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Understanding Black Hole Formation in Cygnus X-1
Tsing-Wai
1 Center
1,2
Wong ,
Francesca
1
Valsecchi ,
Tassos
2
Fragos ,
and Vassiliki
1
Kalogera
for Interdisciplinary Exploration and Research in Astrophysics (CIERA) & Department of Physics and Astronomy, Northwestern University
2 Harvard-Smithsonian Center for Astrophysics
Background and Purpose
Cygnus X-1 is a luminous X-ray binary, hosting a 14.81 ± 0.98 M⊙ black hole (BH) and a 19.16 ± 1.90 M⊙ O supergiant star in a Keplerian orbit of 5.6 days (Orosz 2011). This system is a
persistent X-ray source that emits in two states: low-hard or high-soft state. Although the supergiant is close to filling its Roche-lobe, the observed X-ray emission comes from the partial accretion of
the supergiant’s stellar wind onto the BH. The purpose of this study is to estimate the mass of the BH immediate progenitor and the magnitude of a possible natal kick imparted to the BH.
Formation scenario of Cygnus X-1
We adopt the simplest formation scenario that can explain
all the observations.
• assume both stars, the BH progenitor and the O
supergiant were born at the same time
• assume there was no mass transfer at all in the history of
Cygnus X-1.
(This means we can model the O supergiant as a single
isolated star.)
• the BH immediate progenitor is a He star.
• during the core-collapse event, the binary orbit was
altered by mass loss from the system and the possible
natal kick imparted to the BH.
• the BH has accreted negligible amount of mass since its
birth.
> 120 M⊙
MS
14.81 ± 0.98 M⊙
He
Black
Hole
Core
Collapse
Cygnus X-1
MBH = 14.81 ± 0.98 M⊙
M2 = 19.16 ± 1.90 M⊙
L2 = (2.33 ± 0.42) ! 105 L⊙
natal kick?
MS
MS
Teff = 31000 ± 1000 K
Lx = (1.3 " 2.1) ! 1037 erg/s
MS
Porb = 5.599829(16) days
eorb = 0.018(3)
Fig 1. The adopted formation scenario of Cygnus X-1. The notation MS and He stands for main sequence star and helium star, respectively.
Methodology
Step 1: create stellar models that matched all the observed BH companion’s properties
> 120 M⊙
15.0 ! 20.0 M⊙
• used a modified stellar evolution code, which was originally developed by Paxton (2004)
• computed the X-ray luminosity by Bondi-Hoyle accretion model
the companion
was747:111
a 20 to(12pp),
23 M2012
at 10
zero-age main sequence
• found
MS (ZAMS)
⊙ star
He
The Astrophysical
Journal,
March
• estimated the BH was born 4.8 to 7.6 million years ago
Step 2: find the systemic peculiar velocity (Vpec_postSN) right after the BH’s formation
14.81 ± 0.98 M⊙
• traced the motion of Cygnus X-1 in a galactic potential backwards in time
Cygnus X-1
• derived Vpec_postSN = 22 to 32 km/s
Black
Wong et al.
Hole
Core
4.8 ! 7.6
Myr
± 0.98 M⊙
Step 3: constrain the binary
properties
right before the core-collapseMevent
via Monte
BH = 14.81
Collapse
The Astrophysical Journal, 747:111 (12pp), 2012 March
10
Wong et al. Carlo
simulations
The Astrophysical
Journal, 747:111 (12pp), 2012 March 10
Wong
et al.
Companion Age vs. ZAMS mass
Kinematics of Cygnus X-1 in the past
Mc = 19.16 ± 1.90
Vk " 77 km/s
The Astrophysical Journal, 747:111 (12pp), 2012 March 10
Wong et al.
• important free parameters: BH immediate progenitor mass (MHe), orbital semi-major
the Galactic
plane
and
the
end
points
of
all
trajectories
fall
within
esti
+ current location
mat
axis (ApreSN) & eccentricity (epreSN), and natal kick magnitude (Vkick)
×from
Cyg OB3the Galactic plane, we consider each end point as
ed c
110
pc
omp
anio
MS
MSof the BH. The post-SN MS
a possible birth site
peculiar velocity • properties
of the companion star was given by stellar models created in Step 1.
n ag
e
Vpec,postSN of the binary is obtained by subtracting the local
Galactic rotational
velocity
of
20 ! 23
M⊙ from the center-of-mass
19.8 ! 22.6 velocity
M⊙
the binary at the birth sites. We find Vpec,postSN ranges from
+ current
location
22 to 32 km s−1 and is time independent. The
distribution
of
potential BH birth sites
× Cyg OB3
Vpec,postSN against the time expired since the formation of the
BH are displayed in Figure 5.
