Cygnus
X-3 and the Cosmic Ray Question
Andrew B Collins,
science and history writer reports
Photograph of Cygnus
X-3 taken by the Chandra X-ray Observatory in November 2000.
The horizontal line is thought
to be an artefact of the image(Pic: (Credit: NASA/SRON/MPE).
Abstract
Cygnus X-3 is a high mass X-ray binary
and microquasar, with a compact star, either a neutron star or a black
hole, and a companion star, most probably a Wolf-Rayet (WN7 or 8) with
huge mass loss and powerful stellar wind. First observed in 1966 (Giacconi,
et al, 1967), Cygnus X-3 has been monitored across multiple frequencies,
from radio, infrared, optical, X-ray to gamma-rays. It is one of the
brightest galactic X-ray sources, and is the outright brightest during
the production of bright radio flares, which can reach 20 Jy. Criticisms
regarding Cygnus X-3 being a source of cosmic rays up to PeV (Meinels,
personal communication, 11 July 2006) will necessitate a review of findings
and theories since 1985. I will review recent evidence of Cygnus X-3's
production of relativistic jets, as well as speculation that its core
might be a source of strange quark matter, producing exotic primary
particles, with the H being a possible candidate.
Sections: 1 Introduction; 2 Cygnus X-3 as a gamma-ray source;
3 Characteristics of Cygnet Primaries: 3.1 Production of muon flux deep
underground; 4 Cygnet Identification; 5 Cygnets and strange quark matter;
6 Strange matter; 7 Cygnets, Neutrons and Relativistic Flow; 8 Some
Criticisms of Cygnus X-3 as a Cosmic Accelerator; 9 Conclusions.
Key words: Cygnus X-3, gamma-rays,
x-rays, excess muon fluxes, cygnets, neutrons, beta decay, neutral atoms,
hadron-inducing, underground particle detection, strange quark matter,
strange quarks, H particle, R-odd particle, particle acceleration, neutron
star, strange star, linear acceleration, cosmic rays, relativistic jets,
synchroton radiation, blazar, radio flares, jet velocity, SO particles.
1 Introduction
Cygnus X-3 (RA 307.6 dec 40.8) has been identified as a source of ultra
high energy (UHE) gamma-rays of an extremely energetic nature. Indeed,
their initial discovery in the 1970s was responsible for a complete
reassessment of particle acceleration in compact stars. As early as
1973 the SAS-2 satellite reported gamma-radiation with a narrow phase
interval of 4.8 h, noted separately in connection with x-ray and infrared
observations of Cygnus X-3, estimated to be at 10 kiloparsecs (kpc,
about 30,000 light years). This periodicity is most likely caused by
the eclipsing of the compact star by its companion (Hillas, 1984), since
jet precession is now calculated to be in the range of 5 days (Miller-Jones,
et al 2004). Cygnus X-3 is also thought to be a sporadic 12.6 ms pulsar
(Chadwick, 1985) with gamma-rays produced at or near the maximum (phase
0.6) in the 4.8 h X-ray cycle (Bowden et al, 1992).
2 Cygnus X-3 as a gamma-ray source
The gamma-ray emissions in association with Cygnus X-3 are known to
range between 35 and 200 MeV, although the COS-B satellite between 1975
and 1982 reported no radiation between 70 and 5000 MeV with the point-source
signature of 4.8 h (Cordova, 1986). Yet up to 1986 more than a dozen
groups had reported the detection of gamma-rays from Cygnus X-3 with
energies of at least 1011 eV. Gamma-rays in the higher range E> 1014
ev were subsequently reported and verified by ground-based collaborations
in Germany, England, the United States, India and Italy (Cordova, 1986,
and sources quoted).
The extremely energetic gamma-rays from Cygnus X-3 were early considered
to be 'the products of interactions between even more energetic particles
within the source, mainly protons', leading to speculation that Cygnus
X-3 was 'the first astronomical object to be identified with reasonable
certainty as a source of cosmic rays', i.e. any cosmic radiation above
108 ev (Cordova, 1986), or, indeed, a 'cosmic accelerator' (Dar, 1986).
Moreover, gamma-rays from Cygnus X-3 indicated that 'only a very small
number of sources of like nature would be required to produce most of
the observed high-energy cosmic rays.'(Cordova, 1986).
