APASTRA ProceedingsAPASTRA Proc.2199-3963Copernicus GmbHGöttingen, Germany10.5194/ap-2-1-2015The Local Bubble as a cosmic-ray isotropizerGebauerI.gebauer@kit.eduWeinreuterM.KunzS.GaggeroD.Karlsruhe Institute of Technology, Institut für Experimentelle Kernphysik, 76131 Karlsruhe, GermanySISSA, via Bonomea 265, 34136, Trieste, ItalyINFN, sezione di Trieste, via Valerio 2, 34127, Trieste, ItalyI. Gebauer (gebauer@kit.edu)31July2015221315April201524June201525June2015This 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/2/1/2015/ap-2-1-2015.htmlThe full text article is available as a PDF file from https://ap.copernicus.org/articles/2/1/2015/ap-2-1-2015.pdf
The arrival directions of energetic positrons and electrons convey
fundamental information on their origin. PAMELA, and more recently AMS, have
measured an anomalous population of energetic positrons, which cannot be
explained in standard cosmic ray propagation models. Two possible sources
have been extensively discussed: astrophysical point sources, such as local
pulsars, and dark matter. In the first case an anisotropy in the flux of
energetic particles is expected. Reliable predictions of the level of
anisotropy need to account for the Sun's peculiar environment: the Sun
resides in the so-called Local Bubble, an underdense region, embedded in a
dense wall of molecular clouds. This structure is expected to act as an
efficient cosmic-ray isotropizer. Using realistic assumptions on the impact
of the Local Bubble on cosmic-ray diffusion, we demonstrate that the Local
Bubble can indeed dilute the directional information of energetic positrons
and electrons.
Introduction
We examine the impact of local structures on the cosmic-ray
(CR) electron and positron spectra and anisotropies in CR arrival directions.
Electrons and positrons suffer severe energy losses due to synchrotron
emission and Inverse Compton scattering on the Interstellar Radiation Field:
their propagation length decreases significantly with increasing energy from
values of around 10 kpc at GeV energies to 600–900 pc at 1 TeV. With
propagation distances as low as a few hundred parsecs, structures in the
local interstellar medium (ISM) may have a sizeable effect on local spectra
and arrival directions. This is different for hadrons, where the propagation
length is comparable to the diameter of the gaseous disk for energies above
10 GeV.
The most prominent structure in our local interstellar medium is the
so-called Local Bubble (LB), a particular underdense void containing our
Solar system close to its center, surrounded by a wall of dense molecular
clouds. The shape of the region is similar to a chimney, with radii between
50 and 150 pc ; the asymmetric shape, elongated
perpendicularly to the Galactic plane and opened towards the halo, is shown
in several papers (see e.g. ). The Local Bubble is
connected via low-density “tunnels” to other similar nearby structures (see
e.g. ). These huge connected cavities filled with hot
ionized gas are expected to originate from supernova explosions
and should be present in every region of the
Galaxy, making the Galactic plane a very inhomogeneous structure of
underdense regions surrounded by denser and colder magnetized molecular
clouds, which are expected to confine CRs efficiently.
In the context of interpretations of the so-called positron excess
, the local anisotropy in
positron and electron fluxes is particularly important: a positive detection
of a dipole anisotropy towards a known object (e.g. a pulsar) could prove the
astrophysical origin of the positron excess. No detection of any anisotropy
has been reported so far, but more and more stringent upper limits are being
placed on the sum flux of electrons and positrons and on the separate
positron flux. In this context, a structure like the Local Bubble can work as
an efficient isotropizer of local CRs, even under general assumptions. A
meaningful comparison between data and model prediction requires to properly
take into account the complicated environment CRs have to cross on their way
from the local sources to us.
Left: predicted flux of secondary positrons for a set of about
13 000 models optimized to best decribe the flux of protons, antiprotons,
the B/C ratio and the 10Be/9Be ratio
. The full red line indicates the best fit model to the
above observables, the red band is the uncertainty given by the uncertainty
on the transport parameters. Solar modulation was optimized for AMS-02
for each model. Right: behavior of the
diffusion coefficient in the Local Bubble for the two scenarios considered
here. The gray line shows the pulsar source distribution.
