DYNAMICAL MODELS FOR X-RAY EMISSION FROM MASSIVE STARS
P.I.: Stanley P. Owocki, University of Delaware
Post-doctoral Associate: Ross Parkin, University of Leeds
co-I’s:
David Cohen, Swarthmore College
Asif ud-Doula, Morrisville State College
Collaborators:
Mike Corcoran, NASA/GSFC
Marc Gagné, West Chester University
Rich Townsend, University of Wisconsin
Abstract
Massive stars are prominent sources of X-rays detected by both targeted and survey observations from orbiting X-ray telescopes like Chandra, XMM/Newton, and RXTE. Such X-rays
represent key probes of the dynamics of massive star mass loss, and their penetration through
many magnitudes of visible interstellar extinction makes them effective beacons of massive stars
in distant reaches of the Galaxy, and in young, active star-forming regions. The project proposed here will develop a comprehensive theoretical framework for interpreting both surveys and
targeted observations of high-energy emission from massive stars. It will build on our team’s
extensive experience in both theoretical models and observational analyses for three key types of
shock-based emission mechanisms in the stellar wind outflows of these stars, namely: 1) Embedded Wind Shocks (EWS) arising from internal instabilities in the wind driving; 2) Magnetically
Confined Wind Shocks (MCWS) in magnetic massive stars; and 3) shocks in Colliding Wind Binary (CWB) systems. Taking advantage of commonalities in the treatment of radiative driving,
hydrodynamics, shock heating and cooling, and radiation transport, we will develop radiation
hydrodynamical models for the key observational signatures like energy distribution, emission
line spectrum, and variability, with an emphasis on how these can be used in affiliated analyses of both surveys like the recent Chandra mapping of the Carina association, and targeted
observations of galactic X-ray sources associated with each of the above specific model types.
The promises of new clumping-insensitive diagnostics of mass loss rates, and the connection to
magnetic fields and binarity, all have broad relevance for understanding the origin, evolution,
and fate of massive stars, in concert with elements of NASA’s Strategic Subgoal 3D. Building
on our team’s expertise, the project emphasizes training of a new generation of students and
post-doctoral researchers to model and analyze observations by current and future NASA X-ray
observatories.
Contents
1 Introduction
1
2 Background on Relevant Work by Investigators
2.1 Embedded Wind Shocks (EWS) in single OB stars . . . . . . . . . . . . . . . . . . .
2.2 Magnetically Confined Wind Shocks (MCWS) in magnetic massive stars . . . . . . .
2.3 Colliding Wind Binary (CWB) systems . . . . . . . . . . . . . . . . . . . . . . . . .
2
2
4
6
3 Proposed Research
3.1 Radiation-Hydrodynamical Simulation of X-ray Emission and Absorption . . . . . .
3.2 X-ray Signatures of 3-D MHD simulations of MCWS with Radiative Cooling . . . .
3.3 Radiative Driving Feedback on CWB Shocks & X-rays . . . . . . . . . . . . . . . . .
7
7
8
9
4 Cost, Personnel, & Work Plan
10
4.1 Cost Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.2 Qualifications and Expected Contributions of Investigators . . . . . . . . . . . . . . 11
4.3 Work Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5 Broad Relevance of Proposed Project
5.1 Massive Stars . . . . . . . . . . . . . . . . . . . .
5.2 Connections to Massive-Star Gamma-ray Sources
5.3 Impact on current and future NASA missions . .
5.4 Education and Training Impact . . . . . . . . . .
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1
Introduction
Massive stars are the powerhouses of the Milky Way. Even before exploding as violent supernovae
that seed the galaxy with heavy elements and help trigger new generations of star formation, their
high luminosity lights up and ionizes the nearby interstellar medium, and drives strong, high-speed
stellar wind mass outflows. Massive stars are also prominent stellar sources of X-rays, as detected in
both targeted and survey observations by orbiting X-ray telescopes (e.g. Chandra, XMM/Newton,
RXTE); and they are linked to a growing subset of galactic gamma-ray sources detected by both
ground-based Cerenkov telescopes (e.g. HESS, Veritas, Magic) and orbiting gamma-ray missions
(e.g. Fermi). Collectively such massive-star systems provide important laboratories for the fundamental process generating high-energy radiation. The overarching goal of the project proposed here
is to develop a sound theoretical framework for interpreting both surveys and targeted observations
of such high-energy emission from massive stars.
X-rays represent key probes of the dynamics of massive-star mass loss, and their penetration
through many magnitudes of visible interstellar extinction makes them effective beacons of massive
stars in distant reaches of the Galaxy, and in young, active star-forming regions. Given also the
much greater prominence of X-ray sources, and thus much greater extent of existing X-ray datasets,
our focus in the present project will be on X-ray models, leaving thus to a longer term goal further
extensions and connections to massive-star gamma-ray mechanisms (§5.2).
The PI and research team have broad and extensive experience in both theoretical modeling
and observational analyses of three principal types of massive star X-ray sources, namely: 1)
Embedded Wind Shocks (EWS) arising from intrinsic instabilities in the radiatively driven wind
(see §2.1); 2) Magnetically Confined Wind Shock (MCWS) in magnetic massive stars (§2.2); 3)
Colliding Wind Binary (CWB) shocks in systems of two massive stars (e.g. O+O or O+WR; §2.3).
While there are important distinctions for each type, they all share a commonality that the Xray emission arises from circumstellar shock interaction of material originating from the massive
star’s radiatively driven wind. The project proposed here would exploit and build on our group’s
broad expertise and infrastructure of theoretical codes for radiation hydrodynamics of massivestar winds, and analysis tools for massive-star X-rays. Taking full advantage of the commonalities
in treatment of radiative driving, hydrodynamics, shock acceleration and heating, and radiation
transport, it will derive radiation hydrodynamical models for the key observational signatures like
energy distribution, emission spectrum and variability, and apply these to interpreting both surveys
(e.g. the recent Chandra mapping of Carina) and targeted observations of galactic X-ray sources
associated with each of the above specific model types.
As detailed in §3, key issues for each type are: 1) Effect of clumping and porosity on the X-ray
emission and absorption central to inference of wind mass loss rates; 2) 3-D form of wind magnetic
confinement and interaction in non-axisymmetric cases like tilted dipoles; 3) Role of radiative forces
in altering the wind-wind collision and resulting X-ray emission. The promises of new clumpinginsensitive diagnostics of mass loss rates, and the connection to magnetic fields and binarity, all
have broad relevance for understanding the origin, evolution, and fate of massive stars (§5.1).
