The scale height of gas traced by [CII] in the Galactic plane
aa r X i v : . [ a s t r o - ph . GA ] M a r Astronomy&Astrophysicsmanuscript no. aa˙2013˙23281˙Langer˙final c (cid:13)
ESO 2018August 30, 2018
The scale height of gas traced by [C ii ] in the Galactic plane W. D. Langer, J. L. Pineda, and T. Velusamy ⋆ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109-8099, USAe-mail:
Received 19 December 2014 / Accepted 10 March 2014
ABSTRACT
Context.
The distribution of various interstellar gas components and the pressure in the interstellar medium (ISM) is a result of theinterplay of di ff erent dynamical mechanisms and energy sources on the gas in the Milky Way. The scale heights of the di ff erent gastracers, such as H i and CO, are a measure of these processes. The scale height of [C ii ] emission in the Galactic plane is important forunderstanding those ISM components not traced by CO or H i . Aims.
We determine the average distribution of [C ii ] perpendicular to the plane in the inner Galactic disk and compare it to thedistributions of other key gas tracers, such as CO and H i . Methods.
We calculated the vertical, z , distribution of [C ii ] in the inner Galactic disk by adopting a model for the emission thatcombines the latitudinal, b , spectrally unresolved BICE survey, with the spectrally resolved Herschel
Galactic plane survey of [C ii ]at b = ◦ . Our model assumed a Gaussian emissivity distribution vertical to the plane, and related the distribution in z to that of thelatitude b using the spectrally resolved [C ii ] Herschel survey as the boundary solution for the emissivity at b = ◦ . Results.
We find that the distribution of [C ii ] perpendicular to the plane has a full-width half-maximum of 172 pc, larger than that ofCO, which averages ∼
110 pc in the inner Galaxy, but smaller than that of H i , ∼
230 pc, and is o ff set by -28 pc. Conclusions.
We explain the di ff erence in distributions of [C ii ], CO, and H i as due to [C ii ] tracing a mix of ISM components. Modelsof hydrostatic equilibrium of clouds in the disk predict di ff erent scale heights, for the same interstellar pressure. The di ff use molecularclouds with [C ii ] but no CO emission likely have a scale height intermediate between the low density atomic hydrogen H i clouds andthe dense CO molecular clouds. Key words.
ISM: ions — ISM: clouds — Galaxy: structure
1. Introduction
The star formation rate in the Galaxy may be related to thepressure of the interstellar medium (ISM), which itself is afunction of the interplay of dynamical processes and energysources on the interstellar gas. It has also been suggested thatISM pressure plays a role in the formation of giant molecu-lar clouds Blitz & Rosolowsky (2004, 2006). Thus, the vertical( z ) distribution of the various ISM gas components is an im-portant parameter for understanding these dynamical processesthroughout the Milky Way. In the Galaxy, interstellar cloudsare distributed in a thin disk about the mid-plane at b = ◦ and their scale height depends, in hydrostatic equilibrium, ona number of factors, including thermal pressure, the randommotion of the clouds, magnetic pressure, ionization pressure,and the gravitational force of the stars and gas in the disk.Thus, determining the z –distribution, which may be di ff erentfor various ISM components, provides information about theseparameters. The scale height of the di ff use atomic hydrogenclouds is known from extensive maps of the H i CO J = → i and H (as traced by CO) clouds are dif- ⋆ Herschel is an ESA space observatory with science instrumentsprovided by European-led Principal Investigator consortia and with im-portant participation from NASA. ferent and each varies by a factor of ∼ i and CO, the1.9 THz emission from ionized carbon, [C ii ], traces the H gaswhere carbon is ionized but little, or no, CO or neutral carbonis found (the CO-dark H gas), and also traces the warm ionizedmedium (WIM).The scale height for clouds traced by [C ii ] is not well estab-lished because the necessary spectral line surveys of its 158- µ mline have not, until recently been available. The COBE FIRASinstrument made the only large-scale survey of