If a collision of two large, massive, fast gas clouds occurs, their kinetic energy is converted to radiation in a pair of shock fronts at their interface. The resulting structure is described, and the relevance of this as a radiation source for quasi-stellar objects is considered

Cox, D.

Daltabuit, E.

English

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A PLAUSIBLE ENERGY SOURCE AND STRUCTURE FOR QUASI-STELLAR OBJECTS
by Y
E. Daltabuit and D. Cox
University of Wisconsin
Department of Physics
Madison, Wisconsin 53706
Abstract
If a collision of two large, massive, fast gas clouds occurs, their
ig energy is converted to radiation in a pair of shock fronts at
interface. The resulting structure is described and the relevance
Of this as § radiation source for QSO's is considered.
https://ntrs.nasa.gov/search.jsp?R=19720018092 2020-03-11T18:07:30+00:00Z
. , ' . . " • • • ' . . • . • 2 . '
1. The Mechanism.
. A very simple solution to the long standing problem of the QSO
energy source may exist in a mechanism being considered by Osterbrock
(see, for instance, Osterbrock, 1971) for active galactic nuclei, including
those of Seyfert galaxies. This process involves the conversion of large
scale kinetic energy to electromagnetic radiation at or near a pair of
shock fronts between dense colliding gas clouds. In this section we explore
the basic constraints which are imposed on such a model by observations of
QSO's.
As material flows into a shock front, its energy is first thermalized
and, if time, permits, is radiated. As a consequence, the total luminosity
of a pair of such fronts between clouds of cross-sectional area A is
- 2A x (m
where n is the number density in the clouds and v is the shock velocity
(1/2 of the relative velocity of the clouds).
In the case of a QSO, the shock velocity is limited by the observed
line widths (see, for instance, Burbidge (1967) for a review of QSO
2properties) to be generally about 1000 km/sec, implying from 5kT = mv /2
(m = average mass of the nuclei) that the post shock, temperature is roughly
1.5 x 10 °K, taking the helium abundance to be about 10% by number. In
addition fluctuations on a time scale of order one year require that the
cooling time behind the shock be about 1 year, assuming that the luminosity
fluctuations simply mirror fluctuations in the density of material entering
the shock front. The cooling time is given by 5kT/Ln, where L is the
o
cooling coefficient (in ergs cm /sec). If bremsstrahlung accounts for most
of the cooling (Cox and Daltabuit, 1971) then t ^ 0.1 v /n years.
Therefore we require n- - 10 particles/cm . The total radiation flux is
3 7 2 2then approximately P0V0/2 - 10 ergs/cm sec, or 1 watt/cm , which is
similar to a low wattage light bulb.
If this mechanism is to be the QSO energy source we clearly require a
45
very large shock area. For example 10 ergs/sec are generated by a shock
38 2
area of 10 cm . The radius of the smaller cloud involved in the collision
-must then be about 1.3 pc. The mass of such a cloud is 2.5 x 10 M ,
similar to a large globular cluster. It should be noticed that this"
collision would last pnly for a time 2r/v or 2400 years, implying that the
state of being a QSO is ephemeral or repetitive.
Of course it must be shown that such an energy converter produces the
correct spectrum, and that the physical conditions which would produce the
collision are achievable. These points are discussed briefly in the
subsequent sections.
II. Structure and Spectrum.
h.- Shock.Fronts and Cooling Regions.
As the two clouds come together, the gas of each enters a shock front
where its kinetic energy is thermalized, its density raised to 4n and its
velocity reduced to v /4. These are standard results for high velocity
shock waves (see, for instance, Zel'dovich and Raizer, 1967). Behind each
shock there is a cooling region with nearly constant pressure from which
most of the thermal energy i's radiated as the gas flows through. The width
of this region is approximately equal to the cooling time t multiplied by
the flow velocity vQ/4, or
dc = 7.5 x 105 v*/n0 cm (= 7.5 x 1014 cm)
j • ' '
8
where the number in parentheses corresponds to v = 10 cm/sec and
nQ = 10 cm" .
This shock and cooling region effectively converts the entire kinetic
• • ' ."• • - •
 ;
 ' 4.
energy-of the entering gas to-electromagnetic radiation.