6. ORBITAL DYNAMICS AT CORE COLLAPSE
• conservation of orbital energy and angular momentum gave the binary parameters
19.8
! 22.6
M⊙
right
after
the core-collapse
event
• applied the Vpec_postSN = 22 to 32 km/s constraint derived in Step 2
• evolved
the binary
The Astrophysical
Journal, 747:111 (12pp), 2012 March 10
Binary Orbital Evolution
orbit forward in time to
the current epoch
• if the orbital period
and eccentricity
matched the
measured values, we
used that data to
construct probability
distribution functions
(PDFs)
M⊙
For each successful sequence, we perform a Monte Carlo
simulation which consists of 20 million pre-SN binaries.
estimated life time of BH progenitor
The properties of the BH progenitor’s companion are taken
from the stellar model of that sequence, at the time when the
age of the star is equal to tBH . During a supernova (SN) explosion, the mass loss from the system and possibly the kick
imparted to the BH change the binary’s orbital parameters. The
preand
post-SN
component
masses,
orbital
semimajor
axis,
Fig 4. One possible past evolution of Cygnus X-1’s orbit. Right after
Upper panels:
the gray
dots3.
illustrate
the possible
locations
of Cygnusbirth
X-1 at the
birth of
timethe
of theBH.
BH, obtained
Figure
of tof
against companion
M2,zams . TheFigure
gray-shaded
region
Fig4.2.Variations
Variations
the estimate
age5.against
2 (circles)
Fig
Upper
panels:
potential
sites
Lowerfrom 3000 integrations of its trajectory
in time.
The initial
of the
integrations
are generated randomly
using the methodology
described in Section 5.laws
The plus
and
orbital
eccentricity
are related
by the
conservation
ofsigns indicate the current
the core-collapse event at t = 3.8 Myr, this binary system consists of a
sequences,
which
is conditions
indicates
themass.
range of tBH for the corresponding successfulbackward
ZAMS
panel:
the
distribution
of
systemic
peculiar
velocities
against
location of Cygnus X-1, derived from the mean distance of 1.86 kpc. The crosses represent the current location of Cyg OB3 center, with an adopted distance of 2 kpc.
the
orbital
energy
and
angular
the following, we
calculated by Equation (12). The difference between t2 andLower
tBH panel:
givesthetsys
.
14.8 M⊙ BH and a 21.7 M⊙ main-sequence companion.
distribution
ofthe
post-SN
peculiar
velocities
Vpec,postSN
against
time momentum.
expired since the BHIn
formation.
time
expired
since
the
BHtheformation.
add the subscripts “preSN” and “postSN” to the notation of the
orbital
elements
to the
distinguish
between
their etvalues
just
prior
VHe,preSN is the relative pre-SN
orbital
velocity of
BH
formulae
of Sepinsky
al. (2007).
When
calculating the pre-SN
5. KINEMATIC HISTORY IN THE GALAXY
progenitor,
Roche lobe
we assume
that the pre-SN orbit is pseudoto,
and
right after,
the
SN
explosion
thatradii,
formed
the BH.
Figure 6. OrbitalFigure
evolution
of
a
selected
winning
binary.
Right
after
the
formation
of
the
BH
(t
=
3.8
Myr),
this
binary
consists
a a14.8
MM
BH
and
astellar
21.7MM!
synchronized.
Again,
dueconsists
to theofdifference
in!!calculated
6. Orbital evolution of a selected winning
binary.
Right
after
the
formation
of
the
BH
(t
=
3.8
Myr),
this
binary
of
14.8
BH
and
a
21.7
!
$
!
We
start
with
seven
free
parameters:
the
BH
immediate
1/2
Here, we
assume
that
Cygnus
X-1
formed
in
the
Galactic
disk.
#
"
main-sequence star.
The top panels
show
timeshow
evolution
orbital period
eccentricity.
The bottom
panels
show
the evolution
rates
of
change
ofof
the
axisAAand
and
Results
and
Discussion
radii
among
stellar
codes,
we
consider
an uncertainty
main-sequence
star. The
topthe
panels
the timeofevolution
of orbital
period
The bottom
panels
show
the
rates
of
change
thesemimajor
semimajor
axis
1 and eccentricity.
