Galaxy clusters occupy a special position in the cosmic hierarchy as they are the
largest bound structures in the Universe. There is now general agreement on a
hierarchical picture for the formation of cosmic structures, in which galaxy clusters
are supposed to form by accretion of matter and merging between smaller units.
During merger events, shocks are driven by the gravity of the dark matter in the
diffuse barionic component, which is heated up to the observed temperature.
Radio and hard-X ray observations have discovered non-thermal components
mixed with the thermal Intra Cluster Medium (ICM) and this is of great importance
as it calls for a “revision” of the physics of the ICM. The bulk of present information
comes from the radio observations which discovered an increasing number of Mpcsized
emissions from the ICM, Radio Halos (at the cluster center) and Radio Relics
(at the cluster periphery). These sources are due to synchrotron emission from
ultra relativistic electrons diffusing through µG turbulent magnetic fields. Radio
Halos are the most spectacular evidence of non-thermal components in the ICM
and understanding the origin and evolution of these sources represents one of the
most challenging goal of the theory of the ICM.
Cluster mergers are the most energetic events in the Universe and a fraction of
the energy dissipated during these mergers could be channelled into the amplification
of the magnetic fields and into the acceleration of high energy particles via
shocks and turbulence driven by these mergers. Present observations of Radio
Halos (and possibly of hard X-rays) can be best interpreted in terms of the reacceleration
scenario in which MHD turbulence injected during these cluster mergers
re-accelerates high energy particles in the ICM. The physics involved in this scenario
is very complex and model details are difficult to test, however this model clearly
predicts some simple properties of Radio Halos (and resulting IC emission in the hard
X-ray band) which are almost independent of the details of the adopted physics. In
particular in the re-acceleration scenario MHD turbulence is injected and dissipated
during cluster mergers and thus Radio Halos (and also the resulting hard X-ray
IC emission) should be transient phenomena (with a typical lifetime <» 1 Gyr)
associated with dynamically disturbed clusters. The physics of the re-acceleration
scenario should produce an unavoidable cut-off in the spectrum of the re-accelerated
electrons, which is due to the balance between turbulent acceleration and radiative
losses. The energy at which this cut-off occurs, and thus the maximum frequency
at which synchrotron radiation is produced, depends essentially on the efficiency of
the acceleration mechanism so that observations at high frequencies are expected
to catch only the most efficient phenomena while, in principle, low frequency radio
surveys may found these phenomena much common in the Universe.
These basic properties should leave an important imprint in the statistical
properties of Radio Halos (and of non-thermal phenomena in general) which,
however, have not been addressed yet by present modellings.
The main focus of this PhD thesis is to calculate, for the first time, the expected
statistics of Radio Halos in the context of the re-acceleration scenario. In particular,
we shall address the following main questions:
• Is it possible to model “self-consistently” the evolution of these sources together
with that of the parent clusters?
• How the occurrence of Radio Halos is expected to change with cluster mass
and to evolve with redshift? How the efficiency to catch Radio Halos in galaxy
clusters changes with the observing radio frequency?
• How many Radio Halos are expected to form in the Universe? At which redshift
is expected the bulk of these sources?
• Is it possible to reproduce in the re-acceleration scenario the observed
occurrence and number of Radio Halos in the Universe and the observed
correlations between thermal and non-thermal properties of galaxy clusters?
• Is it possible to constrain the magnetic field intensity and profile in galaxy
clusters and the energetic of turbulence in the ICM from the comparison
between model expectations and observations?
Several astrophysical ingredients are necessary to model the evolution and
statistical properties of Radio Halos in the context of re-acceleration model and
to address the points given above. For these reason we deserve some space in this
PhD thesis to review the important aspects of the physics of the ICM which are of
interest to catch our goals. In Chapt. 1 we discuss the physics of galaxy clusters,
and in particular, the clusters formation process; in Chapt. 2 we review the main
observational properties of non-thermal components in the ICM; and in Chapt. 3 we
focus on the physics of magnetic field and of particle acceleration in galaxy clusters.
As a relevant application, the theory of Alfv´enic particle acceleration is applied
in Chapt. 4 where we report the most important results from calculations we have
done in the framework of the re-acceleration scenario. In this Chapter we show that
a fraction of the energy of fluid turbulence driven in the ICM by the cluster mergers
can be channelled into the injection of Alfv´en waves at small scales and that these
waves can efficiently re-accelerate particles and trigger Radio Halos and hard X-ray
emission.
The main part of this PhD work, the calculation of the statistical properties
of Radio Halos and non-thermal phenomena as expected in the context of the
re-acceleration model and their comparison with observations, is presented in
Chapts.5, 6, 7 and 8.