While the scope entailed in addressing three distinct X-ray source types is admittedly ambitious,
we believe our research team is uniquely qualified to tackle this challenge. As noted in the personnel
and work plan sections (§4.2-4.3), while team members are now spread over many institutions, many
have close connection – as students, post-docs, and visitors – to the UDel massive-star research
group developed by PI Owocki over the past decade or so. The proposed project would preserve
and extend this record of mentoring to a new generation of undergraduates, Ph.D. students, and
post-doctoral researchers (§5.4), and so support a continuing infrastructure for applying dynamical
models to analysis of the wealth of observational data from both current and future NASA high1
v(km/s)
time(hr)
ρ/ρ0
log(ρ)(g/cm3)
r(R*)
v(km/s)
time(hr)
log(ρ)(g/cm3)
Height (R*)
Figure 1: Left: Results of 1D Smooth-Source-Function (SSF) simulation of the line-deshadowing
instability. The line plots show the spatial variation of velocity (upper) and density (lower) at a
fixed, arbitrary time snapshot. The corresponding grey scales show both the time (vertical axis)
and height (horizontal axis) evolution. The dashed curve shows the corresponding smooth, steady
CAK model. Right: For 2DH+1DR SSF simulation, grayscale representation for the deviations
rendered as a time sequence of 2-D wedges of the simulation model azimuthal range ∆φ = 12o
stacked clockwise from the vertical in intervals of 4000 sec from the CAK initial condition.
energy missions (§5.3).
As a background to the specific research proposals described in §3, the following section (§2)
further describes the three target X-ray source types, with particular emphasis on our team’s
experience in modeling these. Later sections describe our personnel, work, and cost plan (§4), and
the broader relevance of the project to NASA’s goals, for science impact (§5.1-5.2), for current and
future NASA missions (§5.2), and for education and training (§5.4).
2
2.1
Background on Relevant Work by Investigators
Embedded Wind Shocks (EWS) in single OB stars
The driving of massive-star winds by line-scattering of the star’s continuum radiation is subject
to strong, intrinsic “Line-Deshadowing Instability” (Lucy 1970; Owocki & Rybicki 1984, 1985).
It is widely presumed that this instability is likely a root cause of the inferred extensive spatial
structure and X-ray emission of such winds. Dating back m re than two decades, PI Owocki
and his collaborators have led efforts to develop numerical radiation-hydrodynamics simulations of
the resulting nonlinear evolution of wind structure (Owocki, Castor & Rybicki 1988). A central
challenge has been that the instability is strongest at scales near and below the Sobolev length
(Owocki & Rybicki 1984), implying that simulations can’t use the local, Sobolev-based treatment
of line-driving that is the basis for the standard CAK (Castor, Abbott & Klein 1975) model for
steady-state winds. A key breakthrough was the development (Owocki 1991; Owocki & Puls 1996)
of the escape-probability-based “Smooth Source Function”(SSF) method that allows estimation of
both the direct and diffuse component of the line-force from a fixed set of profile-weighted column
depth integrals across the spatial grid. As illustrated in the left panels of figure 1, results of 1D SSF simulations (Owocki 1991; Owocki & Puls 1999) show the instability does indeed lead to
2
highly nonmonotonic velocity outflow that compresses the wind into extensive clumps, bounded
by embedded wind shocks (EWS) with velocity amplitudes (500-800 km/s), broadly consistent
with observed X-ray softness (∼ 0.5 keV) and luminosity scaling Lx ≈ 10−7 Lbol (Owocki & Cohen
1999). Modern observation of OB supergiants with the X-ray spectrographs on both Chandra and
XMM/Newton do show wind-broadened X-ray emission lines that seem generally consistent with
this EWS picture (Owocki & Cohen 2001; Kramer, Cohen & Owocki 2003; Leutenegger et al. 2007).
The extensive clumped structure has important implications for determination of the wind
mass loss rate. This is typically inferred from recombination emission diagnostics (e.g., Balmer
emission near the star, and/or radio emission from outer wind) that scale with density-square, and
so overestimate the mass loss rate in√a clumped wind, by a factor set by the inverse square-root
of the clump volume filling factor, 1/ fv . Radially extended 1-D SSF simulations by Runacres &
Owocki (2002, 2005) give fv ≈ 1/10, implying a potential factor 3 reduction in inferred mass loss
rate; but both the inner-wind onset and outer-wind dissipation of this clumping depend on details,
like the level of any base perturbation, or the outer region energy balance. These 1-D simulations
also do not model the lateral scale and 3-D nature of actual clumps.
Since bound-free (b-f) absorption of X-rays scales linearly with density, it can provide a mass
loss diagnostic that is insensitive to wind clumping. Specifically, the shape and asymmetry of X-ray
emission line profiles resolved in OB supergiants by grating spectra Chandra and XMM/Newton
depend sensitively on the b-f absorption of X-rays emitted from the receding wind of the back
hemisphere. Our fitting (Kramer et al. 2003; Cohen et al. 2009) of the observed profile shape and
asymmetry in several OB supergiants yields roughly the factor 3 reduction in mass loss implied by
instability simulations. However, if individual clumps become optically thick, the effective masking
of some material will reduce even the b-f absorption, thus making the wind “porous”. This can
by itself reduce the profile asymmetry and so moderate or eliminate the inferred reduction in mass
loss rate (Oskinova et al. 2004, 2007). Our analysis (Owocki and Cohen 2006) shows that for
porosity to be important, the clump-to-clump mean-free-path or “porosity length”, set by the scale
of clumps divided by their volume filling factor, must be comparable to the stellar radius. Given
that the Sobolev length scale of instabilities is only of order a percent of the stellar radius, this seems
unlikely. But further work is needed to constrain this porosity effect through direct application in
existing 1-D and future multi-D simulations of instability-generated structure.
Development of multi-D simulations of wind structure has so far been hindered by the need to
provide a suitably fast treatment of the inherently non-local radiation transport from line scattering
(Owocki 1992; Owocki & Puls 1996, 1999). There have been limited attempts to use a simple 3-ray
treatment to account for lateral forces and radiative transport along two oblique rays (Owocki 1999;
Dessart & Owocki 2005a), while other efforts have mimicked multi-D structure by assigning timerandomized 1D simulations to fixed conical patches of with an assumed lateral angular scale (Dessart
& Owocki 2002a,b), or used a “2DH+1DR” approach that accounts for full 2-D hydrodynamical
evolution, but limits the radiation transport to 1D along radial rays (Dessart & Owocki 2005b; see
right panel of fig. 1). Even these limited multi-D approximations have mainly been used to analyze
variability high S/N optical wind emission lines, with so far limited direct application to X-rays.
To build on the above semi-empirical results, there is a need now to carry out direct X-ray analyses using simulation models, for example to constrain porosity effects through direct application
in existing 1-D and future multi-D simulations of instability-generated structure.
