With the acquisition of satellite data on the energy spectrum of galactic gamma-radiation, it is clear that such radiation has a multicomponent nature. A calculation of the pulsar gamma ray emission spectrum is used together with a statistical analysis of recent data on 328 known pulsars to make a new determination of the pulsar contribution to galactic gamma ray emission. The contributions from diffuse interstellar cosmic ray induced production mechanisms to the total emission are then reexamined. It is concluded that pulsars may account for a significant fraction of galactic gamma ray emission

Harding, A. K.

Stecker, F. W.

English

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c'.
Technical Memorandum 82028
Pulsar and Diffuse Contributions
to the Observed Galactic
Gamma-Radiation
A. K. Harding and F. W. Stecker
^, -fir►•
OCTOBER 1980
National Aeronautics and
Space Administration
Goddard Specs Flight Center
Greenbeit, Maryland 20771
(NASA —Td-82028) PULSAR AND UIYFUSE	 N61-19918
CONTRIBUTIONS TO THE OBSERVED GALACTIC GA88A
RADIATION (NASA) 15 p HC A02111F A01
CSCL 03B	 Oncla6
G3/93 1D623
i
A. K. Harding
F. W. Stecker
Laboratory for High Energy Astrophysics
NASA/Goddard Space Flight Center
Greenbelt, MO 20771
With the aquisiti•on of satellite data ur, the energy spectrum of
galactic y-radiation, t + 2 it has become clear that such radiation has a
multicomponent nature." -7 In this letter, we make use of a calculation
of the pulsar 1-ray emission spectrum together with a statistical analysis
of recent data on 328 known pulsars to make a new determination of the
pulsar contribution to galactic y-ray emission. We then reexamine the
contributions from diffuse interstellar cosmic-ray induced production
mechanisms to the total emission and conclude that pulsars may
account for a significant fraction of galactic Y-ray emission.
1Models for the production of high energy y-rays in the Galaxy have
dealt primarily with diffuse emission processes, those which involve
interactions between cosmic rays and interstellar matter. The major
contributions are thought to cane from electron bremsstrahlung and the
decay of neutral pions produced in high energy proton collisions, with
a small additional flux from Compton interactions. In determining the
relative contributions of these processes from the shape of the observed
y-ray spectrum, thu contribution of true point sources (as opposed to
enhancements in the spatial distribution from diffuse processes) has been
neglected, largely because the point source spectrum has been u,idetermined.
At present, pulsars can give the best information on a true point source
component of the galactic y-ray flux.
We report here on the first calculation of a Y-ray production spectrum
from pulsars in the Galaxy and on the implications of this point source
contribution to the general interpretation of the observed galactic )-ray
spectrum. The details of this calculation, as well as a determination of
the longitude and latitude profiles of pulsar y-rays will be described
elsewhere.' There have previously been estimates of the pulsar
contribution to the observed galactic y-ray flux,9 -11
 using only 51 pulsars
and very general assumptions about their y-ray luminosities.
	 There are now
328 known radio pulsars, all having independent distance determinations via
their dispersion measures. The local density and galactic distribution can
therefore be much better determined, assuming a value for the mean free electron
density in the galactic plane. Pulsed y-rays have been observed from the
Crab (PSR 0531 + 21) and Vela (PSR 0833-45) pulsars by the SAS-2 satellite,12,1'
and the COS-B satel1ite. 1`
 The energy spectra of these sources have recently
2been determined in the range 50 MeV -2 GeV and they can both be fit with
steep paver laws of similar slope around -2.1 '5 Although these two young
sources represent only a small traction of the known pulsars, their
emission testifies to the fact that some, and possibly all pulsars are 1-ray
