Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://xray.sai.msu.ru/~polar/html/publications/odessa/odessa.ps Äàòà èçìåíåíèÿ: Fri Aug 20 17:48:27 1999 Äàòà èíäåêñèðîâàíèÿ: Sat Dec 22 04:53:26 2007 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: m 35

IMF AND EVOLUTION OF CLOSE BINARIES AFTER
STARFORMATION BURSTS
S.B. Popov 1 , M.E. Prokhorov 1 , V.M. Lipunov 1;2
1 Sternberg Astronomical Insitute
Universitetskii pr. 13, Moscow 119899 Russia, polar@xray.sai.msu.su
2 Department of physics, Moscow State University, lipunov@sai.msu.su
ABSTRACT. This paper is a continuation and de­
velopment of our previous articles (Popov et al., 1997,
1998). We use ``Scenario Machine'' (Lipunov et al.,
1996b) -- the population synthesis simulator (for sin­
gle binary systems calculations the program is avail­
able in WWW: http://xray.sai.msu.ru/ (Nazin et
al., 1998)) -- to calculate evolution of populations of
several types of X­ray sources during the first 20 Myrs
after a starformation burst.
We examined the evolution of 12 types of X­ray
sources in close binary systems (both with neutron
stars and with black holes) for different parameters of
the IMF -- slopes: ff = 1, ff = 1:35 and ff = 2:35 and
upper mass limits, M up : 120 M fi , 60 M fi and 40 M fi .
Results, especially for sources with black holes, are very
sensitive to variations of the IMF, and it should be
taken into account when fitting parameters of starfor­
mation bursts.
Results are applied to several regions of recent star­
formation in different galaxies: Tol 89, NGC 5253,
NGC 3125, He 2­10, NGC 3049. Using known ages and
total masses of starformation bursts (Shaerer at al.,
1998) we calculate expected numbers of X­ray sources
in close binaries for different parameters of the IMF.
Usually, X­ray transient sources consisting of a neu­
tron star and a main sequence star are most abundant,
but for very small ages of bursts (less than ú 4 Myrs)
sources with black holes can become more abundant.
Key words: Stars: binary: evolution;
1. Introduction
Theory of stellar evolution and one of the strongest
tools of that theory -- population synthesis -- are now
rapidly developing branches of astrophysics. Very of­
ten only the evolution of single stars is modeled, but it
is well known that about 50% of all stars are members
of binary systems, and a lot of different astrophysical
objects are products of the evolution of binary stars.
We argue, that often it is necessary to take into ac­
count the evolution of close binaries while using the
population synthesis in order to avoid serious errors.
Initially this work was stimulated by the article Con­
tini et al. (1995), where the authors suggested an un­
usual form of the initial mass function (IMF) for the ex­
planation of the observed properties of the galaxy Mrk
712 . They suggested the ``flat'' IMF with the exponent
ff = 1 instead of the Salpeter's value ff = 2:35. Contini
et al. (1995) didn't take into account binary systems,
so no words about the influence of such IMF on the
populations of close binary stars could be said. Later
Shaerer (1996) showed that the observations could be
explained without the IMF with ff = 1. Here we try to
determine the influence of the variations of the IMF on
the evolution of compact binaries and apply our results
to seven regions of starformation (Shaerer et al., 1998,
hereafter SCK98).
Previously (Lipunov et al., 1996a) we used the ``Sce­
nario Machine'' for calculations of populations of X--
ray sources after a burst of starformation at the Galac­
tic center. Here, as before in Popov et al. (1997, 1998),
we model a general situation --- we make calculations
for a typical starformation burst. We show results on
twelve types of binary sources with significant X­ray
luminosity for three values of the upper mass limit for
three values of ff.
2. Model
Monte­Carlo method for statistical simulations of bi­
nary evolution are now widely used in astrophysics: for
analysis of radio pulsar statistics, for formation of the
galactic cataclysmic variables etc. (see the review in
van den Heuvel 1994).
Monte­Carlo simulations of binary star evolution al­
lows one to investigate the evolution of a large ensemble
of binaries and to estimate the number of binaries at
different evolutionary stages. Inevitable simplifications
in the analytical description of the binary evolution
that we allow in our extensive numerical calculations,
make those numbers approximate to a factor of 2­3.
However, the inaccuracy of direct calculations giving
1

2 Odessa Astronomical Publications, vol. 12 (1999)
0 5 10 15 20
0
20
40
60
80
100
Time, Myrs
NA+Be
0 5 10 15 20
0
10
20
30
40
Time, Myrs
BH+MS
0 5 10 15 20
0
0.5
1
1.5
2
Time, Myrs
BH+Giant
0 5 10 15 20
0
2
4
6
Time, Myrs
BH+WR
Figure 1: Evolution of numbers of binary systems after
a burst of starformation. ff = 1:35. BH+Giant -- A BH
with a He­core Star (Giant). BH+WR -- A BH with a
Wolf--Rayet Star. NA+Be -- An Accreting NS with a
Main Sequence Star (Be­transient). BH+MS -- A BH
with a Main Sequence Star
the numbers of different binary types in the Galaxy
(see e.g. van den Heuvel 1994) seems to be compa­
rable to what follows from the simplifications in the
binary evolution treatment.
