A basic model and simple numerical relations useful for future far infrared studies of the galaxy are presented. Making use of recent CO and other galactic surveys, the diffuse far infrared flux distribution from the galactic plane as a function of galactic longitude alternate theta for 4 deg  or = alternate theta  or = 90 and the far infrared emissivity as a function of galactocentric distance is predicted. Future measurements of the galactic far infrared flux would yield valuable information on the physical properties and distribution of dust and molecular clouds in the galaxy, particularly the inner region

Fazio, G. G.

Stecker, F. W.

English

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1
PREDICTION OF THE DIFFUSE FAR
INFRARED FLUX FROM THE
GALACTIC PLANE
I
G. G. FAZIO
F. W. STECKER
MAY 1976
	
('IASA-T :1-X-71125) PKEUICTION OF THE UIFFUSF
	 N7L-261313FAR IN F GASFD FLUX I= PUM TH-t
- GALACTIC PLANE
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Prediction of the Diffuse Far-Infrared Flux from the Galactic Plane
G. G. Fazio
Center for Astrophysics
60 Garden Street
Cambridge, Mass. 02138
a
	
and
F. W. Stecker
Theoretical Studies Group
NASA Goddard Space Flight Center
Greenbelt, MD. 20771
Received Jan. 19, 1976
To be published in Ap. J. Letters 207, July 1, 1976
1	 `
I
r
ABEIRACT:
A basic model and simple numerical relations useful for
future far-infrared studies of the galaxy are presented. Making
use of recent CO and other galactic surveys, we then predict the
diffuse far-infrared flux distribution from the galactic plane as
a function of galactic longitude t for 4°<R< 900
 and the far-
infrared emissivity as a function of galactocentric distance.
Future measurements of the galactic far-infrared flux would yield
valuable information an the physical properties and distribution
of dust and molecular clouds in the galaxy, particularly the
inner region.
-2-
I. INTRODUCTION
Our picture of the state and distribution of interstellar gas
in the galaxy has been rapidly changing with important implications
for galactic structure theory (Burton 1976, Stecker 1976). These
changes have come about as a consequence of important observational
evidence of CO in molecular clouds at mm wavelengths (Scoville and
Solomon 1975, Burton et al. 1975, Gordon and Burton 1976) and satellite
observations at y-ray wavelengths (Pichtel et al. 1975). The CO
surveys show that the molecular cloud abundance in the galaxy exhibits
a strong radial dependence with a broad maximum in the 5 to 6 kpc region.
A strong increase in the y-ray emissivity peaking in the 5 to 6 kpc
region (Stecker et al. 1974, Puget and Stecker 1974) has now been
associated with the strong increase in the molecular cloud concentration
there (Solomon and Stecker 1974, Stecker et al. 1975). The recent
observations imply that N Z is by far the most abundant form of gas
in the inner galaxy. These results are consistent with the basic
concepts of density wave theory (Burton 1976, Stecker 1976).
Both the CO and y-ray observations require some indirect analysis
in obtaining parameters such as hydrogen den y '.ies. These analyses
lead to different uncertainties so that the CO and y-ray observations
complement each other to some extent (Stecker et al. 1975). 1
 Another
promising technique for studying large-scale galactic structure lies
in comparing the y-ray and radio synchrotron observations (Paul et al.
I See also Puget et al. 1976
j	 j	 I
}	 I	 I
`^	 i
-3-
1976) but again, this type of analysis should ultimately include
independent observational determinations of the gas density.
