Long Gamma-Ray Burst Progenitors: Boundary Conditions and Binary Models
Astrophysics and Space Science
DOI 10.1007/sXXXXX-XXX-XXXX-X
Long Gamma-Ray Burst Progenitors: Boundary
Conditions and Binary Models
E.P.J.van den Heuvel and S.-C. Yoon
c© Springer-Verlag ••••
Abstract The observed association of Long Gamma-
Ray Bursts (LGRBs) with peculiar Type Ic super-
novae gives support to Woosley‘s collapsar/hypernova
model, in which the GRB is produced by the collapse
of the rapidly rotating core of a massive star to a
black hole. The association of LGRBs with small star-
forming galaxies suggests low-metallicity to be a condi-
tion for a massive star to evolve to the collapsar stage.
Both completely-mixed single star models and binary
star models are possible. In binary models the progen-
itor of the GRB is a massive helium star with a close
companion. We find that tidal synchronization dur-
ing core-helium burning is reached on a short timescale
(less than a few millennia). However, the strong core-
envelope coupling in the subsequent evolutionary stages
is likely to rule out helium stars with main-sequence
companions as progenitors of hypernovae/GRBs. On
the other hand, helium stars in close binaries with a
neutron-star or black-hole companion can, despite the
strong core-envelope coupling in the post-helium burn-
ing phase, retain sufficient core angular momentum to
produce a hypernova/GRB.
Keywords Gamma-ray bursts: general — binaries
1 Introduction
About a year after the discovery of the first optical af-
terglow of a Gamma-Ray Burst (GRB) by van Paradĳs
et al. (1997), two of van Paradĳs’ students discov-
ered the first supernova associated with a long-duration
E.P.J.van den Heuvel and S.-C. Yoon
Astronomical Instiutute “Anton Pannekoek” & Center for High
Energy Astrophysics, University of Amsterdam, The Netherlands
and Kavli Institute for Theoretical Physics, University of Califor-
nia, Santa Barbara
GRB: SN 1998bw/GRB980425 (Galama, Vreeswĳk et
al. 1998). This supernova appeared to be highly pecu-
liar and energetic. It is of class Ic, which means that
it has no H or He in its spectrum. Its outflow veloci-
ties of > 30000 km/s were very much larger than the
10000 km/s seen in “ordinary” Type Ic supernovae and
the total kinetic energy in SN1998bw was > 1052 ergs:
at least an order of magnitude larger than in other
supernovae. Theoretical modeling by Iwamoto at al.
(1998) showed that the exploding star must have been
a Carbon-Oxygen star with a mass in the range 6 to 13
M�, which had a collapsing core > 3 M�. The latter
is too large to leave a neutron star, implying that this
was the first-ever observed birth event of a stellar-mass
black hole (Iwamoto et al. 1998). The discovery of
SN1998bw was a beautiful confirmation of the “collap-
sar” (“hypernova”) model proposed by Woosley (1993).
According to this model the collapse of the rapidly ro-
tating core of a massive star to a black hole will leave
behind a rapidly rotating torus of extremely hot nuclear
matter around the black hole. Internal friction in this
keplerian torus causes its matter to spiral in towards the
black hole within a few minutes, generating so much
heat in this process that part of the matter is blown
away in directions perpendicular to the plane of the
torus with relativistic velocities. Woosley speculated
that these relativistic “jets” of matter might produce a
GRB. SN 1998bw appeared to confirm the predictions
of Woosley‘s “collapsar” (“hypernova”) model. Al-
though GRB980425 was, as a GRB, intrinsically quite
faint and nearby (z=0.0085), which at first cast some
doubt on the idea that genuine long-duration GRBs
would in general be the birth events of stellar black
holes, the discovery of the association of the really “cos-
mological” gamma-ray burst GRB 030329 (z= 0.17)
with a supernova with a spectrum and lightcurve almost
identical to those of SN1998bw (e.g. Hjorth et al. 2003)
confirmed beyond any reasonable doubt the association
of long GRBs (abbreviated further as LGRB) with the
death events of very massive stars and the formation of
black holes. Indeed, while the lightcurves of the opti-
cal transients (OTs) associated with LGRBs are often
dominated by the radiation from the relativistic outflow
of the GRB, numerous LGRBs have shown late-time
“bumps” consistent with the presence of underlying su-
pernovae (e.g. Bloom et al. 1999; Galama et al. 1999;
Levan et al. 2005). For a review see Woosley and Bloom
(2006). These discoveries have given strong credence to
Woosley‘s (1993) model as the “standard” model for
the production of the LGRBs, and this model has been
worked out in more detail by Woosley and collabora-
tors (e.g. MacFadyen and Woosley 1999; Woosley and
Heger, 2006). To distinguish these very energetic and
peculiar Ic “supernovae” associated LGRBs from the
more ordinary Ibc supernovae, we will in this paper call
them “hypernovae”. In order to finish with a pure CO-
core of mass > 6M�, a star must have started out on
the main sequence with a mass > 30M�, which implies
that the LGRBs are associated with the most massive
stars. Here we will discuss further evidence linking in-
deed the LGRBs with such stars, and examine under
which circumstances a star could lose its entire H- en
He-rich envelope before collapsing to a black hole. It
appears that the removal of the envelope by a binary
companion might be an attractive possibility.
2 Host Galaxy Characteristics: further
evidence for an association of the LGRBs
with the most massive stars.
In a very important recent paper, Fruchter et al. (2006)
reported that the environments of LGRBs are strik-
ingly different from those of the “ordinary” core col-
lapse supernovae of types Ib,c and II. Using Hubble
Space Telescope imaging of the host galaxies of LGRBs
and core-collapse supenovae they found that the GRB
are far more concentrated on the very brightest re-
gions of their host galaxies than are the supernovae.
Furthermore, they found that the host galaxies of the
GRBs are significantly fainter and more irregular than
the hosts of the supernovae. Theoretical work (Fryer,
2004, 2006) shows that stars which started out on the
main sequence with masses between 8 and 20 M� leave
neutron stars as remnants, while the cores of stars more
massive than about 20M� collapse to black holes. Fig-
ure 1, after Fryer (2006) shows that this happens irre-
spective of initial metallicity, although the black holes
produced at lower metallicity tend to be much more
massive than those from higher metallicity stars. In
view of the slope of the IMF, some 75 per cent of the
Fig. 1.— Mass of collapsed remnant as a function of
initial main-sequence progenitor mass from the analysis
by Fryer (2006), for both the Limongi & Chieffi (2006)
and Woosley et al. (2002) stellar progenitors. The lines
are derived from the Woosley et al. (2002) progenitors:
dotted line refers to solar metallicity, solid line refers to
very low metallicity. The points are derived from the
Limogni and Chieffi (2006) models: circle -solar, square
0.2 solar, triangle - zero, metallicities. Around 20 solar
masses the outcome depends sensitively on the stellar
evolution code used. Credit: C.L.Fryer (2006)
deaths of stars >8 M� arise from the mass range 8-
20M�, and only some 25 per cent from masses > 20M�.
Therefore, the bulk of the core collapse supernovae will
be neutron-star forming events. It thus appears that
the neutron-star forming events follow the normal light
distribution of their host galaxies, whereas the LGRBs
are concentrated strongly on the brightest parts of these
galaxies. Another striking difference is that while half
of the hosts of the “normal” core collapse supernovae
are Grand Design (GD) spiral galaxies, only one out of
the 42 hosts of the LGRBs is a GD spiral, the other
41 being smaller and more irregular galaxies. [In the
case of the one GD spiral it is still very well possible
that the real host is a small SMC- or LMC-like satellite
of this spiral galaxy, which at this distance cannot be
separately recognized].
The brightest patches of the irregular and small host
galaxies of LGRBs are “clumps” of massive stars. This
follows from the fact that these hosts are generally
found to be very blue ( Fruchter et al. 1999; Sokolov et
Long Gamma-Ray Burst Progenitors: Boundary Conditions and Binary Models 3
al. 2001) and have strong emission lines (Bloom et al.
1998; Vreeswĳk et al. 2001), suggesting a significant
abundance of young massive stars. At the large red-
shifts of the GRB hosts it is impossible to distinguish
the stellar content of the bright emission line spots (the
entire HST image of a host is often smaller than an
arcsec), but nearby small irregular starforming (“star-
burst”) galaxies serve as a good example of what is
going on in these small GRB hosts. A nearby exam-
ple of such a galaxy is NGC 3125 which was studied
by Hadfield and Crowther (2006). These authors find
that the bright spots of this galaxy consist of large con-
centrations of O- and WR-type stars, which number of
order 10 000 in this galaxy. The galaxy has a metal-
licity like that of the SMC/LMC (between 0.2 and 0.5
solar) and its brightest clump has at least four dense
star clusters of > 200 000 solar masses, each with some
600 O-stars. A few of the hosts of relatively nearby
LGRBs associated with hypernovae show similar char-
acteristics. The host of SN1998bw is an LMC-size star-
forming galaxy; the host of GRB060218 is SMC size;
the host of GRB030329 is a z=0.17 undetectable, indi-
cating that its size must be smaller than that of the
SMC, and the host of GRB970228 at z=0.67 is not
larger than the LMC.
