On the temperature structure of the Galactic Centre cloud G0.253+0.016
Paul C Clark, Simon C. O. Glover, Sarah E. Ragan, Rahul Shetty, Ralf S. Klessen
DDraft version November 1, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
ON THE TEMPERATURE STRUCTURE OF THE GALACTIC CENTRE CLOUD G0.253+0.016
Paul C. Clark , Simon C.O. Glover , Sarah E. Ragan , Rahul Shetty & Ralf S. Klessen Universit¨at Heidelberg, Zentrum f¨ur Astronomie, Institut f¨ur Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg,Germany. Max Planck Institut f¨ur Astronomie, K¨onigstuhl 17, 69117 Heidelberg, Germany.email: [email protected], [email protected], [email protected], [email protected], [email protected]
Draft version November 1, 2018
ABSTRACTWe present a series of smoothed particle hydrodynamical models of G0.253+0.016 (also known as“The Brick”), a very dense molecular cloud that lies close to the Galactic Centre. We explore howits gas and dust temperatures react as we vary the strength of both the interstellar radiation field(ISRF) and the cosmic ray ionisation rate (CRIR). The cloud has an extent in the plane of the sky ofroughly 3.4 pc × − s − , regardless of the geometries studied. For such high values ofthe CRIR, we find that cooling in the cloud’s interior is dominated by neutral oxygen, in contrast tostandard molecular clouds, which at the same densities are mainly cooled via CO. Our results suggestthat the conditions near G0.253+0.016 are more extreme than those generally accepted for the inner500 pc of the galaxy. Subject headings: stars: formation INTRODUCTION
The environmental conditions in the Galactic Cen-tre (GC) provide an extreme test of our current under-standing of the star formation process (e.g. Papadopou-los 2010; Krumholz et al. 2012; Longmore et al. 2013;Kruijssen et al. 2013). With both stronger backgroundradiation fields and higher cosmic-ray fluxes comparedto clouds in the solar neighborhood, star formation ispredicted to occur at higher volume and column densi-ties than is typical in a standard giant molecular cloud(Elmegreen et al. 2008).One notable example is G0.253+0.016 (also referred toas the “The Brick”), which displays both extremely highcolumn and volume densities, yet very little sign of starformation (G¨usten et al. 1981; Lis et al. 1994; Longmoreet al. 2012). Despite the current lack of star formation,the physical conditions in this object are thought to besimilar to those required for the formation of massivestellar clusters (Longmore et al. 2012).In this paper we investigate the influence of the ex-treme GC environment on the thermodynamics of denseand massive molecular clouds, in an attempt to betterunderstand the initial conditions for star formation inthe inner molecular zone. We adopt values for the inter-stellar radiation field and the cosmic ray ionisation ratethat are significantly higher than those measured in solarneighborhood molecular clouds. For more fundamentalparameters such as the mass, dimensions, and turbulentvelocity dispersion of the clouds, we take the values forG0.253+0.016 reported by Longmore et al. (2012). Incontrast to the other clouds in the GC, the apparentlack of star formation in G0.253+0.016 makes it an idealcandidate for studying the effects of the environmentalconditions on the thermal balance of the cloud.
Fig. 1.—
Column density, and mean gas and dust temperaturesin our fiducial cloud setup (simulation ‘1’ in Table 1), with theISRF set at 1000 G , and the CRIR at 3 × − s − . COMPUTATIONAL METHOD a r X i v : . [ a s t r o - ph . GA ] A p r TABLE 1Summary of the simulations
Model L x L y L z Σ min , n I ISRF 8 I CR 9 x (H ) x (CO) x (C + ) x (O)[pc] [pc] [pc] [cm − ] [cm − ] [G ] [s − ]1 9.4 3.4 3.4 3 . × . × × − . × − . × − . × − . × . ×
100 3 × − . × − . × − . × − . × . × × − . × − . × − . × − . × . ×
100 3 × − . × − . × − . × − . × . ×
100 3 × − . × − . × − . × − . × . × × − . × − . × − . × − Note . — , , Initial physical dimensions of the cloud. Minimum column density, measured along the shortest axis. Initialhydrogen nuclei number density. Strength of the interstellar radiation field, in units of the local value. Cosmic ray ionisationrate. , , , Final fractional chemical abundances in the cloud, measured at the point at which the first core goes into runawaycollapse. These are quoted with respect to the number of H nuclei. A fully molecular gas therefore has x (H ) = 0 .