2.2
Magnetically Confined Wind Shocks (MCWS) in magnetic massive stars
Massive stars lack the strong near-surface convection zones that power the magnetic dynamo in the
sun and other cool stars. Nonetheless, improvements in spectropolarmetric instruments have led
3
log(ρ) t=80 ksec
log(T) t=80 ksec
log(ρ) t=180 ksec
log(T) t=180 ksec
Figure 2: 2-D MHD simulation of the MCWS model for θ1 Ori C, showing the logarithmic density
ρ and temperature T in a meridional plane. Left: at a time 80 ksecs after the initial condition, the
magnetic field has channeled wind material into a compressed, hot disk at the magnetic equator.
Right: at a time 180 ksecs, the cooled equatorial material is falling back toward the star along field
lines, in a complex ‘snake’ pattern. The darkest areas of the temperature plots represent gas at
T ∼ 107 K, hot enough to produce relatively hard X-ray emission of a few keV.
Figure 3: Snapshots of (left to right) differential emission measure, and spatial distribution of
optical, soft, and X-ray emission in a 3-D Rigid-Field Hydrodynamics (RFHD) simulation of the
MCWS model for a titled dipole field.
to direct detection of strong (hundreds to thousands of Gauss), large-scale (often, but not always,
characterized by a tilted dipole) magnetic fields in significant subset (5-10%) of massive stars. The
current Magnetism in Massive Stars (MiMeS) project headed by G. Wade (with participation by PI
Owocki and several other members of the proposed team) aims to use the Espadons spectrograph
on CFHT to detect and characterize the fields at levels down below 100 G.
As first noted by Babel & Montmerle (1997), a likely key effect of such magnetic fields is
to channel the radiatively driven wind outflow from opposite footpoints of a closed loop into a
Magnetically Confined Wind Shock (MCWS) near the loop top. In contrast to the soft X-rays
produced by the wind instability, the directed collision between opposite streams at relative speeds
near twice the wind terminal speed (several times 1000 km/s) can produce a quite hard X-ray
spectrum (2-10 keV). This is indeed what is observed in the O7V star θ1 Ori C, which has an
inferred field of ca. 1200 G.
The first full, time-dependent MHD simulations of magnetic channeling in radiatively driven
winds were carried out by co-I ud-Doula, as part of his UDel Ph.D. thesis research under PI
4
Owocki’s supervision (ud-Doula 2003). These simulations employ fast, localized Sobolev treatment of line-driving that suppresses the small-scale instability to focus larger-scale structure. This
makes tractable a full 2-D (and eventually 3-D; see below) model of the wind interaction with an
axisymmetric, dipole field. An important general result is that the effect of the magnetic field on
the wind can be characterized by a single, dimensionless, wind magnetic confinement parameter,
η∗ , representing the overall ratio of magnetic energy to wind kinetic energy (ud-Doula & Owocki
2002). For η∗ ≪ 1, the wind outflow quickly overwhelms any surface field, pulling it open into a
purely radial form; but for η∗ ≪ 1, there is a region of magnetic dominance out to an Alfvén radius
1/4
RA ≈ R∗ /η∗ wherein the magnetic field does in fact channel the wind into MCWS.
1
For θ Ori C, the inferred field strength and stellar wind parameters give a confinement parameter η∗ ≈ 14, implying a substantial region of MCWS. Observations indicate both the observer and
the dipole field axis are tilted by roughly 45o to the rotation axis, implying the observer alternative
views both the magnetic equator and pole over the 15-day rotation cycle. Since this low rotation has
limited dynamical effect on the wind confinement, one can still use 2-D MHD simulations to model
the X-ray brightness and spectrum as observed from the different viewpoints over the rotational
phase. Working with team-collaborator M. Gagné to analyze ROSAT and Chandra observations
of θ1 Ori C, we found predictions of the MHD simulations to be in remarkably close agreement
with the level, hardness, and rotational phase timing of observed X-ray emission, as well as the
narrowness and nearly unshifted form of X-ray emission lines (Gagné et al. 2005).
For strong confinement with a more rapid rotation that is a fraction W = Vrot /Vorb of the
critical (orbital) rate, cooled material from a MCWS that lies above the Kepler co-rotation radius
RK = R∗ /W 2/3 can be centrifugally supported, while being held down by the loop tension, to form
a “Rigidly Rotating Magnetosphere” (RRM; Townsend & Owocki 2005). Application of this RRM
model to the strongly magnetic (B∗ ≈ 104 G!) B2pV star σ Ori E show the Doppler-shifted Balmer
recombination can reproduce very well the observed dynamic spectrum of Balmer emission vs.
phase and frequency. In cooperation with G. Wade and other member of the MiMeS consortium,
Owocki’s Ph.D. student M. Oksala is using MiMeS and other observations to map the field and
surface abundance patterns of this star.
The enormous magnetic confinement parameter of σ Ori E, η∗ ≈ 107 , makes the field too “stiff”
for direct MHD simulation. But simulations at strong, but more modest confinement η∗ ≈ 1000,
show that as wind material accumulates in the trapped magnetosphere, it causes the confining
field loops to stretch and eventually break and reconnect (ud-Doula, Owocki & Townsend 2008;
2009). The rapid heating associated with this centrifugally driven reconnection provides a potential
explanation for the hard X-ray flares observed from σ Ori E by Rosat and XMM/Newton (ud-Doula,
Townsend, & Owocki 2006). The magnetic torquing of the wind outflow augments its angular
momentum loss and the associated spindown of stellar rotation (ud-Doula, Owocki & Townsend
2009). For the underlying material channeled into MCWS, the resulting X-ray emission can be
conveniently modeled using a Rigid-Field-HydroDynamics (RFHD) approach (Townsend, Owocki
& ud-Doula 2007). Here the 1-D radiatively driven flow and shock collision along a large number
(typically 10,000) field lines are simulated separately (e.g., in separate nodes of a cluster), and then
“stitched” together to form a full 3-D model of the X-ray emitting magnetosphere (see figure 3).
Further work is needed to compare results of such RFHD models with those of full 3-D MHD
simulations that don’t assume a strictly rigid field, but allow for the complex feedback between
magnetic forces and wind inertia. Moreover, our MHD simulation parameter studies of how magnetosphere filling and breakout depend on magnetic confinement and rotation (ud-Doula, Owocki
& Townsend 2008; 2009) have so far assumed a simple isothermal wind outflow. Application to
the interpretation of X-ray surveys will thus require including a full energy balance, and studying
5
10
t = 48d
t = 202d
t = 1011d
10
x
-10
-5
0
x-z Axis Plane
5
-10
Figure 4: Snapshots of 3-D SPH simulation of wind-wind collision in η Car at times that, from left
to right, are -1, +48, +202, and +1,011 days from periastron. The color scale shows the density (on
a logarithmic scale with cgs units) in the x-y orbital plane (top) and in the x-z perpendicular plane
containing the orbital and major axes (bottom). The X marks at the head of the wind-interaction
front makes the position of the assumed X-ray source. See Okazaki et al. (2008) for further details.
how this varies with a parameter characterizing the importance of radiative cooling as a function
of wind density.
