Microquasar jets interacting with their
environments
P. Bordas,1 J. M. Paredes1 and V. Bosch-Ramon2
1
2
Departament d’Astronomia i Meteorologia, Universitat de Barcelona, Martı́ i
Franquès 1, 08028, Barcelona, Spain
pbordas@am.ub.es; jmparedes@ub.edu
Max Planck Institut für Kernphysik, Saupfercheckweg 1, Heidelberg 69117,
Germany
vbosch@mpi-hd.mpg.de
Summary. Microquasars (MQ) are X-ray binary systems showing relativistic jets.
We present a model to estimate the properties of these jets when interacting with
the surrounding interstellar medium (ISM). Given the analogies between MQ jets
and those present in active galactic nuclei (AGN), we suggest that the large-scale
emitting structures observed in the latter could be present in the surroundings of
MQs as well. We provide some estimates for the radiative outcomes of the studied
regions, showing that cocoon and bow shock regions may be detectable by the present
observational facilities.
1 Model Outline
Our model is based on twin jets emerging from the central source in two
opposite directions. The supersonic jets end in strong shock fronts at the location where they impact on the ambient gas. The matter carried by the jets
inflate the cocoon that is overpressured with respect to the environment. The
cocoon therefore expands sidewards and a bow shock is driven into the surrounding ISM. By inflating the cocoon the jets create their own high-pressure
but low-density environment, protecting them from disruption due to turbulent gas entrainment. This ensures that the jets do not widen much on their
way through the lobes, and thus the momentum and energy transported by
the jets are delivered through the jet shocks without significant losses to continue pumping energy in the cocoon and ISM shocked structures. See Fig. 1
for an illustrative picture of our scenario. We use a model that adopts the
same key ideas as those applied to the study of AGN/environemnt interaction. We follow the pioneer works on this field ([1], [2]) that initially stated
the main concepts concerning the mechanisms for the formation of luminous
radio-lobe sources. We adapt to MQ, in a similar way as [3], [4] and [5] for
extragalactic sources, the self-similar treatment developed to explain observed
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P. Bordas, J. M. Paredes and V. Bosch-Ramon
extended radio structures in radio galaxies and radio-loud quasars. We have
roughly estimated the particle acceleration efficiency in the considered regions
applying a first-type Fermi type shock acceleration model.We aim at giving
some predictions concerning the non thermal and thermal radiative outcome
of the outflow/medium interaction. This will allow to constrain later on the
physics of these phenomena in MQs via comparison with observational data,
to be presented in a future work.
Fig. 1. Zones treated in our model: 1 unshocked ISM; 2 shocked ISM; 3 shocked
jet material; 4 unshocked jet material. The strong shocks separating zones 1 and
2 (the bow shock) and 3 and 4 (reverse shock) are able to accelerate non-thermal
particles and increase the temperature, leading to synchrotron and Bremsstrahlung
processes.
1.1 Self-similar treatment
The model assumes an averaged energy rate Q0 outflowing in the jet. The
mass density distribution of the external ambient gas is modeled by a power
law, ρ = ρ0 (r/r0 )−α where r is the distance from the compact object and r0 is
a scale length. In the cases where MQs are situated in the ISM of the Galactic
plane, the ambient gas has roughly a constant density ρ0 and α = 0.
The cocoon and the bow shock evolution is self-similar once the jet extends
beyond a characteristic length scale given by the basic parameters that govern
the whole structure formation, L0 = (ρ20 Q0 /Ṁ03 )−1/4 . Here, Ṁ0 = Q0 /(Γj −
1)c2 is the mass transport rate of the jet, that travels with a Lorentz factor
Γj . Taking reasonable values for the parameters involved (see Table 1) we
find L0 ∼ 105 cm, obviously smaller than the jet length even in its forming
point. As pointed out by Falle (1991) [3], once the jet is larger than L0 ,
MQ Jets Interactions
3
Table 1. Parameter values used throughout the model.