spectrally un-resolved [C ii ] (Wright et al. 1991; Bennett et al. 1994), how-ever, COBE with its 7 ◦ beam and ∼ − velocity res-olution, is unable to resolve the latitudinal distribution. Thereare two moderate-scale Galactic surveys of spectrally unresolved[C ii ], the Far-Infrared Line Mapper (FILM) onboard the InfraredTelescope in Space (IRTS) (Shibai et al. 1994; Makiuti et al.2002) and the Balloon-borne Infrared Carbon Explorer (BICE)(Nakagawa et al. 1998), and an earlier small-scale survey withthe Balloon-borne Infrared Telescope (BIRT) (Shibai et al.1991). However, there is only one spectrally resolved survey,the Herschel open time key program, Galactic Observationsof Terahertz C + , hereafter GOT C + (see Langer et al. 2010;Pineda et al. 2013; Langer et al. 2014). FILM and BICE had anangular resolution of order ten to fifteen arcminutes, su ffi cient todetermine the latitudinal b distribution of [C ii ], but the velocityresolution was, at best, ∼
175 km s − for BICE (for FILM it was ∼
750 km s − and for BIRT 143 km s − ). Only the GOT C + sur-vey had the spectral resolution ( < − ) su ffi cient to resolve ii ] Galactic scale height the velocity structure of individual gas clouds and thus locatetheir Galactic radius using a position–velocity rotation curve.However, GOT C + surveyed [C ii ] sparsely in longitude, l , andlatitude, b .Here we determine the average scale height distribution of[C ii ] in z by combining the high spectral resolution [C ii ] radialdistribution from GOT C + at b = ◦ with the BICE latitudinalangular distribution in b by adopting a hydrostatic model resultfor the distribution in z . We use the BICE survey to determinethe scale height of [C ii ] emission because it had better coveragein both longitude and latitude in the Galactic disk than the BIRTand FILM surveys. BICE had an angular resolution of 15 ′ , andspectral resolution of ∼
175 km s − .The GOT C + survey contains several hundred lines-of-sightof spectrally resolved [C ii ] emission throughout the Galacticdisk from l = ◦ to 360 ◦ and b = ◦ , ± . ◦ , and ± . ◦ . However,because GOT C + is a sparse survey it does not have su ffi cientcoverage in latitude b to derive a smooth continuous distribu-tion in the vertical distribution z . In contrast, the BICE surveyhad insu ffi cient spectral resolution, but had much better cover-age in b , but only observed up to latitudes b = ± ◦ and onlywithin longitude 350 ◦ ≤ l ≤ ◦ . GOT C + has a 3- σ sensitivity ∼ − (Langer et al. 2014) which, over the bandwidthof the velocity resolution of BICE, corresponds to 7.4 × − ergss − cm − sr − . BICE has a 3- σ detection limit ∼ × − ergss − cm − sr − (Nakagawa et al. 1998). Thus GOT C + is almostthree times more sensitive than BICE and capable of detectingthe [C ii ] emission seen by BICE.We also use results from FILM (Shibai et al. 1996;Makiuti et al. 2002), which observed [C ii ] at higher latitudesthan BICE, to recalibrate the results of Nakagawa et al. (1998)for | b | = ◦ to 4 ◦ . FILM observed [C ii ] along a great circlecrossing the plane at l = ◦ (inner Galaxy) and 230 ◦ (outerGalaxy), but measured the [C ii ] intensity for larger latitudes thanBICE. However, Shibai et al. (1996) and Makiuti et al. (2002)smoothed their data to 1 ◦ to improve their sensitivity, insu ffi -cient to use at low latitudes to determine the scale height in thedisk.Nakagawa et al. (1998) compared the latitudinal distributionof [C ii ] from BICE with those of H i , CO, and far-infrareddust emission, finding that H i had the largest distribution in b followed by [C ii ] and then far-infrared dust emission, and thatCO had the smallest distribution in b . However, without know-ing where the [C ii ] emission came from they could not assign aspatial scale height to the gas traced by the [C ii ] 158- µ m line.We begin with a summary of the BICE and GOT C + [C ii ] distri-butions and then derive an approximate relationship between theradial and b distributions that allow us to deconvolve the [C ii ]distribution in z in the disk. Finally, we compare the [C ii ] scaleheight with those of CO and H i and discuss its implications forthe understanding the sources of [C ii ] emission.
2. The z-distribution of [C ii ] To determine the latitudinal distribution of [C ii ] Nakagawa et al.(1998) averaged the [C ii ] line intensity (measured in erg s − cm − sr − ) only over longitudes 5 ◦ < l < ◦ in order to avoidthe Galactic center, and calculated a relative intensity as a func-tion of b such that the peak of this distribution is unity. Herewe define the relative intensity as I ( b ) / I ( b c ), where I ( b ) is theintensity along b , and I ( b c ) is the intensity at the peak of thedistribution located at b c (i.e. this term accounts for any o ff setin the peak from b = ◦ ). However, Nakagawa et al. (1998) setthe normalized intensity to zero at b = ± ◦ , thus suppressing [C II] BICE[C II] {BICE + FILM} I ( b ) /I ( o ) b( o ) Fig. 1.
Distribution of the normalized intensity of [C ii ], I ( b ) / I ( b c ), as a function of latitude as derived by Nakagawa et al.(1998) from the BICE survey (solid line). The modified distribu-tion using the FILM latitudinal data to calibrate the normalizedintensity at b ± ◦ (dashed line).potential contributions from | b | = ◦ to 4 ◦ . The relative intensitydistribution from BICE is plotted in their Figure 9, and recreatedhere in Figure 1. Nakagawa et al. (1998) also plotted the corre-sponding relative intensity of other ISM gas and dust tracers:H i , CO(1 → b , for thesefour tracers and their results are summarized here in Table 1. InFigure 1 it can be seen that the peak in the [C ii ] relative inten-sity is shifted slightly below the plane to b c ∼ − . ◦ ; the far-IRemission also peaks there (see their Figure 9), but their plot ofthe CO and H i peak at b = ◦ .The assumption that I ( b = ± ◦ ) / I ( b c ) = ii ] and could introduce a slight er-ror in determining the FWHM. Shibai et al. (1996) observed that[C ii ] emission in the FILM latitudinal scans extended out to per-haps ± ◦ (see their Figure 1, which plots the [C ii ] intensity dis-tribution in latitude smoothed over a 1 ◦ beam). They interpretedthe latitudinal [C ii ] distribution as having two components: (1)concentrated emission in the disk; and, (2) a weaker component,decreasing slowly with b beyond ∼ ◦ . Makiuti et al. (2002)analyzed the distribution at large b and conclude that it mainlytraces the WIM at high latitudes. We have fit the wings of theFILM inner Galaxy scan from 4 ◦ to 10 ◦ in order to recalibratethe BICE distribution such that the BICE relative intensity cor-responds to the relative intensity ratio observed by FILM at ± ◦ .We do not use the FILM fit beyond ± ◦ because the FILM ob-serving path results in b being a strong function of longitude l and it does not cover the regions needed to compare GOT C + with the BICE survey, and because at large b FILM is surveyingthe Galaxy near the solar radius. The revised BICE distribution isshown in Figure 1 and labeled BICE + FILM. This recalibrationmakes very little di ff erence to the bulk of the [C ii ] distribution,but, as will be seen later, provides a much better fit to the wingsat | b | ≥ ◦ . ii ] Galactic scale height Table 1. b (FWHM) of gas and dust tracers: Nakagawa et al.(1998) Tracer FWHM in b Data sourceH i ◦ Hartmann & Burton (1997)[C ii ] 1.32 ◦ Nakagawa et al. (1998)far-IR dust 1.18 ◦ Beichman et al. (1988)CO 1.07 ◦ Dame et al. (1987)
The GOT C + survey observed spectrally resolved [C ii ]along 151 lines-of-sight covering 0 ◦ < l < ◦ at b = ◦ .The details of the observing mode and data reduction are dis-cussed in Pineda et al. (2013), and representative spectra can beviewed there and in Langer et al. (2014). In Pineda et al. (2013)the [C ii ] spatial-velocity maps were used along with a Galacticrotation curve to assign the intensity as a function of Galacticradius. These intensities were then summed in rings about theGalactic center and then used to calculate the azimuthally av-eraged emissivity for [C ii ], ǫ [CII] ( R gal ) as a function of Galacticradius, R gal , in units of K km s − kpc − , except for the inner-most 0.5 kpc, because this region is undersampled. In Figure 2we reproduce the radial distribution for ǫ [CII] ( R gal ) from Figure 7in Pineda et al. (2013). In Figure 2 it can be seen that the [C ii ]emissivity peaks in the molecular ring at about 5 kpc and mostof the emission comes from R gal = + radial distributionsees all the [C ii ] components observed by BICE including theWIM, which is believed to more prominent at higher latitudesthan in the plane. In the Galactic plane for b = ◦ the contribu-tion of the WIM component in the radial profile was estimatedby Pineda et al. (2013) to be only ∼
4% using the electron abun-dance of low density ionized gas in the plane as given by theNE2001 code (Cordes & Lazio 2002). Note that this value isonly an estimate and is not directly observed in the GOT C + data. However, Velusamy et al. (2012) used the GOT C + data todetect emission from the compressed WIM along selected linesof sight corresponding to the spiral arm tangencies. Combinedwith its higher sensitivity and adequate sampling in the plane, thedistribution of [C ii ] emission in the GOT C + radial profile con-tains all [C ii ] features as seen by BICE, including the emissionfrom the WIM. Therefore we believe that the combined e ff ectsof all [C ii ] components will be fully represented in our solutionfor the z-scale derived below.We can determine the average z distribution in the innerGalactic disk by combining the GOT C + radial distribution of ǫ [CII] ( R gal ) for b = ◦ with the modified BICE + FILM latitudi-nal distribution if we know the functional form of the emissivityin z , and if we assume that the distribution in z is independentof location in the inner Galactic disk. For the first assumption,models of hydrostatic equilibrium of gas in the ISM suggest aGaussian distribution for many ISM components, however, thesecond assumption can only be correct on average, because thepressure in the ISM varies across the Galaxy, and the observedscale heights for CO and H i vary with Galactic radius.Adopting these two assumptions the averaged [C ii ] inten-sity observed by BICE + FILM along a line-of-sight is just theintegral of the emissivity along a path length s from the solarsystem, as illustrated in Figure 3 for l = ◦ . If we know the valueof the emissivity at z = z for a given scale height of the Gaussian distribution. Thus theintensity measured by BICE + FILM as a function of b is relatedto the [C ii ] emissivity, ǫ [CII] ( R gal , l , x , z ), as a function of the dis-tance to the source in the plane, x , the height above the plane, Fig. 2.
Galactic radial emissivity of [C ii ], ǫ [CII] ( R gal ), derived byPineda et al. (2013) using the GOT C + [C ii ] survey at b = ◦ . ! " %&’()!* ! +,! " ! ! " * *-. /! Fig. 3.
Schematic showing two representative lines of sight(dashed lines) from the solar system through the Galactic disk(GC labels the Galactic center and b labels the latitude). The in-tensity of [C ii ] is the integral of the emissivity, ǫ , along the pathlength s (see text). The actual lines of sight used to calculate theintensity cover l = ◦ to 25 ◦ . z , along a line-of-sight longitude l , and latitude, b . Most of theobserved [C ii ] intensity measured by BICE comes from the nearside of the inner Galaxy for | b | ≥ ◦ because at higher latitudesthe line of sight passes far above the plane on the far side of theGalaxy. For example, at b = ◦ the line of sight, s , passes ∼ b = ◦ , it is ∼
450 pcabove the plane, and on the far side of the molecular ring it is >
