Sources of the Radio Background Considered Page: 5 of 12
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Sources of Radio Background 5
Similarly, we can get the inverse Compton (IC) emis-
sivity resulting from the same population of electrons as
[vzicJvp]= dv0 dyen(vo)ne(Ye) 2
16w J v0
(Blumenthal & Gould 1970), where n(vo) = [voU0 ]tot/hvo
is the total spectral number density of the extragalactic
background photon field (including radio, CMB, infrared,
optical/UV, X-ray, etc),
fT=2qT lnqT+qT+1- 2q,
qT - 2 and T2 Gq 1.
The IC emissivity can be related to the IC energy den-
sity by an equation similar to equation 10 with Fsy,(z) re-
placed by Fec(z) which now describes the evolution of the
product n(vo) x ke. Ignoring the differences between these
two evolutions (i.e. assuming that the ratio of the integrals
over redshift involving Fsy,(z) and F>c(z) is of order unity)
and by eliminating ke we can express the IC energy density
in terms of the synchrotron energy density as
v; Upr] (4.2 (BpG) ) 2
[v cU ] B28r v x
I %_e2 (B)
duo v0 'Ye [vOUno ]tot fT '
with v-, - min[v2, v, mec2/4hye] and vmin =
max[vi, v/42]. We note that because the IC emissivity is
dominated by upscattering of the CMB photon field, for
which the energy density increases with redshift, the pre-
sented evaluation of [vcU,] with the cosmological evolu-
tion neglected corresponds strictly to a lower limit.
Figure 3 shows the energy density of the observed ex-
tragalactic background light (thick curve), and the expected
IC energy density resulting from upscattering of these back-
ground photons by electrons producing the radio back-
ground as given by equation 14, for different magnetic fields
B - 0.001, 0.01, 0.1, and 1 pG (dotted, dashed, dot-dashed,
and solid curves, respectively). Spectral energy densities of
the IR/optical, X-ray, and y-ray cosmic photon fields were
constructed to be in agreement with the background levels
provided by Franceschini et al. (2008), Gilli et al. (2007), and
Sreekumar et al. (1998), respectively. Clearly any magnetic
field weaker than 1pG would result in X-ray/y-ray emission
exceeding the observed background, and regions with such
magnetic fields may be excluded as significant sources of the
Importantly, this consideration excludes our own Galac-
tic halo as the origin of the bulk of the isotropic radio signal.
Taylor, Stil, & Sunstrum. (2009) use rotation measure mea-
surements of 37,000 polarized extragalactic radio sources to
determine the intensity of the magnetic field in the Galactic
halo, concluding with a value of approximately 1 G. In our
2 The following expressions are valid in the Thompson regime and
are a good approximation for scattering of photons with hvo ~- 1
ev by the highest energy electrons -2. For scattering of photons
above this energy one must use the Klein Nishina cross section.
Few relevant photons lie above this range so in what follows we
approximate the Klein-Nishina suppression by a sharp cutoff.
log v [Hz]
Figure 3. The thick black curve shows the measured energy
density of the radio, microwave, infrared, optical, ultraviolet,
X-ray, and y-ray extragalactic backgrounds. The other curves
show the energy density produced by inverse Compton scatter-
ing of the photon backgrounds by electrons necessary to produce
the radio background reported by the ARCADE 2 collaboration
via synchrotron emission. The dotted, dashed, dot-dashed and
solid curves are for a 1 nG, 10 nG, 100 nG, and 1 pG level av-
erage magnetic field. Because the intergalactic magnetic field is
known to be ( 1pG, the observed level of the X-ray background
rules out a significant portion of the radio background being pro-
duced by electrons far from galaxies. Spectral energy densities of
the IR/optical, X-ray, and y-ray cosmic photon fields were con-
structed to be in agreement with the background levels provided
by Franceschini et al. (2008), Gilli et al. (2007), and Sreekumar
et al. (1998), respectively.
Galactic halo, the level of the ambient optical and infrared
photon fields will be even higher than that considered in the
calculation here, by an amount depending on the distance
from the Galactic plane, from the Galactic Plane, predict-
ing an X-ray background many times larger than that ob-
served. There are Galactic and solar system components to
the observed diffuse X-ray background, but these are signif-
icant only below 1 keV (Hickox & Markevitch 2006). The
observed level of the XRB therefore strongly disfavours a
Galactic origin for the observed isotropic radio signal..
3.2 Diffuse emission from the IGM
The CRB could in principle result from a population of rela-
tivistic electrons pervading the IGM as as a whole, perhaps
resulting from many generations of AGN. Large scale radio
sources can easily expand to sizes of many Mpc on gigayear
timescales, and so overlap. Almost certainly, however, adi-
abatic expansion losses would result in a very low energy
density, and synchrotron losses would lead to a steep en-
ergy spectrum. Furthermore a variety of arguments suggest
that the magnetic field in the IGM is likely to be very weak,
B ; 0.2 pG (see Vall6e (2004) and references therein). Dif-
fuse emission from the IGM therefore seems unlikely to be
3.3 Diffuse emission from clusters
There is evidence for diffuse radio emission in some but not
all clusters of galaxies. Ever since discovery of this emission
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Singal, J.; Stawarz, L.; Lawrence, A. & Petrosian, V. Sources of the Radio Background Considered, article, August 22, 2011; United States. (digital.library.unt.edu/ark:/67531/metadc928747/m1/5/: accessed November 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.