parameter
Symbol
Value
Injection point
z0
50Rg
Jet’s Lorentz factor
Γj
1.02
Jet kinetic luminosity
Q0 1036 erg/s
Fraction of non thermal particles
χ
1%, 5%
injected e± spectral index
P
2.0
Magnetic field at z0
B0
105
Compression ratio
r
∼4
Self-similar ratio
R
∼2
ISM particle density
nISM 100 cm−3
dimensional arguments demand that the axial coordinate describing the jet
position and the advance velocity follow respectively the relationships Ljet =
c1 (Q0 /ρ0 )1/5 t3/5 and L̇jet = 3Ljet /5t, where t is the age of the jet and c1 ∼ 2
is a dimensionless constant that depends on the thermodynamical properties
of the jet material and on the assumed source self-similar ratio R.
1.2 Particle acceleration
The high pressure jump at the forward and reverse shock fronts makes of these
regions a suitable place for the first-order Fermi process to operate. In the
context of this particle acceleration model, the rate of energy gain by particles
of charge e in a region where a magnetic field Bjet is present can be written
ec2 B
as (dE/dt)accel = 1.5 · 104 η jet where we have taken a diffusion coefficient
D both for up and downstream zones given by some factor η times the Bohm
diffusion coefficient, D = η 31 rgyro c with rgyro the particle gyroradius. The
differential form of the resulting particle energy spectrum can be expressed
r+2
as (see [6] for a detailed calculation) N (E) ∝ E −P where P ≈ r−1
depends
on the ratio of the densities at both sides of the shock front r. The maximum
energy that a particle can reach will be limited by the more important energy
loss mechanism actually present in the region. In our case, the relevant losses
are the escape losses of particles and those from synchrotron and relativistic
Bremsstrahlung processes.
Under the conditions assumed in the jet reverse shock (the hot spot) and
the ISM forward shock (the bow shock), we estimate the maximum particle energy in 10 TeV and 0.1 TeV, respectively. This shows us that, with
equipartition magnetic fields, synchrotron emission will yield luminosities up
to ∼ 8 · 1034 erg/s and ∼ 3 · 1034 erg/s, and Bremsstrahlung up to ∼ 5 · 1032
erg/s and ∼ 1026 erg/s, for the cocoon and the shock ISM regions, respectively. Moreover, the specific luminosity will peak at νmax ∼ 1018 Hz in the
cocoon and at νmax ∼ 1014 Hz in the shocked ISM gas.
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P. Bordas, J. M. Paredes and V. Bosch-Ramon
2 Model results and conclusions
Regarding the shocked ISM region we have estimated the relativistic Bremstrahlung and synchrotron efficiencies since some fraction of the shocked particles can be accelerated to non-thermal energies at the shock front. We have
taken an equipartition magnetic field present throughout the region. To estimate the thermal Bremsstrahlung efficiency, a shocked gas temperature of
∼ 3 · 109 K in the cocoon and ∼ 1.2 · 104 K in the bow shock region have
been derived from the thermodynamical properties of the shocked material
produced either in the reverse shock/hot spot or in the forward shock/bow
shock region.
In comparing both thermal and non-thermal contributions, we have to
chose a phenomenological value for the thermal-non-thermal energy conversion. Looking at the efficiencies of the radiative processes takin place in the
studied zones, we can see that relativistic Bremsstrahlung may be efficient
for reasonable non-thermal to thermal energy ratios (∼ 0.05) only in the
bow shock region. Otherwise, the synchrotron process may produce significant amounts of radiation in both the cocoon and the bow shock, although
the overall production would be probably dominated by the former. Concerning the thermal Bremsstrahlung radiative outcome, we see that the dominant
component will be the bow shock one.
We conclude that the cocoon and the bowshock regions could be efficient
emitters of thermal and non thermal radiation that may be detected at radio
frequencies and, less likely, at X-rays. We note that for the case of a high
mass system with a very bright companion, even at the distant regions we
are concerned here from the MQ the inverse Compton process could be significant and should be considered ([7]). Moreover, accelerated protons could
also produce significant gamma-ray emission via proton proton interactions
with the interstellar medium, generating as well lower energy radiation via
the secondaries produced in the same proton proton collisions ([8])
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