2.3
Colliding Wind Binary (CWB) systems
Massive stars often occur in binary systems, thus placing their winds in proximity for collision
along a broad interaction front. The direct collision at the head of this front can result in shock
velocities characterized by the full wind flow speed (several 1000 km/s), thus leading again to X-ray
emission that is much harder (1-10 keV) than found from EWS. Early simulations of such Colliding
Wind Binary (CWB) systems assumed a simple 2-D asymmetry that effectively fixes the orbital
motion (e.g. Stevens, Blondin, & Pollock 1992). But advances in computing power have recently
made possible the initial exploration of fully 3-D models that include orbital effects (Lemaster et
al. 2007; Pittard 2009).
Members of our proposed team have been an active part of developing such 3-D simulations
and applying them to modeling of observational datasets of CWB systems. Under PI Owocki’s
supervision, UDel Ph.D. student Chris Russel has used 3-D Smoothed Particle Hydrodynamics
simulations to model the RXTE lightcurve of η Carinae in terms of wind absorption of a pointsource of X-rays located at the head of the wind interaction front (Okazaki et al. 2008; see fig. 2.2);
the good fit to the X-ray minimum that occurs near periastron of the highly eccentric (ǫ ≈ 0.9,
5.5-year binary orbit) provides a tight constraint on the observer perspective, as well as other wind
and orbital parameters. Ph.D. research by another student in Owocki’s group, Tom Madura, aims
to use these and other 3-D simulations to model HST STIS slit spectra of η Carinae obtained at
various orbital phases (Madura et al. 2009).
6
log ρ (g cm-3)
x
x
x
-5
0
5
x-y Orbital Plane
t = -1d
Under supervision of J. Pittard at Leeds University, team post-doc candidate Ross Parkin is
currently completing Ph.D. thesis research aimed also at developing 3-D models of CWB systems
(Parkin & Pittard 2008), with initial application also centered on η Carinae (Parkin et al. 2009).
A key issue considered in the latter work is the potential role of radiative forces in modifying
the hydrodynamical collision, including both the “radiative inhibition” (Stevens & Pollock 1994),
by which radiation from each star weakens the initiation of the wind from its companion, and
“radiative braking”, by which the radiation from the weaker-wind star slows or stops the incoming
stronger wind from its companion (Gayley, Owocki, & Cranmer 1997). Analyses of the former
effect have so far assumed a simple illumination model, but our subsequent studies (Owocki 2007)
suggest that reflection from the stellar photosphere can effectively cancel the radial component of
the near-surface force from impinging radiation. The latter effect was first suggested by PI Owocki
(Owocki & Gayley 1995) in the context of the short-period (4.2 day) WR+O binary system V444
Cygni, wherein it was shown that the such braking could prevent shock collapse from the strong
WR wind onto the surface of the O-star, while also weakening the shock velocity and thus X-ray
emission. Such radiative braking effects are most pronounced in close binary systems with highly
asymmetric wind momenta, but our recent work (Tuthill et al. 2008) shows that they can even have
significant influence on the wind interaction in wide, eccentric binaries, especially near periastron.
The recent premature recovery of the X-ray minimum seen in the latest orbital cycle monitoring of
η Carinae by RXTE (M. Corcoran, pc) suggests that such more subtle effects, and not just simple
wind absorption, may be needed to explain the sharp, extended X-ray minimum. Analogous issues
hold for other CWB systems, e.g. WR 140.
3
Proposed Research
Building on this background, we now propose a coordinated theoretical effort to develop and extend
dynamical models for each of the three classes of wind-based X-ray emission from massive stars, as
detailed in the following three subsections.
3.1
Radiation-Hydrodynamical Simulation of X-ray Emission and Absorption
We propose a renewed effort to apply and extend radiation hydrodynamical simulations of wind
structure and shocks arising from the intrinsic instability of line-driving, to model the X-ray emission
and absorption, with a goal to predict and interpret X-ray observational characteristics like energy
distribution, emission line profiles, variability, and scaling of overall emission luminosity. Specific
questions to be addressed are:
• Structure Scale: What sets the spectrum of spatial scales of wind structure? How is it is
influenced by base perturbations from atmospheric pulsation or turbulence, by stellar rotation,
or by lateral coupling of diffuse radiation? In particular, under what circumstances can the
scale be large enough to lead to a substantial porosity in b-f absorption of X-rays?
• Clumping Factor: What sets the magnitude and spatial distribution of the wind clumping
factor? How is the onset affected by base perturbations, or by the details of treatment of
scattering line-drag? How does this affect Balmer emission used to infer mass loss? Likewise,
what controls the outer dissipation of wind structure, and what are the implications for radio
mass loss rates?
• Velocity Dispersion: What sets the magnitude and spatial variation of the wind velocity
dispersion that leads to both compressed clumps and X-ray emitting shocks? What sets the
7
phase relation between velocity and density fluctuations, and how does this influence the
X-ray brightness and hardness?
Our initial efforts will focus on direct application of existing 1-D and pseudo-multi-D SSF simulations, with relatively modest extensions, e.g. to include base perturbations, and better resolution
of radiative cooling of shock-heated gas. Using methods developed in our empirical models, we will
now solve X-ray radiation transport of emission and absorption directly within snapshots of these
dynamical simulations, and use this to derive observational signatures like emission line spectrum
and line profile shapes.
But dramatic advances in parallel computing capacity now make feasible multi-D treatments of
nonlocal radiation transport within a time-dependent hydrodynamical simulation. Taking advantage of this, we plan over the full term of the project to develop 2-D and eventually 3-D versions of
these SSF simulations that take accurate account of the lateral line transport of scattered radiation
along along suitably fine set of rays. The goal is to study of how the associated lateral components
diffuse line-force couples wind structure. Unlike our previous 2DH+1DR approach that ignores
such diffuse lateral transport and so tends to develop lateral variations down to the grid scale, this
coupling could lead to a minimum lateral size, perhaps comparable to the ca. 1 degree scale inferred
by our empirical fits to optical emission line variations (Dessart & Owocki 2002a, 2005a). As noted
above, the results have broad implications for X-ray emission and transport, including the role of
porosity in reducing b-f absorption.
3.2
X-ray Signatures of 3-D MHD simulations of MCWS with Radiative Cooling
Our extension of MHD simulations of the MCWS from massive stars will include both a more
extensive study of the broad role of radiative cooling, and an extension of existing MHD simulations
to full 3-D geometry. Specific questions are:
• Cooling & X-ray Hardness: How do variations in wind mass loss rate, density, and thus
cooling length affect the strength of MCWS and thus X-ray hardness. In weaker winds the
back compression of post-shock gas can push the shock front back into the wind acceleration
region. What is the dynamical nature and stability of this balance for realistic treatments
of the wind driving? How does it depend on variations in parameters characterizing the
magnetic confinement and rotation? What are the predicted scalings in hardness and X-ray
luminosity relevant to targeted and survey observations of massive-star X-ray sources?