B. HII Regions.
Most of the radiation from the cooling regions, however, is beyond
.the Lyman limit and as it propagates either upstream into the clouds, or
downstream into the already cold dense gas flowing out of the cooling
regions it is strongly absorbed to form HII regions, one leading and one
trailing each shock. These two HII regions process nearly equal amounts of
the ionizing radiation, but they differ in size and secondary spectrum
because of their extreme difference in density. The leading HII region
7 - 3 2has a density of 10 cm . The trailing HII region has a pressure p v ,
1 1 - 3 4implying a density of 10 cm if its temperature is 10 °K, or in general
10 /T. cm" , where T , is the local temperature. (This value of the density
depends on the contribution of magnetic fields to the pressure, which has
been neglected here.) -
Again-a-ssuming bremsstrahlung to be the dominant cooling mechanism in
the cooling regions, the average number of ionizing photons which must be
processed by the HII regions is approximately 5 E, (1,,/kT) = 20 for every
atom entering the shock front. In either HII region the density is so high
14that "its thickness is quite small, -about"3 x 10 cm for the leading region
and perhaps 4 x 10 cm for the trailing region, so that all the emitted
radiation is converted to photons with hv <_ 13.6 ev in a pair of thin
sheets sandwiching the narrow cooling region. Even the bremsstrahlung
X-rays are absorbed within a very short distance in the clouds (which are
neutral because of the very short recombination time for hydrogen).
C. Anticipated Spectrum. .
Both the cooling and the HII regions have considerable temperature and
ionization structure. -The HII regions are expected to be similar to those
: • ' • • . - • ' • - 5 .
considered by Mac Alpine (1972) and Davidson (1972), except for the low
radiation density in the primary source considered here. The emission
lines will thus originate from a wide range of ionization stages. Some of
the most intense lines expected from the cooling and HII regions are shown
in Table 1. Since the gas behind the shock slows down as it cools, coming
essentially to rest with respect to the clouds, the lines observed will
have widths up to 1000 km/sec, 'corresponding to the velocity separation
between the emitting regions. In the denser region behind the shock
collisional quenching can be expected for some lines. These lines will
thus suffer only the thermal broadening that occurs in the leading HI I
region. The spectrum will then consist of a mixture of broad and narrow
lines similar to that described by Burbidge (1971).
There is a very dense sheet of material between the two shock fronts.
This consists of material which has passed completely through one or the
other of the shocks, and J.ts.. associated .cooling and HI I -regions. -As has
been mentioned the density in this sheet, in the absence of magnetic fields,
would be 10 /T. cm" , and the sheet thickness would be about 4 x 1 0 T. cm
when the collision is half over. If sufficient dust is present in this
region it may be expected that the radiation reaching it will be absorbed
by molecules and dust, and be re-radiated as characteristic or black-body
radiation. . If so, the effective temperature would be a few hundred degrees.
D. -Opacity of the Neutral Clouds.
The column density of neutral hydrogen in one of these clouds is about
25 -24 x 10 cm . To prevent the entire luminosity of this object from
escaping only in the infrared, it is required that the dust to gas ratio in
4 5the clouds, which surround the emitting regions, be 10 - 10 times smaller
than in the interstellar medium in our galaxy. If the clouds are assumed
6.
to have 10 times less heavy element abundance, similar to population II
3 4
stars, the dust to heavy element ratio need only be 10 - 10 times smaller
than in our galaxy. On the other hand, if the interior cold dense region
is to be thick enough to provide characteristic or thermal infrared radiation,
the dust to gas ratio there should be slightly higher. This may be a
reasonable consequence of the material's density and thermal history, i.e.,
the baking which this gas undergoes in passing through the interior HII
region could have stimulated molecule and dust formation. We have not
pursued this idea numerically.
-The flux of non hydrogen-ionizing radiation produced in the cooling
region and in both HII regions is sufficient to ionize all the heavy
elements with ionization energy below that of hydrogen, and to do so without
diminishing appreciably. This flux is also more than sufficient to ionize
all the H~ that forms in the clouds. This means that the bound-free opacity
from both heavy elements and H" is negligible. The electrons existing
in the cloud have such low abundance, and the HII region is so thin, that
electron scattering is of no consequence. The free-free opacities both
from H~ and the heavy elements only become important in the far infrared or
beyond_because of the low electron abundance.
