: 800 let wavelength photons, and a fraction of the molecules,
76
K for the Southwest region and 870 K for the Northeast insteadofdissociating,de-exciteintotheobservedlower-
region. excitationrotationandvibrationstates. Anumberofob-
Similar to what we find when comparing to other servationaldiagnosticsexisttodistinguishbetweenthese
molecular clouds in the central 500 pc of our Galaxy, two excitation mechanisms, which focus on the relative
the power law index for the temperature distribution in brightness of rotational and highly vibrationally-excited
the Southwest and Northeast regions of CND (about 3) transitions(thelatterofwhichareexpectedtobeweaker
is also flatter than for any galaxies in the sample mea- or absent in the case of shock-excited emission; Shull &
sured by Togi & Smith (2016), which includes galaxies Hollenbach 1978; Black & van Dishoeck 1987; Wolfire &
withstar-formingnuclei,luminousandultraluminousin- Konigl 1991).
frared galaxies (LIRGS and ULIRGS), Low Ionization Although fluorescent emission might seem to be ruled
Nuclear Emission Regions (LINERs), Seyfert Galaxies, out due to the large radii at which the ‘very hot’ H
2
dwarf galaxies, and radio galaxies. Measured power-law traced by the 1-0 Q(1) line is observed, UV radiation
indices for this sample ranged from 3.79-6.4 with an av- from the central star cluster is not the only possible
eragevalueof 4.84. Thestar-forminggalaxiesselected source of this excitation: cosmic rays, which as they im-
from the SING∼S sample (Kennicutt et al. 2003) had a pactthedensegascanalsoexcitetheLymanandWerner
slightlyloweraveragepowerlawindexof4.5,butstilldo bands of H (Prasad & Tarafdar 1983). Due to the lim-
2
not approach the low values that we measure in the Cir- itedsensitivityandwavelengthrangeoftheSWSspectra,
cumnucleardisk. Evenintheextremeshockedregionsof we lack detections of many of these traditional tracers
Stephan’sQuintet,thepowerlawindexisonlymeasured of fluorescent emission (e.g., more highly vibrationally-
to be 4.5 (Appleton et al. 2017). excitedlineslike1-0S(1)and2-1S(1)Shull&Hollenbach
A di∼rect comparison of these values is complicated be- 1978). However, Ciurlo et al. (2016) in their shorter-
causeofthedifferentscalesinvolved: theCNDcomprises wavelength observations of H in the central cavity of
2
onlyafewparsecsinthecenterofourgalaxy,whilemany the CND (the central 36(cid:48)(cid:48) by 29(cid:48)(cid:48)), are able to detect
of the measurements from Togi & Smith (2016) average these lines and use them to discriminate between colli-
over entire galaxies. Of course, the H -emitting region sional and fluorescent excitation. Using ratios of the 1-0
2
of a galaxy may be much more compact: in the sample S(1) line at 2.1217 µm and the 2-1 S(1) line at 2.2476
of ULIRGS, the mid-infrared H emission is typically µm, they find regions where the excitation is dominate
2
concentrated in the central 1 to a few kpc (Higdon et al. by both fluorescent and collisional excitation. However
2006). Differencesthereforecouldbeeitherbecauseeven in the region that is likely most similar to the CND gas
in galaxies more extreme than the milky way, conditions probed by the ISO observations (their ’Zone 1’ on the
similar to the CND of our galaxy are not present over inner edge of the CND, with a far stronger 1-0 S(1) line
larger (hundreds of parsecs) scales, or because such con- fluxthaninotherlocationsanalyzed),theyfindthatthe
ditions are present, but are diluted by abundant H in line ratios are consistent with collisional heating alone.
2
less-extreme conditions at larger radii. In support of the Thisconfirmspriorassumptions(e.g.,Yusef-Zadehetal.
latter scenario, we note that the ‘typical’ power law in- 2001;Leeetal.2008)thatthe1-0S(1)emissiondetected
dices we measure for clouds in the central 500 pc of our in the CND is likely a tracer of shocks in the CND gas.