600 pc above b = ◦ .We can write the intensity as a function of latitude, I ( b ),along a given line of sight in terms of the integration of the emis-sivity as follows, I [CII] ( b ) = Z s max ǫ [CII] ( s ) ds (1)where the integral of the emissivity ǫ [CII] ( s ) is along a line s fromthe solar system, s min = s max , where theemissivity is small. As illustrated in Figure 3 we can relate theintensity of emission at each location along s to the emission ii ] Galactic scale height along the plane at b = ◦ , by changing the integration along s to x in the plane. Substituting x = s cos( b ) in Equation 1 we get, I [CII] ( l , b ) = Z x max ǫ [CII] ( x ) f ( z )( cos ( b )) − dx (2)where f ( z ) is the emissivity distribution in z .We have chosen to integrate up to x max =
28 kpc, which ison the far side of the Galaxy and where the GOT C + [C ii ] emis-sivity is very small. However, for all practical purposes, as dis-cussed above, most of the contribution to the intensity comesfrom the near side of the Galaxy, except for the very lowest val-ues of b . The usual form for f ( z ) derived from equations of hy-drostatic equilibrium balancing the ISM pressure with the grav-itational force of the stars and gas in the Galaxy is a Gaussian(c.f. Spitzer 1978), although other dynamical processes (e.g. su-pernova, outflows) can lead to non-Gaussian terms. Here we as-sume a Gaussian distribution for the [C ii ] emissivity of the form, f ( z ) = f ( z c ) e − . z − z c ) / z ) (3)where z is the scale height, z c accounts for an o ff set in thepeak of the distribution, and f ( z c ) normalizes the distributionto unity. The FWHM([C ii ]) is equal to 2(2ln2) . z . We substi-tute this form in Equation 2 and, as can be seen in Figure 3,rewrite the integral using z = x cos( b ). The relative intensity, F ( b ) = I ( b ) / I ( b c ) is given by, F ( b ) = R x max ǫ [CII] ( x ) e − . xsinb − z c ) / z ) cos ( b ) − dx R x max ǫ [CII] ( x ) e − . z c / z ) dx . (4)where cos( b = ◦ ) is unity in the denominator.As mentioned above, Nakagawa et al. (1998) calculated therelative intensity as a function of b by averaging the BICE ob-servations over longitudes from 5 ◦ to 25 ◦ , to avoid the Galacticcenter, thus omitting [C ii ] over a region with Galactic radius ∼ ◦ to 25 ◦ , where we use the GOT C + radial profiles tocalculate the intensity along l for b = ◦ . We also assume that [C ii ] emission is optically thin because most of the GOT C + [C ii ]spectra have a main beam temperature much less than the kinetictemperature (c.f. discussion of C + excitation and [C ii ] radiativetransfer in Goldsmith et al. 2012).We iterated on the two parameters, z and z c in Equation 4to minimize the rms deviation of the model averaged over fivelongitudes compared to the modified BICE + FILM [C ii ] distri-bution. The best fit is given by z =
73 pc and z c = -28 pc, andis listed in Table 2, along with the corresponding FWHM([C ii ]) =
172 pc. We also fit the original BICE distribution without theFILM correction and find the same o ff set and a slightly di ff er-ent FWHM =
170 pc. The fitting parameters to the BICE andthe BICE + FILM distributions do not di ff er significantly as thecentral ± ◦ dominates the quality of the fit. However, the fitis much better for the modified BICE + FILM distribution for | b | > ◦ . In Figure 4 we show a plot of the relative intensity forthe BICE + FILM combination and for just the original BICEdistribution, compared to the fitted distribution as a function of b . It can be seen that our fit is very good over the complete range b = − ◦ to + ◦ , di ff ering by at most ∼
15% from the modifiedBICE + FILM distribution, except at the bumps in the shoulders( b ∼ ± ◦ ) where the di ff erence is as much as 30%.Nakagawa et al. (1998) calculated the total flux measuredby BICE over the entire mapped angular region | b | ≤ ◦ and [C II] BICE[C II] {BICE + FILM}[C II] fit I ( b ) /I ( b c ) b( o ) Fig. 4.
