Astron. Astrophys. 320, 957-971 (1997)
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.
![[FIGURE]](img144.gif) |
Fig. 9. Kinetic temperature as a function of distance to Sgr B2M as derived from and predicted by models. The thick solid line represents the averaged kinetic gas temperature obtained from our maps. In all cases was obtained by considering gas-dust coupling as the main heating mechanism. The last case also includes the dissipation of turbulent motions. The luminosity of the infrarred sources is . For Scoville & Kwan model see Scoville & Kwan (1976)
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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),
![[EQUATION]](img146.gif)
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,
![[EQUATION]](img149.gif)
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,
![[EQUATION]](img165.gif)
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.
![[FIGURE]](img183.gif) |
Fig. 10. Profiles of the J=5-4, J=8-7 lines towards the position (-100,0) from Sgr B2M. The thin and thick continuous lines superimposed on the observed lines represent the predicted profile for physical conditions =500 K, N( )= and and respectively. The grey line represents the line profile for a two component model: first component: =80 K, N( )= , , second component: =400 K, N( )= , .
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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.
![[FIGURE]](img191.gif) |
Fig. 11. In gray scale, map. The white line represents a level Jy in the 50 µm emission (Goldsmith et al. 1992), which we take as the boundary of the warm dust emission region. The black solid lines correspond to levels 0.2 and 0.4 Jy at 43 GHz; the maximum intensity is 0.8 Jy/beam (Akabane et al. 1988).
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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.
- Photoelectric heating from the UV radiation of the OB stars.
This heating mechanism would be more effective in thin regions with
low visual extinctions (
). Howe et al. (1991)
have estimated that for a molecular hydrogen density of
the layer would be
0.03 pc thick. Therefore the UV radiation would not heat a region with
more than 10 mag. of visual extinction. However clumpiness would allow
the UV photons to penetrate deeper in the cloud. Howe et al. 1991 show
that the UV depth of penetration probed by CII can be 10-100 times
greater than for uniform gas with densities larger than
. In any case one, expects the kinetic
temperature to decrease monotonically from the OB star forming region,
which is not the case for the hot ring which appears separated from
the Sgr B2M and Sgr B2N cores.
- Heating is produced by shock fronts associated to the expansion of
the ionized bubble. This mechanism would better match the morphology
of the hot ring. It has been proposed that the low density high
temperature material of the hot envelope in Sgr B2 observed in
absorption lines is due to the presence of C shocks with a shock
velocity of 25
(Flower et al. 1995). This model
explains the absorption lines of towards Sgr
B2, and the abundance ratios of found in the hot
and diffuse envelope (see section 9.3). It is then very likely that
the absorption lines in Sgr B2 might arise from the hot ring located
in front of the HII region. High angular resolution observations of
will help to elucidate the origin of this
remarkable feature.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998
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