A substantial fraction of the energy emitted in the HII regions, and
to a lesser extent, in the cooling region (Cox and Tucker, 1969) will appear
in the form of Ly a radiation. The cloud is indeed thick at this wave-
length. However, the Ly a produced in the cooling region and in the trailing
HII region is emitted far in the wings of the absorption profile of the
unshocked portion of the cloud. This radiation will diffuse both in space
and in frequency (Osterbrock, 1967) and part of it will eventually escape.
The number of scatterings required for escape, however, is so large that
the probability of conversion to 2 photon Ly a continuum (or to other lines
7.
by collisional quenching of .this continuum) is substantial. This could
contribute to the continuum spectrum of this object. The Ly a emitted in
the leading HII region is emitted in the core of the absorption profile,
and is all converted. All the Ly a that enters the unshocked portion of
the cloud effectively populates the n = 2 level of hydrogen, and this
population could be enough to make the Balmer continuum opacity marginally
significant. '.--••.
The transfer of radiation through the cloud is not a trivial problem,
and its solution requires a knowledge of the spectrum of the cooling and HII
regions. This latter problem is being studied at present. It seems,
however, that in the absence of dust, the clouds are fairly transparent,
and that most of the radiation will emerge almost as emitted by the HII
regions.
III. Origin
, . This energy source requires the collision of two clouds of mass ^ 10 M
 e,
8
and size vl pc, traveling at velocities of 10 cm/sec. If gravitation is
the source of acceleration, the total mass M. required is given by
2 ' .
v = GM./R, where R is the maximum size of the object containing the clouds.
L .
8We have then (with VQ = v x 10" )
v^ , 4.4 (Mt/1012 M 0)/Rkpc .
• • . \
If R = 1 kpc, for example, Mt = 1011 M e .
The Jeans' length for the clouds we consider is
Xt = 2.1 x 10"2 pc (T2/n7)1/2
The clouds will therefore collapse, and the free fall time is
4
* - Ij5 x 10 n years.
" . • ' ' ' . ' • . 8.
-.Ihe_pressure-free .calculation .i.s_appropriate-because -the transparency of
the clouds.keeps the temperature from rising (see, for instance, Mestel,
1965).
The short lifetime of such clouds seems to indicate that in order to
make a collision probable, a number of such clouds must exist within a
fixed volume. By requiring that the time between collisions be of the
order of the duration of one collision we obtain the condition
N2 = (4/3) (R/r)3
-where N is the number of clouds of radius r contained within a radius R.
4If R = 1 kpc, N = 4 x 10 and most of the mass required is contained in
the form of clouds. For smaller values of R fewer clouds are allowed and
a large central mass must supply the required velocities.
t .
All this indicates that a possible location for the occurrence of
collisions is in the early stages of galactic formation. Consider an
12initial mass of 10 M
 0, with a radius of 100 kpc and a temperature of
10°K. Within it assume density fluctuations with Sp/p = 10" , radius of
fi R1 kpc and mass 10 M
 0 . After a .time t = 5 x 10 years the condensations
will be similar to the clouds we have discussed, while the whole object
4 - 3
will be about 1 kpc in radius and will have a mean density of 10 cm .
All this has been calculated using only the simplest arguments of non-
rotating, spherical, pressure-free collapse (see, for instance, Mestel, 1965),
In any case, it seems very likely-that the collision of two massive,
large, dense, fast clouds might occur during the early stages of galactic
formation, as discussed, for instance, by Mestel (1965) or Brosche (1970).
The short lifetime of the clouds and the comparable duration of the collision
indicate that very few collisions will occur in one object. The remnants of
such collisions will be sheets of high density where rapid star formation
. . 9.
...may occur. Also,..magnetic fields might be compressed in-such sheets, and if
illuminated with bursts of high energy electrons from nearby supernovae
explosions might provide the environment for Kellerman's model of the radio
sources (Kellerman, 1966). Another possibility is that the compression and
therefore enhancement of the B field by the shock and subsequent cooling,
and the compression of any ambient cosmic ray electrons (which results in
enhanced electron energies) could alone provide the radio emission. If the
primordial B field were somewhat uniform even the dipolar structure might.
be expected. One very nice feature of this model is that the energy available
54in the original cloud motion amounts to about 4 x 10 -ergs. The energies
required do not then seem too overwhelming.
