ON THE NATURE OF GALACTIO HALO BY S.B. PICKELLNER AND I.S. SHKLOVSKY

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On the nature of Galactic Halo
By S.B.Pickelner and I.S.Shklovsky,
of
1. In 195 2. it was shown by one us (1) that the soiree s..
of galactic nonthermal radioemission form a nearly spherical
system concentrating toward the plane and the centre of `the
Galaxy. It was pointed out independently by the other author
'(2) that the field between the clouds should be sufficiently
strong in order to retain the 'cosmic rays in the. Galaxy. The
density of the kinetic energy of the gas between the clouds
could be. taken as equal to that of the magnetic energy"-'
Thus the velocity, dispersion of the rarefte,d gas in the.
space between the clouds should be large and 'form a spheri?
cal, but not a flat subsystem. 'The spherical distribution,
.ofthe .radioemission supports this suggestion. The wide. H
and K absorption lines appearing in the spectra of. early
supergiants are also an argument in favour of the reality of
fast, movements of the rarefied gas. However, L-Spitzer, .{3)
points.out that at least a part of these lines belong to
the stars. Spectrograms taken by G.Mianch show-that some of
the wide lines consist of a few faint narrow lines. These
phenomena may be explained by the density fluctuations of
rarefied gas (ky oo n2), but some other interpretations
are also probable. This phenomenon supports the hypothesis
that the more rarefied gas possesses a higher velocity dis-
persion. The existence of wide H and K lines is not the
principal. argument of this theory. It will be shown below
that the gas of the halo is too rarefied to give observable
L.Spitzer also pointed out that the existence of super-
sonic motions must lead, to rapid energy dissipation,Conse-
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quently he considered the galactic halo to be real and its
large size to be maintained by its high kinetic temperature
instead of its fast motions. In this ease the temperature of
the gas in the space between clouds should. be about one milli-
on degrees and the concentration derived from the e quilibri-
um. condition between the clouds, and in the interstellar
space must be 5.10-4cm`3.
2: The only.reliable observational.data concerned with
halo are supplied by the nonthermal radioemission of the .
Galaxy. J.Baldwin (4) believes that there are two. subsystems
which could give similar spectra - the spherical halo and,.:'
. the "0.ort-Westerhout distribution*. This suggestion seem
to ` us: artificial and is a consequence of the introduction'
of some simplified procedures in the treatment of the obser-
vational data. Direct observations by B-.Mills by means of
a "cross" show a gradual -increase of brightness towards
the equator and a narrow maximum corresponding to the flat'
subsystem. -The radiogalaxie.s NGC 51281, 4486 and` '1316 also
show bright nuclei and a gradual decrease of brightness i' ,
an outward direction. It may be found from an analysis of':
different radio data and their comparison that the density
of emission near the galactic' plane beyond the flat sub-
system (z 1 kps above the Sun) is about 5-10 tithes ,larger
than that far from the galactic plane. (z 10 kps).
Let the differential energy-spectrum of relativistic
electrons be dN(E) = KE dE. The emission. E~ per unit
volume is then proportional to KH 2 V _ The ave-
rage value of is found to be 2.6, thus Ly oo KH1.8
The slow decrease of E , upwards is the consequence of a
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slow decrease of K and H. As the. electrons move along the
magnetic lines we can assume K to be proportional to H. The
error involved in this assumption is insignificant. Thus
H2' 8 K2.8
. Introducing the ratio of the value:
found; for above at Z" t and 10 kps,. we obtain the..,
value of ,H (and consequently K) in these two come spoAding
points to be different by a factor of,about 2. As, the :;mo
tion of
protons and other cosmic ray particles are similar
to that of electrons, their energy density in the tipper.
la;r is also about twice smaller than that near--'theg
lactic plane and is approximately equal to 0.5 eV/cm3e
The pressure of cosmic rays constitutes a third of its
energy density. It is known that cosmic rays may btu re.-
tamed in the. Galaxy by the magnetic field, if the magre-
+tic .pressure is larger than the cosmic ray pressure, .Con
sequently,' the. lower limit of the field strength is about
H10 3.10 6 and H.1 6.0_6. Possible error involved
here is not very large. If the emission of the flat sub
system were .also of a nonthermal character, as it is stag-
gusted by B.Mills, it might be_explained by that the field
in spiral arms is 'a little stronger than outside these
arms
3. The magnetic and cosmic ray pressure at Z - 10 kps
must be balanced by the weight of the gas above this level.
2
10 T' +f Kr+ 2.Ova +pp
f0
See page 9..
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The scale of height may be taken as 5 kps. .We deduce then
n10 about 0.6.1U- 'cm73, which. is ten times larger than Spit-
zer's' value . The Spitzer's halo cannot be retained in our
Galaxy. 'If the density is large the temperature. cannot be
very high, otherwise the clouds- would not be in equili-
brium. High temperature is not necessary now since the. halo
may be supported by the magnetic and cosmic-ray pressures.
magnetic field can hardly be regular, since the polbi-
',dal,field does not keep the cosmic rays, while the toroi-
dal field prevents the cosmic rays from spreading in the
Galaxy and reveals some other difficulties (large value. of
the magnetic flux and so on). If the field is not regular
.Cannot .be a static one. The magnetic forces will le.':
-a-motion of the matter and the dynamic equilibrium ziust
be established, when the densities of the magnetic and ~ the
kinetic energies are about the same. In this case'. the mean
velocity of macroscopic motions is about, 100 km/sec. Thee
gravitational equilibrium for the layer belween = i kps
and 10 kps gives an average value n about 1?em
4., The principal objection against high velocity mass
motion is the strong energy dissipation in shock mores. '
However the presence of the magnetic field and the :cosmic
rays increases the sound velocity. If the magnetic and ki-
netic energies are the same, the sound velocity in the, di-
rection normal to His equal, or greater, than the gas..ve-
locity. The shook wave is weak in this case and, the 'd1sdi-
patlon" is not so large. An solution for the weak,''
erpend -
cular magneto-hydrodynamic shook waves was obtained: ,Aecor-
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ding to Foiioffmann and E Teller (5) the increase 'of`.:enthropy
in that wave is
/axJ3/2zp~.
4S=- J27 I axe )
where
If
form
the eouation may be reduced to the;
The left side is the ratio of irreversible heatin-,7 per unit
mass to the total amount of kinetic and magnetic ener;ies
,per unit mass as a result of a passage of a single wave o The
radiative cooling increases .the irreversible. dissipation. But
this effect is not very pronounced;: if 'B < 250000. Besides,
the reversible transformation of the::,-kinetic into the magne-
tic energy retards the individual wave, without decreasi. r the
total average amount of the kinetic energy. T.1i.e relative com-
pression. X was calculated by means of general equations
,
of the perpendicular magneto-hydrodynamic waves. If the con-
dition fpv=$ 1-/2 is fulfilled
0.54, COnue-
quently, only about 4 per cent of energy is dissipated, in a
single wave. If the density of the magnetic energy is neater
than that of,the kinetic one (for instance, if the differen-
tial rotation stresses the magnetic lines) the relative dissi-
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pation decreases as H14. A calculation of the dissipation,
.taking into account the pressure and energy densities of the
cosmic rays, had been done. The same value was obtained.
Let the characteristic dimensions of the motions in the
halo be e, loops. The characteristic time t 1 will then be
6
about 10. years. The time-of dissipation in the chaotic mae;-
:netic field to 25 t1, while in the absence of the field,
will be about t 1. The diminution of the dissipation in
To maintain the motions, in the halo a. powerful: source
,of energy is required. The power of this -source must be
about
lem of interstellar gas, but
ti on. in stellar atmospheres.
the magnetic field may be important not only for the prob-
z
*1(4 82
3.10' 'erg/sec.
All known mechanisms - novae and supernovae explosions, the
radiation pressure of hot stars, the expansion of H'.II re-
tic energy is equal. to the kinetic eildrgy and g is propor-.
tional to H then the radioemission of the nucleus must be
about 100 times greater, than the halo of radioemission.
gions and.the. "rocket effect" are insufficient.
The.Dutch scientists showed (6) that the neutral hydro-
gen in the nucleus of the Galaxy (no 0.4 cm-3) has the
radial velocity dispersion of about' 50 km/see. If the magne-
This is in accordance. with observations and may serve as a
proof of the correctness of some of the above. suggestions.
The magneto-hydrodynamic waves must be propagating outward
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from, the nucleus of the Galaxy. The energy flow S fJ U3s
is about. 5.104.1 erg/sec, namely Just sufficient to compensate
.dissipation. The magnetic field of the waves in,the vicinity.
of the. nucleus is larger than the mean field in the halo. It
explains the large extension of the region where the nonther-
mal radioemission is relatively strong. This region is con-
siderably larger, than the 21 cm region. The increase`of non-
,.thermal radioemission towards the nucleus, same as that; -of
the density of the magnetic and the kinetic energies s;`also
an argument in favour of the hypothesis that the nucletls is
the principal factor, explaining the motions in the halo.o
The mechanism supporting the motions in the nucleus is un-
known yet, but the motions are observed.
5. The value of p Q permits us to 'compute: the increa-
se of gas temperature when.a single, wave is passing. For.. the
average conditions a T' 30000?. It was calculated that a
wave ionises one per cent of the hydrogen. After the time
interval t1 the temperature: falls to within 100000 - 15000?.
Every subsequent wave will ionise about one per cent of gas.
After this, the temperature will again fall to ti 10000?.
This. quantity depends but very little from the initial con-
ditions, because at low temperatures the process of cooling
is very slow. The stationary degree of ionisation may be
from 10 to 80 per cent. It is a function of gas density,. of
t 9 and other physical conditions, The ionisation would be
complete, if the magnetic field were absent. The determina-
tion of the ionisation from ,observations permits us to de-
fine more precisely the rate of dissipation,
6. The theoretical computation is based upon simple
models and may be lacking accuracy. It is necessary to con-
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firm the principal results by means of direct observations.
Examples must be given to show the existence of halo and
other, gaseous systems with, a sigh velocity dispersion.,, but
,with low temperature: and' ionisation.' The Australian seien-'
'tists; (,7) received.21 cm isophots for the Magellanic Clouds.
These' isophots cover the region which is much larger than
.the region of optical emission. The radial velocity disper-
sion is about 50 km/seen The computed. concentration of the
neutral hydrogen on the ;periphery of the LMC is about .
0.8.90-2 0M -3. L iC - has traces of spiral structure. It is
probable that I WO has a halo similar to our Ga] axy, The,
nucleus .of our Galaxy also contains partly neutral gas
with high velocity dispersion. Observations in the 21 em
region in the Coma cluster (8) are especially interesting.
The mass of neutral hydrogen is about 10 M ,..which Is
nearly equal to the total. mass of the cluster from the vvi-
rial theorem. The great mass, the large extei4sion and some'
other reasons lead to a supposition. that we have here to do
with intergalactic gas. 'The dispersion of the radial v'el.o-
city of this gas is about. 500 km/sec. If the magnetic field
would be absent this intergalactic gas would be completely
ionised. The field may decrease the dissipation in the shock
wave,' If the energy of 'the fie~d is not less than the kine
tic energy. Consequently, the examples given above grepre-
sent an argument in favour of the equipartition of the mag-
netic and the kinetic energy.
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References
1.. T.S.Shklovsky, USSR Astronomadournal 29, 418, 1952
2. S.B.Pickelner, Publ.-of Crim.Astroph.Obs.10, .74, 1953?
Comptes Rendus de 1'Acad.d.Sci. de
1'URSS 88, 229, 1953.
3.. L.Spitzer,. ApJ 124, 20.,_ 1956
4. J.Baldwin, M.N.115, 684, 691, 1955
5. F0Hoffmann, E.Teller, Phys0Rev.80, 692, 1950
6.K?Kwee, C.Muller, G.V7esterhout, BAN 15 498, 1954
7. F.Kerr, J.Hindmann, B.Robinson, Austr0Journal of Phys.
7,
297,
1954
8.D?Heeshen, ApJ 124,
660,
195.6
The Coefficient 3 is too large, but we retain it since
according to modern data the density of ' the energy. of
cosmic rays exceeds 1 eV/cm3 , because the energy spectrum
of the cosmical particles was prolonged towards the region
of small energies. .
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