Model fit (dotted line) of the normalized intensity usingthe GOT C + observations at b = ◦ compared to the normalizedintensity from the modified BICE + FILM profile (solid line)versus latitude b . The unmodified BICE profiles are shown forcomparison (dashed line).350 ◦ ≤ l ≤ ◦ to be 6 × − ergs s − cm − . The BICE calibra-tion errors are ±
35% and include an estimated uniform o ff setof 2 × − ergs s − cm − sr − , comparable to the calibration un-certainty (see their Section 3.1). FILM observations are bettercalibrated than those of BICE and Makiuti et al. (2002) com-pared FILM with BICE and found that the [C ii ] line intensityfor FILM is ∼
65% of BICE for I ([C ii ]) > − ergs s − cm − sr − and ∼
85% for I ([C ii ]) < − ergs s − cm − sr − . To confirmthat GOT C + and BICE are sensitive to the same ISM gas com-ponents we calculated the total flux that would be detected byGOT C + over this same angular area, | b | ≤ ◦ and 350 ◦ ≤ l ≤ ◦ ,using the emissivity in the plane ( b = ◦ ) in Pineda et al. (2013)and the Gaussian distribution in z with a FWHM =
172 pc. Wecalculate from GOT C + a total flux ∼ × − ergs s − cm − .This value is about 25% less than calculated in the BICE sur-vey, however, it is in good agreement if we recalibrate BICEusing the calibration from FILM. The agreement between GOTC + and BICE is well within the errors of the BICE result, andsupports our assumption that GOT C + and BICE trace the sameISM gas components.The FWHM for CO has been estimated by several au-thors using di ff erent Galactic surveys, including Sanders et al.(1984), Dame et al. (1987, 2001); Bronfman et al. (1988);Clemens et al. (1988), Malhotra (1994), and Jackson et al.(2006). They all find about the same result that CO emissionpeaks between 4 and 7 kpc, and in the Galactic center, and thatthe scale height increases with increasing Galactic radius beyond2 kpc and is o ff set below b = ◦ . Sanders et al. (1984) foundthat the FWHM (or 2 z / in their notation) ranged from 60 to140 pc for R gal increasing from 3 to 8 kpc. To compare the COdistribution with the average derived for [C ii ] we calculated theaverage FWHM(CO) using their results from 3 to 8 kpc wherethe [C ii ] is largest. We find < FWHM > = ∼
110 pc and z c ∼ -25pc, and these values are listed in Table 2. Their CO o ff set below ii ] Galactic scale height Table 2.
Tracer fitting parameters
Tracer z < FWHM > z c F( b c ) F( ± ◦ ) Reference(pc) (pc) (pc)[C ii ] 73 172 -28 1.0 0.04 This paper CO 46.7 110 -25 1.0 1H i
212 -25 i
530 -25 i
403 -25 R gal = ff setin H i to facilitate comparison of the distributions. the plane is very close to what we derived for [C ii ], however, theCO FWHM is noticeably smaller than that for [C ii ].The H i distribution in the Galaxy has been discussed bymany authors (c.f. Boulares & Cox 1990; Dickey & Lockman1990; Narayan & Jog 2002; Kalberla & Dedes 2008;Kalberla & Kerp 2009). Here we will use the parametersfrom Dickey & Lockman (1990) for fitting the distributionof H i relative intensity with z . H i is roughly constant from R gal = z is complicated byhaving several components, some of which extend into the halo.Dickey & Lockman (1990) find that the best estimate of the z mean density distribution, n ( z ), is given by two Gaussians withpeak mean densities of n (0) = n (0) = − andFWHM = of 212 and FWHM =
530 pc, plus an exponentialwith a peak mean density, n (0) = − and scale height403 pc. In Table 2 we list their two Gaussian parametersand one exponential parameter, but to calculate a relative H i intensity we normalize their contributions to the total intensityusing the corresponding central mean densities to weight thecontributions, where the total F ( z ) = F ( z ) + F ( z ) + F ( z ), with F i ( b c ) = n i ( b c ) / n tot ( b c ), and n tot ( b c ) = n ( b c ) + n ( b c ) + n ( b c ).We have included an o ff set z c = −
25 pc for H i in Table 2, tofacilitate comparison of the relative distributions of the three gastracers. The spatial resolution of H i Galactic surveys is not highenough to resolve clearly an o ff set z c (HI) of order 25 pc, butthere is some indication that the solar system is o ff set from thewarped Galactic plane as seen in the Leiden-Argentine-Bonn21-cm survey (see Figure 3 in Kalberla & Kerp 2009).In Figure 5 we plot the Gaussian distributions of the relativeintensities as a function of z for [C ii ], CO, and H i using theaverage FWHM for each of the components listed in Table 2.As can be seen in Figure 5 the average distribution of CO as afunction of z in the Galactic disk is narrower than [C ii ], and bothare narrower than that for H i . The distribution for [C ii ] consistsmainly of a disk component confined to ±
200 pc.
