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Analysis of Doppler-Broadened X-ray Emission Line Profiles from Hot Stars
David Cohen - Swarthmore College
with
Roban Kramer - Swarthmore College
Stanley Owocki - Bartol Research Institute
Outline
0. The astrophysical context
I. Introduction: What line profiles can tell us
II. The basic model
III. Fitting Chandra data from hot stars - Pup: Constraining parameters
IV. What the data are telling us: Integration with other X-ray spectral diagnostics
What produces hot-star X-rays?
Hot stars have massive radiation-driven winds, with a significant amount of continuum opacity
Hot stars are thought not to have convective envelopes, magnetic activity, or coronae
What Line Profiles Can Tell Us
The wavelength of an emitted photon is proportional to the line-of-sight velocity:
Line shape maps emission measure at each velocity/wavelength interval
Continuum absorption by the cold stellar wind affects the line shape
Correlation between line-of-sight velocity and absorption optical depth will cause asymmetries in emission lines
X-ray line profiles can provide the most direct observational constraints on the X-ray production mechanism in hot stars
Emission Profiles from a Spherically Symmetric, Expanding Medium
A uniform shell gives a rectangular
profile.
A spherically-symmetric, X-ray emitting wind can be built up from a series of
concentric shells.
Occultation by the star removes red photons,
making the profile asymmetric
Continuum Absorption Acts Like Occultation
Red photons are preferentially absorbed, making the line asymmetric: The peak is shifted to the blue, and the red wing
becomes much less steep.
We calculate line profiles using a 4-parameter model
3 parameters describe the spatial and velocity distribution of the emission:
Ro is the minimum radius of X-ray emission;
describes the acceleration of the wind;
q parameterizes the radial dependence of the filling factor.
1 parameter,*, describes the level of continuum absorption in the overlying wind.
A wind terminal velocity is assumed based on UV observations, and the calculated line profile is convolved with the appropriate instrument-response function for each line.
In addition to the wind-shock model,
our empirical line profile model can also describe a corona
With most of the emission concentrated near the photosphere and with very little acceleration, the coronal line profiles are very narrow.
Line profiles change in characteristic ways with * and Ro, becoming broader and more skewed with increasing * and broader and more flat-topped with increasing Ro.
A wide variety of wind-shock characteristics can
be modeled
Ro=1.5
Ro=3
Ro=10
=1,2,8
We fit six lines in the Chandra MEG spectrum of Pup
N VIIO VIII
Fe XVII
Ne X
The X-ray lines in O stars are observed to be broad;
Pup is the prototypical O supergiant with a strong wind
For each line, we are able to achieve a good fit with reasonable model parameters
Best-fit model: =1.0, Ro=1.4, q=-0.4, with =1 fixed
blend
We also determine the extent of the confidence limits within the model parameter space – Note how the line profile changes with increasing wind opacity
inc reasin g
68%
95%
99%
inc reasin g
The fitted lines span a range of wind optical depth and X-ray temperature
The Fe XVII line at 15 Å (left) has a more typical profile, while the N VII (right) is more flat-topped and broad. And despite having a
longer wavelength, it doesn’t suffer a lot of attenuation.
The confidence regions define the widest possible variation among acceptable models
The best fit and two other acceptable (at the 95% confidence level) fits
best fit model
lowest highest
The best-fit parameters and 95% confidence limits are derived for all six lines
The formation radii for all lines are close to the surface of the star
Discussion
• A spherically symmetric, distributed wind X-ray source (i.e. ‘wind shock model’) can account for the line profiles in Pup in a reasonable way
• The X-ray formation zone begins close to the photosphere (within 3 R for all lines)
• Continuum absorption by the overlying cool wind is important, but not as strong as models (and UV observations of the wind) would seem to suggest ( is between 8 and 20 according to models calculated by Hillier et al. (1993)).
more Discussion…
• Above Ro, the amount of X-ray emitting gas scales close to density-squared (i.e. the filling factor has very little radial dependence)
• The lower-than-expected absorption could have to do with overestimation of the wind opacity, or possibly with overestimation of the mass-loss rate…but, it could also be due to clumping in the wind (which might also be associated with the wind-shock process itself)
• Other O stars observed with Chandra do not seem to have wind absorption signatures (broad but symmetric lines) and B stars have basically narrow lines – could this have to do with clumping too? Or non-spherical winds? (see Owocki’s poster on MHD simulations of magnetic hot star winds)
Rad-hydro simulations of the line-force instability – copius shock-heated material distributed throughout the wind
The Basic Model
L 8 2 d 1
1
r 2R
(, r)e , r dr
)/1()( * rRvrv
p, z
Rdz'
r'2 1 Rr' z
Rv
M
4
r' p2 z'2
(r ) ~ o 1 v c f (r) ~ r qfor r Ro
Described in Owocki & Cohen (2001, ApJ, 559, 1108), the model assumes a smoothly and spherically symmetrically distributed accelerating X-ray emitting plasma subject to continuum attenuation by the cold stellar wind.
The wind velocity is assumed to have the form:
which dictates the density of
the wind as well.
whereThe optical depth of the wind along a ray with impact parameter p is given by:
The delta function picks out the
resonance velocity, mapping into . q parameterizes the radial fall-off of the emissivity.
Ro parameterizes the lower radius of X-ray emission
Note that while spherical symmetry is natural for the emission, cylindrical symmetry is natural for the absorption; Combining expressions in these two sets of variables requires the transformation: