APASTRA ProceedingsAPASTRA Proc.2199-3963Copernicus GmbHGöttingen, Germany10.5194/ap-2-21-2015Diffuse synchrotron emission from galactic cosmic ray electronsDi BernardoG.bernardo@mpa-garching.mpg.deGrassoD.EvoliC.GaggeroD.MPI für Astrophysik, Karl-Schwarzschild-Strasse 1, 85740 Garching, GermanyIstituto Nazionale di Fisica Nucleare, Sezione di Pisa, Largo B. Pontecorvo, 56127 Pisa, ItalyII. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, GermanySISSA, Via Bonomea 265, 34136 Trieste, ItalyINFN, sezione di Trieste, via Valerio 2, 34127 Trieste, ItalyG. Di Bernardo (bernardo@mpa-garching.mpg.de)22September201522212617April201528July20159September2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://ap.copernicus.org/articles/2/21/2015/ap-2-21-2015.htmlThe full text article is available as a PDF file from https://ap.copernicus.org/articles/2/21/2015/ap-2-21-2015.pdf
Synchrotron diffuse radiation (SDR) emission is one of the major Galactic
components, in the 100 MHz up to 100 GHz frequency range. Its spectrum and
sky map provide valuable measure of the galactic cosmic ray electrons (GCRE)
in the relevant energy range, as well as of the strength and structure of the
Galactic magnetic fields (GMF), both regular and random ones. This emission
is an astrophysical sky foreground for the study of the Cosmic Microwave
Background (CMB), and the extragalactic microwave measurements, and it needs
to be modelled as better as possible. In this regard, in order to get an
accurate description of the SDR in the Galaxy, we use – for the first time
in this context – 3-dimensional GCRE models obtained by running the
Dragon code. This allows us to account for a realistic spiral arm
pattern of the source distribution, demanded to get a self-consistent
treatment of all relevant energy losses influencing the final synchrotron
spectrum.
Introduction
Deflection of ultra-high energy cosmic rays (UHECR), rotation measure,
synchrotron radiation, and polarized dust are just a small sample of
different methods of observation of the galactic magnetized interstellar
medium (ISM). Cosmic rays (CRs) are, doubtless, a unique probe of the ISM
properties. Thanks to a set of successful experiments such as Fermi-LAT,
PAMELA, AMS-02, the last few years have witnessed an incredible progress in
the science of electron, and positron Galactic CRs, over a wide range of
energy, from O (TeV) down to tens of MeV.
Unfortunately, solar modulation complicates matters, since the CR spectra
observed on Earth are – for E≲ 20 GeV – completely
reshaped with respect to their local interstellar spectra (LIS).
Relativistic cosmic ray electrons and positrons (CRE), spiralling around the
interstellar magnetic field lines, are at the origin of the radio diffuse
emission from the Milky Way. For magnetic field intensity of O
(µG), like in the case of our Galaxy, and for electrons/positrons of
[GeV–TeV] energies, the synchrotron emission falls in the
[MHz–GHz] range. Indeed, the SDR offers valuable complementary
checks of the low energy spectrum, and in general of the spatial distribution
of CRs in the Galaxy. Hence, a parallel study of radio emission, together
with CR measurements, can put better constraints on all the interstellar
medium (ISM) components involved . The
interpretation of those measurements requires a proper modelling of
injection, propagation and losses in the Galaxy.
Moreover, the presence in the [20–200] GHz range of several astrophysical
sky signal components – with similar intensities and some spatial correlation – makes
the extraction of the CMB a complex task. In order to achieve
sufficient accuracy on the cosmological signal the component separation needs
to take advantage of the knowledge on the properties of diffuse Galactic emission.
We plan to accomplish the aforementioned study by running the Dragon
code in its 3-dimensional version. Indeed, this is well suited to model the
CRE propagation, when accounting for a realistic spiral arm distribution of
astrophysical sources, gas distributions, magnetic fields models and
different position-dependent models for diffusion in the parallel and
perpendicular directions with respect to the GMF.
Objectives and method
In the present Section, we outline the guidelines of the
multi-wavelength analysis we have performed, in order to model the
CRE spectra consistently with the diffuse synchrotron emission of the Galaxy.
One of our main aims has been:
To explore the physical properties – injection and propagation – of the
local interstellar spectrum (LIS) of CRE, in the realm of low energies
(≲ 7 GeV), by combining the latest e- and e+ measurements
with the diffuse Galaxy radio emission, between 10 MHz and few GHz.