3. Discussion
There is a very simple explanation why the scale height for [C ii ]is more than that of CO but less than that of H i . While H i tracesmainly the atomic hydrogen clouds in the Galaxy and CO tracesthe dense molecular clouds, [C ii ] traces both of these regions, aswell as the di ff use molecular clouds that have [C ii ] but no COemission (CO-dark H clouds), and the WIM. The solution forthe density distribution of clouds in hydrostatic equilibrium is aGaussian function, ∝ exp ( − . z / z ) ), with the scale factor, z proportional to the velocity dispersion, < v i > . , where i labelsthe ISM cloud component. The di ff use atomic clouds with theirlower densities have higher velocity dispersions, < v > . ∼ [C II]COHI I ( z ) /I ( z c ) z(pc) Fig. 5.
Gaussian fits for the normalized intensities of [C ii ], CO,and H i as a function of z . The fits include the measured o ff sets z o ff set for CO and [C ii ], and an inferred o ff set for H i equal tothat for CO. Towards the inner Galaxy CO has, on average, thenarrowest distribution in the disk, followed by [C ii ], and H i hasthe thickest distribution.km s − , while those for the denser CO clouds have < v > . ∼ − (see discussion and models in Narayan & Jog 2002).Thus in hydrostatic equilibrium, for an equal ISM pressure, theH i clouds have a larger scale height than those of the denser COclouds.Pineda et al. (2013) found that the PDRs of dense molecularclouds emit ∼
43% of the total [C ii ] throughout the plane at b = ◦ , di ff use atomic hydrogen clouds ∼ ff use molecularclouds (CO-dark H clouds) ∼ ∼ R gal < ii ] distribution, these percentages are only slightly di ff erent.Therefore, it is no surprise that the distribution of [C ii ], whicharises from all ISM components, would have a distribution in-termediate between that of the dense CO clouds and less denseatomic H i clouds and the WIM. Thus [C ii ] traces a mixture ofclouds of di ff erent mass, density, and velocity dispersion, someof which are also traced by H i and CO, and the WIM. The di ff er-ent scale heights then depend on the di ff erent physical propertiesand energetics of the clouds that enter into the hydrostatic mech-anisms responsible for the distribution of gas in the plane.As seen in Figure 5, the derived z distribution in [C ii ] doesnot follow that of H i for z greater than about ∼
200 pc. At thisheight there are few dense molecular clouds as traced by CO andlikely very few di ff use molecular clouds (CO-dark H clouds),so any [C ii ] would have to come from the H i clouds and / or theWIM. Makiuti et al. (2002) compared the distribution of [C ii ]and H i at high latitudes and conclude that the [C ii ] emissioncomes primarily from the WIM (see their Figure 3). However,the FILM results at high latitude are limited to a region near thesolar radius and cannot be extrapolated across the Galaxy. Thecombined GOT C + and BICE data suggest that this conclusionalso holds for the inner Galaxy as well, because H i clouds highabove the plane have low densities and are not likely to emit[C ii ] e ffi ciently. This low emissivity is due to the di ff erence in ii ] Galactic scale height the excitation conditions for H i and [C ii ]. The intensity of H i isproportional to its column density in the optically thin regime, I ([H I]) = . × − N (H I) , (5)in units of (K km s − ), and is relatively insensitive to densityand kinetic temperature. In contrast the [C ii ] emission is verysensitive to kinetic temperature, T kin because the energy of theupper level P / , E u / k = . K is typically higher than thegas temperature in neutral clouds, and density where the atomic,n(H), and molecular, n(H ), hydrogen densities are much lowerthan the critical densities for thermalizing the C + , n cr ( H ) ∼ − and the recently revised value n cr ( H ) ∼ − (Wiesenfeld & Goldsmith 2014). The radiative transfer equationfor the [C ii ] intensity for optically thin emission is given inGoldsmith et al. (2012) and Langer et al. (2014), and, in the dif-fuse clouds, such that the intensity can be written as, I j ([C II]) = . × − e − ∆ E / kT n ( j ) n cr ( j ) N j (C + ) , (6)where I is in units of K km s − and the index j labels H i orH . Therefore, while the H i intensity depends only on the col-umn density of atomic hydrogen, the [C ii ] intensity also dependsvery sensitively on the density and will be