Issue |
A&A
Volume 518, July-August 2010
Herschel: the first science highlights
|
|
---|---|---|
Article Number | A12 | |
Number of page(s) | 8 | |
Section | Stellar structure and evolution | |
DOI | https://doi.org/10.1051/0004-6361/200913938 | |
Published online | 20 August 2010 |
Gamma-ray absorption and the origin of the gamma-ray flare in Cygnus X-1
G. E. Romero1,2, -
M. V. del Valle1,2,
-
M. Orellana2,3
1 - Instituto Argentino de Radioastronomía (IAR), CCT La Plata (CONICET), C.C.5, (1894) Villa Elisa, Buenos Aires, Argentina
2
- Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional
de La Plata, Paseo del Bosque s/n, 1900 La Plata, Argentina
3 -
Departamento de Física y Astronomía, Universidad de Valparaíso, Chile
Received 22 December 2009 / Accepted 20 April 2010
Abstract
Context. The high-mass microquasar Cyg X-1, the
best-established candidate for a stellar-mass black hole in the Galaxy,
has been detected in a flaring state at very high energies (VHE), E> 200 GeV, by the Atmospheric Cherenkov Telescope MAGIC. The flare occurred at orbital phase
,
where
is the configuration with the black hole behind the companion high-mass
star, when the absorption of gamma-ray photons by photon-photon
annihilation with the stellar field is expected to be highest.
Aims. We aim to set up a model for the high-energy emission and
absorption in Cyg X-1 that can explain the nature of the observed
gamma-ray flare.
Methods. We study the gamma-ray opacity due to pair creation
along the whole orbit, and for different locations of the emitter. Then
we consider a possible mechanism for the production of the VHE
emission.
Results. We present detailed calculations of the gamma-ray
opacity and infer from these calculations the distance from the black
hole where the emitting region was located. We suggest that the flare
was the result of a jet-clump interaction where the decay products of
inelastic p-p collisions dominate the VHE outcome.
Conclusions. We are able to reproduce the spectrum of Cyg X-1
during the observed flare under reasonable assumptions. The flare may
be the first event of jet-cloud interaction ever detected at such high
energies.
Key words: X-rays: binaries - gamma-rays: general - radiation mechanisms: non-thermal - stars: winds, outflows
1 Introduction
Five X-ray binaries have been detected in the very high-energy region of the electromagnetic spectrum,
TeV. Three of them, PSR B1259-63, LS I +61 303 and LS 5039, have been
detected at different orbital phases and show variable emission. Four
gamma-ray flares were detected by the AGILE satellite from the
exceptional X-ray binary Cyg X-3 (Tavani et al. 2009).
The Fermi Large Area Telescope (LAT) has also detected a variable
high-energy source coinciding with the position of Cyg X-3 (Abdo
et al. 2009). The fifth
source, Cyg X-1, has been detected only once during a flare episode.
This latter detection constitutes the first evidence of very
high-energy gamma-ray emission produced in the surroundings of a
stellar-mass black hole (BH) in our galaxy (for further discussion see
Paredes 2008).
Recently, Albert et al. (2007) reported the results from observations of Cyg X-1 at very high energies, E>200 GeV,
performed with the Major Atmospheric Gamma Imaging Cherenkov (MAGIC)
telescope. No persistent emission was detected, but a fast transient
episode was. The satellites INTEGRAL and Swift/BAT detected with some
