Hydrodynamic and Spectral Simulations of HMXB Winds
Christopher W. Mauche1,∗), Duane A. Liedahl1,∗∗), Shizuka Akiyama1,∗∗∗), and
Tomek Plewa2,†)
1Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
2University of Chicago, 5640 South Ellis Avenue, RI-475, Chicago, IL 60615, USA
We describe preliminary results of a global model of the radiatively-driven photoionized
wind and accretion flow of the high-mass X-ray binary Vela X-1. The full model combines
FLASH hydrodynamic calculations, XSTAR photoionization calculations, HULLAC atomic
data, and Monte Carlo radiation transport. We present maps of the density, temperature, ve-
locity, and ionization parameter from a FLASH two-dimensional time-dependent simulation
of Vela X-1, as well as maps of the emissivity distributions of the X-ray emission lines.
§1. Introduction
As described by Castor, Abbott, and Klein (hereafter CAK),1) mass loss in the
form of a high velocity wind is driven from the surface of an OB star by radiation
pressure on a multitude of resonance transitions of intermediate charge states of
cosmically abundant elements. The wind is characterized by a mass-loss rate Ṁ ∼
10−6–10−5 M⊙ yr
−1 and a velocity profile V (R) ∼ V∞(1− ROB/R)
β , where β ≈ 1
the terminal velocity V∞ ∼ 3Vesc = 3 (2GMOB/ROB)
1/2 ∼ 1500 km s−1, R is the
distance from the OB star, and MOB and ROB are respectively the mass and radius
of the OB star. In a detached high-mass X-ray binary (HMXB), a compact object,
typically a neutron star, captures a fraction f ∼ πR2BH/4πa
2 of the OB star wind,
where a is the binary separation, RBH = 2GMNS/[V (a)
2 + c2s ] is the Bondi-Hoyle
radius, cs ∼ 10 (T/10
4)1/2 km s−1 is the sound speed, and T is the wind temperature.
Accretion of this material onto the neutron star powers an X-ray luminosity LX ∼
fGṀMNS/RNS ∼ 10
36–1037 erg s−1, where MNS and RNS are respectively the mass
and radius of the neutron star. The resulting X-ray flux photoionizes the wind and
reduces its ability to be radiatively driven, both because the higher ionization state
of the plasma results is a reduction in the number of resonance transitions, and
because the energy of the transitions shifts to shorter wavelengths where the overlap
with the stellar continuum is lower. To first order, the lower radiative driving results
in a reduced wind velocity near the neutron star V (a), which increases the Bondi-
Hoyle radius RBH, which increases the accretion efficiency f , which increases the
X-ray luminosity LX. In this way, the X-ray emission of HMXBs is the result of a
complex interplay between the radiative driving of the wind of the OB star and the
photoionization of the wind by the neutron star.
Known since the early days of X-ray astronomy, HMXBs have been extensively
∗) E-mail: mauche@cygnus.llnl.gov
∗∗) E-mail: liedahl1@llnl.gov
∗∗∗) E-mail: shizuka@llnl.gov
†) E-Mail: tomek@uchicago.edu
typeset using PTPTEX.cls 〈Ver.0.9〉
http://arxiv.org/abs/0704.0237v1
2 C. W. Mauche, D. A. Liedahl, S. Akiyama, and T. Plewa
studied observationally, theoretically,2)–4) and computationally.5)–8) They are excel-
lent targets for X-ray spectroscopic observations because the large covering fraction of
the wind and the moderate X-ray luminosities result in large volumes of photoionized
plasma that produce strong recombination lines and narrow radiative recombination
continua of H- and He-like ions, as well as fluorescent lines from lower charge states.