5. The totalcarbon and oxygen abundances in the models are 1 . × − and 3 . × − respectively. We perform our simulations using the smoothed par-ticle hydrodynamics (SPH) code
Gadget2 (Springel2005). We have modified the code to include time-dependent chemistry and a treatment of the main heat-ing and cooling processes (described below). We havealso included an implementation of the
TreeCol algo-rithm (Clark, Glover & Klessen 2012), to obtain columndensity maps of the sky as seen by each SPH particle.These maps (including total, H and CO column densi-ties) are used to calculate the influence of the interstellarradiation field (ISRF) on the gas and the dust.We assume for simplicity that the spectral shape ofthe ISRF follows Draine (1978) in the UV and Black(1994) at longer wavelengths. We denote the solar neigh-bourhood value of the strength of the ISRF as G ,and perform simulations with field strengths 100 G and1000 G (see Table 1). Note that this multiplicative scal-ing is done equally at all wavelengths. For our dustmodel, we use a combination of values from Ossenkopf &Henning (1994) (non-coagulated, thick ice mantle grains)for wavelengths longer than 1 µ m, and from Mathis,Mezger & Panagia (1983) at shorter wavelengths. Tocompute the visual extinction, we use the relationship A V = 5 . × − ( N H , tot / − ), where N H , tot isthe total hydrogen column density (Bohlin, Savage &Drake 1978; Draine & Bertoldi 1996). For simplicity,we do not account for any changes in the extinctioncurve that may occur due to dust coagulation. For thecosmic-ray ionisation rate (CRIR), we adopt a value ofI CR , = 3 × − s − as our solar neighbourhood value(van der Tak & van Dishoeck 2000), and assume thateach ionisation event deposits 20 eV of energy into thegas (Goldsmith & Langer 1978). The dependence of theCRIR on column density is highly uncertain (Padovani,Galli & Glassgold 2009), and we assume for simplicitythat no attenuation occurs. We do not include the effectsof ionization by hard X-rays, as this does not appear to bea major heat source in the Galactic Center, given the rel-atively low X-ray luminosity (Rodr´ıguez-Fern´andez et al.2004; Schleicher, Spaans & Klessen 2010)For the chemistry we adopt the reduced CO network ofNelson & Langer (1999). Details can be found in Glover& Clark (2012b), and a description of how the chemistryinteracts with the ISRF via the TreeCol algorithm isgiven in Glover & Clark (2012a). INITIAL CONDITIONS AND MODEL PARAMETERS
For the initial conditions in this study, we take thecloud properties derived in Longmore et al. (2012) forG0.253+0.016 as a guide: a size of 9.4 pc by 3.4 pc, anda mass of 1 . × M (cid:12) . The clouds are simulated us-ing 2 × SPH particles, and so our mass resolution is M res = 0 . (cid:12) (Hubber et al. 2006). We adopt a simplerectangular cuboid geometry, matching the longer of thetwo observed dimensions with the x -axis in the simula-tions, and the shorter with the y -axis, such that all theclouds have particles placed initially from 0 to 9.4 pc in x ( L x ) and 0 to 3.4 pc in y ( L y ). In the z direction weadopt two values for the extent of the cloud, since thetrue dimension of G0.253+0.016 along the line-of-sightis unknown. Our first choice is to make the z -axis thesame length as the y -axis, yielding a mean hydrogen nu-clei number density n = 3 . × cm − . This is thesetup used in our ‘fiducial’ clouds. Our second choice isto make z the longest axis, with L z = 17 . . × cm − and areour ‘low-density’ clouds. All the clouds are given non-thermal support in the form of a turbulent velocity field,which has a power spectrum P ( k ) ∝ k − . The turbu-lence is permitted to decay as the cloud evolves. Wefix the initial 3D turbulent velocity dispersion based onthe observational data: Longmore et al. (2012) report alinewidth of 15.1 km s − for G0.253+0.016, equivalent toa 1D velocity dispersion of 6.4 km s − , and hence to a 3Dvelocity dispersion of 11.12 km s − , assuming isotropicturbulence.We perform three simulations for each of our two cloudmodels, varying the strength of the ISRF and the mag-nitude of the CRIR. An overview of the simulations canbe found in Table 1. A central assumption here is thatthe shape of the radiation field and the cosmic ray en-ergy spectrum are the same locally and in the GalacticCentre, and that it is only the normalization of each thatchanges.In view of the high densities probed by our initial con-ditions, we assume that the hydrogen in our clouds startsas H . However, we start with the carbon in the formof C + , and allow it to self-consistently evolve to form Cand CO. As we discuss in §