Recently Wolf and Podsiadlowski (2006), statis-
tically studying part of the host galaxy sample of
Fruchter et al. (2006), concluded that the typical
LGRB host galaxy is of LMC size. They found, on
the basis of the metallicity-luminosity relation for star-
forming galaxies, that LGRB models that require a
sharp metallicity cut-off below 0.5 solar metallicity are
effectively ruled out as they would require fainter host
galaxies than are observed. They therefore conclude
that metallicities up to 0.5 solar must be allowed by
models for LBRBs/hypernovae. As, however, in these
irregular galaxies the metallicity may vary wildly from
place to place, it is not clear to us whether not the
LGRBs might arise from areas in the hosts of much
lower metallicity, while the average metallicity of the
host might still be up to of order 0.5 solar.
3 Possible reasons why small “starburst-like”
galaxies are the prime sources of LGRBs
These reasons can be divided into two broad categories:
(1) Metallicity-related, (2) Starburst-related.
As to Category (1): the wind mass-loss rates from
massive stars are known to be metallicity-related: Mok-
iem at al.(2006) find from observations of O- and B-
supergiants in the Local Group galaxies that he wind
mass-loss rates scale roughly as Ṁw ∝ Z0.78, where Z
is the abundance of the elements heavier than helium.
This implies that at lower metallicities, such as in the
SMC and LMC (0.2 and 0.5 solar, respectively) massive
stars lose (much) less mass during their evolution than
in our galaxy. Therefore, they are more likely to finish
as a black hole. Indeed, one observes that in the LMC
half of the four known persistent High Mass X-ray Bina-
ries (HMXB) harbour a black hole while in our Galaxy
only one out of the over 20 known persistent HMXBs
harbours a black hole (Cygnus X-1). It thus appears
that at low Z, black-hole production is more efficient.
In addition, a requirement for producing a “hypernova”
is that at the time of the core collapse, the star is still
rotating sufficiently rapidly to enable the formation of
a disk or torus around the black hole (MacFadyen and
Woosley 1999). Lower wind mass-loss rates imply also
lower angular momentum loss rates, which will increase
the probability of having still a sufficiently rapidly ro-
tating stellar core at the time of the collapse.
As to Category (2): It is well-known that during a
starburst massive dense star clusters form with many
hundreds, if not thousands, of massive OB stars. For
example, many such massive young globular clusters are
observed in the pair of Antennae Galaxies. In massive
young globular clusters a variety of dynamical interac-
tions take place between massive stars, massive binaries
and stellar remnants (black holes, neutron stars) rang-
ing from direct collisions to companion exchanges in
binary systems, and to the formation of so-called In-
termediate Mass Black Holes (IMBHs) with masses of
order 100 to 1000 solar masses (Portegies Zwart et al.,
2002, 2004, 2006). These can be unique events, which
do not occur in any other stellar environment. Kulkarni
(2006) suggested that LGRBs might be related to such
unique events that can occur only in starburst galax-
ies. This interesting idea merits to be further worked
out, but at present not much further can be said about
it. For this reason we will here only concentrate on the
possible relation between LGRBs and metallicity. In
order to make a hypernova such as the ones observed
to coincide with the LGRBs, the two following condi-
tions should be fulfilled:
(1) the star must have lost its H- and He-rich outer lay-
(2) At the time of core collapse, the core should have
specific angular momentum in the range
J(CO − core) = (3− 20)× 1016[cm2/s] (1)
In order to fulfill these two conditions, two possible sce-
narios have been proposed:
(i) Completely-mixed single-star evolution of a rapidly-
rotating low-metallicity star (Yoon and Langer 2005;
Woosley and Heger 2006).
(ii) Binary mass exchange, where the star achieves and
maintains its rapid rotation due to tidal synchroniza-
tion in a close binary (Izzard et al. 2004; Podsiadlowski
et al. 2004).