IV. Conclusions.
If two clouds with the appropriate characteristics collide with
relative velocity of about 2000 km/sec, their kinetic energies are transformed
3 times before an observable spectrum is produced. -The kinetic energy is
first gradually thermalized as the cloud flows into a standing shock front.
The thermal energy is then radiated by the cooling region as high energy
photons. These photons are'absorbed and the energy re-radiated by the HII
—regions. A fraction of-the HII region radi-ation is lost as it flows, out
of the object to the opacity of the neutral clouds. The spectrum which is
then observable is expected to be rather similar to those calculated by
Mac Alpine (1972) and Davidson (1972) [see Mac Alpine (1971) for preliminary
results]. Our results suggest that such collisions could be expected in
the normal process of galaxy formation, making QSO's rather unexceptional
objects. Our discussion in no way requires this; however, it is a straight-
forward way of getting the required cloud..kinetic energies.
In closing it should be noticed that there are some superficial and
some not so superficial" resemblances between the model described here and
. . ' - . . - •
 :
 1 0 .
.conclusions reached by Davidson (1972). The cloud-cloud collisions
described by Davidson were used only to provide regions of differing
density. The radiation produced by the shock waves during the collisions
was ignored in favor of an external unspecified UV source with a power
law spectrum. Since we propose a specific energy source, whose spectrum
can be computed, we feel that this work is complementary to that of Mac Alpine
and Davidson. As previously mentioned, we are now working to produce a
reliable spectrum of a 1000 km/sec shock wave and cooling region which we
then expect to use with the photoionization program of Mac Alpine (1972) to
find the ultimate spectral results of our model.
We would like to thank D. E. Osterbrock, J. Mathis, G. Mac Alpine,
C. Goeble, and B. Savage for useful discussions of the astronomy and physics
involved in this model. Similarly we appreciate the critical reading of
this manuscript by D. McCammon and D. Osterbrock. We further would like to
thank the referee for comments'useful in preparing a readable version of
this letter.
This project was supported by C.O.N.A.C.Y.T. (Mexico), The Universidad
Nacional Autonoma de Mexico, The Wisconsin Alumni Research Foundation, and
NASA Grant NGL 50-002-044. .
11
Table 1
Strongest Lines That May Appear in the Spectra of the
Emitting Regions (Not Including H and He Lines)
Cooling Region /-,\ HII Region /?x
X(A) -..' X(A)
CII 1334 ' CIII] 1909
CII] 2326 CIV 1550
CIII] 1909 NV 1239-1243
CIV 1550 [OIII] 5007-4363
NV 1239-1243 01V] 1406
OIV] 1406 OVI 1033
0V] 1213 NIV] 1488
OVI 1033 [Nelll] 3869
Mgll 2748 [NeV] 3426
Sill 1824 Mgll 2798
(1) Preliminary results of a calculation of the spectrum of
the cooling region.
(2) Estimated from the results of.Mac Alpine (1971, 1972).
• ' •• References
Brosche, P. 1970, Ast. and Astrophys., 6, 240.
Burbidge, E. M. 1967, Ann. Rev. Ast. & Astrophys., 5, 399.
1971, Pontificiae Academiae Scientiarum, Scn'pta Van'a
No 35, p. 122.
Cox, D., and Daltabuit, E. 1971, Ap. J., 167, 113.
Davidson, K. 1972, Ap. J.,.J7J. 213.
Kellerman, K. I. 1966, Ap. J., 146, 621.
Mac Alpine, G. M. 1971, Thesis, University of Wisconsin.
1972, preprint.
Mestel, L. 1965, Q. J. Roy. Ast. Soc., 6, 161.
Osterbrock, D. E. 1962, Ap. J., K35, 195.
1971, Pontificiae Academiae Scientiarum, Scripta Van'a
No 35, p. 151. •
Zel"'dovich, Ya. B., and Raizer, Yu. D. 1967, "Physics of Shock Waves and
High Temperature Hydrodynamic Phenomena". Academic Press, N.Y. and
London.


A plausible energy source and structure for quasi-stellar objects

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