delay a related flare at hard X-rays, while only a statistically poor
detection was found in the RXTE/ASM data at soft X-rays. This
wavelength-dependent behavior may suggest that different emitting
regions were involved. The gamma-ray excess occurred at orbital phase
.
This can help to set constraints on the location of the emission
region. More recently, the flaring nature of Cyg X-1 in gamma rays
has been confirmed with the AGILE satellite (Sabatini et al. 2010).
This work is devoted to a study of the absorption of high-energy
photons in Cyg X-1 and the implications of the resulting constraints.
The paper is organized as follows: in the next section we describe the main characteristics of the source under study. Section 3 deals with the gamma-ray opacity by pair creation in the stellar radiation field. The production mechanism of the flare emission is then examined in the context of existing models (e.g. Bosch-Ramon et al. 2006; Romero et al. 2003). In particular, we explore the physical conditions required by the energy budget and spectrum of the flare event. In Sect. 4 we present a simple modelization for the non-thermal emission and compare our calculations with the observational results. Finally, in Sect. 5, we present a brief discussion and the conclusions.
2 Cygnus X-1
The binary system Cyg X-1 is composed by a massive star and a compact
object. The X-ray and radio monitoring of the source over the last
decades have shown that Cyg X-1 is most of the time in a hard X-ray
state and powers collimated jets (e.g. Stirling et al. 2001),
which makes it a confirmed high-mass microquasar (HMMQ, Mirabel &
Rodríguez 1999). It is located at a distance of kpc (Ziólkowski 2005). The massive star is an O9.7 Iab of
and the compact object is the best-established candidate for a stellar-mass BH in the Galaxy, with
(Ziólkowski 2005). The orbit of the system is circular, with a period of 5.6 days and an inclination between 25
and 65
(Gies & Bolton 1986).
At radio wavelengths, a semi-ring surrounds Cyg X-1. This feature is
thought to be the result of a strong shock at the location where the
jet impacts onto the ambient interstellar medium (Gallo et al. 2005).
Regarding the flare event at VHEs, the observed energy spectrum is well
fitted by a relatively soft power law (Albert et al. 2007)
The star provides an intense radiation field that can absorb gamma-rays by pair creation within the binary system. The detection by MAGIC occurred near the superior conjunction, when this opacity to gamma-ray propagation from a region close to the compact object is expected to be maximum.
The massive star has a strong wind. Considerable observational evidence supports the idea that winds of high-mass stars are clumpy (e.g. Owocki & Cohen 2006; Moffat 2008). In a HMMQ, some clumps could eventually penetrate into the jet of the system enhancing the non-thermal emission, as proposed by Owocki et al. (2009).
3 Gamma-ray opacity due to e+e- pair creation in the stellar radiation field
3.1 Calculations
In a HMMQ the radiation field of the massive star provides soft photons that can annihilate gamma-rays by pair creation:
.
We consider the opacity treatment for gamma-ray absorption in a massive
X-ray binary system as in Dubus (2006) and Romero et al. (2007). The differential opacity for a gamma-ray at P traveling in the direction given by
due to photons of an energy
emitted at S in the direction
is (Fig. 1)
where d