emitters at some stage of their evolution. Though these others may be
individually below the present limits of detectability, the contribution
of their Y rays to the observed galactic emission could be significant, as
has been previously suggested.e
We assume that the 1-ray emission above 100 MeV is produced by curvature
radiation from primary particles which have been accelerated to high energies
in the electric fields of the pulsar's magnetosphere. Some of these 1-rays are
converted to electron-positron pairs in the strong pulsar magnetic field. The
electric field induced perpendicular to the magnetic field by the star's
rotation also contributes to the pair production rate and has a large effect
on the optical depths in short period pulsars. 16 The shape of the numerically
calculated spectra in this model depend on the initial energy of the primary
particles and on the pulsar magnetic field strength and period. ,7 For an
initial energy of 1.5 x 10` GeV and a. field strength of 10,a gauss, the
resulting calculated spectrum for a pulsar period of .033 s reproduces the
shape of the observed Crab pulsar spectrum. The observed 100 MeV flux from
the Crab pulsar at 2 ;.pc is used to determine the normalization factor
(— 10') which is the ratio of the primary particle density above the polar
cap to the corotation charge density. Using this same normalization factor,
primary particle energy, and magnetic field strength, the calculated spectrum
for a period of .089 s. fits the observed Vela pulsar spectrum quite well.
3It may be reasonable to assume, then. that these values of the parameters
determining the spectrum are valid for all pulsar periods.
An expression for the Y-ray luminosity can be derived by integrating
the spectra calculated for different periods, P, and surface magnetic field
strengths, B (in units of 10 4 gauss). The best fit for the dependence of
t^
luminosity on these quantities qives:
L (> 100 MeV) = 1.2 x 10^ 6 B°'a " P-1.1 photons s-'	 (1)
Y	 t :^
The Y
-
ray
 luminosities and fluxes for the known radio pulsars have been calculated
from equation (1) and compared to the upper limits obtained by SAS-2j 8 and
the sources in the COS-B catalogt9 . Eight pulsars have predicted fluxes
above the point :,:turce detectability limit of COS -B but most are toward the
galactic center where the diffuse background is high. Only two lie in the
longitude range 90° e j < 2700 where the search is considered complete down
to 1.3 X 10-6 cm-2 s-1 ; however, they both lie just outside the latitude
range of the search. Four pulsars have predicted fluxes above their SAS-2
upper limits, but exceed them by no more than the estimated uncertainties
in either the measurements or the moc.el.
In calculating these pulsar spectra and luminosities, it has been assumed
that the magnetic field is a pure dipole and that the angle between the dipole
axis and spin axis is 90°, since we are concerned here with the collective
properties of the pulsar population, and a random distribution of angles would
give an average of 90°. More details of the model are given in Reference 17.
4If all pulsars produce pulsed 1-rays according to this model, then the
local differential production spectrum will be,
gPSR(EY) 
z 
7F
Dg a
 o I 1
(P,E7 ) a (P) dP,
where D8 is the local surface density of pulsars which are beamed in our
direction, h is their scale height above the plane, a(P) is their period
distribution and I I (P,EY ) is the x-ray spectrum of an individual pulsar
with period P. I I (P,EI is also directly proportional to surface magnetic
field strength, so that gPSR will be proportional to the average pulsar
magnetic field strength. We take an average field of 10 2 gauss, which is
consistent with measured pulsar spindown rates. The derived local density
and scale height depend on a determination of <n 
e
> * the mean electron
density in the galactic plane, which, through dispersion measure observations,
fixes the pulsar distance scale. Unfortunately, the galactic distribution
of n  is not well known and is difficult to determine.
	