We now separately discuss these two possible scenarios.
4 Completely mixed single-star models of low
metallicity
In this case the rapid rotation of the star keeps it com-
pletely mixed by meridional circulation during its en-
tire H-burning evolution. The low metallicity causes
the wind mass- and angular-momentum-loss rates to
be small such that the star keeps rotating rapidly until
the end. The complete mixing makes that by the end
of hydrogen burning the star has become a complete
helium star (the weak wind has by that time carried off
the thin hydrogen envelope that still surrounded the
helium core). Yoon and Langer (2005) calculated such
an evolution for a star which started out with M= 40
M� and Z= 10−5 and find that it evolves into a rapidly
rotating pure helium star of 32 M�, which after 600
years of C-burning undergoes core-collapse to a black
hole with sufficient angular momentum to make a hy-
pernova. They find that this type of evolution follows if
the star starts out with an equatorial rotation velocity
of 0.5 times the critical one. Later calculations by these
authors suggest that up to Z =0.2 solar the stars still
follow this evolutionary path. Woosley and Heger find
that it would still work up to Z = 0.33 solar. For higher
Z this single star model no longer works. If the conclu-
sion of Wolf and Podsiadlowski (2006) mentioned in
section 2 would strictly hold, i.e. if models should work
up to Z =0.5 solar, these single star models would be
ruled out. However, as mentioned at the end of section
2, due to the patchy distribution of metallicity in irregu-
lar starburst galaxies, there could easily be patches with
SMC-like (Z=0.2) metallicities in the irregular hosts
and therefore certainly these completely mixed single
star models cannot be ruled out. In the calculations of
Yoon and Langer (2005) these stars still have a helium-
rich envelope, which would lead to a Type Ib supernova,
but later calculated models (Yoon, Langer and Norman
2006) and also some of the Woosley and Heger (2006)
models lose this envelope by wind such that they would
produce a Type Ic supernova.
5 Binary Models; can LGRBs be the formation
events of Black-Hole X-ray Binaries?
5.1 Introduction
The first ones to consider binary models for making
LGRBs were Fryer and Woosley (1998). Their model
was, however, not a core-collapse model, but one in
which an already existing black hole in an X-ray bi-
nary spiraled down into the helium core of its massive
companion, as a result of a Common-Envelope phase.
Although interesting, we will not consider such models
here and only concentrate on “hypernova” models in
which the LGRB coincides with the core-collapse event
in which a black hole is formed.
Izzard et al. (2004) and Podsiadlowski et al. (2004)
were the first to consider the role that binary systems
might play in producing such “hypernova” events. At
present some twenty close X-ray binaries are known
that consist of a black hole and a low-mass companion
star (see McClintock and Remillard, 2006). The black
hole in such systems typically has a mass between 3
and 20 M�, and the companion is a Roche-lobe filling
star with a mass < 2M�. The orbital periods are in
general less than a few days, and in many cases less
than 0.5 day. In the system of X-ray-Nova Sco 1994
(J1655-40) the F-type companion of the 7 M� black
hole has an overabundance of alpha-type elements such
as S, Mg and Si of more than one order of magnitude
(Israelian et al. 1999). This is just what one expects if
the outer layers of the star of which the core collapsed
to the black hole were ejected in a supernova-like event
and polluted the outer layers of the F-type companion.
It thus appears that in this black-hole X-ray binary a
hypernova-like event took place. Podsiadlowski et al.
(2004) propose that in all of these low-mass black hole
X-ray binaries the formation event of the black hole
produced a LGRB. The formation of these BH-LMXBs
requires a preceding Common-Envelope (CE) phase of
an initially wide binary system consisting of the massive
progenitor star of the black hole together with a dis-
tant low-mass companion star (e.g. see van den Heuvel
and Habets 1984; Brown et al. 1996; Nelemans and
van den Heuvel, 2001). During this CE phase the low-
mass companion spiraled down deeply into the envelope
of the massive companion resulting in a very close bi-
nary system consisting of the helium core of the mas-
sive star together with its low mass-mass main-sequence
companion (< 2M�). Izzard et al. (2004) and Podsi-
adlowski et al. (2004) suggested that tidal forces in
this close binary keep the helium star in synchronous
(=rapid) rotation, allowing it to have sufficient angular
momentum at the time of its core collapse to produce a
Long Gamma-Ray Burst Progenitors: Boundary Conditions and Binary Models 5
hypernova. These authors, however, did not calculate
the timescales on which tidal synchronization in such
binaries can be achieved. In order to see whether such
a model can work, one has to calculate these timescales
as well as the timescales on which the rotation of the
contracting stellar core is synchronized with the outer
envelope of the star. These two problems we will con-
sider here.
