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Ïîèñêîâûå ñëîâà: http xrays mystery html 02
Populations of close binaries in galaxies with
recent bursts of starformation
S.B. Popov,
(http://xray.sai.msu.su/~ polar/)
M.E. Prokhorov & V.M. Lipunov
Sternberg Astronomical Institute
Moscow State University
Abstract
This paper is a continuation and development 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 available in WWW:
http://xray.sai.msu.su/sciwork/scenario.html (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: 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 starformation bursts.
Results are applied to several regions of recent starformation 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. Usially, X­ray
transient sources consisting of a neutron 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.
1

1 Introduction.
Theory of stellar evolution and one of the strongest tools of that theory -- pop­
ulation synthesis -- are now rapidly developing branches of astrophysics. Very
often only the evolution of single stars is modelled, 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 account the evolution of close binaries
while using the population synthesis in order to avoid serious errors.
Initially this work was stimulated by the article Contini et al. (1995), where
the authors suggested an unusial form of the initial mass function (IMF) for the
explanation 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 ``Scenario Machine'' for cal­
culations of populations of X-- ray sources after a burst of starformation at the
Galactic 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 binary evolution was originally
proposed by Kornilov & Lipunov (1983a,b) for massive binaries and developed
later by Lipunov & Postnov (1987) for low­massive binaries. Dewey & Cordes
(1987) applied an analogous method for analysis of radio pulsar statistics, and
de Kool (1992) investigated by the Monte­Carlo method the formation of the
galactic cataclysmic variables (see the review in van den Heuvel 1994).
Monte­Carlo simulations of binary star evolution allows one to investigate
the evolution of a large ensemble of binaries and to estimate the number of bina­
ries 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 the numbers of different binary types
in the Galaxy (see e.g. Iben & Tutukov 1984, van den Heuvel 1994) seems to
be comparable to what follows from the simplifications in the binary evolution
treatment.
2

In our analysis of binary evolution, we use the ``Scenario Machine'', a com­
puter code, that incorporates current scenarios of binary evolution and takes
into account the influence of magnetic field of compact objects on their obser­
vational appearance. A detailed description of the computational techniques
and input assumptions is summarized elsewhere (Lipunov et al. 1996b; see also:
http://xray.sai.msu.su/~ mystery/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 compact remnants: neutron stars (NSs) and black
holes (BHs). Therefore we consider only massive binaries, i.e. those having the
mass of the primary (more massive) component in the range of 10 \Gamma 120 M fi .
The distribution in orbital separations is taken as deduced from observations:
f(log a) = const ; max f10 R fi ; Roche Lobe M (M 1 )g ! log a ! 10 7 R fi :
(1)
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 than ¸ (10 \Gamma 20)% of its initial mass during
the evolution with a strong stellar wind.
The most massive stars are assumed to collapse into a BH once their mass
before the collapse is M ? M cr = 35 M fi (which would correspond to an initial
mass of the ZAMS star as high as ¸ 60 M fi since a substantial mass loss due
to a strong stellar wind occurs for the most massive stars). 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 corresponds to a hard equation of state of the NS matter.
We made calculations for several values of the coefficient ff:
dN
dM / M \Gammaff (2)
We calculated 10 7 systems in every run of the program. 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.
We took into account that the collapse of a massive star into a NS can be
asymmetrical, so that an additional kick velocity, v kick , presumably randomly
oriented in space, should be imparted to the newborn compact object. We used
the velocity distribution in the form obtained by Lyne & Lorimer (1994) with
the characteristic value 200 km/s (twice less than in Lyne & Lorimer (1994),
see Lipunov et al. (1996c)).
3

3 Results.
On the figures we show the results of our calculations. On all graphs on the X­
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
(not the birth rate of the sources!).
On figures 1­3 we show our calculations for X­ray sources of 12 different
types for different parameters of the IMF.
ffl Figure 1 --- ff = 1,
ffl Figure 2 --- ff = 1:35,
ffl Figure 3 --- ff = 2:35.
For upper mass limits:
ffl 120M fi -- solid lines,
ffl 60M fi -- dashed lines,
ffl 40M fi -- dotted lines.
The calculated numbers were normalized for 1 \Delta 10 6 M fi in binary stars. We
show on the figures 1­3 and in tables 1­9 only systems with the luminosity of
compact object greater than 10 33 erg=s (it should be mainly X­ray luminosity).
Curves were not smoothed so all fluctuations of statistical nature are pre­
sented. We calculated 10 7 binary systems in every run, and then the results
were normalized.
We used the ``flat'' mass ratio function, i.e. binary systems with any mass
ratio appear with the same probability. The results can be renormalized to any
other form of the mass ratio function.
4 Application of our calculations
We apply our results to seven regions of recent starformation. 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 simplification). As far as for several regions ages are uncertain, we
made calculations for two values of the age, marked in SCK98.
Results are presented in tables 1­9 (regions NGC3125A and NGC3125B have
similar ages and total masses). We made an assumption, that binaries contain
50% of the total mass of the starburst. Numbers were rounded off to the nearest
integer (i.e. n sources means, that calculated number was between n­0.5 and
n+0.5).
4