There are several
indications that n  is not uniform throughout the galactic plane and that it
does not have a simple exponential Z dependence"- '1, 42 ,  both of which have
been previously assumed in determining pulsar densities. However, in view
of the difficulties entailed in a detailed spatial modeling of n e , given the
present observational data, we choose to adopt the simple constant density
model of Taylor and Manchester' which is sufficient for estimating the mean
contribution from pulsars to the galactic r-radiation. For <n0'- _ . n3 cri-',
a value consistent O th HI ihsnrption distanco s, to pulsars in local regions
of the Galaxy' o , a statistical analysis of data on the 328 known pulsars
gives D8 ° 480 pulsars kpc-' and hp 1 325 pc. The resulting 7-ray production
spectrum per cm-' is shown in Figure 1 along with the production spectra for
n
5y„` mayor diffuse processes calculated by Stecker,` assUani ng a local inter-
stellar hydrogen density of 1 atom per cm-% This spectrum gives volume-
averaged integral pulsar 1-ray production rates at 10 kpc of 2.2 X 10-"
photons am-' s-I above 100 MeV and 4.6 Y 7 0-86 photons cm-' s-' above 35 MeV.
Although the calculated pulsar spectrum has been extrapolated below 100 MeV,
the model does not accurately predict the low energy spectrum because the
synchrotron radiation from secondary particles, which may extend to the
y-ray region, has not been included. This contribution would tend to steepen
the spectrum and increase the estimated flux level below around 100 MeV.
The diffuse production spectra illustrated in Figure 1 have widely
differing uncertainties. The pion production spectrum is least uncertain,
since it primarily involves cosmic ray protons with energies in the 1-10
GeV range where uncertainties in determining galactic fluxes owing to solar
modulation effects produce small uncertainties (4 15 percent) in the total
production rate. 26 Even the differential 7-ray source spectrum for E  4
10 GeV is insensitive to the kinematical model chosen, as evidenced by the
excellent agreement between calculations of Stecker, 2 ' -26 Ganguli and
Sreekantan. 211 and Badhwar and Stephens.'e
The Compton production mechanism produces a small expected contribution
in our region of the Galaxy, however, this process could be significant near
the galactic enter.° Since this component is small over most of the galaxy
and various theoretical estimates ,211 0 0 are in reasonable agreement with
Figure 1, we conclude that little error in determining the total galactic
flux is introduced via the Compton process.
6The situation is quite different in the case of electron bremsstrahlung.
The curve shown in Figure 1 for this component was determined using a
conservative "standard" cosmic ray electron spectrue l . However, the
electron spectrum cannot be easily determined from cosmic-ray data awing
to large solar modulation effects. Theorists have thus had much leeway in
invoking large electron fluxes to account for discrepancies in both the
spectrum and intensity of the observed galactic y-rays with "standard"
predictions" • 33 . Indeed, the spectral data have even been used to
speculate on drastic fluctuations in both electron and proton fluxes in the
Galaxy" although, in our view, inherent systematic errors as well as
statistical errors in the spectral data make such a radical analysis
unwarranted.
The calculated pulsar contribution, as presented here, has clear
implications for analyzing the total galactic spectrum. Pulsars contribute
a soft power law flux component similar to that expected from electron
bremsstrahlung. In addition, the pulsar component as estimated in Figure 1
is as large as the "standard" bremsstrahlung component.
It is also expected that the pulsar contribution to the total galactic
flux should be roughly independent of galactic longitude except in the outer
Galaxy. The argument is as follows. We have used the longitude and distance
data for the full sample of observed pulsars, together with corrections for
selection effects, to determine the radial distributions of pulsars in both
the northern (00 <t< 1800 ) and southern (1800 <,< 3600 ) Galactic longitudes.
The results for the inner Galaxy (R < 8 kpc) are strikingly similar to the
distributions of total 7-ray emissivity determined previously. e
 Thus, the
Wiz-.._	
----•^-1
7
ratio of pulsar to total emissivity (i.e., the fraction of the flux from the
pulsar component) should be roughly constant with longitude, for longitudes
within 600 of the Galactic center. This fraction is calculated to be 15 to
'	 20 percent above 100 MeV (as derived from both Figure 1 and a comparison of
the longitude distribution of pulsar an(i observed 7-ray emission' using the
data in Figure 2.) It can easily be of the order of 50 percent at lower
energies (see Figure 1), obviating the need to invoke large law energy
electron fluxes to explain the shape of the observed 7-ray spectrum.
The latitude distribution of pulsar 7-ray emission will be yarrow but
will extend somewhat beyond b = 100 (Ref. 8). Pulsars may therefore be
able to account for some of the flux observed at galactic latitudes above
100 ?b+'s . According to the model, the younger pulsars are the strongest
i-ray emitters. They are also more confined to the galactic plane". Thus,
the pulsars at high b have a higher mean age and are weaker. This would be
consistent with the lack of observed point sources at high b.
We therefore conclude that the integrated flux from distant 7-ray
emitting pulsars may provide an important fraction of the low to medium
energy galactic y-ray flux (although a smaller fraction of the flux above
100 MeV) ar, 1 the inclusion of the pulsar component in analyzing the galactic
-ray spectrum supports a coherent integrated relationship with galactic
cosmic-ray theory as previously discussed°°'4a.
REF)
Paul, J. A., ems. , Astron,I
Hartman, R. C., et a1., Astrophys. J. 230 9 597-606 (1939).
Stecker, F. W., Cosmic Gamma Rays, Mono Book Co., Baltimore (1971).
Stecker, F. W., Puget, J L., Strong, A. W., and Bredekamp, J. H.,
Astrophys, J. 188, L59-L61 (1974).
Fichtel, C. E., et al., Mstrophvs. J. 208, 211-219 (1976).
Stecker, F. W., Astrophys. J. 212 9 60-70 (1977).
Higdon, J. C., Astro h s J. 232, 113-128 (1979).
Harding, A. K., Astropoys. J., in press (1981).
Higdon, J. C. and Lingenfelter, R. E., Astrophys. J. 208 9 L107-L110 (1976).
Strong, A. W., Wolfendale, A. W., and Dahanayake, C. Mon. Not. R. Ast
i
r Soc.
179, 69-72 (1977).
11. Hartman, R. C., et al., in The Structure and Content of the Galaxy and
Galactic Gamma Rays ed. C. E. Fichtel and F. W. Stecker, pp. 15-25,
NASA CP-002, U.S. Govt. Printing Office, Washington, DC (1977).
12. Kniffen, D. A. et al., Nature 251, 397-398 (1974).
13. Thompson, D. J., Fichtel, C. E., Kniffen, D. A., and Ogelman, H.,
Astrophys. J. 200, L79-L82 (1975).
14. Bennett, K., et al., A-tron. Astrophys. 61, 279-284 (1977).
15. Lichti, G. G., et al., Non-Solar Gamma Rays (COSPAR Symp.) ed. R. Cowsik
and R. D. Wills (New York; Pergamon) pp.49-53 (1980).
16. Harding, A. K., Tademaru, E. and Esposito, L. W., Astrophys. J. 225,
226-236 (1978).
17. Harding, A. K., Astrophys. J., in press (1981).
1.
2.
3.
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5.
6.
7.