5, the clouds are already inchemical equilibrium at the point at which we performour analysis. GAS AND DUST TEMPERATURE
Fig. 2.—
Gas (blue) and dust (red) temperatures as a function of x . The top row contains the clouds that have the fiducial setup ( x is thelongest axis), while the bottom row contains the low density clouds (those with z as the longest axis). The lines denote the mass-averagedtemperature along the line of sight. Vertical bars denote the 1- σ dispersion. Fig. 3.—
Gas (blue) and dust (red) temperatures as a functionof density in our fiducial cloud (model ‘1’ in Table 1).
Using
Herschel observations, Longmore et al. (2012)show that the dust temperature varies smoothly from19 K in the cloud centre to 27 K at the edge. Ob-servational constraints on the gas temperature ofG0.253+0.016 have existed for some time: G¨usten et al.(1981) derive rotation temperatures of ∼
45 K using am-monia transitions, corresponding to an average kinetictemperatures of ∼
80 K (Walmsley & Ungerechts 1983).A recent formaldehyde survey (Ao et al. 2013) findsaverage kinetic temperatures of 65–70 K, which agreeswithin the uncertainties. However, observations of high- excitation ammonia lines suggest that G0.253+0.016 hasa complex gas temperature structure, with componentsup to 400 K, that has yet to be modeled (E. Mills, 2013,private communication). What environmental condi-tions are required to produce such temperatures?The typical features of our cloud are illustrated inFig. 1, which shows the column densities of one ofthe clouds in the x - y plane (i.e. integrating along z ),and the accompanying mean gas and dust temperaturemaps. This cloud is our most extreme case studied, withI ISRF = 1000 G , and I CR = 1000 I CR , , and our ‘fidu-cial’ cloud geometry. However, the features of this cloudare mirrored in our other simulations – the clouds havea hot skin and a relatively cool interior, and are highlystructured by the supersonic turbulence. The images inFig. 1 are taken just as the first collapsing core exceedsa density of around 10 cm − , and so represent the stateof the cloud at the onset of star formation. All the otherclouds in this study will be presented at the same pointin their evolution.In Figure 2, we show the gas and dust temperaturesin the clouds as a function of the position along the x -axis. The most obvious feature of these profiles is thatthe gas and dust have different temperatures throughoutthe cloud. They are not thermodynamically coupled onthe scales shown here, consistent with the observationsmentioned above.The profiles also reveal how the environment affectsthe cloud temperature. We see that the cosmic raysare responsible for heating the gas, while the ISRF isprimarily responsible for heating the dust. Such a re-sult is expected. The high column density of this cloudmeans that photo-electric emission in the cloud interioris strongly suppressed, as the UV photons responsiblefor it are readily absorbed near the surface of the cloud.As such, the ISRF can play only a minor role in directlyheating the gas. On the the other hand, as the cosmicrays have no attenuation in our model, they are free toheat the cloud’s gaseous interior throughout. The ISRFcan, however, heat the dust at the centre of the cloud,as this heating comes primarily from longer wavelengthphotons, which are able to penetrate much further thanthe UV photons. In summary, for clouds with such anextreme column density as G0.253+0.016, the heating ofthe dust and gas is effectively split into two components.Our 3D modelling results suggest that for our fiducialcloud model, the environmental parameters that best re-produce the observed temperatures are I ISRF = 1000 G ,and I CR = 1000 I CR , . Reducing either of these values bya factor of ten results in gas or dust temperatures thatare too low to agree with the observations.One potential source of error is simply that we haveunderestimated the extent of G0.253+0.016 along theobserved line-of-sight, and so the true effective columnof the cloud is much smaller than we are assuming in thefiducial models. However we find that similar environ-mental conditions are also