§2. Vela X-1
Vela X-1 is the prototypical detached HMXB, having been studied extensively in
nearly every waveband, particularly in X-rays, since its discovery as an X-ray source
during a rocket flight four decades ago. It consists of a B0.5 Ib supergiant and a
magnetic neutron star in an 8.964-day orbit. From an X-ray spectroscopic point of
view, Vela X-1 distinguished itself in 1994 when Nagase et al.,9) using ASCA SIS
data, showed that, in addition to the well-known 6.4 keV emission line, the eclipse
X-ray spectrum is dominated by recombination lines and continua of H- and He-like
Ne, Mg, Si, S, Ar, and Fe. These data were subsequently modeled in detail by Sako
et al.,10) using a kinematic model in which the photoionized wind was characterized
by the ionization parameter ξ ≡ LX/nr
2, where r is the distance from the neutron
star and n is the number density, given by the mass-loss rate and velocity law of
an undisturbed CAK wind. Vela X-1 was subsequently observed with the Chandra
HETG in 2000 for 30 ks in eclipse11) and in 2001 for 85, 30, and 30 ks in eclipse and at
binary phases 0.25 and 0.5, respectively.12), 13) Watanabe et al.,13) using very similar
assumptions as Sako et al. and a Monte Carlo radiation transfer code, produced a
global model of Vela X-1 that simultaneously fit the HETG spectra from the three
binary phases with a wind mass-loss rate Ṁ ≈ 2 × 10−6 M⊙ yr
−1 and terminal
velocity V∞ = 1100 km s
−1. One of the failures of this model was the velocity
shifts of the emission lines between eclipse and phase 0.5, which were observed to be
∆V ≈ 400–500 km s−1, while the model simulations predicted ∆V ∼ 1000 km s−1.
In order to resolve this discrepancy, Watanabe et al. performed a 1D calculation to
estimate the wind velocity profile along the line of centers between the two stars,
accounting, in an approximate way, for the reduction of the radiative driving due to
photoionization. They found that the velocity of the wind near the neutron star is
lower by a factor of 2–3 relative to an undisturbed CAK wind, which was sufficient to
explain the observations. However, these results were not fed back into their global
model to determine the effect on the X-ray spectra.
§3. Hydrodynamic Simulations
To make additional progress in our understanding of the wind and accretion
flow of Vela X-1 in particular and HMXBs in general — to bridge the gap between
the detailed hydrodynamic models of Blondin et al. and the simple kinetic-spectral
models of Sako et al. and Watanabe et al. — we have undertaken a project to
develop improved models of radiatively-driven photoionized accretion flows, with
the goal of producing synthetic X-ray spectral models that possess a level of detail
commensurate with the grating spectra returned by Chandra and XMM-Newton.
This project combines (1) XSTAR14) photoionization calculations, (2) HUL-
Hydrodynamic and Spectral Simulations of HMXB Winds 3
(a) (b) (c) (d)
x x x
Fig. 1. Color-coded maps of (a) log T (K) = [4.4, 8.3], (b) log n (cm−3) = [7.4, 10.8], (c)
log V (km s−1) = [1.3, 3.5], and (d) log ξ (erg cm s−1) = [1.1, 7.7] in the orbital plane of Vela X-1.
The positions of the OB star and neutron star are shown by the circle and the “×,” respectively.
The horizontal axis x = [−5, 7]× 1012 cm, and the vertical axis y = [−4, 8]× 1012 cm.
LAC15) emission models appropriate to X-ray photoionized plasmas, (3) improved
models of the radiative driving of the photoionized wind, (4) FLASH16) three-
dimensional time-dependent adaptive-mesh hydrodynamics calculations, and (5) a
Monte Carlo radiation transport code.17) Radiative driving of the wind is accounted
for via the force multiplier formalism,1) accounting for X-ray photoionization and
non-LTE population kinetics using HULLAC atomic data for 2× 106 lines of 35,000
energy levels of 166 ions of the 13 most cosmically abundant elements. In addi-
tion to the usual hydrodynamic quantities, the FLASH calculations account for (a)
the gravity of the OB star and neutron star, (b) Coriolis and centrifugal forces, (c)
radiative driving of the wind as a function of the local ionization parameter, temper-
ature, and optical depth, (d) photoionization and Compton heating of the irradiated
wind, and (e) radiative cooling of the irradiated wind and the “shadow wind” be-
hind the OB star. To demonstrate typical results of our simulations, we show in
Fig. 1 color-coded maps of the log of the (a) temperature, (b) density, (c) velocity,
and (d) ionization parameter of a FLASH simulation with parameters appropriate
to Vela X-1. This is a 2D simulation in the binary orbital plane, has a resolution
of ∆l = 9.4 × 1010 cm, and, at the time step shown (t = 100 ks), the relatively
slow (V ≈ 400 km s−1)∗) irradiated wind has reached just ∼ 2 stellar radii from the
stellar surface. The various panels show (1) the effect of the Coriolis and centrifugal
forces, which cause the flow to curve clockwise, (2) the cool, fast wind behind the
OB star, (3) the hot, slow irradiated wind, (4) the hot, low density, high velocity
flow downstream of the neutron star, and (5) the bow shock and two flanking shocks
formed where the irradiated wind collides with the hot disturbed flow in front and
downstream of the neutron star.
