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4 J. Singal et al.
2.1 2.2 2.3 7. I
2. 2.2 2.3 2 .1
S -- - -
-. 2 . .
Figure 2. TOP: The lower flux density of sources Si, at
1.4 GHz required so that the extrapolated source counts from
S0 1 mJy, with a faint end index y, can account for observed
CRB as reported by the ARCADE 2 collaboration, including a
16% (solid lines) or 25% (dotted line; see 4) contribution to
the background from S;So sources. The upper and lower solid
curves are for the two extreme values of the 1 mJy normaliza-
tions no of the surveys we consider. For y ~ 2.5 an extrapolation
to Smi, O.IpJy is needed, while the needed lower flux density
falls rapidly with decreasing faint end index. BOTTOM: Same
as the top panel, but for the minimum number of sources below
So needed to produce the observed CRB.
customary, is more than likely an over-simplification. A more
realistic description would involve a smoothly curved func-
tion with the integrated contribution per log flux bin (Figure
1, lower panel) peaking around Smin and then falling off, but
including some contribution from objects with fluxes lower
than Smin. The large population of dwarf galaxies may be
the sources that increasingly become relevant at fluxes below
3 DIFFUSE SOURCES
In this section we consider the possibility that the CRB re-
sults from truly diffuse emission associated with the large
scale structure of the Universe, such as the intracluster
medium (ICM), intergalactic medium (IGM), or the fil-
. . .
47r 87rkBv/ vr0.
VrUrI - -vBCRB(vr) 1.17 k3 -- ,
C C3 kv*,
where v* - 1 GHz. We are considering the background span-
ning frequencies from v1 ~1 MHz to v2 ~10 GHz.
For a density of ultrarelativistic electrons with a power-
law energy spectrum
n (-Y,) = keye-s for 'Ye, ye Y2,
where ke is a normalization constant in units of cm-3, and
ye and ye2 correspond here to the Lorentz factors of the
electrons producing radiation primarily around v1 and v2,
respectively, the synchrotron emissivity may be approxi-
mated as (see e.g. Rybicki & Lightman 1979)
COT UB yr 2
where UB = B2/87r is the energy density of the magnetic
field, and ve = (3eB/47rmc) y ~ 4.2 (B/pG) ye Hz is the
critical (radio) synchrotron frequency for a given ye.
For production of the observed radio background we
need s = 2.2, ye = 5 x 102(B/pG)-1/2, and e2 =
5 x 104(B/pG)-1/2, with the value of ke being determined
from the following relation between the emissivity and the
observed energy density.
We relate the (radio) synchrotron energy density to the
47r dV dz .
c dz 47rd2(z)vrJ ri
47r Fsyn(z) dz
(vr jvr] H0f (1 + z)(s+1)/2E(z)
where yr = vr (1 + z), H0 = 70 km-1 Mpc-1 is the Hubble
constant, and Fsyn (z) describes the evolution of the product
UB x ke. Here E(z) - Q2M (1 + z)3 + QA for the assumed
flat cosmology, and the comoving volume element is
c347, [ dz'
H0sE(z) [1 E(z')l
H0 (1 + z)2 E(z) .
aments connecting the clusters containing warm-hot gas
(WHIM). First we consider very general constraints, and
then look at specific possibilities.
3.1 General constraints on diffuse emission
The simplest constraint on any population of electrons pro-
ducing the CRB is that it must have a relatively flat energy
spectrum, in order to produce the observed spectral index
of a ~ 0.6. Less obviously, we show below that it must be
associated with a magnetic field of at least 1 pG. This is
because otherwise the magnetic field energy density in such
systems is much less than the energy density of the cosmic
- .. microwave background (CMB) and other background radi-
2. 5 .( ations. As a result, the relativistic electrons responsible for
the radio emission would lose most of their energy produc-
ing hard X-ray and gamma radiation via inverse Compton
scattering of the other background fields. We now derive this
t limit more carefully.
Given the observed power law spectrum, the energy
density of the radio background per frequency dex at r,
is given by
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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/m1/4/: accessed January 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.