5 Discussion and conclusions
Different types of close binaries show different sensitivity 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, another 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, X­
ray transients, which are the most numerous systems in our calculations, 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 variations in
the IMF. If it is possible to distinguish systems with BH, it is much better to
use them to test the IMF.
The results of our calculations can be easily used to estimate the number
of X­ ray sources for different parameters of the IMF if the total mass of stars
and age of a starburst are known (in (Popov et al., 1997, 1998) analytical
approximations for source numbers were given). And we estimate numbers of
different sources for several regions of recent starformation (tables 1­9).
In this poster we also tried to show, that, as expected, populations of close
binaries 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.
6 Acknowledgements
We want to thank Dr. K.A. Postnov for discussions and G.V. Lipunova and Dr.
I.E. Panchenko for technical assistance.
This work was supported by the grants: NTP ``Astronomy'' 1.4.2.3., NTP
``Astronomy'' 1.4.4.1 and ``Universities of Russia'' N5559.
We are also thankful to the organizers of the conference for support and
hospitality.
5

References
[1] Contini, T., Davoust, E., & Considere, S., 1995, A & A 303, 440
[2] de Kool, M. 1992, A&A, 261, 188
[3] Dewey, R.J. & Cordes, J.M. 1987, ApJ, 321, 780
[4] Iben, I., Jr. & Tutukov, A.V. 1984, ApJ, 284, 719
[5] Kornilov, V.G. & Lipunov, V.M. 1983b, AZh, 60, 574
[6] Kornilov, V.G. & Lipunov, V.M. 1983a, AZh, 60, 284
[7] Lipunov, V.M., Ozernoy, L.M., Popov, S.B., Postnov, K.A. & Prokhorov,
M.E., 1996a, ApJ 466, 234
[8] Lipunov, V.M., Postnov, K.A. & Prokhorov, M.E., 1996b, Astroph. and
Space Phys. Rev. 9, part 4
[9] Lipunov, V.M., Postnov, K.A., & Prokhorov, M.E., 1996c, A & A 310, 489
[10] Lipunov, V.M. & Postnov, K.A. 1987, Ap.& Sp.Sci. 145, 1
[11] Lyne, A.G., & Lorimer, D.R., 1994, Nature 369, 127
[12] Nazin, , S.N., Lipunov, V.M., Panchenko, I.E., Postnov, K.A., Prokhorov,
M.E. & Popov, S.B., 1998, Grav. & Cosmology, 4, suppl. ``Cosmoparticle
Physics'' part.1, 150 (astro­ph 9605184)
[13] Popov, S.B., Lipunov, V.M., Prokhorov, M.E., & Postnov, K.A., 1997,
astro­ph/9711352
[14] Popov, S.B., Lipunov, V.M., Prokhorov, M.E., & Postnov, K.A., 1998,
AZh, 75, 35 (astro­ph/9812416)
[15] Schaerer, D., 1996, ApJ 467, L17
[16] Schaerer, D., Contini, T., & Kunth, D., 1998, A&A 341, 399 (astro­
ph/9809015) (SCK98)
[17] Schaller, G., Schaerer, D., Meynet, G., & Maeder, A., 1992, A & A Supp.
96, 269
[18] van den Heuvel, E.P.J., 1994, in `Interacting Binaries'', Eds. Shore, S.N.,
Livio, M., & van den Heuvel, E.P.J., Berlin, Springer, 442
6

TWELVE TYPES OF X­RAY SOURCES
BH+N2 --- A BH with a He­core Star (Giant)
NA+N1 --- An Accreting NS with a Main Sequence
Star (Be­transient)
BH+WR --- A BH with a Wolf--Rayet Star
BH+N1 --- A BH with a Main Sequence Star
BH+N3G --- A BH with a Roche­lobe filling star, when
the binary loses angular momentum by grav. radiation
NA+N3 --- An Accreting NSt with a Roche­lobe filling
star (fast mass transfer from the more massive star)
NA+WR --- An Accreting NS with a Wolf--Rayet Star
BH+N3E --- A BH with a Roche­lobe filling star (nu­
clear evolution time scale)
NA+N3G --- An Accreting NS with a Roche­lobe filling
star, when the binary loses angular momentum due to
gravitational radiation
NA+N3M --- An Accreting NS with a Roche­lobe fill­
ing star, when the binary loses angular momentum due
to magnetic wind
NA+N2 --- An Accreting NS with a He­core Star (Gi­
ant)
NA+N3E --- An Accreting NS with a Roche­lobe filling
star (nuclear evolution time scale)
7