• Magnetic Reconnection and X-ray Flaring: How does the centrifugal mass ejection and reconnection of rotating magnetospheres scale with rotation and confinement parameters? What
sets the frequency, luminosity, and hardness of the resulting X-ray flares?
• 3-D Form of Magnetic Structure: How are the properties of MWCS affected by a fully 3-D vs.
2-D MHD simulation? Even in field-aligned rotation models with global 2-D axisymmetry,
what processes lead to azimuthal breakup, and at what scale? In tilted dipole, or nonaxisymmetric multipoles, what is the nature of MCWS, and how does it differ from what’s
inferred from our existing Rigid-Field HydroDynamics (RFHD) approach? Do streams from
open-field regions form the Co-rotating Interaction Regions (CIR: Mullan 1984; Cranmer
& Owocki 1995) inferred from UV line modulation? How do the X-rays from CIR shocks
compare with those from MCWS?
8
Implementation of radiative cooling will take advantage of the new exact integration scheme developed by Townsend (2009), which is faster and more accurate than previous algorithms.
The computational demands for 3-D MHD are such that practical use requires operation on
parallel clusters. Our previous 2-D simulations were based mostly on both scalar and MPI versions
of Zeus (viz. Zeus-2D, Zeus-3D, and Zeus-MP), operating in spherical polar coordinates. We have
recently begun tests of 3-D simulations with both Zeus-3D and Zeus-MP, but not yet carried out any
detailed studies. In parallel with our other projects, we have also carried out 3-D hydro simulations
( e.g. for CWB; see below) using the more-modern Athena MHD code (Stone et al. 2008). This
cross-fertilization of experimentation with various options for codes operating in HD or MHD mode
represents one example of the synergy of our multi-faceted research effort.
3.3
Radiative Driving Feedback on CWB Shocks & X-rays
Building on our existing work on 3-D hydrodynamical simulations of CWB, our further simulations
will incorporate a generalized CAK/Sobolev treatment of radiative driving from each of the two
companion stars. Instead of assuming a fixed outflow speed from the stellar surface, this will allow
taking proper account of the each wind’s outward radiative acceleration against gravity. It will also
allow study of the mutual effects of the radiation of the companion star on the other star’s wind,
including both the radiative inhibition (Stevens and Pollack 1994) and radiative braking (Gayley,
Owocki, & Cranmer 1997) effects. Specific questions are:
• Shock Reduction and Collapse: How does incorporation of wind acceleration alter the form
and strength of shock interaction front. What are the conditions for shock collapse in cases
where the ram balance brings the stronger wind past the point of maximum momentum flux
for the weaker wind? In an eccentric binary how does such collapse start and end as the stars
approach and recede on each side of the periastron? Could this provide an explanation for
the extended, and now variable, X-ray minimum observed from η Carinae by RXTE.
• Radiative Braking: How are the shock interaction, and indeed the nature and operation of
shock collapse, affected by braking of the stronger wind by the radiation of the weaker-wind
star? How does this depend on the assumptions about the line-opacity of the two winds? In
particular, can observational signatures of radiative braking in WR+O binaries be used to
constrain the effective opacity of WR winds?
• Radiative Inhibition: Similarly, how are these wind interactions affected by inhibition of the
initial acceleration of each wind by the radiation of its companion? How does each star’s photospheric reflection of the companion’s light alter the simple, pure-illumination formulation
used in the standard analysis of radiative inhibition? Would the expected cancellation of the
near-surface normal component of any external force (cf. Owocki 2007) effectively “inhibit”
any radiative inhibition? What are the implications for modeling X-ray lightcurves, especially
around X-ray minimum?
The basic methods and codes for implementing radiation forces in CWB simulation codes were
initially developed from our earlier analyses of radiative braking (Owocki & Gayley 1995; Gayley,
Owocki & Cranmer 1997). Post-doc Parkin, working with his Ph.D. thesis advisor J. Pittard,
have independently implemented radiative driving terms in their simulation codes. The initial
phase our project will thus focus on comparison and synthesizing the two approaches, along with
generalizations to include reflection. Implementation in our combined suite of 3-D codes (both SPH
and finite-difference based) should be straightforward.
9
4
Cost, Personnel, & Work Plan
4.1
Cost Plan
To accomplish the ambitious and multi-faceted research goals outlined in this proposal, this project
will leverage the broad and extensive research experience of the PI and team of co-I’s and collaborators toward guidance and training of a group younger members at the undergraduate, Ph.D.
student, and post-doctoral level. Salary, computer, and travel expenses for these junior members
forms the bulk of the proposed budget. Specifically, we request:
• Full-time, 3-year support for named post-doctoral researcher Ross Parkin, who is currently
completing his Ph.D. from Leeds University on modelling X-ray emission from colliding wind
binary systems.
• Full-time, 3-year support a new graduate student researcher, who will initiate Ph.D. thesis
research in one of the subtopics of the project. This would maintain continuity with PI
Owocki’s current group of (3) Ph.D. students, who are fully supported by other projects and
fellowships, and expected to complete their theses within the first half of the proposed project.
Such visibly successful progress of existing students provides a key advantage in attracting
and providing the initial training for new students to work in the high-energy processes central
to this project.
• Summer research by an undergraduate student from either UDel or nearby Swarthmore College, where co-I (and former UDel post-doc) D. Cohen is a faculty member. This will build on
the success both Owocki and Cohen have had in mentoring undergraduate research projects.
• Salary support for a one-month summer visit each year to UDel by former UDel student and
post-doc, and current project co-I, A. ud-Doula, who is now a faculty member at Morrisville
State College. In light of his heavy teaching demands during the academic year, this will enable active continuation of magnetic wind modelling begun during student and post-doctoral
collaborations with PI Owocki, with now more direct focus on the X-ray emission properties
central to this project.
• One month summer salary support for PI Owocki, in partial compensation for his year-round
efforts to lead, guide, and coordinate the overall project.
• In addition to travel support for the post-doc and/or students to present results at scientific
conferences, we also request modest travel support for team members to attend regular team
one- or two-day meetings to discuss and coordinate the various science efforts. Such regular
meetings have been a key to the success of our ongoing collaborations on massive stars and
their X-ray properties.
• $5K funds (with waived overhead) toward purchase of a workstation for post-doc Parkin,
to facilitate local analysis of simulations carried out on various local and remote clusters
and supercomputers, including time obtained through separate but affiliated applications at
NASA computing centers.