Model
We use the DRAGON
The code is public and available at:
www.dragonproject.org.
code, which numerically
solves the CR transport equation for all CR species, to simulate the
propagation of e± accelerated by a nearby point source through the
environment of the Local Bubble. The transport model was chosen to describe
the locally measured proton and antiproton spectrum, the B/C ratio and the
10Be/9Be fraction. Using the given transport model,
the contribution of secondary e± from proton-gas interactions in the
ISM can be calculated. The predicted flux of secondary positrons is shown in
Fig. . The solution is obtained separately for continuously
distributed supernova remnants (where primary CR acceleration takes place for
both, leptons and for hadrons; the latter also produce secondary positrons
and electrons in subsequent interactions with the ISM), and for a pulsar
point source (considered as electron-positron pair emitter). We model the
source as a Gaussian with a width of 60 pc to account for the extension of
the pulsar wind nebula; the source is assumed to be located at a distance d=200 pc towards the Galactic center, just outside the bubble wall. The
common electron and positron spectrum from pulsars is assumed to follow a
power law with spectral index γ and an exponential cutoff at energy
Ecut: Qe+,e-pulsar=q0(E/E0)γexp(-E/Ecut). The position and extension of the source with
respect to the Local Bubble is illustrated by the gray line in
Fig. . The source parameters are fixed to best describe the AMS-02
positron data.
To model the Local Bubble we implemented a region with increased spatial
resolution surrounding the Sun in the DRAGON code. Within this
region the normalization of the diffusion coefficient is allowed to vary as
described in the following. In the most realistic model the bubble is a
region of large diffusion coefficient surrounded by a thin, very confining
region characterized instead by a low diffusion coefficient. The diffusion
coefficient has the lowest value at a distance of 160 pc from the Sun. We
discuss two scenarios: (a) a decrease of diffusion coefficient in the bubble
wall by a factor of 100 with respect to the galactic value and an increase by
a factor of 100 with respect to the galactic value at the Sun's position
(dark blue line in Fig. ). (b) a decrease of diffusion coefficient
in the bubble wall by a factor of 100 with respect to the galactic value,
while the diffusion coefficient at the position of the Sun is identical to
the galactic value (sea green line in Fig. ). More details on the
technical implementation of the Local Bubble will be presented in a
forthcoming publication.
Left: local positron flux. The solar modulation is optimized for the
data in each case. Data: AMS-02 .
Right: electron + positron sum flux anisotropy. The x axis is in
cumulative energies, with a maximum energy of 1 TeV. Data: Fermi-LAT
.
Anisotropy and electron/positron spectra
For each scenario the injection spectrum of primary electrons from the
continuous supernova remnant distribution is optimized to best describe the
AMS-02 electron data. The pulsar injection spectrum index, cutoff energy and
relative normalization of the pulsar contribution is optimized to the
positron flux and positron fraction measured by AMS-02. The left side of
Fig. shows the impact of the Local Bubble scenarios on the
electron and positron spectra. In the reference scenario (no Local Bubble,
black line in Fig. ) the data cannot be explained by a single
pulsar. The plot shows how the Local Bubble, in both the implementations
described here, has a sizable effect on the positron flux at low energy (we
postpone a complete discussion to a more detailed work, given the huge
uncertainties involved in this part of the spectrum on the modelling side).
The corresponding anisotropies are numerically calculated for the position of
the Sun according to δ=3D(E)/c⋅∇ne/ne, where D(E) is the local diffusion coefficient
and ne is the local electron density .
The spatial resolution of our model around the position of the Sun is 10 pc.
The right side of Fig. shows the anisotropy of the electron and
positron sum flux. The standard scenario with no Local Bubble yields
anisotropies at the level of 0.5 % in the entire energy range from
60 GeV to 1 TeV, which is comparable to the 95 % CL upper limits from
Fermi. In the bubble + wall scenario the level of anisotropy is decreased
by a factor of 2.3 in the entire energy range, while the wall only scenario
yields a decrease by a factor of about 4.
Conclusion
We used general assumptions on the behavior of the
diffusion coefficient in the Local Bubble to investigate the level of
isotropization of electron and positron fluxes coming from a nearby point
source (e.g. a pulsar). We tuned the source parameters so that the emission
from the source provides a good fit of AMS e+ and e- spectra. We showed
that the level of anisotropy expected from a local point source can be
decreased by a factor of 4 by local changes in the diffusion coefficient,
while the description of the local spectra of electrons and positrons is
improved. We conclude that, under simple assumptions, the Local Bubble acts
as an efficient CR isotropizer, with strong impact on the comparison between
the prediction of the dipole anisotropy from local pulsars and the observed
upper limit from Fermi-LAT.
Acknowledgements
We thank the anonymous referees for helpful input. The computational
resources for this project are provided by the bwGRiD.
Edited by: K. Scherer
Reviewed by: two anonymous referees
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