In Chapt.5 we present a first approach to semi-analytical calculations of
statistical properties of giant Radio Halos. The main goal of this Chapter is to model
cluster formation, the injection of turbulence in the ICM and the resulting particle
acceleration process. We adopt the semi–analytic extended Press & Schechter (PS)
theory to follow the formation of a large synthetic population of galaxy clusters and
assume that during a merger a fraction of the PdV work done by the infalling
subclusters in passing through the most massive one is injected in the form of
magnetosonic waves. Then the processes of stochastic acceleration of the relativistic
electrons by these waves and the properties of the ensuing synchrotron (Radio Halos)
and inverse Compton (IC, hard X-ray) emission of merging clusters are computed
under the assumption of a constant rms average magnetic field strength in emitting
volume. The main finding of these calculations is that giant Radio Halos are
naturally expected only in the more massive clusters, and that the expected fraction
of clusters with Radio Halos is consistent with the observed one.
In Chapt. 6 we extend the previous calculations by including a scaling of the
magnetic field strength with cluster mass. The inclusion of this scaling allows us to
derive the expected correlations between the synchrotron radio power of Radio Halos
and the X-ray properties (T, LX) and mass of the hosting clusters. For the first
time, we show that these correlations, calculated in the context of the re-acceleration
model, are consistent with the observed ones for typical µG strengths of the average
B intensity in massive clusters. The calculations presented in this Chapter allow
us to derive the evolution of the probability to form Radio Halos as a function of
the cluster mass and redshift. The most relevant finding presented in this Chapter
is that the luminosity functions of giant Radio Halos at 1.4 GHz are expected to
peak around a radio power » 1024 W/Hz and to flatten (or cut-off) at lower radio
powers because of the decrease of the electron re-acceleration efficiency in smaller
galaxy clusters. In Chapt. 6 we also derive the expected number counts of Radio
Halos and compare them with available observations: we claim that » 100 Radio
Halos in the Universe can be observed at 1.4 GHz with deep surveys, while more
than 1000 Radio Halos are expected to be discovered in the next future by LOFAR
at 150 MHz. This is the first (and so far unique) model expectation for the number
counts of Radio Halos at lower frequency and allows to design future radio surveys.
Based on the results of Chapt. 6, in Chapt.7 we present a work in progress on
a “revision” of the occurrence of Radio Halos. We combine past results from the
NVSS radio survey (z » 0.05 − 0.2) with our ongoing GMRT Radio Halos Pointed
Observations of 50 X-ray luminous galaxy clusters (at z » 0.2−0.4) and discuss the
possibility to test our model expectations with the number counts of Radio Halos
at z » 0.05 − 0.4.
The most relevant limitation in the calculations presented in Chapt. 5 and 6 is
the assumption of an “averaged” size of Radio Halos independently of their radio
luminosity and of the mass of the parent clusters. This assumption cannot be
released in the context of the PS formalism used to describe the formation process
of clusters, while a more detailed analysis of the physics of cluster mergers and of
the injection process of turbulence in the ICM would require an approach based on
numerical (possible MHD) simulations of a very large volume of the Universe which
is however well beyond the aim of this PhD thesis.
On the other hand, in Chapt.8 we report our discovery of novel correlations between
the size (RH) of Radio Halos and their radio power and between RH and the cluster
mass within the Radio Halo region, MH. In particular this last “geometrical”
MH − RH correlation allows us to “observationally” overcome the limitation of
the “average” size of Radio Halos. Thus in this Chapter, by making use of this
“geometrical” correlation and of a simplified form of the re-acceleration model based
on the results of Chapt. 5 and 6 we are able to discuss expected correlations
between the synchrotron power and the thermal cluster quantities relative to the
radio emitting region. This is a new powerful tool of investigation and we show that
all the observed correlations (PR − RH, PR − MH, PR − T, PR − LX, . . . ) now
become well understood in the context of the re-acceleration model. In addition, we
find that observationally the size of Radio Halos scales non-linearly with the virial
radius of the parent cluster, and this immediately means that the fraction of the
cluster volume which is radio emitting increases with cluster mass and thus that the
non-thermal component in clusters is not self-similar.
| Identifer | oai:union.ndltd.org:unibo.it/oai:amsdottorato.cib.unibo.it:346 |
| Date | 11 April 2007 |
| Creators | Cassano, Rossella <1978> |
| Contributors | Setti, Giancarlo |
| Publisher | Alma Mater Studiorum - Università di Bologna |
| Source Sets | Università di Bologna |
| Language | English |
| Detected Language | English |
| Type | Doctoral Thesis, PeerReviewed |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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