The remaining budget items include nominal allotments for materials and supplies, plus the
federally negotiated UDel rates for overhead and benefits.
10
4.2
Qualifications and Expected Contributions of Investigators
Although very ambitious, the project here builds quite directly on our prior research, combining
the varied experience and expertise of the proposed investigators. PI Owocki has worked for more
than 20 years on the physics of radiatively driven mass loss, with extensive experience in all 3 of
the targeted X-ray mechanisms; the basic methods used and codes developed in that work will form
the basis for the analysis and modelling efforts proposed here. He will lead, guide, and coordinate
the overall project.
Post-doctoral candidate Parkin is currently completing his Ph.D. thesis on CWB at U. Leeds.
His initial involvement will thus naturally focus on that mechanism, but he is also interested in the
other two areas, particularly development of multi-D sims of EWS.
Co-I ud-Doula’s work both as a graduate student and post-doc in Owocki’s group at UDel was
centered on MHD simulation of magnetic wind channeling, and so his efforts will focus on the
development of the MCWS models, catalyzed by month-long summer visits to UDel, as well as
in between academic year teaching as a tenure-track faculty at Morrisville College in upstate New
York.
Co-I Cohen was also a former post-doc in Owocki’s group at UDel, focused on applying Owocki’s
simulation results toward empirical analyses of intrinsic X-rays from single OB stars. Since joining
the faculty at nearby Swarthmore College, he and Owocki have maintained a very active collaboration, highlighted also by his remarkable success in supervising multiple undergraduate research
projects. Working with future students, Cohen plans to focus efforts on guiding the application of
instability simulations to interpretation of X-ray emission lines.
Collaborator Townsend was also a post-doc in Owocki’s group, working with him to develop the
RRM and RFHD models of magnetic massive stars. He is now a tenure-track faculty at University
of Wisconsin in Madison. His contributions will center on applying the RFHD sims toward X-ray
emission models, and working with ud-Doula to compare these with MHD simulations.
Collaborators Gagné and Corcoran both have broad experience with X-ray datasets, and have
worked extensively with PI Owocki on topics in this proposal, through frequent mutual visits
to/from their nearby home institutions (West Chester University and NASA/GSFC, respectively).
Gagné was undergrad advisor to Owocki’s current Ph.D. student Mary Oksala. Corcoran is currently NASA-center advisor on the GSRP fellowship funding another of Owocki’s UDel Ph.D.
students, Chris Russel, whose thesis also includes analysis CWB X-rays. Together they will provide an observation perspective to ensure that the theoretical results are well-positioned to augment
interpretation of both targeted and survey observation of massive stars, with particular emphasis
on analysis of the recent large Chandra survey of the Carina region (PI L. Townsley).
4.3
Work Plan
Within the caveat that the most fruitful research often comes about from following interesting new
avenues arising from intermediate results, we offer the following general outline of our time plan
for carrying out our proposed project:
• Year 1: Begin initial implementations in all 3 areas. For EWS, apply existing SSF simulations
to analyze porosity effects on X-ray emission lines; led by co-I Cohen, working with PI and
newly recruited undergrad and/or grad students. For MCWS, implement new cooling routine
and initiate parameter study, while also testing 3-D MHD options; led by co-I ud-Doula. For
CWB, merge Parkin and Owocki radiative driving approaches and implement reflection effect
modifications; led by PD Parkin.
11
• Year 2: Extend above and add emphasis on longer-term challenges. For EWS, develop
2-D SSF incorporating lateral diffuse force; led by PI Owocki, working with PD Parkin
and possibly new grad student. For MCWS, begin full operation of 3-D MHD, guided by
comparison to RFHD models; led by co-I ud-Doula, working with collaborator Townsend and
PI Owocki. For CWB, compute 3-D models and derive X-ray light curves, with emphasis on
radiative force effects in softening or quenching emission around periastron.
• Year 3: Full operation of 3 topics, but with added emphasis on forging theory advances
into suite of diagnostic signatures for application in separate analysis efforts for targeted and
survey observations; theory efforts as above, with heavy input from observational collaborators
Cohen, Gagné and Corcoran.
5
Broad Relevance of Proposed Project
5.1
Massive Stars
Massive stars are powerhouses of the galaxy, with broad influence on the mass and energy budget
of the interstellar medium, especially in young, star forming regions. In the context of the current
proposal, some particular items of broad relevance include:
• Mass Loss: This is a key to both the evolution of the star’s themselves, and the surrounding
circumstellar and interstellar medium. As such, there is vital need for accurate determinations
of mass loss rate that minimize or account for wind clumping, as provided by the b-f X-ray
absorption and associated simulation models proposed here. Our fundamental simulations
of massive-star wind driving moreover serve as a prototype for key dynamical processes in
other luminous systems, such as winds from luminous accretion disks around both stellar or
supermassive central objects.
• Magnetism in Massive Stars: As reflected in extensive survey programs like MiMeS, the
detection and study of magnetic fields in massive stars is an area of emerging prominence. It
challenges the classical notion that massive star atmospheres are idealized, radiative spheres.
The detection of strong, nearly constant, large-scales fields in the absence of a near-surface
convective dynamo represents a marked counterexample to the magnetic activity cycles seen in
the sun and other cool, low-mass stars. The magnetic torquing of the wind outflow augments
angular momentum loss and associated spindown of stellar rotation. Our study of wind
magnetic channeling and MCWS is thus a part of broader efforts to understand the nature,
origin, and consequences of such massive-star magnetic fields.
• Binarity: Massive stars occur commonly, even predominantly, in binary (or still higher multiple) systems, and this has important implications for understanding their formation and
evolution. CWB of type O+O and O+WR provide snapshots of an evolutionary stage before
the more massive star explodes as supernova, leaving behind a compact companion seen in
high-mass mass-transfer systems. In some key examples, e.g. η Carinae, the primary evidence
for presence of a high-mass secondary (which is still not clearly detected directly) is in fact
through the clock-like, periodic variation in X-ray emission. Our study of CWB X-rays is
part of a broader effort to understand the incidence, properties, and consequences of binarity
in massive stars, while the focus on radiative forces in such collisions provides a novel variant
on their role in stellar and disk wind driving.
• Shocks: Shocks are fundamental and pervasive by-products of interactions in hypersonic astrophysical flows. The 3 specific examples studied here provide a varied laboratory of conditions
12
and characteristics for determining the X-ray signatures of resulting shock properties. As
such, the results and analysis methods here share a broad relevance for studies of many other
types of astrophysical shocks.
• X-rays as Beacons: Moreover, the relative penetration of X-rays through many magnitudes of
visible interstellar extinction makes them effective beacons of massive stars in distant reaches
of the Galaxy, or in young, active star-forming regions. The proper identification of massive
stars in X-ray surveys, in particular determining the type of source, depends on predictions
from the associated theoretical models in this study.