Given these maps, it is straightforward to determine where in the binary the
X-ray emission originates. To demonstrate this, we show in Fig. 2 color-coded maps
of the log of the emissivity of (a) SiXIV Lyα, (b) SiXIII Heα, (c) FeXXVI Lyα,
and (d) FeXXV Heα. The gross properties of these maps agree with Fig. 24 of
Watanabe et al., but they are now (1) quantitative rather than qualitative and (2)
specific to individual transitions of individual ions. The maps also capture features
that otherwise would not have been supposed, such as the excess emission in the H-
∗) Note that this velocity reproduces the value that Watanabe et al. found was needed to match
the velocity of the emission lines in the Chandra HETG spectra of Vela X-1.
4 C. W. Mauche, D. A. Liedahl, S. Akiyama, and T. Plewa
(a) (b) (c) (d)
x x x x
Fig. 2. Color-coded maps of the log of the X-ray emissivity of (a) SiXIV Lyα, (b) SiXIII Heα,
(c) FeXXVI Lyα, and (d) FeXXV Heα. In each case, two orders of magnitude are plotted.
and He-like Si lines downstream of the flanking shocks. Combining these maps with
the velocity map (Fig. 1c), these models make very specific predictions about (1)
the intensity of the emission features, (2) where the emission features originate, and
(3) their velocity widths and amplitudes as a function of binary phase.
The next step in our modeling effort is to feed the output of the FLASH simula-
tions into the Monte Carlo radiation transfer code, to determine how the spatial and
spectral properties of the X-ray emission features are modified by Compton scatter-
ing, photoabsorption followed by radiative cascades, and line scattering. This work
is underway.
Acknowledgements
This work was performed under the auspices of the U.S. Department of Energy
by University of California, Lawrence Livermore National Laboratory under Contract
W-7405-Eng-48. T. Plewa’s contribution to this work was supported in part by the
U.S. Department of Energy under Grant No. B523820 to the Center for Astrophysical
Thermonuclear Flashes at the University of Chicago.
References
1) J. I. Castor, D. C. Abbott, and R. I. Klein, Ap.J. 195 (1975), 157, CAK.
2) S. Hatchett and R. McCray, Ap.J. 211 (1977), 552.
3) R. McCray, T. R. Kallman, J. I. Castor, and G. L. Olson, Ap.J. 282 (1984), 245.
4) I. R. Stevens and T. R. Kallman, Ap.J. 365 (1990), 321.
5) J. M. Blondin, T. R. Kallman, B. A. Fryxell, and R. E. Taam, Ap.J. 356 (1990), 591.
6) J. M. Blondin, I. R. Stevens, and T. R. Kallman, Ap.J. 371 (1991), 684.
7) J. M. Blondin, Ap.J. 435 (1994), 756.
8) J. M. Blondin and J. W. Woo, Ap.J. 445 (1995), 889.
9) F. Nagase, G. Zylstra, T. Sonobe, T. Kotani, H. Inoue, and J. Woo, Ap.J. 436 (1994), L1.
10) M. Sako, D. A. Liedahl, S. M. Kahn, and F. Paerels, Ap.J. 525 (1999), 921.
11) N. S. Schulz, C. R. Canizares, J. C. Lee, and M. Sako, Ap.J. 564 (2002), L21.
12) G. Goldstein, D. P. Huenemoerder, and D. Blank, A.J. 127 (2004), 2310.
13) S. Watanabe, et al., Ap.J. 651 (2006), 421.
14) T. Kallman and M. Bautista, Ap.J.S. 133 (2001), 221
15) A. Bar-Shalom, M. Klapisch, and J. Oreg, Phys. Rev. A38 (1988), 1773
16) B. Fryxell, et al., Ap.J.S. 131 (2000), 273.
17) C. W. Mauche, D. A. Liedahl, B. F. Mathiesen, M. A. Jimenez-Garate, and J. C. Raymond,
Ap.J. 606 (2004), 168.