Among the suspected method of production of gamma-rays were two popular
models. Either they were protons accelerated by the electric field induced
in the accretion disk held in the magnetic field of the compact star,
or they were accelerated by shocks in the matter accreted on to a neutron
star or black hole.
3 Characteristics of Cygnet Primaries
Between 1983 and 30 October 1985 various ground-based air shower arrays,
including Kiel (Samorski and Stamm, 1983a, 1983b) and Fly's Eye (the
latter from 1981 through till 1988) reported extensive air showers with
the direction and periodicity of Cygnus X-3 (See Marshak et al, 1985;
Cassiday et al, 1989). In Kiel's case, particles were detected in the
1016 eV range (initially assumed to be gamma-rays). This was later confirmed
(Lloyd-Evans et al, 1983) with the pulse being narrow (duty cycle 2%)
and occurring at a phase 0.25 after the X-ray maximum. Thus it was concluded
that Cygnus X-3 accelerated particles to at least 1016 eV, and that
if these were electrons, then protons might reach a higher level still
(Hillas, 1984). Indeed, at Kiel the EAS reached energies of > 1018
eV (Cassiday et al, 1989; Sommer and Elbert, 1990).
At the same time two underground nucleon-decay detectors set up originally
to observe proton decay, Soudon (Marshak et al, 1985) and NUSEX (Battistoni,
1985, Baym, 1985), reported excessive muon fluxes either with a time
modulation of the 4.8-h period of Cygnus X-3, or coincident to its daily
transit. The flux from single-muon events was greater than several orders
than that expected from high energy photon flux, suggesting most probably
either a primary of unique characteristics, dubbed the 'cygnet', or
a new mechanism for very efficient muon production in high energy photon-initiated
air cascades (Dar, 1986).
3.1 Production of Muon Flux Deep Underground
Excess muon quanta reported deep underground (at a depth equivalent
of 2 to 5 kilometres of water) produced an angular spread highly suggestive
of the primaries interacting in the rock overhang down to a depth of
a few hundred metres (Kolb, 1985, Ruddick, 1986). This was confirmed
by the differences in flux between the Soudon and NUSEX detectors, with
the latter's flux being ten times less than the former, leading to the
conclusion that this effect 'can only be explained by attenuation of
the cygnet beam in the rock' (Ruddick, 1986). It also explained the
zenith angles of the muons, which were similar to the background flux
produced by EAS. Furthermore, the underground muon energy measurements
predicted a characteristic variation of the quanta according to depth,
with detectors on the surface only being able to detect them at near
the horizontal, due to the large interaction length of the primaries.
This meant 'such detectors would have to be very large to detect a signal'(Ruddick,
1986).
4 Cygnet Identification
Identification of the relativistic primaries (Ruddick, 1986) responsible
for these signal events has proved extremely difficult, highly controversial
and even questionable (Thomsen, 1986). The enhanced muon flux recorded,
particularly by the Soudon I group, was far too high for them to be
gamma-rays, which produced a mere 1/300 of the muons (µ-mesons)
characteristic of the reported muon excess (Baym, 1986). Their 4.8-hour
periodicity meant that they had to have travelled in a more or less
straight line at relativistic speeds, otherwise a spread of lower velocities
would have washed out the signal. Clearly, the path of the cygnets was
not curved by the galactic magnetic field, otherwise this would have
randomised or deflected their arrival directions (Dar, Lord and Wilkes,
1986).
The fact that the cygnets produced excessive muon (µ-mesons) quanta,
implied that they acted to produce hadron-induced cascades. In other
words, they were strongly-interacting particles, rather than electromagnetic
particles, like gamma-rays or weak particles such as neutrinos (Dar,
Lord and Wilkes, 1986). Further evidence against them being neutrinos
was the fact that the cygnet-produced muon flux increased when Cygnus
X-3 was overhead, and faded when it was not in view, the so-called 'horizon
effect'. This is not a characteristic of neutrinos, which do not interact
in this manner.
Thus the conclusion was that cygnet primaries, either measured in ground-based
air shower arrays or in underground detectors, were long-lived neutral
particles with energies anything up to at least PeV (Kolb, 1985; Maiani,
1985; Berezinsky, Ellis and Ioffe, 1986; Cordova, 1986; Ruddick, 1986;
Cassiday et al, 1989; Czapek et al, 1990). However, the only obvious
candidate was the neutron, which is unstable to beta decay and has a
half-life of approximately 10-15 minutes. Thus the only way that they
could have reached the earth was by travelling at relativistic speeds.
Quashing this possibility was the fact that it would require neutrons
with 100 times the energy of the monitored cygnet events. Neutral atoms
could be eliminated since their electrons would have been stripped away
by the 5g per cm2 interstellar hydrogen, causing their decay long before
they ever reached the Earth. This is unless they had an incredibly high
energy in the range of 1018 ev (Baym, 1986). As already noted, the Kiel
collaboration did indeed register EAS with energies >1018 eV.
Initial findings strongly indicated that the cygnet primary bore the
following characteristics: 1) no electric charge; 2) no magnetic charge;
3) a rest mass estimated to be between zero and 1/20 of a proton mass,
and less than its energy by a factor of around 104 (Baym, 1986; Ruddick,
1986); 4) it was strongly interacting, in that it was hadron-inducing,
and, lastly; 5) it possessed a half-life relative to its assumed passage
at relativistic speed. Protons, neutrons, nuclei, atoms, and micrograins
of ordinary matter could all be ruled out.
The cygnets were not charged cosmic particles since they are affected
by the galactic magnetic field which randomizes their directional flow
and ruins any chances of ascertaining their astronomical source, which
can only be determined if they correlate with activity in other frequencies
that might contain a known periodicity or direction.
Since neutral primaries arrive directly from source without being affected
by the galactic magnetic field, they are crucial to determining the
original trajectory of any cosmic ray. Gamma-rays are neutral, and so
can also arrive directly from source, why we can trace the astronomical
source of GRBs.
Thus in order to determine point sources of cosmic rays it is better
to examine neutral particles, which retain their primary trajectory
across the galaxy and when travelling at relativistic speeds will also
retain their unique signature, which has been the case with Cygnus X-3
and Hercules X-1.
Indeed, as long ago as 1983 it was suggested that 'since the galactic
magnetic field seems sufficient to randomize all charged particles during
their long flights through space, pristine cosmic rays may not be charged
particles at all.' (See Hecht and Torrey, 1983). A study of the five
strongest recorded UHE cosmic ray events (E>1020 eV) by Farrar and
Torrey (1998) led to the conclusion that their trajectory pointed back
to extra-galactic QSOs (quasar stellar objects) with a margin of error
of 0.005. In order that the primaries do not violate the Greisen-Zatsepin-Kuzmin
(GZK) cutoff for distance travel of a photon or nuclei, they saw them
as long-living, neutral hadrons of a possible exotic nature (Farrar,
et al, 1998).
5 Cygnets and Strange Quark Matter
As far back as the mid 1980s it was proposed that cygnets were exotic
hadrons resulting from strange quarks produced in strange quark matter
in the core of Cygnus X-3. Maiani (1985), for instance, noted the observation
of 'very energetic particles' arriving from Cygnus X-3, with estimated
energies up to 104 TeV, as well as the observation underground of high
energy muons correlated with a 4.8h modulation. He also accepted that
poorer statistics might have been behind why other collaborations failed
to register these increased muon fluxes underground, such as FREJUS
and HPW. The primaries, he suggested, could be photons, which produce
high energy showers in the atmosphere, and might well explain underground
muon fluxes like those observed by Soudon and NUSEX. Yet results from
these collaborations showed an increased muon flux too high for photons
to be the simple answer (Dar, 1986). In contrast to Kolb and Ruddick,
Maiani saw an anticorrelation in the reported muon flux versus the depth
of the traversed rock, and the fact that NUSEX results were less than
Soudon I. This was evidence, he felt, merely of the 'absorption effect'
(Maiani, 1985).
6 Strange Matter
Kolb (1985) asserted that quark nuggets might lead to an enhancement
in muon production over normal nuclear matter, yet even then only by
a factor of two. He additionally considered the R-odd particle from
supersymmetry and also the H-particle, after Jaffe. This last cited
he saw as having a lifetime long enough to reach the earth, because
of its double beta decay. Moreover, it bears four of the main characteristics
of the proposed cygnet, although whether it can produce the enhanced
muon flux depended upon its method of production. Despite this, the
mass of the H, might not be low enough, something that only experimentation
could determine. Even if the mass was close to that of the cygnet, the
muon flux would be smaller than that reported. Moreover, the H cannot
account for the angular spread of the underground muon flux. For instance,
the NUSEX signal was seen coming from a 10 degree by 10 degree window
in celestial coordinates, larger than the 0.5 degrees expected for an
angular resolution.