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
50
Time, Myrs
BH+MS
0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
Time, Myrs
BH+Giant
0 5 10 15 20
0
2
4
6
Time, Myrs
BH+WR
0 5 10 15 20
0
1
2
3
4
Time, Myrs
NA+N3
0 5 10 15 20
0
2
4
6
Time, Myrs
BH+N3E
0 5 10 15 20
0
10
20
30
Time, Myrs
BH+N3G
0 5 10 15 20
0
0.1
0.2
0.3
0.4
Time, Myrs
NA+WR
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
0.2
0.4
0.6
0.8
1
Time, Myrs
NA+Giant
Figure 1
8

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
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
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
9

0 5 10 15 20
0
5
10
15
20
Time, Myrs
NA+Be
0 5 10 15 20
0
0.5
1
1.5
2
Time, Myrs
BH+MS
0 5 10 15 20
0
0.02
0.04
0.06
0.08
0.1
Time, Myrs
BH+Giant
0 5 10 15 20
0
0.1
0.2
0.3
0.4
Time, Myrs
BH+WR
0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
Time, Myrs
NA+N3
0 5 10 15 20
0
0.1
0.2
0.3
0.4
Time, Myrs
BH+N3E
0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
Time, Myrs
BH+N3G
0 5 10 15 20
0
0.02
0.04
0.06
0.08
0.1
Time, Myrs
NA+WR
0 5 10 15 20
0
0.05
0.1
0.15
0.2
Time, Myrs
NA+N3M
0 5 10 15 20
0
0.02
0.04
0.06
0.08
0.1
Time, Myrs
NA+N3E
0 5 10 15 20
0
0.1
0.2
0.3
0.4
Time, Myrs
NA+N3G
0 5 10 15 20
0
0.02
0.04
0.06
0.08
0.1
Time, Myrs
NA+Giant
Figure 3
10

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 1.01 1.01 1.01
Up.mas. 120 60 40 120 60 40 120 60 40
bh+n1 0 0 0 16 0 0 28 0 0
bh+n2 0 0 0 0 0 0 0 0 0
bh+n3e 1 0 0 9 4 0 12 6 1
bh+n3g 4 1 0 62 10 0 84 4 0
bh+wr 0 0 0 1 0 0 3 0 0
na+n1 24 22 15 187 241 165 190 321 221
na+n3 0 0 0 0 0 0 0 1 0
na+wr 0 0 0 0 0 0 0 0 0
na+n3m 0 0 0 0 0 0 0 0 0
na+n3e 0 0 0 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0 0 0 0
na+n2 0 0 0 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 1.01 1.01 1.01
Up.mas. 120 60 40 120 60 40 120 60 40
bh+n1 0 0 0 9 0 0 17 0 0
bh+n2 0 0 0 1 0 0 2 0 0
bh+n3e 1 0 0 9 4 0 11 6 1
bh+n3g 4 1 0 65 11 0 88 4 0
bh+wr 0 0 0 0 0 0 0 0 0
na+n1 29 30 22 198 283 233 202 367 322
na+n3 0 0 0 0 1 1 0 1 1
na+wr 0 0 0 0 0 0 0 0 0
na+n3m 0 0 0 0 0 0 0 0 0
na+n3e 0 0 0 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0 0 0 0
na+n2 0 0 0 0 1 0 0 1 1
11

Table 3: NGC3125A, B; age 4.5 Myrs; total mass 10 6:1 M fi
Slope 2.35 2.35 2.35 1.35 1.35 1.35 1.01 1.01 1.01
Up.mas. 120 60 40 120 60 40 120 60 40
bh+n1 1 0 0 11 0 0 16 0 0
bh+n2 0 0 0 0 0 0 0 0 0
bh+n3e 0 0 0 2 1 0 3 1 0
bh+n3g 1 0 0 11 2 0 14 1 0
bh+wr 0 0 0 1 0 0 1 0 0
na+n1 2 2 0 21 24 5 24 33 6
na+n3 0 0 0 0 0 0 0 0 0
na+wr 0 0 0 0 0 0 0 0 0
na+n3m 0 0 0 0 0 0 0 0 0
na+n3e 0 0 0 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0 0 0 0
na+n2 0 0 0 0 0 0 0 0 0
Table 4: NGC3125A, B; age 5.0 Myrs; total mass 10 6:1 M fi
Slope 2.35 2.35 2.35 1.35 1.35 1.35 1.01 1.01 1.01
Up.mas. 120 60 40 120 60 40 120 60 40
bh+n1 0 0 0 7 0 0 8 0 0
bh+n2 0 0 0 0 0 0 0 0 0
bh+n3e 0 0 0 2 1 0 3 1 0
bh+n3g 1 0 0 12 2 0 16 1 0
bh+wr 0 0 0 1 0 0 1 0 0
na+n1 3 3 1 29 36 18 34 52 25
na+n3 0 0 0 0 0 0 0 0 0
na+wr 0 0 0 0 0 0 0 0 0
na+n3m 0 0 0 0 0 0 0 0 0
na+n3e 0 0 0 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0 0 0 0
na+n2 0 0 0 0 0 0 0 0 0
12