5.2 Timescales for synchronization of helium stars in
close binaries with a main-sequence companion.
We consider helium stars of 8 and 16 M�, which are
probably representative for the progenitors of the black
holes in LGRBs. Helium-burning helium stars with
such masses are almost completely convective. In 8
and 16 M� helium stars the convective cores have radii
of about 60 and 70 per cent, respectively, of the stellar
radii, and occupy most of the stellar mass (Paczynski
1971).
According to Zahn (1975, 1977) the tidal synchro-
nization timescale for a star with a convective core and
a radiative envelope is given by:
1/tsync = 52
)1/2 MR2
q2(1 + q)5/6E2
where q = M2/M is the mass ratio of the compan-
ion (M2) and of the star to be synchronized (M), and
gs, R and I are the surface gravity, radius and mo-
ment of intertia, respectively, of the latter star, a is the
orbital radius and E2 is the tidal torque constant for
stars with a radiative envelope and a convective core.
E2 is proportional to (Rc/R)6, where Rc is the radius
of the convective core (Zahn, 1975, 1977). Zahn (1975)
calculated the values of E2 for main-sequence stars of
various masses. For such stars in the mass range 7 to
15M� he found E2 to be around 10−4. In order to cor-
rect for the much larger relative radius of the convec-
tive cores in helium stars, one has to multiply the E2-
values for main-sequence stars of similar masses with
(RcHe/Rcms)6 , where Rcms is the relative radius if the
convective core of the main-sequence star, and RcHe is
the one of the helium star. To this end we used for the
8M� helium star (Rc = 0.7R) the E2 value of Zahn’s
10M� main-sequence star (Rc = 0.27R) and for the
16M� Helium star (Rc = 0.8R) we used the E2 value of
Zahn‘s 15M� main-sequence star (Rc = 0.30R). This
yields E2 = 4.4 × 10−4 for the 8M� helium star and
E2 = 1.7× 10−2 for the 16M� helium star.
In order to get the shortest possible orbital periods,
we now assume that after the CE phase the low-mass
main-sequence companion of the helium star fills its
Roche lobe.
We then find for the 8M� helium star that with
Roche-lobe-filling companions of 1, 2 and 4 M�, re-
spectively, the orbital periods are 8.78, 10.45 and 12.43
hours, respectively; using equation (2) we then find
that with these three companion masses the tidal syn-
chronization timescales of these three systems are 1800,
1400 and 1130 years, respectively. For a 16M� helium
star the orbital periods with these three main-sequence
companion masses are exactly the same and the tidal
synchronization timescales are 440, 400 and 370 years,
respectively. The lifetimes of helium stars of 8 and 16
M�, respectively, are of order 5 × 105 yrs (Paczynski
1971). Thus one expects, as already assumed by Izzard
et al. (2004) and Podsiadlowski et al. (2004), that these
helium stars will be fully synchronized with their or-
bital motion throughout their core-helium-burning evo-
lution. Could after the end of helium burning the con-
tracting Carbon-Oxygen core of the helium star keep
the angular momentum which it obtained in its state
of synchronized helium star and maintain that angular
momentum until core collapse? As we will now show,
it is unlikely that it will be able to take this barrier.