2 and
− accretion
=
G(M
+M
. the
(17)
VHe,preSN
(He-rich)
progenitor
mass
(M
), Rpre-SN
orbital
semimajor
He
2 ) wind
eccentricityof
e due
to OB3
tidal effects
(solid
line),
mass
and
wind
accretion
onto
theonto
BH
(dashed
line),
and
gravitational
radiation
(dotted
ofHe
±2.5
the companion
radius
(Valsecchi
et al. 2010). The
The consideration
Cyg
being
the
association
of
The Astrophysical Journal, 747:111 (12pp), 2012 March 10
eccentricity
e due to
tidalparent
effectswind
(solid
line),loss
wind
mass
loss
and
BH (dashed
line),
and
radiation
(dottedline).
line).
" ongravitational
r
ApreSN
of the
BH immediate
progenitor
can be approximated by
PDFs
of MHe and
2D joint
M
2D joint epreSN−ApreSN PDF
kick
He−Vkick PDF
axis (ApreSN ) and eccentricity radius
(epreSN
), the
mean
anomaly
(m),
Cygnus X-1 is discussed in Section1D9.2.
Given
the Vobserved
Equations (3) in Fryer & Kalogera (1997), since we assume
throu
The
angle
ψ
is
the
polar
angle
of
the
position
vector
of
the
BH
the
magnitude
(V
),
and
direction
(θ
,
φ)
of
the
kick
velocity
position and measured proper motion of Cygnus X-1, we derive
k
that it is a Helium star. Second, the pre-SN spin of the BH
with respect to its pre-SN orbital velocity in the companion’s
the b
3σ to be less than the
imparted
to
the
BH.
θ
is
the
polar
angle
of
the
kick
with
respect
the post-SN peculiar velocity of the binary’s center
of
mass
by
immediate
progenitor
and
its
companion
need
frame. It is related to the pre-SN parameters as
3 1/2
find
breakup
angular
velocity Ωc just
≈ (GM/R
)to . As the calculated
to the relative
orbital
velocity
of
the
BH
progenitor
prior
tracing its orbit in the Galaxy back to the time of BH formation.
Figure 6. Orbital evolution of a selected winning binary. Right after the formation of the BH (t = 3.8 Myr), this binary consists of a 14.8 M! BH
%
&
2 2
2
2
stellar
radius
R
associates
with
an
uncertainty
∆R
=
2.5 R"
a ran
2
ψ = G(MHethe
+ MSN
1 − epreSNand
. (18)
r VHe,preSN
explosion,
φ is the
corresponding
azimuthal
angle
2 )ApreSN
main-sequence
star. The top panels show the time evolution of orbital period and eccentricity. The bottom panels show the rates of change of the semim
We describe the motion of the binary with respect
to a sin
right(Valsecchi et al. 2010),
max
eccentricity e due to tidal effects (solid line), wind mass loss and wind accretion onto the BH (dashed line), and gravitational radiation (dotted line).
(see
Figure
1
in
Kalogera
2000
for
a
graphical
representation).
hand Cartesian reference frame, whose originSince
coincides
with
the core collapse is instantaneous, r remains unchanged.
' 2σ (
limit
)
The
first
five
parameters
are
drawn
from
uniform
distributions,
3 ∆R
GM2
the Galactic center. The Z-axis points to the northern
This gives Galactic
a constraint
recei
1
+
(20)
Ωc =
3
while
the
last
two
are
drawn
from
isotropic
distributions.
It
is
2 R2
pole, while the X-axis points in the direction from the projected
R2
fiden
r = ApreSN (1 − eobvious
preSN cos Ethat
preSN )the progenitor must of course1σ
be
more
massive
than
position of the Sun onto the Galactic plane to the Galactic center.
a no
= ApostSN (1 − epostSN cos EpostSN ),
(19)
for
the
BH
companion.
the BH, but there is no absolute upper limit for the progenitor
In this reference frame, the Sun is located at (X! , Y! , Z! ) =
rentl
mass.