Table 5: 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 1.01 1.01 1.01
Up.mas. 120 60 40 120 60 40 120 60 40
bh+n1 0 0 0 5 0 0 8 0 0
bh+n2 0 0 0 0 0 0 0 0 0
bh+n3e 1 0 0 10 0 0 13 0 0
bh+n3g 1 0 0 11 0 0 15 0 0
bh+wr 0 0 0 0 0 0 0 0 0
na+n1 0 0 0 0 0 0 0 0 0
na+n3 0 0 0 0 0 0 0 0 0
na+wr 0 0 0 0 0 0 0 0 0
na+n3m 0 0 0 0 0 0 0 0 0
na+n3e 0 0 0 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0 0 0 0
na+n2 0 0 0 0 0 0 0 0 0
Table 6: 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 1.01 1.01 1.01
Up.mas. 120 60 40 120 60 40 120 60 40
bh+n1 1 0 0 21 0 0 26 0 0
bh+n2 0 0 0 1 0 0 1 0 0
bh+n3e 1 0 0 7 3 0 8 4 0
bh+n3g 2 1 0 36 7 0 49 3 0
bh+wr 0 0 0 3 0 0 2 0 0
na+n1 11 10 5 92 112 58 106 163 80
na+n3 0 0 0 0 0 0 0 0 0
na+wr 0 0 0 0 0 0 0 0 0
na+n3m 0 0 0 0 0 0 0 0 0
na+n3e 0 0 0 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0 0 0 0
na+n2 0 0 0 0 0 0 0 0 0
13

Table 7: 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 1.01 1.01 1.01
Up.mas. 120 60 40 120 60 40 120 60 40
bh+n1 0 0 0 4 0 0 6 0 0
bh+n2 0 0 0 0 0 0 0 0 0
bh+n3e 0 0 0 1 0 0 1 0 0
bh+n3g 0 0 0 4 1 0 6 0 0
bh+wr 0 0 0 0 0 0 1 0 0
na+n1 1 1 0 9 9 2 10 13 2
na+n3 0 0 0 0 0 0 0 0 0
na+wr 0 0 0 0 0 0 0 0 0
na+n3m 0 0 0 0 0 0 0 0 0
na+n3e 0 0 0 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0 0 0 0
na+n2 0 0 0 0 0 0 0 0 0
Table 8: Tol 89; age 5.0 Myrs; total mass 10 5:7 M fi
Slope 2.35 2.35 2.35 1.35 1.35 1.35 1.01 1.01 1.01
Up.mas. 120 60 40 120 60 40 120 60 40
bh+n1 0 0 0 3 0 0 3 0 0
bh+n2 0 0 0 0 0 0 0 0 0
bh+n3e 0 0 0 1 0 0 1 0 0
bh+n3g 0 0 0 5 1 0 6 0 0
bh+wr 0 0 0 0 0 0 0 0 0
na+n1 1 1 1 12 14 7 13 21 10
na+n3 0 0 0 0 0 0 0 0 0
na+wr 0 0 0 0 0 0 0 0 0
na+n3m 0 0 0 0 0 0 0 0 0
na+n3e 0 0 0 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0 0 0 0
na+n2 0 0 0 0 0 0 0 0 0
14

Table 9: NGC3049; age 5.5 Myrs; total mass 10 6:4 M fi
Slope 2.35 2.35 2.35 1.35 1.35 1.35 1.01 1.01 1.01
Up.mas. 120 60 40 120 60 40 120 60 40
bh+n1 0 0 0 7 0 0 11 0 0
bh+n2 0 0 0 0 0 0 0 0 0
bh+n3e 0 0 0 4 2 0 5 2 0
bh+n3g 2 0 0 24 4 0 33 2 0
bh+wr 0 0 0 1 0 0 1 0 0
na+n1 9 9 6 74 96 66 76 128 88
na+n3 0 0 0 0 0 0 0 0 0
na+wr 0 0 0 0 0 0 0 0 0
na+n3m 0 0 0 0 0 0 0 0 0
na+n3e 0 0 0 0 0 0 0 0 0
na+n3g 0 0 0 0 0 0 0 0 0
na+n2 0 0 0 0 0 0 0 0 0
15