Baym (1986) likewise proposed that the cygnet primary was the theorised
H particle. Should its mass be less than that of the lambda (?) (1.1
16 GeV) plus that of the neutron (0.938 GeV), then it was possible that
the lifetime of the H could be sufficiently long for it to be the cygnet
primary, since it would not undergo the rapid decay into a single lambda
or neutron.
Wilk and Wlodarczyk (1996) acknowledged 'anomalous cosmic ray bursts
from Cygnus X-3' as the result of strange quark matter existing in its
presumed neutron star (Wilk and Wlodarczyk, 1996). This supposition
was explored further by Rybczynski, Wlodarczyk and Wilk (2004).
In similar to Kolb and Baym, Weber (2005) saw further support for the
existence of strange matter in Cygnus X-3, which he speculates produces
cosmic rays that to arrive as point-source signal events means that
they have to be 'electrically neutral', like the cygnet primaries. Acknowledging
their main characteristics, he confirms also that to survive the trip
from Cygnus X-3 such particles are 'long-lived'. In his opinion, the
'only known particle which can quantitatively satisfy this constraint
is the photon'. This is despite the fact that, as he states, they would
only produce air showers with a 'small muon component'.
Weber goes on to predict that the 'natural candidate' for the cygnet
is the H particle. Their potentially long lifetime means that they 'may
be present as components of existing neutral particle beams' (Weber,
2005). Yet in order to give it long life, it would need to have 'mass
below single weak decay stability'. Furthermore, in order to generate
enough H particles, the source would have to be a strange star. Weber
admits that the problem with Cygnus X-3 is that, 'it is accreting mass
and thus has a crust, such that there is no exposed strange matter surface
where small strangelets could be produced and subsequently accelerated
electrodynamically to high energies into the atmosphere of the companion
star where H particles were created via spallation reactions.'(Weber,
2005). Yet other evidence of strangelets in balloon-borne counter experiments,
air-shower arrays and large emulsion chambers has convinced Weber that
'some primary cosmic rays may contain non-nucleus components which generate
extended air showers that contain both a large number of muons as well
as very high energetic photons', with Cygnus X-3 being a unique candidate.
7 Cygnets, Neutrons and Relativistic
Flow
The idea that cygnet primaries are the result of exotic nuclei within
Cygnus X-3's compact star being accelerated towards the earth is based
on the view that they interact as hadrons to induce cascades uncommon
to the normal production of muons in the atmosphere. However, should
it be shown that the particles travel at relativistic speeds and thus
contain considerably higher energies than previously reported, then
they might be explainable in more conventional terms. Soudon reported
that the muon excess from Cygnus X-3 was coincident to major radio flares
(from 0.1 mJy up to 20Jy), which have themselves occurred coincident
with X-ray and infrared observations (Baym, 1986). Moreover, gamma-rays
with the 4.8 h periodicity of Cygnus X-3 monitored by ground-based air
arrays have also coincided with considerable excess muon flux underground
as mentioned earlier.
Sommers and Elbert (1989) examined the evidence for EeV neutrons and/or
photons from Cygnus X-3, based on the Fly's Eye data, and stated that
'because of synchroton radiation losses, EeV particle acceleration cannot
occur gradually while a particle orbits in a strong magnetic field.'
As a consequence, Sommers and Elbert suspected that 'if particles are
accelerated in a neutron star's magnetosphere, some type of linear accelerator
must be responsible (my italics)'.
Accepting that the cosmic rays from Cygnus X-3 are neutral, since charged
particles would be dispersed by the galactic magnetic field at EeV energies,
the question remains of how neutral particles might be produced by accelerated
charged particles. According to Sommers and Elbert, the range of possible
models for the production of EeV neutral particles 'is greater than
the range considered for the production of 1015 eV neutral particles
from Cyg X-3. This is partly because the EeV neutral particles can be
neutrons as well as gamma-rays' (Sommers and Elbert, 1989).