Fig. 2.— Solid curve: specific angular momentum as
a function of mass in a synchronized 8 solar mass he-
lium star with a 0.8 solar mass Roche-lobe filling main-
sequence companion. Dotted curve: specific angular
momentum distribution required for the formation of a
hypernova in case the mass interior toMr collapses to a
Schwarzschild black hole; dash-dotted curve: the same
for the case of a Kerr black hole
5.3 Timescales for core-envelope coupling
The fully drawn curve in Figure 2 shows the specific an-
gular momentum distribution in a synchronized helium
star of 8M� in a close binary with a 0.8M� Roche-lobe
filling companion (Porb = 7.17h), compared with the
minimum specific angular momentum required to form
an accretion disk around a Schwarzschild and a Kerr
black hole, as a function of the black hole mass. One
observes from this figure that if the inner part of the
helium star can maintain its specific angular momen-
tum also when it becomes a contracting CO-core (which
then will spin much faster than its helium envelope)
then indeed the inner parts of such helium stars would
be able to produce a hypernova/GRB if the black hole
is of the Kerr type. However, whether the contracting
CO-core can maintain its specific angular momentum
which it had as a helium star, depends on the timescale
of core-envelope coupling. It is expected that this cou-
pling in a convective differentially rotating star will be
due to magnetic fields generated in this star, and Spruit
(2002) has derived the order of magnitude timescale for
this coupling. Yoon (2006) calculated the evolution of
rotating helium stars with masses between 8 and 40M�
using Spruit’s (2002) mechanism for core-envelope cou-
pling. He found that the inner 3M� of the CO-cores of
these stars at the moment of core collapse have retained
a fraction f of their initial specific angular momentum
which they had as a helium star in solid-body rotation:
For MHe = 8-16 M�: f = 0.2; 20M�: f = 0.4; 25M�: f
= 0.6; 30M�: f = 0.65; 40 M�: f = 0.75.
Using these values for 8-16 M� stars in Figure 2 one
sees that the specific angular momentum in the central
parts of the 8 M� helium star (the fully drawn curve)
moves downwards by a factor 5 and thus falls below
the Kerr as well as the Schwarzschild curves. The same
holds for the 16M� helium star. This means that while
a Helium star in a close binary with a Roche-lobe fill-
ing low-mass main-sequence star has achieved tidal syn-
chronization during core-helium burning, still its core
at the time of its collapse will be unable to produce a
hypernova/LGRB. We thus see that the progenitors of
the black holes in the Black-Hole X-ray Binaries with
low-mass companion stars in all likelyhood did not pro-
duce a hypernova/LGRB.
5.4 Timescales for synchronization of helium stars in
close binaries with a compact companion
Such binaries will form by the spiral-in of a neutron-
star or black-hole companion of a massive star in a wide
High-Mass X-ray Binary (HMXB). Recently, with IN-
TEGRAL such a wide system was discovered, consist-
ing of a blue supergiant and a compact star in a 330
day orbit (Sidoli et al. 2006). [In HMXBs with orbital
periods shorter than about 100 days, the compact star
is expected to spiral into the core of its companion such
that no binary will be left (e.g. Taam 1996)]. Presently
three close X-ray binaries consisting of a helium star
(Wolf-Rayet star) and a compact object are known:
Cygnus X-3 (Porb = 4.8 h; van Kerkwĳk et al. 1992),
and the extragalactic sources IC10 X-1 (Porb = 34.8
h, Prestwich et al. 2007; ATel 955) and NGC 300 X-
1 (Porb = 32.8 h; Carpano et al. 2007). The short-
est possible orbital periods of helium star plus compact
star binaries will occur if the helium star fills its Roche
lobe. For helium stars of 8M� and 16M� these short-
est possible orbital periods are 2.046 and 2.466 hours,
respectively, independent of the mass of the compact
companion. Using equation (2) one finds that the syn-
chronization timescales in these systems are extremely
short, of the order of years to decades at most, such
that they will remain synchronized throughout their
core-helium- burning evolution. The specific angular
momentum is here 3.7×1017 and 6.0×1017 cgs, respec-
tively. As mentioned above, the cores of these stars
can maintain some 20 per cent of this up till core col-
lapse. Equation (1) shows that this is sufficient to make
a LGRB/hypernova. Thus the post-in-spiral remnants
of HMXBs are suitable for producing Long GRBs.
Some example progenitor HMXBs that might pro-
duce a LGRB: We use Webbink‘s (1984) equation to
calculate the ratio of the final and initial orbital radius
in the case of Common-Envelope evolution (e.g. see
also van den Heuvel 1994). We will assume that the
product αλ = 1, where α is the efficiency parameter
for the ejection of the envelope, and λ is a parameter
characterizing the density structure of the star. Our
first example is Cygnus X-1, for which we adopt a mass
of 35M�, with a 14M� helium core for the supergiant
and a mass of 15M� for the black hole (e.g. Gies and
Bolton, 1982, 1986). The initial orbital period of 5.6
days of this system then results into a final orbital pe-
riod of 2.4 hours for the 14M� helium star plus the
15M� black hole. In this case the helium star will be
very close to filling is Roche lobe, so we expect the final
product of the Cygnus X-1 system to be able to pro-
duce a hypernova/LGRB when the core of the helium
star collapses to a black hole.