required when we consider ourlower-density version of G0.253+0.016. These models areshown on the bottom row of Fig 2. Even in these lowercolumn density clouds, we see that the ISRF is mainlyresponsible for determining the dust temperatures (i.e.there is very little gas-dust thermodynamic coupling),and the CRIR is mainly responsible for determining thegas temperatures. Our dust temperatures are now a lit-tle higher than the observed values throughout the cloud,suggesting that for this geometry the I ISRF would need tobe lower than 1000 G . However we see that by 100 G ,the ISRF is already too low to explain the observed tem-peratures. Also, we see that I CR = 100 I CR , results ina gas temperature of around 30 K in the interior of thecloud – again, this is inconsistent with the observations.Figure 2 also shows that the geometry of the cloud af-fects the temperature gradients along the cloud. This isparticularly evident when one looks at the gas tempera-ture, especially when I ISRF is high (see e.g. the bottomright panel). This implies that it should be possible toconstrain both the total ISRF and the cloud’s geome-try by fitting the gradient of the gas temperature in thecloud modelling. Such a study is worth revisiting oncemaps of the gas temperature with sub-parsec resolutionbecome available.Finally, we note that both the gas and dust tempera-tures can vary considerably along a line of sight from theaverages shown in Fig. 2. This can already be seen inthe images in Fig. 1. However, we also show in Fig. 3how the temperatures vary as a function of density in ourfiducial case. We see that at high densities ( > cm − ),once the dust and gas thermally couple, the temperaturescan be relatively cold. HEATING AND COOLING PROCESSES
In this section we investigate the heating and cool-ing processes for the gas in more detail. The dominantprocesses that govern the gas temperature are shownas functions of density in Fig. 4 for the two most ex-treme cases: our fiducial cloud (n = 3 . × cm − )with I ISRF = 1000 G and I CR = 1000 I CR , , and one ofthe lower-density clouds (n = 6 . × cm − ), with Fig. 4.—
Processes responsible for heating and cooling the gasin two very different cloud models (clouds 1 and 4 from Table1). Heating processes are shown in red and orange and coolingprocesses are represented in blue. Two processes – p d V work andgas-dust thermal coupling – can produce either heating or coolingdepending on the circumstances. Heating and cooling associatedwith compression and expansion are denoted by Γ p d V and Λ p d V ,respectively, while the transfer of energy from the gas to the dustis denoted by Λ GD and that from the dust to the gas by Γ DG . Theplotted quantities represent the median values at each density. I ISRF = 100 G and I CR = 10 I CR , .In both clouds, the dominant heating processes followa broadly similar pattern. At the lowest densities, whichrepresent the outskirts of the clouds in these simulations,the dominant heat source is photoelectric emission fromdust grains. This falls off sharply as we move to higherdensities as a result of the increasing extinction as onemoves into the cloud’s interior. At slightly higher densi-ties, the heating caused by cosmic rays starts to dominatethe thermal balance. In the case of the hotter, densercloud, this process remains the main heating source untilwe reach a number density n = 10 cm − , correspond-ing to our resolution limit. In the lower density cloud,embedded in the less extreme environment, shock heat-ing becomes the main source of heat input to the gas atdensities above n ∼ cm − . Note that since neithercompression nor shock-heating are dominant in the highCRIR case, the temperature of the cloud cannot be usedto determine its age.When we compare the main cooling processes, we alsofind some similarities. In the low-density outskirts, wherethe gas is warm and there is little CO, we find that C + and neutral oxygen emission are the main coolants, as inthe low-density ISM. Given the high densities and tem-peratures of the cloud’s skin, and the fact that we startwith the hydrogen in molecular form, we also find thatH can be an effective coolant at the outskirts.As we move into the cloud, however, the gas tem-perature drops and the C + recombines to form C andthen CO. The identity of the dominant coolant thereforechanges. In the low-density cloud, CO cooling dominatesin this