Below that energy, we modelled the LIS of e++e- on the basis of the observed
synchrotron spectrum of the Galaxy, which is unaffected by propagation in the
heliosphere (see also e.g. ).
In parallel to that, the current study has pushed us to give an important
constrain on the vertical scale height of the diffusion region in the Galaxy,
by looking simultaneously at the radio spectrum, the latitude profile of the
synchrotron emission, and the positron fraction at energies below ∼ 5 GeV.
The structure of the GMF is still not well understood. Generally, a
realistic, and accurate description of the synchrotron emission, as well as
of its angular distribution, requires to consider two main components for the
GMF: the regular and turbulent ones. Regarding the ordered one, here we rely
on a recent model, based on a wide and updated compilation of Faraday
rotation measurements . It consists of two
different components: a disc field, with a magnitude in the vicinity
of the solar system, B0, taken to be 2 µG, and a toroidal
halo field, with a thickness of ∼ [0.2–0.4] kpc, and
extended – above, and below – out of the galactic plane (GP) for
[1–2] kpc.
We have included the regular field in order to make our
model compatible with the current information. However, in our analysis, we
have checked that only the halo component (Bhalo= 4 µG)
for the regular GMF plays, albeit marginal, a role.
A
new, and much-improved model for the regular GMF has been recently brought to
the attention of the community . In addition to a
disc field and an extended halo field, the peculiarity of this GMF model is
its X-shape in the r–z directions. The main implications based on
such a ordered GMF model will be addressed in our future work.
Regarding the random component – actually, the main responsible for the
diffusion of charged particles in the ISM – there is still a poor knowledge
about its geometrical structure. As in , we have
assumed it to fill a thick disk, modelled with an exponential vertical
profile, and an effective scale-height zh, accordingly to the equation:
Bran(z)=Bran(0)exp-z/zh.
For the aforementioned purposes, we first run Dragon, a new
numerical package aiming to solve the diffusion equation of CRs in the Galaxy
environment .
Differently form other semi-analytical and numerical codes, in this
contribution we account for a possible spatial dependence of the diffusion coefficient,
D(ρ,R,z)=D0βηf(z)ρρ0δ,ρ being the rigidity of the particle, β the particle speed in
units of speed of light c, and f(z) indicates the spatial dependence of
the diffusion coefficient. As predicted by the quasi-linear theory (QLT),
that should be related to the fluctuating magnetic field, and hence as
D(z)-1∝Bran(z)∝exp(-z/zh).
The CRE models considered in the present analysis. The reported
values of γinj(e-) refer to energies below/above 4 GeV.
In this paper, for simplicity, only two representative classes of propagation
regimes have been taken in consideration: the KRA (Kraichnan), and
the KOL (Kolmogorov). The main parameter characterizing those two
models are reported in Table .
For each of them, we varied the scale-height of the diffusive halo in the
range zh= [1–16] kpc, and the main diffusive parameters were
determined in order to minimize the combined χ2 against the
boron-to-carbon ratio and the proton observed spectra.
Finally, at high energies (≳ 7 GeV), unlike our previous
results presented in , here we fix the spectral index,
and the normalization of the injection spectrum of the primary electrons and
of the extra-component by tuning our models against the new data, as recently
released by PAMELA and AMS-02 collaborations, respectively, rather than on
e-+e+ spectrum measured by Fermi-LAT .
With reference to Fig. , we want to make it clear that
the assumption of a simple power-law (PL) distribution for energetic
electrons and positrons, whose sources are smoothly distributed in the entire
Galactic disc, leads to large overestimation of their energy densities in
comparison with the values deduced when a 3-dimensional spiral arm
distributions are used. In our opinion, the impact of this more realistic
modelling of the particle distribution on the final synchrotron spectral maps
is a crucial issue (see also the comparison between the Figs.
and ).
The synchrotron emission of the galaxy
It is known that the synchrotron intensity depends on the spatial, and
energetic distribution of CRE density, ne, and the strength of the
magnetic field (B⟂), perpendicular to the line of sight (LOS) to the
observer. Once the CRE densities are computed by Dragon – at all
points of the computational grid – we use Gammasky, a dedicated code
recently used in, e.g. , and
to get the emissivities (i.e. power per unit volume
per unit frequency per unit solid angle), for the regular and random fields,
according to the standard formalism , after having
integrated over the particle energy.