Galaxy (a region known to have higher temperatures, We thus conclude that it is likely that the H lines we
2
density, andturbulencethanthediskofourGalaxy)ap- observe toward the Northeast and Southwest regions of
pearquitecomparabletothoseonkiloparsecscalesinthe the CND are collisionally excited.
centersofmoreextremestar-formingandinfrared-bright We also search for anomalous ortho to para ratios in
galaxies. our observed H lines. The typical signature of disequi-
2
librium in the ortho-para ratio is a zigzag or saw-tooth
4.2. The heating mechanism for the CND patternintheBoltzmanndiagram,wheretheortho(odd
J)linesappearsystematicallyweakerthanlinesfromthe
4.2.1. The excitation mechanism of H in the CND
2 para (even J) transitions. We do see a slight sawtooth
For highly-excited lines of H like those we analyze pattern in the S(1) through S(5) lines from the South-
2
here, there are two possibilities for their excitation: col- west region, however the magnitude of the variation in
lisional excitation, in which the observed levels are pop- these lines is consistent with the random scatter seen in
ulated by collisions with other H molecules, atoms, the higher pure-rotational lines. We find no evidence for
2
8
an anomalous ortho to para ratio in the observed pure- expected for a PDR driven by the central star cluster.
rotational lines of H for the other two positions: this C-shocks as the dominant mode of heating the CND
2
characteristicpatterndoesnotappearintheresidualsof would be consistent with Rodr´ıguez-Fern´andez et al.
the temperature fits for the Northeast region or toward (2004), who find that PDRs can only contribute 10-30%
Sgr A*. Anomalous ratios have previously been seen in of the heating for gas in Galactic center clouds outside
the pure-rotational 0-0 S lines of several Galactic center oftheCND.Theyfavormoderate-velocityshocks(v 25
clouds (Rodr´ıguez-Fern´andez et al. 2000), as well as in km s−1) induced by turbulent motions as the prim∼ary
the1-0SlinesobservedbyCiurloetal.(2016)inseveral heating source in these clouds, for example contribut-
positions in the central cavity of the CND. Such ratios ing to the warm H measured by Rodr´ıguez-Fern´andez
2
have been attributed to the recent formation and/or de- et al. (2001) toward a number of these sources. For the
structionofH2 beforeitcanreachorthotoparaequilib- CND, chemical modeling by Harada et al. (2015) favors
rium via e.g., proton-exchange collisions with H+, H+3, shocks with v>40 km s−1 for reproducing the observed
or H3O+(Gerlich 1990; Le Bourlot et al. 1999). abundances of species in millimeter and submillimeter
observations. However, such velocities are near those re-
4.2.2. Shock heating quired to dissociate H molecules, and so velocities (cid:38)
2
40 km s−1 are likely ruled out by our observations of
Based on the continuous distribution of warm to very
H at temperatures > 2600 K, which are also consistent
hot temperatures we measure with the pure rotational 2
withwhatisfoundforthepeaktemperaturesinC-shock
lines of H and the line ratios measured by Ciurlo et al.
2 models with v 25-30 km s−1. Shock velocities > 25
(2016), we favor a scenario in which the warm/hot H2 km s−1 and co∼rrespondingly higher temperatures in the
in the CND is heated in shocks. The presence of gas at
CNDwouldbeconsistentwithrecentworkthatsuggests
temperatures in excess of 2000 K rules out dissociative
turbulentheatingisresponsibleforacorrelationbetween
shocksasthesourceofthisheating, astheH molecules
2 temperature and linewidth in Galactic center molecular
must survive to the post-shock phase in order to reach
clouds(Immeretal.2016),astheCNDhasmuchbroader
these temperatures, as opposed to dissociating and re-
linewidths than other Galactic center clouds (σ 10-40
MforcmKieneg1a9t89c)o.oler temperatures (∼500 K; Hollenbach & km s−1on 0.2 pc scales; Montero-Castan˜o et al.∼2009),
Althougheithershocksorahighcosmicrayionization comparedtopredictedandobservedσ 0.5-5kms−1for
rate are favored by chemical modeling of millimeter and other Galactic center clouds (Shetty e∼t al. 2012; Kauff-
submillimeter molecular lines in the CND (Harada et al. mann et al. 2013; Rathborne et al. 2015). In order to
2015),heatingbycosmicraysappearsunlikelytobesuf- explain the higher temperatures measured in the South-
ficient to produce the observed fractions of gas at these west,wewouldpredictthatcarefulanalysisoftheNorth-
high temperatures (Clark et al. 2013). This is consistent east and Southwest regions would find larger linewidths
with the observed Herschel far-infrared line ratios mea- in the Southwest, and more signatures of shocks.