A second example is the system of 4U 1223-62/Wray
977, which consists of a neutron star and a blue hyper-
giant (B1.5Ia0) in an eccentric orbit with P = 41.5 days
(e.g. see Kaper et al. 2006). The hypergiant is likely
to have a mass 35M�, so we again we assume here
a helium core of 14M�. For the neutron star we as-
sume a mass of 1.8M� (like in the system of Vela X-1,
which also is a very massive X-ray binary). Assuming
the same values for alpha and lambda as in the first
case, we find that the final orbital period after spiral-in
is 2.1 hours, such that again the helium star just fits in-
side its Roche lobe. So also here the core of the helium
Long Gamma-Ray Burst Progenitors: Boundary Conditions and Binary Models 7
star at the time of collapse will have enough angular
momentum to make a hypernova/LGRB.
6 Discussion and Conclusions
We saw in section 4 that completely rotationally mixed
single star evolution at relatively low metallicities (Z ≤
0.33 solar) may well provide a viable model for the
production of LGRBs/hypernovae. As to binary mod-
els: the results from section 5 show that, assuming
Zahn’s (1975, 1977) model for the tidal synchroniza-
tion of helium stars in close binaries, massive helium
stars with main-sequence companions will be quickly
synchronized, within a few centuries to millennia, with
their orbital motion. However, we find that as a conse-
quence of efficient core-envelope coupling in the post-
helium burning phase it is unlikely that these stars by
the time of core collapse will have sufficient core angu-
lar momentum to produce a hypernova/GRB. On the
other hand, if the companion of the helium star is a
compact object and the helium star is close to filling its
Roche lobe (implying a very short orbital period, of the
order of a few hours) we find that by the time of core
collapse the core can still have sufficient angular mo-
mentum to produce a hypernova/GRB. The fact that
we already know two potential progenitors of close he-
lium star plus compact star companion binaries among
the HMXBs within 3.5 kpc distance from the sun im-
plies that there must be several dozens such progenitor
systems in our galaxy. Assuming a lifetime of some
50000 years for the HMXB phase, and 25 such systems
in the Galaxy, one would expect one hypernova/LGRB
from such systems every 2000 years. This is about 5
per cent of the SN rate in our galaxy. Assuming that
the GRBs are beamed within a cone of opening half-
angle 5 degrees (Frail et al. 2001), we would expect
to observe one LGRB from such binary systems per 2
million years from a Galaxy like our own.
We note that although this binary model appears
viable, it remains puzzling why LGRBs have such
a strong preference for the small irregular starburst
galaxies. A possible explanation might be that at
low metallicity a much larger fraction of the massive
stars collapses to black holes. In such galaxies one
would already expect most of the persistent “standard”
HMXBs (that is: the ones with massive blue supergiant
donor stars) to harbour black holes, while then also
the donor stars in such systems are likely to collapse
to black holes. This would imply that, if indeed the
LGRBs originate from binary systems, a considerable
fraction of the hypernovae/LGRBs will be the forma-
tion events of close double black hole systems. We note
that also Tutukov and Cherepaschuck (2004) have pro-
posed that LGRBs are later evolutionary products of
HMXBs. They assumed (but did not calculate) that
the helium star plus compact star remnants from such
systems would be synchronized and also assumed that
the collapsing cores would have retained the angular
momentum from the time a synchronized helium star.
We have shown here quantitatively that this is indeed
the case.
This research was supported in part by the National
Science Foundation under Grant No. PHY99-07949.
The first author thanks the Mount Stromlo Observa-
tory for its hospitality during the conference and the
Netherlands research School for Astronomy NOVA for
financial support for participation in this meeting.
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	Introduction
	Host Galaxy Characteristics: further evidence for an association of the LGRBs with the most massive stars. 
	Possible reasons why small ``starburst-like'' galaxies are the prime sources of LGRBs
	Completely mixed single-star models of low metallicity
	Binary Models; can LGRBs be the formation events of Black-Hole X-ray Binaries?
	Introduction
	Timescales for synchronization of helium stars in close binaries with a main-sequence companion.
	 Timescales for core-envelope coupling
	Timescales for synchronization of helium stars in close binaries with a compact companion
	Discussion and Conclusions