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F-
9
REFERENCES (Cont'd.)
18. Ogelman, H., Fichtel, C. E., Kniffen, D. A. and Thompson, D. J.
Al trop ys. J.. 2199 584-591 (1976).
19. Swanenburg, B. N. et al. Al troDhys. J., in press.
20. Weisberg, J. M., Rankin, J. and Boriakoff, V., Astron. Astrophys. 58,
84-93 (1980).
21. Ables, J. G. and Manchester. R. N. Astron. Astrophys., % 177 -184 (1976).
22. Harding, A. K. Pulsars, ed. W. Sieber and R. Wielebinski (Dordrecht:
Reidel), in press.
23. Taylor, J. H. and Manchester, R. N. Astrophys. J., 215, 885-896 (1977).
24. Stecker, F. W., Astrophys. and Space_ Sci. 6, 377-389 (1970).
25. Stecker, F. W., Astrophys. J. 185, 499-504 (1973).
26. Stecker, F. W., Astrophys. J. 22 ,  919-927 (1979).
This is basically a neutrino paper, but the new high-energy )-ray
spectrum results are discussed and shown in Figure 1 of this reference.
27. Ganguli, S. N. and Sreekantan, B. V., J. Phys. A9, 311-321 (1976).
28. Badhwar, G. D. and Stephens, F. A., Proc. 15th Intl. Cosmic Ray Conf.,
Plovdiv 1, 198-203 (1977).
29. Stecker, F. W., Origin of Cosmic Rays, ed. J. L. Osborne and
A. W. Wolfendale (Dordrecht: Reidel) pp. 267-334 (1975).
30. Piccinotti, G., and Bignami, G. F., Astron. Astrophys. 5, 69-75 (1976)
31. Daugherty, J. K., Hartman, R. C., and Schmidt, P. J., AI trouhvs. J.
198, 493-505 (1975).
32. Cesarsky, D. J., Paul, J. A. and Shukla, P. G., Astrophys. Space Sci. 59,
73-83 (1978).
33. Schlickeiser, R. and Thielheim, K. 0,, Mon. Not. R. Astr. Soc, 182,
103-109 (1978).
^F.
s 10
REFERENCES (Contd.)
34. Strong, A. W., Wolfendale, A. W., Bennett, K., and Wills, R. D., Mbn.
Not, R. Astr, Soc. 182, 751-760 (1978).
35. Fichtel, C. E., Simpson, G. A. and Thompson, D. J., Astroghys., J., 222,
833-849 (1978).
35. Lebrun, F. and Paul, J. A. Proc. 16th Intl. Conf, Cosmic Rays, pp. 13-18
w	 ...r^r	 r.- n .r^w^.
(1979).
37. Taylor, J. H. The Lame-Scale Characteristics of the Galaxy, ed.
W. B. Burton (Dordrecht: Reidel), pp. 119-123 (1979).
38. Stecker, F. W. Phys. Rev. Lett. 35, 188-1:, (1975).
39. Stecker, F. W., Nature, aq, 412-414 (1976).
40. Stecker, F. W. and Jones, F. C., Astrophys. J. 217, 843-858 (1977).
41. Stecker, F. W., Amer. Sci. 66, 570-576 (1978).
42. Stecker, F. W., The Large Scale Characteristics of the Galaxy, ed.
W. B. Burton (Dordrecht: Reidel) pp. 475-782 (1979).
11
FIGURE CAPTIONS
Figure 1--Differential production spectra for pulsars and the major diffuse
processes. The Vo . bremsstrahlung and Compton spectra are from
Stecker• *" and the total spectrum includes the pulsar contribution.
SAS-2 and COS-B data points for the longitude range 3550 <I< 150
are also shown.' a The left and right hand scales refer
to the theoretical production rates at 10 kpc from the galactic
center and the observed 7-rav flux, respectively.
Figure 2--Surface density of pulsars° and 7-ray surface emissivity plotted
against galacto-centric radius for northern and southern halves
of the Galaxy.
f.
1 0
10"2
I^ 24
IE
(D 10 25
Z
IL
w IC 26
tY
HARTMAN st. al.1979
PAUL. et. al. 1978
16-3
0
co
10-4 0bw
'aN
0
v^
10-5 0
0
a
10-6
10 -2 	 10 - 1	 1	 10
E y (GeV)
Figure 1
2000
1500
M,
s t
T
1i
i
1
E
N 1000
V
Y 500
Q
J
2000
1500
1000
500
8
6 zH
4
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2 V
Q ^
N1C
C
8
Y
Q '
^ o
6
4 g
0
O
2 ^
	
' ;	 0° s 2 < 180°
i y -RAY EMISSION
'	 (STECKER 1977)
— PULSAR DENSITY
DISTRIBUTION
Iv!	 `^	 T 1	 T T
1-i
10
	
15
	
r •
	 1800 s P 3600
r
rl
1
i
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Figure


Pulsar and diffuse contributions to the observed galactic gamma radiation

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