slightly denser regime, just as is the case in localmolecular clouds. In the denser cloud model, however,CO never dominates; instead, atomic oxygen becomesthe main coolant. This difference in behaviour is a resultof the CRIR in these two clouds. In the higher densitycloud, the much higher CRIR creates many He + ionsthat react destructively with the CO molecules:CO + He + → C + + O + He . (1)It also keeps the gas warm enough to excite the fine struc-ture lines of atomic oxygen. In the lower density cloudwith the much lower CRIR, both of these effects are lessimportant, and hence atomic oxygen never becomes thedominant coolant. Since we need a large CRIR to ex-plain the observed gas temperatures, the implication isthat the cooling of gas in G0.253+0.016 (and probablyalso in other Galactic Centre clouds) is dominated overa significant range in densities by emission from atomicoxygen.At very high densities, dust becomes the most effec-tive source of cooling. However this does not occur un-til the gas density is more than an order of magnitudehigher than the mean cloud density, and hence we ex-pect that T gas = T dust only in the densest gas withinG0.253+0.016, with most of the volume of the cloud hav-ing T gas (cid:54) = T dust . As already noted, this expectation issupported by the available observational data on the gasand dust temperatures.The effect of the clouds’ environment on the chemicalbalance is summarised in Table 1. We see that strongISRFs and CRIRs have little effect on the H fraction,and so we would expect the true molecular state of thecloud to be relatively independent of the environment.However, the CO fraction varies by around an order ofmagnitude in the models, implying that its ability totrace the molecular state of the gas is a strong functionof the environment. Since the clouds initially have allof their carbon in the form of C + , one might argue that we have simply ended our simulations too soon to pickup all of the CO. However, we see that in the cloudswith smaller CRIRs over half of the carbon is in CO,suggesting that there is sufficient time available for it toform in large quantities. As such, the low CO abundancesin the clouds with high CRIR are due to real differencesin their chemical evolution. DISCUSSION
Our results suggest that the CRIR and ISRF aroundG0.253+0.016 should be 1000 times the solar neighbour-hood values, in order to obtain temperatures consistentwith the values derived from observations. Such radia-tion and CR fields could be produced by enhanced starformation activity, higher stellar densities, or some com-bination of both. Yusuf-Zadeh et al. (2009) measured thestar formation rate (SFR) in the GC to be 50–100 timesthe local SFR. If the CRIR and ISRF are set solely bystar formation, our results suggests that the local SFRnear G0.253+0.016 is about an order of magnitude higherthan the mean SFR of the central molecular zone (Morris& Serabyn 1996; Yusuf-Zadeh et al. 2009).Similarly, the CRIR that we require is significantlyhigher than the values found for local dense clouds. How-ever, there is considerable observational evidence thatthe ionization rate is higher in the Galactic Centre.For example, Oka et al. (2005) estimate a value of 2–7 × − s − in diffuse gas along several GC sightlines,while Yusuf-Zadeh, Wardle & Roy (2007) infer a value of2–50 × − s − within GC clouds, based on observationsof the fluorescent 6.4 keV K α iron line. Our requiredvalue of a few times 10 − s − is compatible with thesevalues, given the large uncertainties.Our models also suggest that the neutral oxygen emis-sion coming from G0.253+0.016 should be significantlyhigher than that seen typical molecular clouds. Thiscould provide an independent test of the models pre-sented in this paper. ACKNOWLEDGEMENTS
The authors would like to thank Katharine Johnstonand Elizabeth Mills for their enlightening discussions onG0.253+0.016. We acknowledge financial support fromthe DFG via SFB 811 “The Milky Way System” (sub-projects B1 and B2), and from the Baden-W¨urttemberg-Stiftung by contract research via the programme Interna-tionale Spitzenforschung II (grant P- LS-SPII/18). PCCand SER are supported by grant CL 463/2-1 and RA2158/1-1, respectively, which are part of the DFG-SPP1573. The simulations presented in this paper were per-formed on the
Milkyway supercomputer at the J¨ulichForschungszentrum, funded via SFB 811.