much smaller in lowdensity atomic hydrogen clouds above the plane.The scale height for [C ii ] derived here depends on the ra-dial distribution derived from the GOT C + sampling at b = ◦ ,which as noted above is a sparse sample. The premise of theGOT C + survey was that a well designed unbiased sampling inlongitude would represent statistically the distribution of [C ii ]in the Galactic plane. Therefore, the fact that GOT C + , alongwith our model of the z distribution, reproduces the total fluxobserved by BICE (rescaled to the FILM calibration) supportsthis approach.Another potential uncertainty is the adoption of a Galacticrotation curve in Pineda et al. (2013) to locate the source ofthe [C ii ] emission. In Langer et al. (2014) we adopted a rota-tion curve based on gas-flow hydrodynamical models to assigna distance based on velocity. We found that it made a di ff erencemainly in the inner Galaxy, | l | ≤ ◦ , but this region is mostly ex-cluded from the BICE analysis (see above). There are also re-gions where clouds have peculiar velocities due to Galactic dy-namics, where the rotation curve may assign the wrong distance.For example, Zhang et al. (2014) find non-rotational cloud mo-tions at the end of the Galactic bar from parallax observations ofmasers at l ∼ ◦ . While 30 ◦ is outside of the longitudinal rangeobserved by BICE, this region contributes to our GOT C + dataset. We cannot quantitatively assess the error introduced into ourradial distribution but note that, because we average lines of sightfrom all across the Galaxy, the edges of the bar contribute a smallfraction of the emission in any given ring.We cannot calculate the radial dependence for the [C ii ]FWHM from the GOT C + survey without a better samplingin b . However, to gain some insight on the e ff ect of a variableFWHM( R gal ), we assume that it varies similar to that for CO.Sanders et al. (1984) and Clemens et al. (1988) found that theCO scale height varied roughly as R . between 3 and 9 kpc.We replaced z o in Equation (3) with one that varied ∝ R . for R gal > b , similar to what was doneto determine an average scale factor. We find that the best fit isgiven by, FWHM( R gal ) = R gal / . . pc. Thus the averagevalue for FWHM for [C ii ] of 172 pc corresponds to the radial solution at ∼ ∼ ∼
230 pc over Galactic radii 3 kpc to 8 kpc.
4. Summary
We have combined the GOT C + spectrally resolved [C ii ] surveyin the Galactic plane at b = ◦ with the latitudinal distributionderived from the BICE survey of spectrally unresolved [C ii ] toderive, for the first time, the average scale height of [C ii ] overthe inner Galactic plane. GOT C + is slightly more sensitive thanBICE and the total flux measured by GOT C + is close to that ofBICE given the uncertainties of the BICE calibration. Thereforethese two surveys are likely tracing the same ISM gas compo-nents. The average distribution in the inner Galactic disk is wellfit by a single Gaussian with FWHM([C ii ]) =
172 pc and ano ff set -28 pc below the plane ( b = ◦ ).In this paper we find that the [C ii ] distribution is larger in z than that of CO, but smaller than H i . The origin of the [C ii ]emission has been attributed to di ff erent sources by various au-thors based on the spectrally unresolved surveys. However, theresult here suggests to us a more complicated picture with [C ii ]tracing a mix of ISM cloud categories. The GOT C + data for b , ◦ may be able to give some insights on the distributionof the di ff erent ISM components, but to determine completelythe distribution of [C ii ] for the separate ISM components as afunction of Galactic radius and z , we will need more detailedspectrally resolved latitudinal maps across the Galaxy and withfiner steps in b . We also need to extend the spectral line observa-tions to higher values of b than observed in the GOT C + surveyto understand the contributions of the warm ionized medium andlow density high latitude H i clouds to the [C ii ] emissivity abovethe disk. Acknowledgements.
We thank the referee for a careful reading of the manuscriptand several suggestions that improved the discussion. We also thank P. F.Goldsmith for constructive comments and edits. This work was performed atthe Jet Propulsion Laboratory, California Institute of Technology, under contractwith the National Aeronautics and Space Administration.
References