Crucially, Sommers and Elbert go on to state that 'although free neutrons
decay with a mean proper lifetime of 898 seconds', time dilation allows
some neutrons at these energies to travel the distance from Cyg X-3.
On this basis, the energy threshold (0.5 EeV) for the data used in the
Fly's Eye analysis suggests that the reported increased muon flux could
be neutrons, even though the collaboration was at the time unable to
distinguish between a neutron-initiated shower and a gamma-ray shower
(Sommers and Elbert, 1989). In final conclusion, they stated that 'Cyg
X-3 is a strong source of EeV cosmic rays'.
The significance of Sommers and Elbert's proposal is that with a relativistic
linear acceleration through jet production, the view that cygnets are
exotic strange quark particles becomes unnecessary. The neutral particles
might indeed be neutrons, reliant on a new model based upon synchrotron
radiation loss through relativistic flow.
Cygnus X-3 during its major radio flare in September
2001 (after Miller Jones, et al, 2004).
|
A one-side relativistic
jet was observed in association with radio flare activity in Cygnus
X-3 by Mioduszewski, et al (2001) using the VLBA in February 1997.
It was estimated to have an opening angle of 12 degrees, and a small
inclination angle of > 12 degrees towards the Earth, leading
to the conclusion that it constituted the galaxy's first blazar.
A precessional phase of 30 days with an anticlockwise movement was
also noted in association with jet production. These parameters
were comparable with those obtained during the observation in September
2001 of a separate major radio flare by Miller-Jones, et al. (2004)
using the VLBA over a period of six days following a peak outburst.
The southern jet was estimated to be moving within 10.5 degrees
to the line of sight, with a precessional phase in a clockwise motion
of 5.3 days. The northern jet was weakly observed. Clearly, the
implication was that both the precession cycle and the direction
of the jets had shifted between 1997 and 2001. Through extrapolation
of the jet motion back to source Miller-Jones estimated that the
jets were ejected about 2.5 days after the radio brightness of Cygnus
X-3 began to increase. Overall the parameters of the southern jet
have been found to be consistent with what Mioduszewski et al. had
previously observed. |
Bipolar jets were also observed in
October-November 2000 using the VLA and examined by the NRAO (Marti,
et al, 2002), although whether or not these were a separate mechanism
to the observed north-south orientated jets observed in 2001 has still
to be decided.
The speed of Cygnus X-3's suspected one-sided jet was originally estimated
at 0.35c (Cordova, 1986). More recent assessments of the relativistic
jets following the 1997 VLBA observations by Mioduszewski, et al (2001),
provided a revised speed up to 0.81c, while Miller Jones, et al, following
the 2001 observations concluded that the rate was 0.63c. Yet they accepted
that faster speeds could precede the observable appearance of the series
of bead-like knots marking the whereabouts of the jets; see also Hannikainen,
et al (2003, poster) for further discussion on this subject.
Such speeds might be enough to enable short-lived neutrons to reach
the Earth, indicating a realistic process for the arrival of low-mass
neutral particles, and the possible production of increased air showers
and underground muon quanta from Cygnus X-3.
It has been pointed out that an observed velocity of Cygnus X-3s jet
at a maximum of 0.81c would be too slow to compress time so that neutrons
might have time to decay into protons (Meinel, private communication,
11 July 2006).
The 0.81c for the speed of Cygnus X-3s southern jet for the February
1997 observations (Mioduszewski et al, 2001) is based on estimates of
jet motion in radio flaring, and does not necessarily relate to the
initial velocity of ejecta on all frequencies. Moreover, it is clear
that the speed of the jets change, as is seen in the 2001 observations,
where a velocity of just 0.63c was deduced (Miller-Jones, 2004). Earlier
estimates of jet speed were even lower. Moreover, the bipolar jets monitored
by the NRAO using the VLA in 2000 (Marti, et al, 2001) determined that
they had an infrared speed of just 0.48c, which is much slower than
the higher speed radio flares. Thus there is no reason why UHE and HE
cosmic rays and gamma-rays from Cygnus X-3, or indeed any point source,
might not exceed the velocity speed of radio flares.