In our analysis of binary evolution, we use the ``Sce­
nario Machine'', a computer code, that incorporates
current scenarios of binary evolution and takes into
account the influence of magnetic field of compact ob­
jects on their observational appearance. A detailed
description of the computational techniques and in­
put assumptions is summarized elsewhere (Lipunov et
al. 1996b; see also: http://xray.sai.msu.ru/~ mys­
tery/articles/review/), and here we briefly list only
principal parameters and initial distributions.
We trace the evolution of binary systems during the
first 20 Myrs after their formation in a starformation
burst. Obviously, only stars that are massive enough
(with masses – 8 \Gamma 10 M fi ) can evolve off the main
sequence during the time as short as this to yield com­
pact remnants: neutron stars (NSs) and black holes
(BHs). Therefore we consider only massive binaries,
i.e. those having the mass of the primary (more mas­
sive) component in the range of 10 M fi -- M up .
We assume that a NS with a mass of 1:4 M fi is
formed as a result of the collapse of a star, whose core
mass prior to collapse was M \Lambda ¸ (2:5 \Gamma 35) M fi . This
corresponds to an initial mass range ¸ (10 \Gamma 60) M fi ,
taking into account that a massive star can lose more
0 5 10 15 20
0
0.1
0.2
0.3
0.4
Time, Myrs
NA+N3M
0 5 10 15 20
0
0.05
0.1
0.15
0.2
Time, Myrs
NA+N3E
0 5 10 15 20
0
0.5
1
1.5
2
Time, Myrs
NA+N3G
0 5 10 15 20
0
0.1
0.2
0.3
0.4
Time, Myrs
NA+Giant
Figure 2: Evolution of numbers of binary systems after
a burst of starformation. ff = 1:35. NA+N3G -- An
Accreting NS with a Roche­lobe filling star, when the
binary loses angular momentum due to gravitational
radiation. NA+Giant -- An Accreting NS with a He­
core Star (Giant). NA+N3M -- An Accreting NS with
a Roche­lobe filling star, when the binary loses angu­
lar momentum due to magnetic wind. NA+N3E --An
Accreting NS with a Roche­lobe filling star (nuclear
evolution time scale).
than ¸ (10 \Gamma 20)% of its initial mass during the evolu­
tion with a strong stellar wind. The most massive stars
are assumed to collapse into a BH once their mass be­
fore the collapse is M ? M cr = 35 M fi . The BH mass
is calculated as M bh = k bh M cr , where the parameter
k bh is taken to be 0.7.
The mass limit for NS (the Oppenheimer­Volkoff
limit) is taken to be MOV = 2:5 M fi , which corre­
sponds to a hard equation of state of the NS matter.
We made calculations for several values of the coef­
ficient ff:
dN
dM / M \Gammaff
We calculated 10 7 systems in every run of the pro­
gram. Then the results were normalized to the total
mass of binary stars in the starformation burst. We
also used different values of the upper mass limit, M up .
3. Results
On the figures we show some of the results of our
calculations (full results can be found in the electronic
preprint (Popov et al. 1999)). On all graphs on the X­

Odessa Astronomical Publications, vol. 12 (1999) 3
0 5 10 15 20
0
1
2
3
4
Time, Myrs
NA+N3
0 5 10 15 20
0
1
2
3
4
Time, Myrs
BH+N3E
0 5 10 15 20
0
5
10
15
20
Time, Myrs
BH+N3G
0 5 10 15 20
0
0.1
0.2
0.3
0.4
Time, Myrs
NA+WR
Figure 3: Evolution of numbers of binary systems after
a burst of starformation. ff = 1:35. BH+N3G -- A BH
with a Roche­lobe filling star, when the binary loses an­
gular momentum by gravitational radiation. NA+WR
-- An Accreting NS with a Wolf--Rayet Star. NA+N3
-- An Accreting NS with a Roche­lobe filling star (fast
mass transfer from the more massive star). BH+N3E --
A BH with a Roche­lobe filling star (nuclear evolution
time scale).
axis we show the time after the starformation burst in
Myrs, on the Y­ axis --- number of the sources of the
selected type that exist at the particular moment.
On the figures results are shown for three values of
upper mass limits: 120M fi -- solid lines, 60M fi -- dashed
lines, 40M fi -- dotted lines.
The calculated numbers were normalized for 10 6 M fi
in binary stars. We show on the figures and in tables
only systems with the luminosity of compact object
greater than 10 33 erg=s.
Curves were not smoothed so all fluctuations of sta­
tistical nature are presented. We calculated 10 7 binary
systems and then the results were normalized.
We apply our results to seven regions of recent star­
formation (see the tables, the full set can be found in
(Popov et al., 1999)). Ages, total masses and some
other characteristics were taken from SCK98 (we used
total masses determined for Salpeter's IMF even for the
IMFs with different parameters, which is a simplifica­
tion). We made an assumption, that binaries contain
50% of the total mass of the starburst. Numbers were
rounded off to the nearest integer.