suredbyGoicoecheaetal.(2013)towardthecentralcav-
ity,whicharealsosuggestedtoruleoutbothcosmicrays 4.3. The spatial distribution of the warm gas
andX-raysforheatingthehot(T 1300K)gas. Photon-
Given that the ISO spectra analyzed here consist of
dominated regions (PDRs) as th∼e sole source of heating
three large-aperture pointings toward the central par-
in the CND were initially ruled out by Bradford et al.
secs and thus have extremely limited spatial informa-
(2005), based on the observed ratio of CO 7-6 and [OI]
tion, one question is where the measured H is actually
2
63 µm lines compared to predictions from PDR models
located. Prior observations (e.g., Etxaluze et al. 2011;
(e.g.,Kaufmanetal.1999). However,thisconclusionwas
Goicoechea et al. 2013; Lau et al. 2013; Ciurlo et al.
basedontheassumptionthataclumpyPDRmodelwith
2016) have pointed to the central cavity and the inner
high-density gas like that applied to the Orion bar (e.g.,
edge of the CND as the location of both the hottest gas
Burton et al. 1990) is not applicable to the CND, when
and dust. However, the resolution of our ISO data is
in fact more recent analyses have found that there is gas
not sufficient to distinguish between these locations, nor
with significantly higher densities (n 2 105 3 106
are the kinematics sufficiently precise to be indicative
cm−3;Requena-Torresetal.2012;M∼illse×tal.2−013)×than of a particular location (though, the average velocities
the Bradford et al. (2005) measurement (n 5 6 104 of the ISO Northwest and Southwest region spectra are
cm−3). The presence of higher-density clum∼ps−cou×ld al- broadly consistent with the kinematics of dense gas in
low for a more sizable contribution from PDR heating, the CND, e.g., Christopher et al. 2005). However, the
howevergiventhattheCO7-6to[OI]63µmratiointhe high-resolution maps of the 1-0 Q(1) line published in
CNDisstillanorderofmagnitudebelowaclumpyclassi- Feldmeier et al. (2014) and reproduced here in Figure 1
calPDRliketheOrionBar(Staceyetal.1993),andthat can give some insight into the distribution of the hottest
apparently very hot gas is also located at large separa- H in the central parsecs. We can clearly see peaks in
2
tionsfromthecentralstarcluster,itisstillnotlikelythat the flux of the 1-0 Q(1) line at the positions of our ISO
thisisthesolesourceofheatingintheCND.SomePDR apertures centered on the Northeast and Southwest re-
heatingcouldbesupportedbyourmeasurementthatthe gion. Importantly, even in this highly-excited H line
2
Southwestregion(theedgeofwhichisionized)iswarmer (which, as noted above is consistent with being thermal-
than the Northeast region. However, higher spatial res- ized at T < 2600 K), these peaks in the highest column
olution observations of the H emission in conjunction density of the very hot H are nearly cospatial with the
2 2
with an improved 3D model of the molecular gas in the peaks of cooler molecular gas and dust (e.g., as seen in
CND are needed to determine whether this difference is Figure of 2 of Montero-Castan˜o et al. 2009). In fact,
consistent with a radial trend in heating that would be emission from the 1-0 Q(1) line is clearly not confined
9
just to the central cavity or a narrow inner edge of the derived from our power-law temperature fitting as a sig-
CND, but is present at radii from 1 pc to 5 pc from Sgr nificant component (or even all) of the molecular gas in
A* and the central nuclear cluster. So, although prior theCND(withintheISOaperture). ThefirstisthatT=
observationsofhotmoleculargasanddustinthecentral 50 K (or T= 100 K)is a valid cutoff temperaturefor the
parsecs have suggested that this gas is primarily found gas in the CND. A second major assumption is that the
in the central cavity and minispiral (Cotera et al. 1999; extrapolation of the power-law index derived using the
Goicoechea et al. 2013; Ciurlo et al. 2016) and the inner S(1) lines and above is valid for the lower temperatures
edge of the CND (Lau et al. 2013; Ciurlo et al. 2016), of interest here. A third assumption is that we are able
the observations of Feldmeier et al. (2014) suggest that to detect all of the emitting H in our aperture (there
2
itismorebroadlydistributedthroughouttheCND.This are no local extinction effects). Finally, in order to put
is important for understanding what is heating the gas, themeasuredquantitiesincontext,wemustassumethat
and we return to this point in Section 4.2. CO (or dust) is a (more) reliable indicator of the total
As expected, the column of hot H is not greatest to- H column of all of the H gas, encompassing the cold,
2 2 2
ward Sgr A* (in the central cavity, which is believed to warm, and hot components.