The cross-section for photon annihilation is (Gould & Schréder 1967)
where




where


![]() |
Figure 1:
Gamma-ray photon at P travels in the direction given by
|
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Because the massive star completely dominates the spectral distribution
of the radiative field at low energies, any other source of radiation
for the production of pairs with gamma rays is neglected here. The star
has a radius ,
and for simplicity we asume a blackbody density radiation of a temperature
:
The geometry considered for the gamma-ray absorption is shown in Fig. 2. If emission occurs at a height h above the compact object and perpendicular to the orbital plane, the distance d from the star becomes



![]() |
(6) |
The parameters adopted for the calculations are shown in Table 1.
![]() |
Figure 2: Sketch of the geometry considered for the gamma-ray absorption of a photon that is produced above the compact object. |
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Table 1: Model parameters.
Under adequate conditions, the absorption, resulting in the creation of
energetic pairs, and the Inverse Compton (IC) emission from them, can
operate in an effective way to develop electromagnetic cascades which
can considerably modify the original gamma-ray spectrum (see e.g.
Bednarek 1997; Orellana et al. 2007,
for detail treatments). Electrons with TeV energies in the stellar
radiation field may also lead to this situation. At TeV energies the
rate of electron energy losses in the Klein-Nishina regime is reduced
by the diminution of the IC cross-section. The ambient magnetic field
must be smaller than a critical value
for the synchrotron losses not to overcome the IC ones. In order to
determine if effective electromagnetic cascading can occur within the
system it is then necessary to know the magnetic field strength in the
gamma-ray propagation region. Such a field is dominated by the stellar
magnetic field. Magnetic fields measured in massive stars can reach
103 G, which is much greater than the critical value
.
For close binaries like Cyg X-1 we can expect that
(Bosch-Ramon et al. 2008) over the whole region of gamma-ray production. We here assume that
,
and neglect the effects of electromagnetic cascades, as well as the
reprocessing of the absorbed energy by synchrotron radiation. The
latter situation was considered by Bosch-Ramon et al. (2008),
who deal with the diffusion of secondary pairs into the system.
Zdziarski et al. (2008), on the other hand, do consider that the
HE photons iniciate a spatiallty extended pair cascade, but we will
comment on this below (Sect. 5).
3.2 Results
In Fig. 3 we show a 2D-map of the attenuation coefficient
as a function of the energy E and the height h above the orbital plane. This absorption map corresponds to the orbital phase
,
when the flare occurred. As can be seen from the figure, the
attenuation is high at energies between 10 GeV and 10 TeV, close to the
compact object, which makes the absorption problem in the energy range
where MAGIC detected the flare very relevant.
In Fig. 4 we show a 2D-map of the attenuation coefficient for E= 1 TeV as a function of the orbital phase
and the height h. It can be seen that the absorption drops strongly as the height above the compact object increases for
h > 1011 cm. When
h < 1011 cm the absorption does not present
major changes, due to the distances involved that make the photon
density remain rather constant (i.e.
cm and
cm; see Fig. 2).
Bosch-Ramon et al. (2008)
find out from opacity calculations near the superior conjunction that
the TeV emitter in Cyg X-1 should be located at a distance greater than
1012 cm above the compact object. Our absorption
calculations agree with this result. Notice that our results cover a
much larger parameter space.
![]() |
Figure 3:
Absorption map as a function of the height h above the compact object and the energy E for orbital phase
|
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![]() |
Figure 4:
Absorption map as a function of the orbital phase |
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From Albert et al. (2007) the observed flux is a power law (Eq. (1)),
in the energy range between 150 GeV and 3 TeV. Considering
that the intrinsic flux from the flare is also a power law
,
we can relate both expressions through
![]() |
(7) |
From the computed numerical values of




![]() |
Figure 5: Range within the error bars of the intrinsic flux index as a function of the height h. |
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4 Flare production mechanism
A hadronic MQ model for Cyg X-1 has been already considered in Orellana et al. (2007) based on ideas advanced by Romero et al. (2003).
We here revisit that scenario with the addition of the interaction
between the steady jet and a more dense target: a clump from the
stellar wind that allows through locally generated shocks the
reacceleration of the particles that produce VHE emission far from the
BH, as in Araudo et al. (2009).
The jet+clump system is assumed to be momentarily in steady state. As
observed in the stable configuration of a microquasar in a low-hard
X-ray state (e.g. Fender et al. 2004), we assume a continuous jet. The calculations of the emission are based on the works by Bosch-Ramon et al. (2006) and Romero & Vila (2008).
The jet is considered perpendicular to the orbital plane, and launched at a distance h0
above the compact object. We consider that farther down the jet the
magnetic field reaches values well below equipartition. Following
Bosch-Ramon et al. (2006) the magnetic field in the jet reference frame can be calculated as
In Eq. (8)


![]() |
(9) |
where





A small fraction of the jet power is transformed into relativistic
particles in a ``one-zone'' acceleration region located above the
compact object, at the height of the impact with the clump. Here we
assumed
cm, based on our opacity constraints.
The kinetic power in the form of relativistic particles is assumed to be proportional to the jet's power,
,
with
and
erg s-1 (Gallo et al. 2005). We considered both hadronic and leptonic content,
.
The ratio of relativistic protons to electrons luminosity
in the jet is unknown. We adopted a = 100, a similar value to what is observed in the galactic cosmic ray spectrum (e.g. Berezinskii et al. 1990).
The minimum kinetic energy is taken to be on the order of the rest mass
energy of the corresponding particles. The maximum energy for the
electrons is obtained equating the cooling rates with the acceleration
rate. The acceleration rate by Fermi mechanism,
dE/dt, of a particle with energy E in a magnetic field B, is given by
![]() |
(10) |
with




For adiabatic losses, the cooling rate is
![]() |
(11) |
The synchrotron losses rate is
![]() |
(12) |
where

The IC loss rate can be calculated from (Blumenthal & Gould 1970)
![]() |
(13) |
where


![]() |
(14) |
with
![]() |
(15) |
Here

![$q = \epsilon_{1}/[b(E_{\rm e}-\epsilon_{1})]$](/articles/aa/full_html/2010/10/aa13938-09/img98.png)

![]() |
(16) |
where





The relativistic Bremsstrahlung losses for a completely ionized plasma were computed according to (Berezinskii et al. 1990)
![]() |
(17) |
where