5.2
Connections to Massive-Star Gamma-ray Sources
Of particular note for our project’s broader impact are potential connections with emerging detections of massive stars in gamma-rays ranging up to TeV energies. Massive stars represent a
growing subset of galactic TeV gamma-ray sources detected by ground-based Cerenkov telescopes
(e.g. HESS, Veritas, Magic), with a few of these now also detected at MeV-GeV energies by orbiting gamma-ray telescopes (Fermi, AGILE, Integral, Swift), and more anticipated with extended
monitoring. For example, the Be-Xray binary LS I +61 303 is a strong Fermi source, and may
have even been detected by the gamma-ray burst monitor on Swift (Dubus and Giebels 2008, ATel
#1715). Both Fermi and AGILE identify a source near η Carinae, with unconfirmed inference of
variability that might be associated with the orbital variations of the CWB (Tavini et al. 2009).
Particle acceleration in CWB shocks has been proposed as one mechanism for massive-star gamma
rays (Pittard & Dougherty 2006; Pittard 2009), but if the above association with η Car is confirmed,
it would represent the first CWB system actually detected in gamma-rays. For LS I +61 303, one
proposed model also invokes particle acceleration in the shock between the Be-star wind and a
relativistic pulsar wind from the compact companion.
PI Owocki has been working with collaborators (Romero et al. 2007) to compare predictions
of this pulsar-wind model to those of a competing “microquasar” model, in which gamma-rays are
produced by interactions of the stellar wind with relativistic protons in a jet from the compact
companion. A recent analysis (Owocki et al. 2009) shows how the “porosity” formalism developed
to study effect of wind clumps on X-rays can also be used to characterize the statistical fluctuations
in gamma-rays that would arise from jet propagation through a highly clumped wind. Together
with UDel Professor Jamie Holder, whose research is focused on analyzing TeV gamma-ray sources
detected by the Veritas Cerenkov telescope, Owocki is currently supervising summer research by
UD junior undergraduate Dan Hertenstein, supported through a summer fellowship from NASA’s
Delaware Space Grant College consortium; the initial plan is for Dan to focus on extensions to
the porosity analysis to include a power-law clump distribution, and also to work with Holder on
characterizing the variability in Veritas observations of massive-star TeV sources. Together with
our team’s background in CWB models, including post-doc Parkin’s affiliation with Ph.D. advisor
J. Pittard and his related development of CWB-shock acceleration mechanism for gamma-rays,
these projects a provide good basis for further links to high-energy processes.
Thus, while we elected not to make gamma-ray modeling an additional explicit focus for the
already quite multi-faceted effort proposed here, over the full project term and beyond we do plan
to actively pursue such emerging connections and applications of our X-ray models to interpretation
of gamma-rays from massive stars.
13
5.3
Impact on current and future NASA missions
Our project will have a significant aspect in the interpretation of data from nearly all important
NASA missions, highlighted as follows:
• Chandra and XMM imaging data. The theoretical developments we propose here have
particular significance for interpretation of X-ray emission (luminosities and spectra) from
large surveys carried out by Chandra and XMM/Newton, especially in important regions of
massive star formation in the Milky Way and other nearby galaxies (the LMC, SMC and
M31 in particular). A prime example of this is the Chandra Very Large Carina survey
project that is currently underway. This project provides the first survey of the Carina
Nebula star forming region, home to many of the most massive stars known and probable
home to the next Galactic hypernova. This survey has resulted in the detection of more
than 14,000 stellar sources, including hundreds of known OB stars. The massive star X-ray
data will provide the first census of X-ray emission from unevolved massive OB stars along
with emission from massive evolved WR stars. Our modeling work may help determine the
distribution of massive colliding wind binaries and magnetically active massive stars, which
has important implications on the binary fraction, stellar formation and the role of magnetic
fields in the evolution of these stars. Theoretical understanding of the importance of radiative
braking, emission from wind-wind collisions, and magnetically-confined winds are all crucial to
understanding the survey data and to determining how X-rays from massive stars help shape
the circumstellar environment both dynamically and radiatively. Collaborators Corcoran and
Gagné are leading the analysis of the X-ray emission from massive stars and Owocki, Cohen,
and Parkin are invited collaborators in the data analysis and modeling of the survey data.
• Dynamics from X-ray Line Profiles. The best diagnostic of the dynamics of the strong
flows associated with OB and WR single and binary stars are the profiles of strong, resolved X-ray emission lines. Such profiles constrain the flow geometry, and (for the He-like
lines) provide important information about densities, temperatures, and the local ionizing
radiation. A handful of bright, important massive stars have already been observed at high
resolution by the gratings on Chandra and XMM/Newton. Upcoming observations with the
X-ray calorimeters on ASTRO-H and the International X-ray Observatory (IXO) will greatly
increase the number of massive stars that can be observed at high spectral resolution. Realistic, 3-D models of the wind outflows of the kind we can provide are needed in order to tease
out the flow geometry and mass and radiation densities from the line profiles.
• X-ray Variability. Variability is most common in CWBs and magnetically confined wind
systems due to orbital or rotational motion. Variability can be modelled using data from
RXTE, ROSAT, ASCA, XMM/Newton, Chandra, Suzaku, Swift and upcoming missions like
ASTRO-H and IXO. Understanding the physical mechanisms producing the variability requires detailed 3-D models including subtle effects like radiative braking that is a focus of our
theory study.
• Spatially-resolved Spectra of Circumstellar Nebulosity. HST/STIS observations of
circumstellar nebulosity around η Car provide a unique, 3-D view of the variable emission
produced by the central binary star. There is currently active application of our CWB
simulations of η Car to the Treasury Project data on HST, centered on UDel Ph.D. student
T. Madura’s thesis project to model the slit spectra accounting for the time-variable wind
interaction fronts.
14
5.4
Education and Training Impact
A prominent feature of both past and planned research in our group is the heavy emphasis on
education and training of both undergraduate and graduate students, as well as post-doctoral
researchers. As noted, Cohen, Townsend, and ud-Doula were all post-docs at UDel (ud-Doula
also being a grad student there) who have since moved to tenure or tenure-track faculty positions.
Owocki is currently supervising 3 Ph.D. students (Tom Madura, Chris Russel, and Mary Oksala),
all of whom have existing fellowship or other support lines, and all of whose theses are thematically
related to this proposal. In addition to above-noted co-advising of the summer undergraduate
research by Dan Hertenstein on gamma-rays (§5.2), Owocki is also jointly supervising with UDel
Professor Mike Shay a second undergraduate summer student, Chris Bard, in this case to use Shay’s
reconnection codes to study simplified representations centrifugally driven reconnection found in
our group’s MHD sims (§2.2).