We
adopt
provide a discussion on this
to be satisfied with
| cos E
| ! 1. MHe ! 20 M! ,7.and
(−8.5, 0, 0.03) kpc (Joshi 2007; Ghez et al. which
2008;needs
Gillessen
postSN
only
ORBITAL EVOLUTION AFTER THE SN EXPLOSION
mass loss
the system
a natal
kick imparted
upperand
limit
in Section
9.1.
et al. 2009; Reid et al. 2009) and has a peculiarThemotion
(Ufrom
!,
amo
The
orbital
evolution
of
the
simulated
binaries,
which
are
to
the
BH
can
induce
a
post-SN
peculiar
velocity
(V
)
pec,postSN
3σ
The relations between pre- and
post-SN parameters have been
V! , W! ) = (11.1, 12.24, 7.25) km s−1 (Schönrich
al. 2010).
∼2 ×
generated from the Monte Carlo simulations described in
at the et
binary’s
center of mass. Its magnitude is determined by
by Hills
Cygnus X-1 is currently located at a distance Equations
of 1.86+0.12
kpcin Paper Iderived
Section 6, is calculated up to the current epoch. After the
(28)–(32)
and is required
to fall(1983):
within the
BH
−0.11
−1
formation of the BH, the orbital parameters of the binary are
derived
in Section 5, which is 22–32 km s .
from the Sun, with a Galactic longitude l = 71.◦range
3, and
a Galactic
by m
subject
to
secular
changes
due
to
the
tidal
torque
exerted
by
In
addition,
there
are
two
more
restrictions
on
the
properties
of
2σ
2
2
plica
latitude b = 3.◦ 1 (Lestrade et al. 1999; Reid etpreal.and
2011).
This
Vk +First,
VHe,preSN
+ 2V
VHe,preSNthecos
M2due
) to the loss of orbital angular
BH + and
BHθon=
its G(M
companion,
post-SN binary components.
we require
thatkboth
" and stellar wind. Since
!
colla
means Cygnus X-1 is currently ∼130 kpc above
the Galactic
momentum via gravitational
radiation
components
have to fit within their pre- and post-SN Roche lobe
the tidal interactions2depend on1 both the orbital and rotational
at periapsis. We impose this condition to avoid complications
a ma
1σ
plane.
,
−
×
properties of the MSr companion,
arising from MT-induced changes in the stellar structure of the
ApostSNthe star’s rotational angular
and
To model the Galaxy, we adopt the Galactic
potential
of
velocity (Ω) right after SN explosion that formed the BH
MS companion that later becomes the BH companion of the
ecce
Carlberg & Innanen (1987)
with
updated
model
parameters
(13)
enters
the
problem
as
an
additional
unknown
quantity.
Here,
XRB.
To
calculate
the
Roche
lobe
radius
of
each
component
Figure 7. Probability distribution functions of the BH immediate (He-rich)
ecce
we assume the rotational angular velocity of the BH companion
in kick
eccentric
pre-the
and
we adopt the fitting
of Kuijken & Gilmoreprogenitor
(1989).mass
The(Mequations
magnitude
(Vk ) post-SN
imparted orbits,
to the BH.
He ) and natal governing
at th
system’s motion in the Galaxy are integrated backward in time,
7
#
$ joint Vjoint
Figure
Two-dimensional
joint ApreSNjoint
–epreSN e
confidence
levels: 68.3%
(red),
Th
Fig
7. 9.The
two dimension
probability
Fig
5.
The
probability
distribution
functions
of
M
and
V
.
Figure
7.
Probability
distribution
functions
of
the
BH
immediate
(He-rich)
preSN−ApreSN
Figure
8.
Two-dimensional
confidence
68.3% (red),
95.4%
He
kick
k –MHe
Fig
6.
The
two
M
probability
distribution
2 dimension
up to the time corresponding to the current system’s age tsys
He−Vkick levels:
G(M
1 and
− e99.7%
95.4% (yellow),
and 99.7% (blue).
BH + M2 )ApostSN
postSN(blue).
(yellow),
studi
progenitor
mass
(M
)
and
natal
kick
magnitude
(V
)
imparted
to
the
BH.
In
Figure
7,
we
present
the
probability
distribution
functions
distribution
function.
He
k
function.
given by the successful sequences. We follow the methodology
Figure 7. Probability distribution functions of the BH immediate (He-rich)
#
color version of this figure is available in the online journal.)
2He ) 2
2(A color2 version of this figure is available in the online journal.) progenitor mass (M ) and natal kick magnitude(A
(200
(PDFs)
of
the
BH
immediate
(He-rich)
progenitor
mass
(M
(V
)
imparted
to
the
BH.