be largely evacuated, containing only a few tens of solar
4.4.1. The cutoff temperature
masses of ionized gas and a few hundred solar masses
of neutral gas; Jackson et al. 1993). It is also not clear We first address the assumption that a temperature
in these ISO observations whether we are even detecting of 50 or 100 K is a valid cutoff temperature for the dis-
central cavity gas in the pointing toward Sgr A*. Due tribution of gas temperatures in the CND. The coolest
to large noise and poor baseline shapes for this position, rotational temperature we can directly measure through
we only detect enough lines of H to constrain a sin- our discrete temperature fits is 580 K in the Southwest
2
gle 1110 K tempertaure component. The velocity of regionand520KintheNortheastregion. Fromournon-
the∼H lines toward this position (28 25 km s−1) could detection of the S(0) line, we also have a limit of >110
2
be consistent with the velocity of ga±s in the nearby 50 K (>130 K) for T32 in the Northeast (Southwest) re-
and 20 kms clouds, which recent orbital models place gion. However, rotational temperatures like this are not
(cid:38) 50 pc in the foreground of Sgr A* (Kruijssen et al. stronglyconstraininginthepresenceofmultipletemper-
2015). Thespectraalsodonotclearlyhaveabroaderline atures,as50or100Kgascouldexistalongwithwarmer
widththantheotherpositions,whichwouldbeexpected gas that has a larger contribution to the S(1) column
ifthiswasindeedgasclosertoSgrA*,withhigherorbital and thus increases the measured T32. There could also
speeds consistent with those seen in the ionized minispi- beyetcoldergasnotpickedupbytheS(0)line. Thebest
ral (Zhao et al. 1993). So, although Ciurlo et al. (2016) constraint on this cold material comes from the dust, as
appeartodetectgasinthecentralcavityintheirhigher- temperatures as low as 25 K have been measured for the
resolution maps of near-infrared rovibrational lines, we CND(Etxaluzeetal.2011). Althoughdustandgastem-
cannot clearly say that the gas we detect toward Sgr A* peratures are not globally observed to be in equilibrium
is any closer to the central black hole than the CND gas in the Galactic center, dust temperatures of 20-30 are
detected in other positions. associated with gas temps of 50-70 K in other Galactic
Despite the lack of detailed spatial information in the centerclouds(Ginsburgetal.2016). Asacutofftemper-
ISO data, we do notice several key differences between ature of 50 K recovers a significantly smaller amount of
theH2 emissiontowardtheNortheastandSouthwestre- the dust or CO-inferred total H2 column in the South-
gions of the CND. First, the H lines are stronger for a west compared to the Northeast, this also suggests that
2
given J in the Northeast region than in the Southwest theremaybealowercutofftemperatureintheSouthwest
region. Notsurprisingly,thetotalcolumnofwarmH in than in the Northeast. As this seems somewhat incon-
2
theNortheastregionistwiceaslargeasintheSouthwest sistent with the general trend seen that the Southwest
region. However, even though the lines are brighter in region is warmer than the Northeast, we discuss some
the Northeast region, the extinction toward the North- alternatives to this in the following sections.