	Introduction
	Vela-0.25 X-1
	Hydrodynamic-0.25 Simulations

  We describe preliminary results of a global model of the radiatively-driven
photoionized wind and accretion flow of the high-mass X-ray binary Vela X-1.
The full model combines FLASH hydrodynamic calculations, XSTAR photoionization
calculations, HULLAC atomic data, and Monte Carlo radiation transport. We
present maps of the density, temperature, velocity, and ionization parameter
from a FLASH two-dimensional time-dependent simulation of Vela X-1, as well as
maps of the emissivity distributions of the X-ray emission lines.

Introduction
As described by Castor, Abbott, and Klein (hereafter CAK),1) mass loss in the
form of a high velocity wind is driven from the surface of an OB star by radiation
pressure on a multitude of resonance transitions of intermediate charge states of
cosmically abundant elements. The wind is characterized by a mass-loss rate Ṁ ∼
10−6–10−5 M⊙ yr
−1 and a velocity profile V (R) ∼ V∞(1− ROB/R)
β , where β ≈ 1
the terminal velocity V∞ ∼ 3Vesc = 3 (2GMOB/ROB)
1/2 ∼ 1500 km s−1, R is the
distance from the OB star, and MOB and ROB are respectively the mass and radius
of the OB star. In a detached high-mass X-ray binary (HMXB), a compact object,
typically a neutron star, captures a fraction f ∼ πR2BH/4πa
2 of the OB star wind,
where a is the binary separation, RBH = 2GMNS/[V (a)
2 + c2s ] is the Bondi-Hoyle
radius, cs ∼ 10 (T/10
4)1/2 km s−1 is the sound speed, and T is the wind temperature.
Accretion of this material onto the neutron star powers an X-ray luminosity LX ∼
fGṀMNS/RNS ∼ 10
36–1037 erg s−1, where MNS and RNS are respectively the mass
and radius of the neutron star. The resulting X-ray flux photoionizes the wind and
reduces its ability to be radiatively driven, both because the higher ionization state
of the plasma results is a reduction in the number of resonance transitions, and
because the energy of the transitions shifts to shorter wavelengths where the overlap
with the stellar continuum is lower. To first order, the lower radiative driving results
in a reduced wind velocity near the neutron star V (a), which increases the Bondi-
Hoyle radius RBH, which increases the accretion efficiency f , which increases the
X-ray luminosity LX. In this way, the X-ray emission of HMXBs is the result of a
complex interplay between the radiative driving of the wind of the OB star and the
photoionization of the wind by the neutron star.
Known since the early days of X-ray astronomy, HMXBs have been extensively
∗) E-mail: mauche@cygnus.llnl.gov
∗∗) E-mail: liedahl1@llnl.gov
∗∗∗) E-mail: shizuka@llnl.gov
†) E-Mail: tomek@uchicago.edu
typeset using PTPTEX.cls 〈Ver.0.9〉
http://arxiv.org/abs/0704.0237v1
2 C. W. Mauche, D. A. Liedahl, S. Akiyama, and T. Plewa
studied observationally, theoretically,2)–4) and computationally.5)–8) They are excel-
lent targets for X-ray spectroscopic observations because the large covering fraction of
the wind and the moderate X-ray luminosities result in large volumes of photoionized
plasma that produce strong recombination lines and narrow radiative recombination
continua of H- and He-like ions, as well as fluorescent lines from lower charge states.