He
k
V
sin
θ
cos
φ
+
[sin
ψ(V
+
V
cos
θ
)
=
r
of Gualandris et al. (2005) to initialize the parameters for the
He,preSN
k
k
the c
Figure
8.
Two-dimensional
joint
Vnatal
confidence
levels: 68.3%
(red),
95.4%
and
natal
kick
magnitude
(V
).
We
find
M
to
be
in
a
$
k –MHekick
k
He
We
found
that
the
BH
immediate
progenitor
mass
(M
)
is
between
15
to
20
M
,
and
the
magnitude
(V
)
imparted
to
the
BH
is
≤
77
km/s,
both
at
95%
confidence.
As
shown
in
the
two
He
⊙
kick
2
integration, which accounts for the uncertainties in the estimated
−1
Figure 8. Two-dimensional joint Vk –MHe confidence levels:
68.
−
V
.
(14)
cos
ψ
sin
θ
sin
φ]
(yellow),
and
99.7%
(blue).
dyna
k
In
Figure
7,
we
present
the
probability
distribution
functions
range
of
15.0–20.0
M
,
and
V
to
be
!77
km
s
,
both
at
!
k
a∗event,
> 0.95if at
3σ
.isTo< and
determine
whether
theMBH
dimensional
joint velocity
Vkick−MHe
probability
natal
coreparameter
collapse
MHe
1799.7%
M⊙(blue).
. For
small
distance
and measured
components.
Wedistribution
generate thefunction (see Fig. 6), the BH might probably have received a non Inzero
(yellow),
He, a
Figure
7, we kick
presentatthethe
probability
distribution
functions
earli
95%
confidence.
Figure
8 illustrates
the two-dimensional
joint(A color20version
M! . We
impose
limit based
the journal.)
physics involved
in
of this
figurethis
is available
in theon
online
(PDFs)
of
the
BH
immediate
(He-rich)
progenitor
mass
(M
)
He
was
born
with
an
extreme
spin,
we
first
estimate
how
much
(A color version of this figure is available in the online journal
(PDFs) of the
BH immediate
(He-rich)
progenitor
mass (MHe )
initial
system’sVposition
by the
Galactic
coordinates
(l, b) andall the observed properties of Cygnus X-1. For a more detail presentation
minimum
km/s
is
necessary
to
explain
of
this
work,
see
Wong
et
al.
(2012).
kick of ~55
durin
Vk –M
evolution
of massive
stars.
A discussion
limit
cankick magnitude (V ). Wemass
levels,
which
shows
that
ifbe
M
thanorbital the
Here,
is the
separation
between
the BH
progenitor
and on thisand
He confidence
Heinis rless
and
natal
kick
magnitude
(V
).
We
find
M
to
a
the
BH
could
have
accreted
from
its
companion’s
stellar
natal
find
M
to
be
in
a
k
He
k
He
a random distance drawing
from
a
Gaussian
distribution.
We
since
−1
−1
found
in Section
9.1. Given our understanding ofrange
mass of
loss
∼17 M!M
, the
BH might
have
received
asnon-zero
natal
kickat the be
its
companion
time
of
SN
explosion,
15.0–20.0
M
,
and
V
to
be
!77
km
s
,
both
at
wind
since
the
time
of
BH
formation.
The
winning
binaries
range
of
15.0–20.0
,
and
V
to
be
!77
km
,
both
at
!
k
! by drawing
k
generate initial system’s
velocity
earli
from Helium stars, it seems that the BH has potentially
received
at the
core-collapse
event.randomly
For small the
MHe , a minimum Vk of
95%
confidence.
Figure
8
illustrates
the
two-dimensional
joint
20
M
.
We
impose
this
limit
based
on
the
physic
!
of
all
successful
sequences
show
that
at
maximum
the
BH
has
95% confidence.
Figure
8 illustrates radial
the two-dimensional
joint
20 M . We impose this limit based Reference
on the −1
physics involved in
proper motions
(µR.A. , ∼55
µdecl.
) and
velocity the current
cons
−3
natal
kick
velocity
of
!77
km
s
km
s−1 heliocentric
is necessary for explaining
observedr = A!a small
(95% confidence)
Vk –MHe confidence levels, which shows
the evolution
of massive
stars.the
A discussion
on t
that if M∼2
less
than
He is
accreted
×
10
M
.
Since
it
is
impossible
to
spin
BH
(1
−
e
cos
E
),
(15)
%
preSN
preSN
preSN
V
the
evolution
of
massive
stars.