![]() |
(18) |
where




Relativistic protons lose energy through adiabatic expansion,
synchrotron radiation, and by losses produced by hadronic interactions.
The energy loss rate produced by proton-proton interactions is
![]() |
(19) |
where np is the density of target protons and


where

![]() |
Figure 6:
Acceleration and cooling rates at
|
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In Fig. 6 we show the rates
of cooling and energy gain for electrons and protons in the
acceleration region, which is considered to be the bow-shock between
the jet and the clump. The electrons reach TeV energies while the
protons can attain energies 102 TeV.
In the one zone approximation the steady state particle distributions N(E) result from the transport equation (Ginzburg & Syrovatskii 1964)
![]() |
(21) |
where

The exact analytical solution of the equation is
![]() |
(22) |
with
![]() |
(23) |
The particle injection function, Q(E), is assumed to be a power-law in the energy of the particles,
![]() |
(24) |
This distribution is expected to be the result of diffusive particle acceleration by the reverse shock. The index


![]() |
(25) |
where V is the co-moving one-zone volume.
4.1 Radiative processes
We consider synchrotron emission from both electrons and protons, inverse Compton emission from electron interactions with the stellar photon field, internal and external relativistic Bremsstrahlung, and inelastic collisions between relativistic protons in the jet and the cold material that forms the jet, plus with the matter of the clump and the background wind. We checked that the emission produced by secondary particles is negligible, as well as the synchrotron self-Compton (SSC).
The synchrotron emission was computed with the approximation
where
![]() |
(27) |
and the usual meaning for the constants c, h, e.
The IC emission by the electron population was calculated as
where the spectrum of scattered photons is
![]() |
(29) |
with
![]() |
(30) |
and

![$ q = (E_{\gamma})/[({\Omega}E_{\rm e}(1-E_{\gamma}/E_{\rm e}))]$](/articles/aa/full_html/2010/10/aa13938-09/img130.png)
![]() |
Figure 7: Computed SED and the MAGIC observational data from Cyg X-1 (Albert et al. 2007). A two-temperatures corona with a non-thermal component is presented as well. The data are from McConnell et al. (2000). The similar data from Malzac et al. (2008) can be easily fitted (see Romero et al. 2010). |
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The relativistic Bremsstrahlung contribution is given by
![]() |
(31) |
where
![]() |
(32) |
and
![]() |
![]() |
||
![]() |
(33) |
All luminosities were calculated in the jet co-moving RF. Photon energies in both frames are related by the Doppler factor D as
![]() |
(34) |
where
![]() |
(35) |
The luminosity in the observer frame is given by (e.g. Lind & Blandford 1985)
![]() |
(36) |
In order to compute the gamma-ray emission produced by neutral pion decay we note that the p-p cross-section parametrization (Eq. (20)) is given in the laboratory RF. Then, we convert the flux of relativistic protons to the laboratory frame:
![]() |
(37) |
where A is a normalization constant. The flux of protons, which is isotropic in the jet RF, is beamed in the lab RF, as indicated by the dependence on the viewing angle

The gamma-ray luminosity, for
TeV, can be obtained straightforwardly as
![]() |
(38) |
with



![]() |
(39) |
with



![]() |
(40) |
Here


The gamma-ray luminosity in the range 0.1 TeV
TeV can be obtained from (Kelner et al. 2006)
![]() |
![]() |
||
![]() |
(41) |
with



In order to reproduce the observed spectral energy distribution (SED),
the density ratio between the clump and the wind at the base is
,
i.e.
cm-3.
Figure 7 shows the computed
SED. We have included the thermal emission by the star, which largely
dominates at optical energies. At X-rays, the components of the
emission by the accretion disk and a corona should be added to our
results. These components in the low-hard state have luminosities 1037 erg s-1 and extend up to
150 keV (see Romero et al. 2002),
in a way that they completely dominate over the non-thermal radiation.
The emission from the corona and a non-thermal tail (McConnell
et al. 2000; Malzac et al. 2008) are also shown. The model for this emission is from Romero et al. (2010) and is presented in detail elsewhere. Here we show only the results relevant to Cyg X-1.
4.2 Internal absorption
Internal photon-photon annihilation within the region of gamma-ray
production can result in strong attenuation of the radiation (Aharonian
et al. 2008; Romero & Vila 2008). The opacity is again an integral of Eq. (2), but now considering the locally produced photons with density
.
We can use the symmetry in one of the angles to write
![]() |
(42) |
Here,