Far-infrared observations provide a powerful alternative
technique for exploring the physics and galactic distribution of
cold molecular clouds. The basic source of far-infrared radiation
in a molecular cloud or HII region is the reradiation of dust
heated by light from early type stars or young stellar associations
located in or near a cloud and having an evolutionary connection
with it as extreme population I. Judging from measurements of CO
excitation temperatures in these clouds (Scoville and Solomon 1975,
for example), the dust temperature in them is expected to be of the
order of 10-20 K and that they are expected to radiate most of their energy
in the wavelength range between 100 pm and 300 pm in distinct contrast to the
hotter strong infrared sources at shorter wavelengths (<100pm) which
are primarily associated with HII regions. Stein (1966) and Pipher
(1973) have previously proposed the existence of a diffuse infrared
flux from the galactic plane due to thermal radiation by dust grains,
but the recent CO observations now permit a more detailed prediction
of the properties of this radiation.
In this Letter we will assume that the ratio of total gas to
dust is roughly the same as that in more diffuse atomic clouds (Ryser
et al. 1975) and that the physical properties of the dust are roughly
uniform throughout the Galaxy. We will then propose a framework for
future far-infrared surveys by suggesting some basic numerical relations
for predicting flux distributions and emissivities. Using dust tempera-
tures derived from CO and other measurements, we then predict the
f
-4-
diffuse far-infrared flux distribution in the galactic plane as
a function of galactic longitude R in the range 4 0 < R < 900 and
the far-infrared emissivity distribution as a function of galacto-
centric distance.
II. GALACTIC PLANE EMISSION
If we assume the dust is at an equilibrium temperature, Td , and
radiates with an absorbtivity, QIR, then the energy emitted in the
wavelength interval da per unit volume of the dust cloud per second
is given by
JIR (1)da=4n2 a 2ndQIR (A)Bl (Td ) da	 (1)
where a is the radius of the dust grain, n  the density of dust part-
icles, and B,(T) is the Planck function.
The value of n  is related to the total hydrogen density by
n  = (3mH/4irpa3) (Md/MH) n 
	 (2)
where m  is the mass of the hydrogen atom n  the total hydrogen den-
sity (nH 2nH2+nHI), p is the grain density, and Md/MH the dust-to-gas
mass ratio. The column density NH 1n Hds in any direction can be re-
lated to the CO emission in that direction as follows:
NH = 4.6 x 1020 1 C cm 2	 (3)
where ICO = jTAdv is the integrated CO intensity in units of K km s-1
(Solomon 1973, Scoville and Solomon 1975, Gordon and Burton 1976).2
Based on the CO measurements alone, eq. (3) is uncertain by a factor
of 5 (Scoville and Solomon 1975). However, arguments taking into
account infrared and x-ray absorption measurements reduce this
uncertainty to within a factor of 2 (Stocker at al. 1975).
t
I
r-5-
The dust parameters are p, a, and QIR. The value of pa can
be (letermined using a hydrogen column density at R=0° (excluding.
the galactic nucleus) of 7 x 10 22cm 2 (Stecker et al. 1975) and
an optical depth in that direct TV= 28, (Becklin and Neugebauer 1968,
Spinrad et al. 1971). Then
Tv = 0.92 A  = va 2 QvNd	(4)
where v is the visual extinction in magnitudes, Qv is the extinction
efficiency at visible wavelengths and N  is the column density of
the dust. If we assume the canonical values (Md /Ml l ) = 10-2 and Qv 1,
we find
pa = 3.1 x 10 -5 g cm-2
	