A
discussion
on
this
limit
can
–M
confidence
levels,
which
shows
that
if
M
is
less
than
(V0 ) from kGaussian
distributions.
current
age isHe
He
prog
Belczynski,
Bulik,and
T., Fryer, C.,during
et al. 2010,
714, 1217 event.
Lestrade, J.-F., Preston,
Jones,
et al.
1999,received
A&A, 344,a 1014
be found
in Section amount
9.1. Given
our
understanding
∼17 MR.A.,
BHD.L.,
might
have
non-zero
natal by
kick
properties ofThe
Cygnus
X-1.system’s
Furthermore,
both
the MHeK.,PDF
the ApJ,
core-collapse
! , the
up
to
a
>
0.95
accreting
that
negligible
of
mass,
∗
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K.,
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V.,
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F.
A.,
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223
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uniformly∼17
distributed
between
4.8
and
7.6
Myr
(see
Figure
4).
be
found
in
Section
9.1.
Given
our
understanding
of
mass
loss
M! , the
BH
might
have
received
a
non-zero
natal
kick
histo
from Helium
stars,
it seems
that
thespin
BH has potenti
at
the
core-collapse
event.
For
small
M
,
a
minimum
Based on the dynamical model of Orosz et al. (2011), Gou
the two-dimensional joint Vk –MHe confidence levels show that
HeBH needs to V
k of an extreme
the
have
spin
at
birth.
This
high
Brocksopp,
C., E
Tarasov,
A.eccentric
E., Lyuty, V.M,
& Roche,and
P. 1999,
A&A, 343,
861
Orosz, J. A., McClintock,
J. E.,
−1Aufdenberg, J. P, et al. 2011, ApJ, 742, 84
−1
where
is the
anomaly
is related
tothe
m BH
asin has
Figureat5 the
shows
the the
possible
positions
of
Cygnus
X-1
at
a
small
natal
kick
velocity
of
!77
km
s
∼55
km
s
is
necessary
for
explaining
the
current
observed
(95%
from
Helium
stars,
it
seems
that
potentially
received
core-collapse
event.
small
M
,
a
minimum
V
of
Fi
He
k
et
al.
(2011)
found
that
the
BH
Cygnus
X-1
has
a
spin
maximum
MFor
is
constrained
by
our
adopted
upper
limit
of
He
Cadolle
Bel,
M.,
Sizun,
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Goldwurm,
A.,
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2006,
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Paxton,
B.,
2004,
PASP,
116,
699
has
implications
about
BH
formation
and
the
role
of
rotation
−1
properties
of Cygnus X-1. Furthermore, both
the MHe PDF and
during the core-collapse event.
the time ∼55
of BH
obtainedfor
from
integrating
our a
a
small
natal
kick
velocity
of
!77
km
s
kmformation,
s−1 is necessary
explaining
the 3000
current
observed
(95%
confidence)
Frontera, F., Palazzi, E., Zdziarski, A. A., et al. 2001, ApJ, 546, 1027
Reid, M.
J., McClintock,
J. E., Narayan, R., et al. 2011, ApJ, 742,
83
in
core
collapse.
Axelsson
et
al.
(2011)
also
concluded
that
the
Based on the dynamical model of Orosz et al.
the two-dimensional
joint VV.
confidence
levels show that
k –M
He ApJ,
trajectories
backward
in
time.
As
there
is
no
trajectory
crossing
Gies,
D.
R.,
Bolton,
C.
T.,
Thomson,
J.
R.,
et
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2003,
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583,
424
Wong,
T.-W.,
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F.,
Fragos,
T.,
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747
111
m
=
E
−
e
sin
E.
(16)
9
properties of Cygnus X-1. Furthermore, both the MHe PDF and
during the core-collapse event.
observed
spin connects
involved
et al. (2011)
found in
thatcore
the collapse
BH in Cygnus X-1
the maximum MHe is constrained by our
adopted upper
limit of to processes
Gou, L., McClintock, J. E., Reid, M. J., et al. 2011, ApJ, 742, 85
Based on the dynamical model of Orosz et al. (2011), Gou
the two-dimensional joint Vk –MHe confidence levels show that
and is not likely to originate from the synchronous rotation of
6 limit of
the BH progenitor.
et al. (2011) found that the BH in Cygnus X-1 has a spin
the maximum MHe is constrained by our adopted upper
9
U