9. The kinetic temperature distribution of the Sgr B2 molecular cloud
The kinetic temperature structure of the main molecular clouds in Sgr B2 can be characterized by four components: the hot cores, the warm and dense envelope, and the hot ring. The first 3 components can be easily recognized in Fig. 9, where we show the averaged kinetic temperature as a function of the distance to Sgr B2M. As discussed in section 5.3 our data also show the presence of an additional component, a hot and diffuse envelope.
In order to explain the overall thermal distribution of the molecular clouds in Sgr B2 we have constructed a simple model which determines by balancing heating and cooling mechanisms as a function of distance from the star forming region. The main heating mechanisms in the interstellar medium have been reviewed recently by Black (1987) and Genzel (1991). The photoelectric effect, the photoionization of C atoms and the photodissociation and deexcitation of molecular hydrogen are the most relevant agents in Photo Dissociation Regions. However these processes are generated by the ultraviolet radiation from OB stars which are attenuated at visual extinctions of less than 10 magnitudes (i.e. 0.02 pc at densities of ) and therefore should have little importance in dense molecular cloud cores. As main heating mechanisms to explain the thermal distribution we have considered in our model the heating of the dust by the radiation from the stars, gas dust collisions and the dissipation of turbulent motions. Heating by cosmic rays and Alfven wave dissipation may also be important, so we included them in our analysis.
9.1. The hot cores
The high kinetic temperature of the gas in dense cores is mainly due to the presence of newly formed stars. As previously mentioned heating agents associated with PDRs can be ignored because these are not effective for visual extinctions higher than 10 magnitudes, and the column density near the hot cores causes much larger extinctions. Most of the gas is heated by collisions with dust grains, which have been heated by the absorption of stellar radiation. The amount of energy transferred by the dust grains to the gas through collisions considered in our model is given by (Lis & Goldsmith 1991),
where is the grain temperature and the kinetic temperature of the gas. The grain temperature which decreases with the distance to the star depends on the luminosity of the heating sources. The radial distribution of dust temperatures has been obtained by two different methods:
1. we use the Scoville and Kwan (1976) approximation which applies for the low opacity limit,
where is the grain emissivity at 50 µm and the source luminosity in . This approximation was obtained assuming that the emissivity depends on the frequency as .
2. we solve the radiation transfer equation numerically, for a spherical cloud with a 3 pc radius and two density regimes. Within the internal 0.07 pc radius we used a constant density of and up to a distance of 3 pc the density law derived in section 5. Dust opacities were obtained from the Hildebrand relation (1983), assuming a mass density of 3.3 gr and a radius of 0.1 µm for the dust grains. We used 1.1 for the spectral index for the dust emissivity law (Martín-Pintado et al. 1990) with an emissivity value at 1300 µm of (Righini-Cohen & Simon 1977; Goldsmith et al. 1987a). The radial dust distribution was evaluated for three different bolometric luminosities of the central source, , and . The dust temperature distribution derived from our model is in very good agreement with that obtained by Lis & Goldsmith (1990) for radii between pc and 10 pc.
The cooling has been estimated using the analytical expression given by Lis and Goldsmith (1990) that takes into account several molecular species (Goldsmith & Langer 1978). Fig. 9 shows the kinetic temperature distribution predicted when heating is by gas-dust collisions. We used one and two infrared sources, and two methods to estimate dust temperatures.
In order to compare the results from these models with our data, we have convolved our results of the calculations with a beam. The closest distance to the star forming region considered for the convolution was 0.001 pc. The convolved kinetic temperature near the hot cores is strongly dependent on this distance. Our model for one heating source predicts a kinetic temperature for the hot cores which is substantially lower than that derived from for all positions even with the highest luminosity for the central source. However when considering the heating by a second IR source (Sgr B2N) at a distance of 0.1 pc from Sgr B2M, the predicted kinetic temperatures agree quite well with the observed kinetic temperature distribution within a region of 0.5 pc around Sgr B2M. Thus, the spatial distribution of the molecular gas close to the Sgr B2M hot core ( pc) can be explained by the heating of dust by radiation from the young stars in the star forming regions, Sgr B2M and Sgr B2N.
For Sgr B2N there is a discrepancy between the size of the observed hot core (0.34 pc) and the size of the region at 300 K derived from the previous model and the assumed luminosities. This discrepancy can be due to the fact that Sgr B2N is a very complex region with multiple HII regions which could heat the gas at larger distances than expected for a point-like source as considered in our model. Interferometric mesurments of J=12-11 are needed to confirm the large extent of the hot material in Sgr B2N.
9.2. The warm envelope
Fig. 9 shows that for distances greater than 1 pc the dust grain temperatures ( K) agree with those obtained by Lis & Goldsmith (1990) and Gordon et al. (1993) but are systematically lower than the predicted kinetic gas temperature observed from , K. Based on absorption lines Wilson et al. (1982) and Huttemeister et al. (1995) showed that the dust is cooler than the gas and a heating mechanism acting only on the gas is required.