Normalized electron density profile along the radial direction. The
black line corresponds to a 2-dimensional, smooth CR. The red one corresponds
to a 3-dimensional spiral arm pattern of sources.
The emissivity (in erg s-1 Hz-1) – in an
uniform magnetic field – is partially linearly polarized,
For a
monochromatic and isotropic distribution of CRE.
and usually subdivided in
two components, ϵ∥,⟂, respectively parallel and
perpendicular to B⟂≡B(r)sinα, with α the
angle between the direction of the magnetic field and the LOS. The
polarization formulation will be used in our future work. Here, we show
results based only on the total intensity, given by
ϵ(ν,r)=3e3mc2B⟂(r)F(x);
where x=ν/νcreg, being νcreg=(3/4π)(e/mc)B⟂γ2 the critical synchrotron frequency,
γ the particle (electron or positron) Lorentz factor, and F(x) is
defined in terms of Bessel functions. In the case of a randomly oriented
magnetic field, the expected isotropic emissivity is computed according to .
The average synchrotron spectra, for zh= 4 kpc. We show
the spectra obtained with (solid lines) and without (dashed lines) the
spectral break in the e- source spectra. Dotted lines are the
contribution of secondary e- source spectra. The contribution of the
regular GMF is shown as the dot-dashed line. The normalization required
for the random component field strength is
Bran(0) = 7.6 µG.
The total synchrotron intensity
Given a GMF model, and for the representative CRE density models
aforementioned, the next step is to compute the Galactic synchrotron
spectrum. We take care of correctly reproducing the observed 408 MHz
radio synchrotron radiation as in , by tuning – time
to time – the normalization value for the turbulent component of the GMF
(see the Eq. ). We get the sky maps in Gammasky
by integrating the Galactic emissivity along the LOS,
I(ν)=∫l.o.sϵ(ν,r)ds,
where ϵ(ν, r) is the total emissivity given by
Eq. (). In Fig. we refer to the observed
brightness temperature (in K), defined as T(ν)=c2I(ν)2kBν2.
Normalization of random GMF vs. the vertical scale height. The
3(5)σ allowed by RM are represented in grey (light grey) bands. The
red squares are the values used in our KRA models in order to
reproduce the observed spectrum at 408 MHz.
The sky maps are subdivided into equal area pixels following the
HEALPix
http://healpix.jpl.nasa.gov/
pixelization scheme
of . We average the flux over the sky regions
40∘<l< 340∘, 10∘<b< 45∘, -45∘<b<-10∘,
where l and b are Galactic longitude and latitude,
respectively. We restrict the analysis to the regions out of the Galactic
plane – but avoiding the polar regions – being the contamination from
point-like and local extended sources expected to be the smallest. In
addition to that, we avoid absorption effect at radio frequencies, and
free-free emission at higher frequencies .
Therefore, the observed Galactic diffuse emission in the radio band is,
almost entirely, due to the synchrotron radiation of CRE moving errantly in
the GMF.
From tens of MHz to 23 GHz (and up to 94 GHz for
Wmap), in such sky region we directly compare our simulated models
with the synchrotron spectra measured by a wide set of radio surveys at
22, 45, 408, 1420, 2326 MHz as well as Wmap satellite data at
23, 33, 41, 61 and 94 GHz.
With reference to Fig. , it is immediate to realize
that the radio data (≲O(100) MHz) are clearly
incompatible with a single PL electron spectrum, suitable to fit the CRE
data. Rather, we find that introducing – below a few GeV – either a
break or an exponential infrared (IR) cut-off in the population of
primary e-, that helps us in providing a very good description of the
radio data.
As immediate consequence of that, the total electron flux (at E≲ 4 GeV),
and hence the radio spectrum below 100 MHz, are
dominated by secondary particles, which are produced in nuclear collision
with the nuclei of the gas present in the ISM, offering thus a direct probe
of the interstellar proton spectrum. In this regard, we found that once the
low energy e- source spectrum is tuned to reproduce the observed e+
spectrum, only models featuring low re-acceleration can reproduce the
observed e+ spectrum and fraction, in total agreement with what found in
.