(5)
This is consistent with the values given by Allen (1973) of p = 1 g cm-3
and a = 3 x 10- 5 cm estimated from Qv and which we now adopt. We then
obtain from eq. (2)
N  = 1.4 x 10-13 NN	 (6)
The value of QIR is assumed to be of the form A1X- 1 with Al = 4.5 x
10-5 cm (Pottasch 1973). 3 The optical depth of the dust is then
T IR - QlR"a2Nd = 8.2 x 10'6Xcm ICO	 (7)
For the range of values for ICO given by Scoville and Solomon (1975)
and taking 1 = 300 pm, it is found that the galaxy is optically thin
-3—The 	 QIR = 1-n with n = 1 is somewhat uncertain at long wave-
lengths. Pottasch (1973) and Soifer et al. (1972) find evidence in far of
an overall dependence given by n = 1. Scoville and Kwan (1975) and Leung (1975)
suggest the dependence may be better represented by n ti 1.5 for a ti 30 pm,
although Leung also gives several examples of grains for which n = 1.
Andriesse (1974) suggests that n = 2 for a > A c with a c between 50 pm and
200 pm.
T
Ir
I
-6-
at far-infrared wavelengths.
From equations (1) and (3) the infrared brightness can be
computed as a function of galactic longitude Q
1IR da	 47r f JIRds - 0.97 x 10-10	 (8)
x{I CO (Z) da a-6 (exp(1.44/1T) - 1)-1)
erg >r.,-2s-1Sr'"1
with a in em. The total infrared brightness is
I ° f0 IIRda - 3.8 x 
10-11Td5 ICO (R) wm 2 Sr-1 (9)
IR
The total emission per grain is
cg
 = nd-1 f JIR d% = 7.7 x 10-24 T d 5 w	 (10)
The temperature of the dust can be derived by relating it to
the CO kinetic temperature, TCO. Goldreich and Kwan (1974) and
Scoville and Kwan (1975) have investigated the thermal coupling
between radiatively heated dust and ambient molecular gas (H2)
and indicate that the gas will approach thermal equilibrium with
the dust (TH 4 Td ) via collisions of H2 with grains for n  > 104cm-3.
2	 2
However, at n  - 104 cm-3 the collision rate is sufficient to give
2
only T  = 1/2 Td . Observational evidence, however, suggests the
2
coupling may be stronger. Scoville: and Solomon derive an average
value of TCO of 6.6K. We shall assume that a lower limit to Td is "7K.
An upper limit to the dust temperature can be derived by assuming
the dust particle absorbs all the incident visible and ultraviolet
radiation and reradiates it in the infrared. At equilibrium:
47r2a2fo QIR BX (Td ) da = n a 2cuY	(11)
where u  is the density of radiation in interstellar space = 7 x 10-13
erg/cm 3 (Allen, 1973). Solving for Td we get Td = 15K. Kaplan and
..7-
Pikelnor (1970) and Greenberg (1971) obtain similar estimates. u 
may vary somewhat throughout the galaxv but eq. (11) gives only a
0.2
slight u 	 dependence for Td.
In presenting our results in graphical form, we shall assume a
value Td=10K. In figlire 1 we have plotted the total infrared
brightness, IIR as a function of galactic longitude derived from
eq. (9) using the data of Scoville and Solomon for ICO and excluding
the galactic center. Of particular importance is the predicted large peak
at R = 30o tangent to the maximum interstellar gas density near 5 kpc.
A further consequence of our model which can be used as an experimental
test is the prediction that the width of the galactic far-infrared disk
should be comparable with that of the molecular cloud disk. The full width
of the cloud disk is given by Scoville and Solomon to be ti 1 0 at k = 300.
The infrared spectrum can be obtained from equation (8). The
maximum in the spectral curve is given by
lm = (he/5.98Td ) = 0.24 Td-1 cm	 (12)
where for Td - 10K, am = 240 pm. With QIR of the form Ana n (n>0).
X  = he/f(n+5) kTd ) = (n+5)Tm	 (13)
d
In the Raleigh-Jeans approximation he «akT, the far infrared spectrum
takes the power-law form
IIR (a) dl x a-(4+n)da	 (14)
It follows from eq. (11)(also Andriesse (1974)) that assuming n > 1
would result in higher Td estimates and smaller differential fluxes at
long wavelengths, although the total infrared flux integrated over all
X as shown in the figures remains unchanged (Greenberg 1971). For example,
Andriesse (1974) with n = 2, obtains Td x, 24K with am ti 85 pm. For the
intermediate case, n = 1.5 1 ti 150-200 jim. Future spectral measurements over the
M
s
j
-8-
galactic plane in the far-infrared could thus help determine the wave-
length dependence of QIR•
Using the relations dorived by Stecker at al. (1975) in conjunction
with equations (6) and (10) and employing the data of Scoville and
Solomon on the molecular cloud d:.r . Lribution in the galaxy, the total
far-infrared emissivity from molecular clouds as a function of galacto-
centric distance was calculated. The results are given in figure 2.
III. GALACTIC CENTER REGION
In the galactic center region 
I L I < 3 0 , Scoville, Solomon and
Jefferts (1974) hove already shown that; a correlation exists, as a
function of galactic longitude, between the 100 um flux and the
maximum CO brightness temperature at each longitude. These authors
conclude that the CO and dust coexist in nearly thermal equilibrium.
The CO measurements indicate that the molecular cloud disk sur-
rounding the galactic nucleus has a radius of ti 600 pe and that the
