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Next: X-ray
Luminosity Evolution Up: Black
Holes in Binaries Previous: Cyg
X-1 as a
As we have seen, evolutionary considerations based on our current understanding
of massive binary systems lead to the conclusion that BH+PSR binaries must
constitute a rather numerous subclass of all binary PSR (
1
per 1000 isolated pulsars; Lipunov et al., 1994b[124]).
It seemed a priori that the binary radio pulsar PSR B0042-73
in the SMC (Kaspi et al., 1994[81])
could belong to one of these two classes. A 16th magnitude B1 star detected
inside the radio error box of this pulsar was suggested as a possible optical
companion to the pulsar. Reliable identification (or absence) of the optical
companion would be detecting the orbital variations of the B-star radial
velocity. This indeed was found by Bell et al. (1995)[11],
so that PSR B0042-73 is the first dual-line pulsar. However, some important
questions about this pulsar do remain unanswered, and we think it is worth
repeating some of the unusual properties of the optical companion to this
pulsar.
close to periastron), requires 
, where 
yr
)
is the rate of the wind, 
cm s
(see more detailed considerations of pulsar with optical
companions in Lipunov et al., 1994a[123])
A similar restriction on 
follows from the observed 
upper limit of variation in dispersion measure 3.2 pc cm
(Kaspi et al., 1994[81]). Standard
radiation-driven stellar wind for a B1 star with bolometric luminosity
3 
erg s
is of the order of 
- 
yr
, which would completely absorb radioemission, unless one assumes an unusually
weak stellar wind for the normal B1 star. In principle, weaker stellar
mass loss rates in the Magellanic Clouds (MC)
could be connected to the observed deficit of metals ( 
), as absorption in their lines leads to radiation-driven stellar winds.
However, analysis shows that 
(Kudritzki et al., 1987[89]); this
reduces
maximum two to three times, and the observed lack of absorption of the
pulsar's radiation and dispersion measure constancy cannot be fully explained
by the stellar wind chemical composition. In addition, the low stellar wind rates cannot be a general property
of all B-stars in MC, because this would contradict the observational fact
of high X-ray luminosity of massive wind-fed MC X-ray binary sources. We
also note, that stellar wind from B-stars which is transparent for pulsar
radioemission in a binary with 
separation, would imply a high fraction 10
percent of visible radiopulsars with massive normal stars (50
per 700 observed isolated pulsars). This also does not fit current observations.
165 km s
, whereas high orbital eccentricity 
, that must have been acquired during the last supernova explosion
in this system, implies a high space velocity of the barycenter after the
supernova explosion, 
where 
and 
are masses of the pulsar and its companion in solar units, respectively.
With 
and 
we obtain 
km s
, much higher than peculiar velocity dispersion in the SMC.
yr
as the sum of tidal quadrupole and relativistic periastron advance for
a BV-star, even the
upper limit yields the upper mass limit 
, too small for a reported 16th magnitude candidate (Kaspi et al., 1994[81]).
Instead, if we assume pure relativistic periastron advance that high, we
get a total mass of the binary PSR J0045-7319 
yr)
. This does not contradict the existence of a massive BH in this system.
Minimum companion mass of
, as suggested by the companion's mass function 
(Kaspi et al., 1994[81]), corresponds
to at least the B3 spectral class implying that we would observe it as
a 
star, which is not the case.
The pulsar itself is a very efficient one, i.e. it has the highest ratio
of radio luminosity (
erg s)
to total rotational energy loss of neutron star (
erg s)
(Kaspi et al., 1994[81]). The
number of such pulsars in the SMC can be estimated by scaling the galactic
pulsar number (
)
by the ratio of the amount of SMC massive X-ray sources to that in our
Galaxy, 
1/10.
Further, this figure must be reduced by a factor 1/100
(fraction of the efficient galactic isolated pulsars; Taylor et al. (1993)[190])
times 1/20
(fraction of galactic pulsars with high radio luminosity; Taylor et al.
(1993)[190]). Possible selection
effects, such as pulsar beaming, leave only a few pulsars to be detected
at the current sensitivity of 1 mJy.
The fact of the binarity of the first pulsar discovered in the SMC may
seem to be very strange, because in our Galaxy the fraction of binary pulsars
with massive companions is 1/500.
Independently of the nature of the secondary companion, this fact can be
explained only by a noticeable deficit of single stars and wide binaries
at least among massive stars in the SMC. This independently follows from
the observed lack of type II supernovae in the MC (Shklovskii, 1983[181]).
The second independent factor that can augment the fraction of binary
PSR with massive companions, is a burst-like behavior
of star formation in the MC. Indeed, if one assumes a star formation burst
to occur some million years ago, one can expect a substantially larger
fraction of massive binary pulsars, because the bulk of single pulsars
are from 
stars, which have not yet exploded. These massive binaries
with pulsars preferentially will hide BH formed from the most massive stars
(> 
). To illustrate this idea, we modeled the evolution of different types
of radiopulsars (single and entering binary systems) after a star formation
burst using the Scenario Machine. The results are presented in Figure 35.
The relative numbers of different types of radiopulsars depend very much
on time after the burst, especially during the first
millions years. So it becomes clear that in a galaxy with a non-stationary
star formation one can expect quite different ratios of different types
of radiopulsars.
Figure 35: Relative number of visible binary radiopulsars with
different secondary companions among single radiopulsars as a function
of time (in million years) after a star formation burst
(Lipunov et al., 1995c). The evolution of 
binary systems was tracked. Initial binary distributions and evolutionary
parameters were the same as in Lipunov et al. (1994b[124]),
but the fraction of mass that collapses to form BH was 
.
Within the framework of different assumptions about parameters of the
binary evolution scenario, we have estimated the relative number of binary
radiopulsars with BH companions, not subjected to selection
effects. For the probable parameters of BH formation ( 
- 
, 
-0.5) we obtained the expected number of BH+PSR binaries to be of order
of unity per 700 radiopulsars (see Table 11).
This means that such binary pulsars should be discovered in the near future.
From the point of view of future observations of relativistic effects,
all such systems must be highly eccentric (e>0.5 with 90 percent probability),
with orbital periods lying in the range of 10 days to several years. We
also estimated the number of BH+PSR binaries, formed through possible AIC
of NS during the common envelope stage of binary evolution,
to be an order of magnitude less than those formed directly from very massive
stars.