Signal events from
Cygnus X-3 which feature the arrival of GeV gamma-ray emissions
and hadron-like neutral particles have coincided with intense bursts
of energies across multiple frequencies during the production of
jets. For instance, this occurred in October 1985 when an increased
muon flux at PeV levels coincided with intense bursts of radio emissions
(Berenzinsky, 1988). In addition to this, there was a correlation
between the excess muon flux recorded by the Soudon II deep underground
experiment between 1991 and 2000 and Cygnus X-3's production of
large or intermediate radio flares (Thomson, 1991; Marshak, 2000;
Allison, 1999). Thus there is every reason to conclude that the
production of gamma-rays and long-lived neutral particles in Cygnus
X-3 might well be the result of narrow, magnetically driven relativistic
jets within a small angle of the Earth. |
NRAO image showing the production
of bipolar jets by Cygnus X-3 in October-November 2000 (pic:
NRAO/AUI) .
|
8 Some Criticisms of Cygnus X-3
as a Cosmic Accelerator
It has been suggested that the cone angle of Cygnus X-3 poses a problem
regarding any working model for it being a cosmic accelerator in its
role as a blazar. In order to send cosmic rays in the Earth's direction
with the solar region being significantly inside the limit to the probability
distribution has been estimated to be about 0.5 radian (Meinel, private
communication, 11 July 2006).
Work has yet to be undertaken on this level, and the recorded data from
both particle physics and astrophysics needs careful evaluation in this
respect. Much of the findings cited from the 1980s of long lasting neutral
particles from Cygnus X-3 has largely been ignored. This is a shame,
for it clearly suggests that Cygnus X-3 possesses an extraordinary acceleration
mechanism for the production of cosmic rays. As we have seen , their
appearance correlates well with radio flaring and hard X-ray outbursts.
Nothing has so far been published on any possible correlations between
cygnets and major radio flaring during the years 1997, 2000, 2001 and
2006.
The question with regards Cygnus X-3 is not whether it can accelerate
out cosmic rays and UHE gamma-rays, but how exactly they might be produced.
In my opinion, it is the production of relativistic jets, or shock waves
in association with their production, that remain the best mechanism
for their production, something predicted by Sommers and Elbert as far
back as 1989. What is important about this and other similar conclusions
during the 1980s is that there was no hard data available then suggesting
that Cygnus X-3 might be a blazar. This came only through the February
1997 observations (see Mioduszewski, et al, 2001), and confirmed during
the 2001 observations (Miller-Jones, et al, 2004). In other words, working
models for the acceleration process of cosmic rays from Cygnus X-3 were
shown to be correct, making the evidence of long-lasting neutral particles
originating from here an extremely likely possibility. What is more,
they have continued to be reported. Soudon II, announced in 1999 that
in its first ten years of operation the collaboration had regularly
tracked excess muon events in the Tev range or above from the direction
of Cygnus X-3, and again in 2000 (Marshak, 2000). There is every likelihood
that cygnets are accelerated from source during jet production, and
that at such energies only stable, neutral particles can travel the
10 kpc distance from Cygnus X-3 to the earth 'along trajectories which
point back to the source' (Allison, 1999). Moreover, the Soudon II collaboration
conclude that since known stable neutral particles - photons and neutrinos
- have only small probabilities of producing detectable muons 'Tev muons
associated with Cygnus X-3 requires either exotic interactions of known
primaries, exotic primaries or very large fluxes of neutrinos or photons'
(Allison, 1999).
9 Conclusions
Despite the Soudon and NUSEX observations of an increased muon flux
underground during the 1980s remaining controversial, there exists good
evidence for the existence of long-lived, low-mass, strongly-interacting
neutral primaries from Cygnus X-3.
Exotic primaries have been proposed to explain the reported EAS and
increased muon flux underground, with strange quark matter from a strange
matter compact star, most likely a neutron star, being currently the
most popular model. However, with the introduction of a relativistic
flow for the acceleration of the neutral primaries, it is possible that
cygnet primaries are simply neutrons. Regardless of this, the idea of
them being produced within neutron stars by strange matter remains an
attractive theory, and exploration into this area of astrophysics is
to be encouraged. It is ironic that the absence of a well-defined mechanism
of production of these neutral primaries, along with their erratic data,
has diminished the impact of these extremely important findings, which
arguably hold the key to determining the first confirmed point source
of galactic cosmic rays.
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Andrew B Collins is the author
of THE CYGNUS MYSTERY,
which features the mysteries of Cygnus X-3 and its role as a cosmic
accelerator. For further information and signed copies click here.