Since joining the faculty at nearby Swarthmore College in fall of 2000, co-I Cohen has been even
more active and successful in mentoring undergraduate students and supervising multiple student
research projects, as evidenced by the impressive list of 9 refereed journal papers co-authored with
students over the past 6 years. His Vita gives further details.
Continuing this extensive record of undergraduate, graduate, and post-doctoral research training
is a major focus of this proposal. We propose to support one undergrad summer research project
per year, recruited either from UD or Swarthmore, to work on development of theoretical models
into observational diagnostics. We also propose full-time support for a new graduate student to
begin thesis research in one of the 3 focused model areas. Finally, a major focus is on the initial
post-doctoral development of Ross Parkin, to follow his expected completion of thesis research on
CWB at Leeds. Such ongoing training helps fulfill and sustain a central need for qualified young
researchers to analyze and interpret the wealth of existing and future data from a range of NASA
missions.
15
References
Babel, J., & Montmerle, T. 1997, ApJL, 485, L29
Castor, J. I., Abbott, D. C., & Klein, R. I. 1975, ApJ, 195, 157
Cohen, D., Leutenegger, M., Wollman, E., Zsargo, J., Hillier, D.J., Townsend, R., & Owocki, S.
2009, MNRAS, submitted
Cranmer, S. R., & Owocki, S. P. 1995, ApJ, 440, 308
Dessart, L., & Owocki, S. P. 2002a. A&A, 383, 1113.
Dessart, L., & Owocki, S. P. 2002b. A&A, 393, 991.
Dessart, L., & Owocki, S. P. 2005a, A&A, 432, 281
Dessart, L., & Owocki, S. P. 2005b, A&A, 437, 657
Gagné, M., Oksala, M. E., Cohen, D. H., Tonnesen, S. K., ud-Doula, A., Owocki, S. P., Townsend,
R. H. D., & MacFarlane, J. J. 2005, ApJ, 628, 986
Gayley, K. G., Owocki, S. P., & Cranmer, S. R. 1997, ApJ, 475, 786
Gull, T., Nielsen, K., Corcoran, M, Madura, T., Owocki, S., Russel, C., Hillier, D.J., Hamaguchi,
K., Kober, G., Weis, K., Stahl, O., & Okazaki, A.T. 2009, MNRAS, in press.
Kramer, R. H., Cohen, D. H., & Owocki, S. P. 2003, ApJ, 592, 532
Lemaster, M. N., Stone, J. M., & Gardiner, T. A. 2007, ApJ, 662, 582
Leutenegger, M. A., Owocki, S. P., Kahn, S. M., & Paerels, F. B. S. 2007, ApJ, 659, 642
Lucy, L. B., & Solomon, P. M. 1970, ApJ, 159, 879
Madura, T., Gull, T., Owocki, S., Okazaki, A., & Russell, C. 2009, Bulletin of the American
Astronomical Society, 41, 205
Mullan, D. J. 1984, ApJ, 283, 303
Okazaki, A. T., Owocki, S. P., Russell, C. M. P., & Corcoran, M. F. 2008, MNRAS, 388, L39
Oskinova, L. M., Feldmeier, A., & Hamann, W.-R. 2004, A&A, 422, 675
Oskinova, L. M., Hamann, W.-R., & Feldmeier, A. 2007, A&A, 476, 1331
Owocki, S. P., & Rybicki, G. B. 1984, ApJ, 284, 337
Owocki, S. P., & Rybicki, G. B. 1985, ApJ, 299, 265
Owocki, S. P., Castor, J. I., & Rybicki, G. B. 1988, ApJ, 335, 914
Owocki, S. P. 1991, NATO ASIC Proc. 341: Stellar Atmospheres - Beyond Classical Models, 235
Owocki, S. P. 1992, Nonisotropic and Variable Outflows from Stars, 22, 273
Owocki, S. P., & Gayley, K. G. 1995, ApJL, 454, L145
Owocki, S. P., & Puls, J. 1996, ApJ, 462, 894
Owocki, S. P. 1999, IAU Colloq. 169: Variable and Non-spherical Stellar Winds in Luminous Hot
Stars, 523, 294
Owocki, S. P., & Puls, J. 1999, ApJ, 510, 355
Owocki, S. P., & Cohen, D. H. 1999, ApJ, 520, 833
Owocki, S. P., & Cohen, D. H. 2001, ApJ, 559, 1108
Owocki, S. P., & Cohen, D. H. 2006, ApJ, 648, 565
Owocki, S. 2007, Massive Stars in Interactive Binaries, 367, 233
Owocki, S. P., Romero, G. E., Townsend, R. H. D., & Araudo, A. T. 2009, ApJ, 696, 690
Parkin, E. R., & Pittard, J. M. 2008, MNRAS, 388, 1047
Parkin, E. R., Pittard, J. M., Corcoran, M. F., Hamaguchi, K., & Stevens, I. R. 2009, MNRAS,
394, 1758
Pittard, J. M., & Dougherty, S. M. 2006, MNRAS, 372, 801
Pittard, J. M. 2009, arXiv:0904.0164
Pittard, J. M. 2009, arXiv:0905.3315
Romero, G. E., Okazaki, A. T., Orellana, M., & Owocki, S. P. 2007, A&A, 474, 15
1
Runacres, M. C., & Owocki, S. P. 2002, A&A, 381, 1015
Runacres, M. C., & Owocki, S. P. 2005, A&A, 429, 323
Stevens, I. R., Blondin, J. M., & Pollock, A. M. T. 1992, ApJ, 386, 265
Stevens, I. R., & Pollock, A. M. T. 1994, MNRAS, 269, 226
Stone, J. M., Gardiner, T. A., Teuben, P., Hawley, J. F., & Simon, J. B. 2008, ApJS, 178, 137
Tavani, M., et al. 2009, arXiv:0904.2736
Townsend, R. H. D., & Owocki, S. P. 2005, MNRAS, 357, 251
Townsend, R. H. D., Owocki, S. P., & Ud-Doula, A. 2007, MNRAS, 382, 139
Townsend, R. H. D. 2009, ApJS, 181, 391
Tuthill, P. G., Monnier, J. D., Lawrance, N., Danchi, W. C., Owocki, S. P., & Gayley, K. G. 2008,
ApJ, 675, 698
ud-Doula, A., & Owocki, S. P. 2002, ApJ, 576, 413
Ud-Doula, A. 2003, Ph.D. Thesis
ud-Doula, A., Townsend, R. H. D., & Owocki, S. P. 2006, ApJL, 640, L191
Ud-Doula, A., Owocki, S. P., & Townsend, R. H. D. 2008, MNRAS, 385, 97
Ud-Doula, A., Owocki, S. P., & Townsend, R. H. D. 2009, MNRAS, 392, 1022
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