The magnetic halo height
The vertical – perpendicular to the Galactic plane – size of the CR diffusion
region represents, undoubtedly, a cornerstone in modern
Astro-particle physics. The accurate knowledge of it goes beyond the target
of conventional CR astrophysics; it is also worth for Dark Matter (DM)
indirect search, since that the local flux of DM decay, and annihilation
products are expected to depend significantly on such physical length.
So far, the diffusive vertical boundary has been constrained purely on the
basis of CR radioactive nuclide 10Be, hence the 10Be / 9Be ratio
most commonly. However, this method is subject to the severe uncertainties
connected to local distribution of sources, gas, and especially by the solar modulation.
The latitude profile for the synchrotron emission at 408 MHz, at
different magnetic halo height.
To the contrary, the synchrotron emissivity of the Galaxy offers a much more
genuine probe of the scale height zh. In that regards, we may notice
that, when a realistic vertical distribution is adopted for the radiation
interstellar field (ISRF) and for the GMF, energy losses in the
O (GeV) energy range - hence in the radio energy band – do not
affect significantly the CRE vertical distribution, determined predominantly
by the diffusion and therefore coincident with that of CR nuclei (see Fig. 5
in ).
Our first argument aiming to constrain the value of zh is the following
one: for a given propagation set up, the synchrotron flux depends, from
Eq. (), only on the random field normalization
Bran(z= 0), dominant respect to the regular one, and on
zh, the scale-height of the diffusion region (I(ν, r)∝∫B(r)ne(r) ds).
As it is possible to appreciate in Fig. , the fit of radio data suggests a tight
relation Bran2(z= 0) ∝zh-1.
Spectral index map between 408 MHz and 23 GHz, with the assumption
of a smooth 2-D CR sources. Given the total intensity
I(ν)∝(ν/ν0)βs, the map has been
computed according the standard formalism:
βs= 0.248 log(I23/I408).
Secondly, we compare the observed latitude profile of the synchrotron
emission at 408 MHz to that calculated for the KRA set up,
setting different values for zh. For each zh we tune the value of
Bran(z= 0) so that the average spectrum in these regions is
reproduced (Fig. ). Low values of zh are disfavoured:
a χ2 analysis showed that zh≤ 2 kpc are excluded at
3σ level.
Future directions and conclusions
To fully observe and understand the GMF, more effort is required. With our
analysis, we exploited the SDR as a way to measure the low energy LIS
spectrum of CRE. For the first time, we have placed a constraint on the CR
diffusive halo scale height, based on the comparison of the computed
synchrotron emission intensity with radio observations. Moreover, we stress
out that – for the first time in this framework – our modelling of the SDR
emission accounts for the presence of the e±charge-symmetric extra-component, required not only to consistently model PAMELA and AMS-02
high energy data, but also to correctly estimate the e- source spectrum
from CRs and radio data. In our opinion, the combination of high precision
CRE data, and current radio observations, can be a viable method to
disentangle the contribution of the extra-component to the total synchrotron spectrum.
One of the greatest challenges of observing the Cosmic Microwave Background (CMB)
in the [20–200] GHz range resides in the separation
between the CMB and the superimposed foreground emission: free-free,
synchrotron, thermal dust. We pointed out that transport of charged
relativistic particles, and magnetic fields models should be studied
simultaneously, because both have influence on the synchrotron modelling.
Synchrotron spectra may reveal signatures of spatially inhomogeneous particle
source distributions and magnetic fields. In our treatment here, instead of a
smooth CR distribution invariant for rotations about the Galactic disc axis,
we rather calculate self-consistently the synchrotron maps emitted by
electrons whose spectral density is inhomogeneous, due to all the relevant
energy losses sustained while traversing regions with different distributed
gas, magnetic and radiation fields.
Finally, the frequency range of Gammasky synchrotron simulations,
from O(10) MHz to O(100) GHz,
covers radio telescopes such as Planck, LOFAR, and SKA. We have developed
Gammasky code with the aim to support the scientific exploitation of
the data provided by these experiments.
As in Fig. , but with the important
assumption of a 3-D spiral arm structure.
Acknowledgements
G. Di Bernardo and C. Evoli would like to thank Klaus Scherer,
Julia Becker Tjus and Paolo Desiati for the invitation to the workshop:
“Cosmic Ray Anisotropies 2015”.
The articleprocessing charges for this open-access publication
were covered by the Max Planck Society.
Edited by: P. Desiati
Reviewed by: two anonymous referees
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