![]() |
(43) |
where



The geometry considered requires
and
.
We find that
is completely negligible (at the level of
), implying that the attenuation coefficient is
1.
5 Discussion
The VHE transient emission of Cyg X-1 occurred when the BH was behind
the star with respect to the observer. Because of the high absorption
in the flare detection energy range, the emission close to the BH is
not enough to explain the observations, unless the photons travel far
away from the star, initiating a spatially extended pair cascade as
considered by Zdziarski et al. (2008). This requires a fine tunned
magnetic field, which allows the instantaneous isotropization of the
electrons, but does not overcome their IC radiative losses. A more
realistic/accurate calculation of the electromagnetic cascade
propagation is then desirable. Such simulations (following the electron
trajectories) will be available in a future work as an application of
the code developed by Pellizza et al. (2009).
Previous 1D cascade simulations (Orellana et al. 2007) are consistent with a strong absorption and steep spectrum at TeV energies. The results by Bosch-Ramon et al. (2008)
have shown that if the cascades are suppressed by effects of the
magnetic field, the synchrotron emission of the secondary pairs peaks
at lower energies (GeV).
Romero et al. (2002) have suggested that Cyg X-1 could go through occasional microblazar phases and have estimated that the luminosity in the observer RF can be up to one order of magnitude higher than the luminosity in the jet RF. Even taking this into account, a flare triggered at the base of the jet is undetectable due to absorption at phase 0.91. A remaining option could be a very short episode with a highly increased accretion/ejection rate, but this is speculative given the lack of evidence at lower energies supporting the hypothesis.
Under the geometry considered here (a jet perpendicular to the orbital plane, which has an inclination of 30 deg),
the high-energy emission should have occurred at a large distance above
the compact object where the absorbing photon field is diluted. In
order to quantify the radiative outcome in this scenario we have
considered the interaction of relativistic particles accelerated in a
narrow region of the jet with the target particles of a dense clump of
the wind.
The flare timescale is related to the permanence of the clump inside the jet. For a spherical clump with a radius
smaller than the jet radius
cm we can make a zerolth order estimation of the time that it takes the clump to cross the jet:
.
The clump velocity is the wind velocity, which at this height is simply
:
![]() |
(44) |
The flaring episode had a timescale shorter than one day and a rising time of about one hour, which is on the same order as the

The simple model presented here for the broadband spectrum of Cygnus X-1 reproduces fairly well the observed SED by MAGIC during the flare using a set of parameters that agrees with reasonable values for this source. Interactions between the clumpy winds of massive stars with the relativistic jets in HMMQ are expected to produce flaring episodes at high and very high energies, and may be detectable by the new high-energy detectors, like Fermi, MAGIC II, and VERITAS.
AcknowledgementsWe thank Florencia Vieyro and Gabriela Vila for help on several aspects of this work. We also thank an anonymous referee for valuable comments. This work was partially supported by grant ANPCyT (PICT 2007-00848, BID 1728/OC-AR). G.E.R. acknowledges support from the Ministerio de Educación y Ciencia (Spain) under grant AYA 2007-68034-C03-01 FEDER funds.
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Footnotes
All Tables
Table 1: Model parameters.
All Figures
![]() |
Figure 1:
Gamma-ray photon at P travels in the direction given by
|
Open with DEXTER | |
In the text |
![]() |
Figure 2: Sketch of the geometry considered for the gamma-ray absorption of a photon that is produced above the compact object. |
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Absorption map as a function of the height h above the compact object and the energy E for orbital phase
|
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Absorption map as a function of the orbital phase |
Open with DEXTER | |
In the text |
![]() |
Figure 5: Range within the error bars of the intrinsic flux index as a function of the height h. |
Open with DEXTER | |
In the text |
![]() |
Figure 6:
Acceleration and cooling rates at
|
Open with DEXTER | |
In the text |
![]() |
Figure 7: Computed SED and the MAGIC observational data from Cyg X-1 (Albert et al. 2007). A two-temperatures corona with a non-thermal component is presented as well. The data are from McConnell et al. (2000). The similar data from Malzac et al. (2008) can be easily fitted (see Romero et al. 2010). |
Open with DEXTER | |
In the text |
Copyright ESO 2010
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