The Scoville & Kwan solution, which is valid in the low opacity limit, approximately fits the data in the 0.5 to 1.5 pc. This may indicate a clumpy structure which allows a deeper penetration of radiation that heats the dust farther inside the cloud.
Heating by cosmic rays and the dissipation of Alfven waves will not significantly affect the total heating rate for the typical densities we have obtained and the expected cosmic ray flux in the Sgr B2 molecular cloud. The cosmic rays flux would have to be 3 orders of magnitude higher than that of the solar system () in order to account for the heating in the molecular cloud. This is unrealistic since then a large fraction of molecules would be dissociated. It has been proposed that turbulent heating could account for the high kinetic temperature in the Galactic Center (Wilson et al., 1982). Heating by turbulent motions can be estimated according to Black (1987) by,
where is the turbulent velocity. We have assumed that ranged from 17 to 13 from the nearest high density regions to the farthest lower density regions mapped. was estimated as 8 pc. Since the turbulence may extend farther than mapped, we used a scale factor F to adjust the observed kinetic temperatures to the model prediction. The best value was which corresponds to a region of a radius of pc.
The dissipation of turbulent motions can explain the observed kinetic temperature distribution of the gas in the warm envelope (Fig. 9) but does not heat the dust. Under these conditions dust-gas collisions act as a cooling agent. The large turbulent state in the Galactic Center is probably due to the velocity shear caused by the differential rotation, which is stronger at the Galactic Center molecular clouds (Wilson et al. 1982).
9.3. The diffuse and very hot envelope
In addition to the warm envelope, which requires "moderate" energy input to be heated, there is a very hot (500 K) and low density () component, seen from the absorption of some lines. Though the kinetic temperature of the hot component is similar to that derived by Flower et al. (1995) our derived densities for this component are one order of magnitude smaller than those inferred by Flower et al. (1995). Based on the absorption data of Hüttemeister et al. (1995) these authors proposed that the envelope of Sgr B2 is filled by a very hot (500 K) and relatively dense () material. We have searched for this extended component in a position offset from the main continuum sources. Fig. 10 shows, superimposed on J=5-4 and J=8-7 spectra taken at a position west from Sgr B2M, the profiles predicted for these lines for 500 K, and two hydrogen density regimes, and . From the fits we conclude that the data do not support a very hot (500 K) and relatively dense () envelope around Sgr B2. The data is in better agreement with a two component model in which the star forming region cores are surrounded by a dense () and warm (80 K) envelope and a more diffuse () and hotter component.
The column density of in the diffuse and hot envelope is . When compared with the column density of other molecules like or we obtain that and . We used the value obtained by Huttemeister et al. (1995).
In spite of the different physical conditions the previous abundance ratios are similar to those found in the hot core in Orion (Irvine, 1987), though the origin of the diffuse and hot envelope in Sgr B2 is unknown. A similar chemistry between these two regions might support the idea that, like for the hot core, the chemistry of the envelope is strongly affected by the evaporation of grain mantles. These data support the suggestion by Flower et al. (1995) that C shocks might heat and evaporate grain mantles in the diffuse and hot envelope.
9.4. The hot ring
The most remarkable feature of the kinetic temperature maps, the hot ring is clearly seen in the plots of averaged kinetic temperature as a function of distance to Sgr B2M (Fig. 9). As shown in Fig. 9 none of the above mechanisms previously discussed explains this structure.
The origin of the hot ring is unclear. In order to gain insight, we have compared the morphology of the hot ring with the morphology of other types of emission. We find that the morphology of the hot ring resembles the morphology of the "hole" of emission at radial velocities of 40-50 reported by Hasegawa et al. (1994). From the spatial distribution of at 20-40 , 40-50 and 70-80 , the authors proposed that cloud-cloud collisions are responsible for this morphology, and that during the course of the collision, dense and massive cores may have formed in the interface between the colliding clouds. However the hot ring appears at different radial velocities than the "hole", and does not match exactly with it; the HII regions are at the edge of the "hole" but in the center of the hot ring. We also do not observe any density enhancement associated to the morphology. Therefore it is not clear that the hot ring is associated with the "hole" reported by Hasegawa et al (1994).
Fig. 11 shows the comparison between the kinetic temperature (grey contours) and the radio continuum emission at 43 GHz from Akabane et al. (1988), shown as a solid line, and the continuum at 50 µm from Goldsmith et al. (1992), shown as a white line. The radio continuum at 7 mm traces the ionized gas with a small contribution from dust and molecular lines (Martín-Pintado et al. 1990) while the continuum at 50 µm samples mainly hot dust heated by the radiation from the OB stars. The hot ring surrounds both the hot dust and the free-free emission.
This morphological relation between the hot ring and both tracers of activity from OB stars suggests that the hot ring may be related to the massive star formation activity in Sgr B2. Very likely the hot ring is a thin interface between the molecular cloud and the ionized "bubble" created by the young OB stars in the core of Sgr B2. In this picture two possibilities can be considered to explain the increase of in the hot ring.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998