east region is slightly larger. Interestingly, this is the re- Acutofftemperatureof50Kalsoimpliesthatthebulk
verse of what is typically observed in the emission from of the gas ( 70 80%) is cold (T<100 K). Although
othermolecularspecies,wheretheNortheastregiongen- gas tempera∼tures−of 50 K are not excluded by excitation
erally appears much weaker than the Southwest region analyses of HCN (Mills et al. 2013), the CO analysis of
(Requena-Torres et al. 2012; Mills et al. 2013). Requena-Torres et al. (2012) found the temperature of
the CO must be greater than 150 K (based on the ob-
4.4. Interpreting the mass of warm H2 in the CND served ratio of 12CO and 13CO lines). Although this
In order to determine if we can draw any strong con- would appear to rule out cutoff temperatures as low as
clusions about the molecular gas mass of the CND from 50or100 K,wenotethat thepresenceofthiscoolgas is
thetemperaturedistributionswehavefittotheobserved neededforourextrapolatedH columnfromdirectmea-
2
H lines in the CND, we first examine the assumptions surementsofH tobeatallconsistentwiththetotalH
2 2 2
that underly these analyses. We focus on the results ob- column inferred from these same CO observations. We
tained from fitting a continuous, power-law distribution thusdonotyetruleoutthepossibilityofacutofftemper-
of temperatures, as it has the potential to infer proper- ature as low as 50 K for the CND gas (though the cutoff
ties for a larger fraction of the gas in the CND, rather temperature is likely to be higher for the Northeast re-
thanthesmallfractionofgasatT>500Kmoredirectly gion, as a cutoff temperature of 50 K yields a larger gas
probed in our discrete temperature fits. mass than is seen with CO or dust). However, this sce-
We identify several key assumptions in this analysis nario then requires a significant burden of observational
thatwemustevaluateinordertointerprettheH masses proof, including an explanation of the observed CO iso-
2
10
tope ratios (either as an average on large scales that is higherclumpyextinctionforoneregionshouldnotman-
notrepresentativeoftheisotoperatiosonsmallerscales, ifestasanychangeintemperature,asemissionwouldbe
or due to some type of anomaly), and verification of T= uniformlymissingforalloftheobservedrotationallines.
50 or 100 K gas with direct measurements using other However, the fact that the extinction is actually mea-
tracers (e.g. NH , CH CN, CH CCH). suredtobeslightlyhigherintheNortheastregion(while
3 3 3
we would need it to be higher in the Southwest region
4.4.2. The extrapolation of a single power-law temperature to hide more of the H2 emission) would seem to argue
fit against the scenario we propose. Ultimately, higher spa-
tial and spectral resolution observations are needed to
In order to infer a total gas mass by extrapolating our
directly compare the clumpy structure observed in other
H data to temperatures below those which are mea-
2 molecules with the structure of the H emission, and to
sured, the power law temperature distribution we fit to 2
and compare the kinematic components directly traced
theS(1)andhigherlinesmustalsobevalidforthelower-
by H and other molecules to confirm that H is not
temperaturegas. Inobservationsofthecentersofnormal 2 2
subject to significant local extinction, and that the H
spirals and star forming galaxies that include the detec- 2
is indeed observed to be fully and proportionately inter-
tion of the S(0) line, there is no evidence for a break in
mixed with the gas traced by other molecules.