§2. Vela X-1
Vela X-1 is the prototypical detached HMXB, having been studied extensively in
nearly every waveband, particularly in X-rays, since its discovery as an X-ray source
during a rocket flight four decades ago. It consists of a B0.5 Ib supergiant and a
magnetic neutron star in an 8.964-day orbit. From an X-ray spectroscopic point of
view, Vela X-1 distinguished itself in 1994 when Nagase et al.,9) using ASCA SIS
data, showed that, in addition to the well-known 6.4 keV emission line, the eclipse
X-ray spectrum is dominated by recombination lines and continua of H- and He-like
Ne, Mg, Si, S, Ar, and Fe. These data were subsequently modeled in detail by Sako
et al.,10) using a kinematic model in which the photoionized wind was characterized
by the ionization parameter ξ ≡ LX/nr
2, where r is the distance from the neutron
star and n is the number density, given by the mass-loss rate and velocity law of
an undisturbed CAK wind. Vela X-1 was subsequently observed with the Chandra
HETG in 2000 for 30 ks in eclipse11) and in 2001 for 85, 30, and 30 ks in eclipse and at
binary phases 0.25 and 0.5, respectively.12), 13) Watanabe et al.,13) using very similar
assumptions as Sako et al. and a Monte Carlo radiation transfer code, produced a
global model of Vela X-1 that simultaneously fit the HETG spectra from the three
binary phases with a wind mass-loss rate Ṁ ≈ 2 × 10−6 M⊙ yr
−1 and terminal
velocity V∞ = 1100 km s
−1. One of the failures of this model was the velocity
shifts of the emission lines between eclipse and phase 0.5, which were observed to be
∆V ≈ 400–500 km s−1, while the model simulations predicted ∆V ∼ 1000 km s−1.
In order to resolve this discrepancy, Watanabe et al. performed a 1D calculation to
estimate the wind velocity profile along the line of centers between the two stars,
accounting, in an approximate way, for the reduction of the radiative driving due to
photoionization. They found that the velocity of the wind near the neutron star is
lower by a factor of 2–3 relative to an undisturbed CAK wind, which was sufficient to
explain the observations. However, these results were not fed back into their global
model to determine the effect on the X-ray spectra.
§3. Hydrodynamic Simulations
To make additional progress in our understanding of the wind and accretion
flow of Vela X-1 in particular and HMXBs in general — to bridge the gap between
the detailed hydrodynamic models of Blondin et al. and the simple kinetic-spectral
models of Sako et al. and Watanabe et al. — we have undertaken a project to
develop improved models of radiatively-driven photoionized accretion flows, with
the goal of producing synthetic X-ray spectral models that possess a level of detail
commensurate with the grating spectra returned by Chandra and XMM-Newton.
This project combines (1) XSTAR14) photoionization calculations, (2) HUL-
Hydrodynamic and Spectral Simulations of HMXB Winds 3
(a) (b) (c) (d)
x x x
Fig. 1. Color-coded maps of (a) log T (K) = [4.4, 8.3], (b) log n (cm−3) = [7.4, 10.8], (c)
log V (km s−1) = [1.3, 3.5], and (d) log ξ (erg cm s−1) = [1.1, 7.7] in the orbital plane of Vela X-1.
The positions of the OB star and neutron star are shown by the circle and the “×,” respectively.
The horizontal axis x = [−5, 7]× 1012 cm, and the vertical axis y = [−4, 8]× 1012 cm.
LAC15) emission models appropriate to X-ray photoionized plasmas, (3) improved
models of the radiative driving of the photoionized wind, (4) FLASH16) three-
dimensional time-dependent adaptive-mesh hydrodynamics calculations, and (5) a
Monte Carlo radiation transport code.17) Radiative driving of the wind is accounted
for via the force multiplier formalism,1) accounting for X-ray photoionization and
non-LTE population kinetics using HULLAC atomic data for 2× 106 lines of 35,000
energy levels of 166 ions of the 13 most cosmically abundant elements. In addi-
tion to the usual hydrodynamic quantities, the FLASH calculations account for (a)
the gravity of the OB star and neutron star, (b) Coriolis and centrifugal forces, (c)
radiative driving of the wind as a function of the local ionization parameter, temper-
ature, and optical depth, (d) photoionization and Compton heating of the irradiated
wind, and (e) radiative cooling of the irradiated wind and the “shadow wind” be-
hind the OB star. To demonstrate typical results of our simulations, we show in
Fig. 1 color-coded maps of the log of the (a) temperature, (b) density, (c) velocity,
and (d) ionization parameter of a FLASH simulation with parameters appropriate
to Vela X-1. This is a 2D simulation in the binary orbital plane, has a resolution
of ∆l = 9.4 × 1010 cm, and, at the time step shown (t = 100 ks), the relatively
slow (V ≈ 400 km s−1)∗) irradiated wind has reached just ∼ 2 stellar radii from the
stellar surface. The various panels show (1) the effect of the Coriolis and centrifugal
forces, which cause the flow to curve clockwise, (2) the cool, fast wind behind the
OB star, (3) the hot, slow irradiated wind, (4) the hot, low density, high velocity
flow downstream of the neutron star, and (5) the bow shock and two flanking shocks
formed where the irradiated wind collides with the hot disturbed flow in front and
downstream of the neutron star.