total mass of molecular gas, mostly H 2 , within the cloud is ti 5 x 107M.
In accordance with our assumed gas-to-dust ratio, the implied dust
mass is then M  ro 5 x 10 5
 MD or about 1039 g. The total number of
grains is then
Ng = (3Md /47ra 3p)11052
	(15)
and, from equation (10), the total luminosity of the galactic center source
is estimated to be
LG.C. ^ Ngeg ti 8 x 1028 T d 5 w	 (16)
which, using the data given by Hoffman, Frederick and Emery (1971),
yields an estimated temperature Td,G.C.of the order of 25 K. The mean
E ^	 Vi
_9-
temperature of the CO gas, expected to be somewhat cooler, is
of the order of 20 K (Scoville, Solomon and Jeff • erts 1974) so that
our model gives reasonable results for the galactic center source.
IV.
Our results indicate that much can be learned about the physics
and conditions of interstellar dust and molecular clouds as well as
the galactic dust and cloud distribution by making far-infrared studies
of the galactic plane. In the inner galaxy, most of the interstellar
medium is in the form of the cold clouds. Far-infrared surveys, in
conjunction with other observations, will enable us to get better
estimates of quantities like N11 , N  and Td . In this paper, we have
predicted the intensity, angular distribution and spectrum of the diffuse
far-infrared radiation over that region of the galactic plane where
sufficient CO data are available (4° < R < 90°) using the data of
Scoville and Solomon (1975). Comparison of our model with 100 Um
observations of the galactic center source, which is expected to ue
about three times hotter than the average galactic molecular cloud,
gives us confidence in the basic relations given in this Letter.
We believe the flux estimates calculated here to be reasonable pre-
dictions, however, one should bear in mind the assumptior.^ made, in
particular the wavelength dependence of QIR, the u.certainty in the
relationship between I CO and n  and the assumption of a uniform value
of Td = 10 K since the predicted flux has a steep temperature
consitivity.
1
1r
i
a
-10-
ACKNOWLEDGMENT:
The authors would like to thank C. D. Andriesse and J. M.
Greenberg for their helpful comments relating to our paper.
..11_
REFERENCES
Allen, G. W. 1973. Astrophysical Quantitites, 3rd ed., Athlono Press, London.
Andtiessa, C. D. 1974, Astr. and Ap. 37, 257.
Becklin, E. E. and Neugebauer, C. 1968, Ap. J. 151, 145.
Burton, W. B. 1976, Ann. Rev. Astr. and Ap., in press.
Burton, W. B., Gordon, M. A., Bania, T. M., and Lockman, F. J. 1975, Ap. J.
202, 30
Fichtel, C. E., Hartman, R. C., Kniffen, D. A., Thompson, D. J., Bignami,
G. F., 8gelman, H., 8zel, M. F., and Turner, T. 1975, Ap. J. 198, 163.
Greenberg, J. M. 1971, Astr. and Ap. 12, 240.
Goldreich, P. and Kwan, J. 1974, Ap. J. 187, 243.
Gordon, M. A. and Burton, W. B. 1976, preprint.
Hoffman, W. F,, Frederick, C. L., and Emery, F. J. 1971, Ap. J. (Letters)
164, L23.
Kaplan, S. A. and Pikelner, S. B. 1970, The Interstellar Medium, Harvard U.
Press, Cambridge, Mass.
Leung, C. M. 1975, Ap. J. 199, 340.
Paul, J., Cass6, M. and Cesarsky, G. J. 1976, preprint.
Pipher, J. L. 1973, Interstellar Dust and Related Topics, p. 559 (J. M.
Greenberg and H. C. Van de Hulst, ads.) Reidel Pub. Co. Holland (IAU Symp.
No. 52)
Pottasch, S. R. 1974, Astr. and Ap. 30, 371.
Puget, J K., Ryter., C. E., Serra, B. and Bignami, G. 1976, Astron. and Ap.,
in press.
Puget, J. L. and Stecker, F. W. 1974, Ap. J. 191, 323
Ryter, C. E., Cesarsky, C. J. and Audouze, J. 1975, Ap. J. 198, 103.
Scoville, N. 2., and Kwan, J. 1975, Ap. J., in press.
^	 I
-12-
Scoville, N. Z., and Solomon, P. M. 1975, Ap. J. (Letters) 199, L105.
Scoville, N. Z., Solomon, P. M•, and Jefferts, K. B. 1974, Ap. J. (Letters)
187, L63.
Soifer, B. T., Pipher, J. L., and Houck, J. R. 1972, Ap. J. 177, 315.
Solomon, P. M. 1973, Physics Today 26, 32.
Solomon, P. M. and Stecker, F. W. 1974, Proc. ESLAB Symp. on the Context and
Status of y-ray Astronomy, Frascati (EGRO SP-106) p. 253.
Spinrad, H., Liebert, J., Smith, H. E., Schweitzer, F., and Kuhi, L. 1971,
Ap. J. 165, 17.
Stecker, F. W. 1976, Nature, 260, 412.
Stecker, F. W., Puget, J. L., Strong A. W., and Bredekamp, J. H. 1974, Ap. J.
(Letters) 188, L59.
Stecker, F. W., Solomon, P. M., Scoville, N. Z., and Ryter, C. E. 1975,
Ap. J. 201, 90.
Stein, W. 1966, Ap. J. 144, 318.
I
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FIGURE CAPTIONS
a
Fig. 1.
	
	
Predicted longitude dependence of the galactic far- 	 r
infrared flux based on the model in the text (equation 9)
using the CO data of Scoville and Salomon (1975) and a
temperature of 10K.
v
.	 V
Fig. 2.	 Predicted galactic far-infrared emissivity distribution using
equations (6) and (10) together with the data of Scoville and
i
Solomon (1975) and the values of n
H
 deriver] by Stecker et
2
al. (1975). Again, a cloud temperature of IOK has been assumed.
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Prediction of the diffuse far infrared flux from the galactic plane

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