the power law between the S(0) and S(1) lines (Togi &
Smith 2016). Further, extrapolating the power-law dis-
4.4.4. Proxies for the total H mass
tribution of H column densities to a temperature of 50 2
2
K in these galaxies appears to consistently recover the We find that the total molecular mass inferred from
total H column as inferred through measurements of twoproxiesforH : observationsofmultiplelinesof12CO
2 2
CO. This would support the adoption of a single power- and13CO(Requena-Torresetal.2012)andcolumnden-
lawdistributionfordescribingtherangeoftemperatures sitymapsderivedfromHerscheldustemission(Battersby
present in the CND gas. Alternatively, if the gas in the etal. inprep;privatecommunication)aregenerallycon-
CND were not consistent with a single power-law de- sistent. The dust-derived masses are slightly lower than
scription of the temperature, this could account for the the CO-derived masses: by a factor of 1.2 in the South-
small(andvarying;6-140%)fractionofthetotal(COand westand1.1intheNortheast. However, theCO-derived
dust-derived) H column that is recovered in the South- mass has been scaled to the size of the ISO aperture
2
westandNortheastregionsoftheCNDbyextrapolating (as the aperture for the CO observations is significantly
a single power law for the observed H lines down to a larger)assumingthattheemissionisuniformacrossthis
2
cutoff temperature. However, a more complicated tem- aperture. Ifthisemissionisnotuniform,thentherecould
perature profile would seem to require a unique physical bealargerdiscrepancybetweenthesemasses. Giventhat
mechanism in this region that does not operate on kilo- the dust-derived mass is consistent with the CO-derived
parsecscalesinthecenterofothergalaxies. Althoughthe mass, and that the Galactic center consists of relatively
local line widths and densities in CND may be slightly high-metallicitygas,wealsodonotexpectthatCO-dark
more extreme than the average conditions over kilopar- gas is a substantial component of the CND.
sec scales in the center of our own and other galaxies While it is possible that there could be additional
(e.g. Montero-Castan˜o et al. 2009; Mills et al. 2013), at systematic uncertainties in these mass determinations
present we do not have a good justification for invoking (for example, in the adopted [12CO]/[H ] abundance of
2
the additional complexity of a varying power-law index. 8 10−5 used by Requena-Torres et al. (2012) to deter-
m×ine the CO to H conversion, or in the assumption for
2
4.4.3. Local variations in the extinction thedustofaconstantgastodustratioof100andaβ of
1.75 over the entire Galactic center), the consistency of
Anotherpossiblefactorthatcouldexplainthefactthat
the masses inferred from both CO and dust suggest that
total H column derived from our power-law extrapola-
2 these are unlikely to be significant.
tion of the pure-rotational lines, and that derived from
CO or dust are not completely consistent (especially in
4.4.5. The total H mass
the Southwest region) is clumpy extinction. In this sce- 2
nario, the lower column of pure-rotational line emission Wecanmakeanextremelyroughestimateofthetotal
observed in the Southwest region (where stronger emis- molecular mass of the CND by using the maps of the
sionfromdensegastracersisobserved;Montero-Castan˜o Q(1) line flux from Feldmeier et al. (2014), to scale the
et al. 2009) might be due to having more of the gas hid- masses determined from the rotational H lines in the
2
den by higher local extinction in the clumpy structures observedISOapertures. Thetwo14(cid:48)(cid:48) 20(cid:48)(cid:48)ISOapertures
that carry the bulk of the mass. If extinction did hide covering the Northeast and Southw×est regions contain
some of the H emission in the CND, this could relax only 1/13 of the total Q(1) emission seen by Feldmeier
2
the tension we found from comparison with the CO ob- etal.∼(2014)overthecentral9.5 8parsecsoftheCND.If
servations of Requena-Torres et al. (2012) that both re- the brightness distribution of th×e rotational lines we use
quire the H to be hotter than 150 K, and infer a larger to determine the mass and the rovibrational Q(1) line of
2
total H column than can be matched with our direct H is similar, then we would infer that the total mass of
2 2
observations of H even when extrapolating to 50 K. A gaswithT>50KintheCNDis 8600M . Thisis 15-
2 (cid:12)
cutoff temperature of 150 K would then not be inconsis- 40% of the total molecular ma∼ss of gas (2-5 104 ∼M )
(cid:12)
tent with a total column inferred directly from H that estimatedtobepresentintheCND(Etxaluze×etal.2011;
2
is much less than that derived with CO (or dust). Requena-Torresetal.2012). However,therearelikelyto
We note that due to the flat shape of the extinction be significant differences in the distribution ofrotational
law from 2-20 µm (Fritz, and our plots of extinction), androvibrationallines,sothisestimateshouldbetreated