As far as for several regions ages are uncertain, we
made calculations for two values of the age.
Different types of close binaries show different sen­
Table 1: He 2­10; age 5.5 Myrs; total mass 10 6:8 M fi
Slope 2.35 2.35 2.35 1.35 1.35 1.35
Up.mas. 120 60 40 120 60 40
bh+ms 0 0 0 16 0 0
bh+giant 0 0 0 0 0 0
bh+n3e 1 0 0 9 4 0
bh+n3g 4 1 0 62 10 0
bh+wr 0 0 0 1 0 0
na+ms 24 22 15 187 241 165
na+n3 0 0 0 0 0 0
na+wr 0 0 0 0 0 0
na+n3m 0 0 0 0 0 0
na+n3e 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0
na+giant 0 0 0 0 0 0
Table 2: He 2­10; age 6.0 Myrs; total mass 10 6:8 M fi
Slope 2.35 2.35 2.35 1.35 1.35 1.35
Up.mas. 120 60 40 120 60 40
bh+ms 0 0 0 9 0 0
bh+giant 0 0 0 1 0 0
bh+n3e 1 0 0 9 4 0
bh+n3g 4 1 0 65 11 0
bh+wr 0 0 0 0 0 0
na+ms 29 30 22 198 283 233
na+n3 0 0 0 0 1 1
na+wr 0 0 0 0 0 0
na+n3m 0 0 0 0 0 0
na+n3e 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0
na+giant 0 0 0 0 1 0
sitivity to variations of the IMF. When we replace
ff = 2:35 by ff = 1 the numbers of all sources increase.
Systems with BHs are more sensitive to such variations.
When one try to vary the upper mass limit, an­
other situation appear. In some cases (especially for
ff = 2:35) systems with NSs show little differences for
different values of the upper mass limit, while systems
with BHs become significantly less (or more) abundant
for different upper masses. Luckily, X­ray transients,
which are the most numerous systems in our calcula­
tions, show significant sensitivity to variations of the
upper mass limit. But of course due to their transient
nature it is difficult to use them to detect small varia­
tions in the IMF. If it is possible to distinguish systems
with BH, it is much better to use them to test the IMF.
4. Discussion and conclusions
The results of our calculations can be easily used
to estimate the number of X­ ray sources for differ­
ent parameters of the IMF if the total mass of stars

4 Odessa Astronomical Publications, vol. 12 (1999)
Table 3: NGC5253A; age 3.0 Myrs; total mass 10 6:6 M fi
Slope 2.35 2.35 2.35 1.35 1.35 1.35
Up.mas. 120 60 40 120 60 40
bh+ms 0 0 0 5 0 0
bh+giant 0 0 0 0 0 0
bh+n3e 1 0 0 10 0 0
bh+n3g 1 0 0 11 0 0
bh+wr 0 0 0 0 0 0
na+ms 0 0 0 0 0 0
na+n3 0 0 0 0 0 0
na+wr 0 0 0 0 0 0
na+n3m 0 0 0 0 0 0
na+n3e 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0
na+giant 0 0 0 0 0 0
Table 4: NGC5253B; age 5.0 Myrs; total mass 10 6:6 M fi
Slope 2.35 2.35 2.35 1.35 1.35 1.35
Up.mas. 120 60 40 120 60 40
bh+ms 1 0 0 21 0 0
bh+giant 0 0 0 1 0 0
bh+n3e 1 0 0 7 3 0
bh+n3g 2 1 0 36 7 0
bh+wr 0 0 0 3 0 0
na+ms 11 10 5 92 112 58
na+n3 0 0 0 0 0 0
na+wr 0 0 0 0 0 0
na+n3m 0 0 0 0 0 0
na+n3e 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0
na+giant 0 0 0 0 0 0
and age of a starburst are known (in (Popov et al.,
1997, 1998) analytical approximations for source num­
bers were given). And we estimate numbers of different
sources for several regions of recent starformation.
Here we tried to show, that populations of close bi­
naries are very sensitive to the variations of the IMF.
One must be careful, when trying to fit the observed
data for single stars with variations of the IMF. And,
vice versa, using detailed observations of X­ray sources,
one can try to estimate parameters of the IMF, and test
results, obtained from single stars population.
Acknowledgements. We want to thank K.A. Postnov
for discussions and G.V. Lipunova and I.E. Panchenko
for technical assistance. SBP also thanks organizers of
the conference for support and hospitality.
This work was supported by the grants: NTP ``As­
tronomy'' 1.4.2.3., NTP `Astronomy'' 1.4.4.1 and ``Uni­
versities of Russia'' N5559.
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Table 5: Tol 89; age 4.5 Myrs; total mass 10 5:7 M fi
Slope 2.35 2.35 2.35 1.35 1.35 1.35
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bh+ms 0 0 0 4 0 0
bh+giant 0 0 0 0 0 0
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bh+wr 0 0 0 0 0 0
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na+n3e 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0
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