Given these maps, it is straightforward to determine where in the binary the
X-ray emission originates. To demonstrate this, we show in Fig. 2 color-coded maps
of the log of the emissivity of (a) SiXIV Lyα, (b) SiXIII Heα, (c) FeXXVI Lyα,
and (d) FeXXV Heα. The gross properties of these maps agree with Fig. 24 of
Watanabe et al., but they are now (1) quantitative rather than qualitative and (2)
specific to individual transitions of individual ions. The maps also capture features
that otherwise would not have been supposed, such as the excess emission in the H-
∗) Note that this velocity reproduces the value that Watanabe et al. found was needed to match
the velocity of the emission lines in the Chandra HETG spectra of Vela X-1.
4 C. W. Mauche, D. A. Liedahl, S. Akiyama, and T. Plewa
(a) (b) (c) (d)
x x x x
Fig. 2. Color-coded maps of the log of the X-ray emissivity of (a) SiXIV Lyα, (b) SiXIII Heα,
(c) FeXXVI Lyα, and (d) FeXXV Heα. In each case, two orders of magnitude are plotted.
and He-like Si lines downstream of the flanking shocks. Combining these maps with
the velocity map (Fig. 1c), these models make very specific predictions about (1)
the intensity of the emission features, (2) where the emission features originate, and
(3) their velocity widths and amplitudes as a function of binary phase.
The next step in our modeling effort is to feed the output of the FLASH simula-
tions into the Monte Carlo radiation transfer code, to determine how the spatial and
spectral properties of the X-ray emission features are modified by Compton scatter-
ing, photoabsorption followed by radiative cascades, and line scattering. This work
is underway.
Acknowledgements
This work was performed under the auspices of the U.S. Department of Energy
by University of California, Lawrence Livermore National Laboratory under Contract
W-7405-Eng-48. T. Plewa’s contribution to this work was supported in part by the
U.S. Department of Energy under Grant No. B523820 to the Center for Astrophysical
Thermonuclear Flashes at the University of Chicago.
References
1) J. I. Castor, D. C. Abbott, and R. I. Klein, Ap.J. 195 (1975), 157, CAK.
2) S. Hatchett and R. McCray, Ap.J. 211 (1977), 552.
3) R. McCray, T. R. Kallman, J. I. Castor, and G. L. Olson, Ap.J. 282 (1984), 245.
4) I. R. Stevens and T. R. Kallman, Ap.J. 365 (1990), 321.
5) J. M. Blondin, T. R. Kallman, B. A. Fryxell, and R. E. Taam, Ap.J. 356 (1990), 591.
6) J. M. Blondin, I. R. Stevens, and T. R. Kallman, Ap.J. 371 (1991), 684.
7) J. M. Blondin, Ap.J. 435 (1994), 756.
8) J. M. Blondin and J. W. Woo, Ap.J. 445 (1995), 889.
9) F. Nagase, G. Zylstra, T. Sonobe, T. Kotani, H. Inoue, and J. Woo, Ap.J. 436 (1994), L1.
10) M. Sako, D. A. Liedahl, S. M. Kahn, and F. Paerels, Ap.J. 525 (1999), 921.
11) N. S. Schulz, C. R. Canizares, J. C. Lee, and M. Sako, Ap.J. 564 (2002), L21.
12) G. Goldstein, D. P. Huenemoerder, and D. Blank, A.J. 127 (2004), 2310.
13) S. Watanabe, et al., Ap.J. 651 (2006), 421.
14) T. Kallman and M. Bautista, Ap.J.S. 133 (2001), 221
15) A. Bar-Shalom, M. Klapisch, and J. Oreg, Phys. Rev. A38 (1988), 1773
16) B. Fryxell, et al., Ap.J.S. 131 (2000), 273.
17) C. W. Mauche, D. A. Liedahl, B. F. Mathiesen, M. A. Jimenez-Garate, and J. C. Raymond,
Ap.J. 606 (2004), 168.
	Introduction
	Vela-0.25 X-1
	Hydrodynamic-0.25 Simulations
