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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 - z 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 are thought not to have convective envelopes, magnetic activity, or coronae Hot stars have massive radiationdriven winds, with a significant amount of continuum opacity 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; b describes the acceleration of the wind; q parameterizes the radial dependence of the filling factor. 1 parameter, t*, 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. A wide variety of windshock characteristics can be modeled Line profiles change in characteristic ways with t* and Ro, becoming broader and more skewed with increasing t* and broader and more flat-topped with increasing Ro. t=1,2,8 Ro=1.5 Ro=3 Ro=10 The X-ray lines in O stars are observed to be broad; z Pup is the prototypical O supergiant with a strong wind Ne X Fe XVII O VIII N VII We fit six lines in the Chandra MEG spectrum of z Pup For each line, we are able to achieve a good fit with reasonable model parameters blend Best-fit model: t=1.0, Ro=1.4, q=-0.4, with b=1 fixed We also determine the extent of the confidence limits within the model parameter space – Note how the line profile changes with increasing wind opacity 68% 95% 99% 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 highest t best fit model lowest t The best fit and two other acceptable (at the 95% confidence level) fits 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 very little radial dependence of the X-ray filling factor Wind optical depth is only moderate, and only varies weakly with wavelength Discussion • A spherically symmetric, distributed wind X-ray source (i.e. ‘wind shock model’) can account for the line profiles in z 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 (t 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) Extra Slides Rad-hydro simulations of the lineforce instability – copius shockheated material distributed throughout the wind The Basic Model 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. L 8 1 1 d R r (, r)e 2 t , r dr v(r ) v (1 R* / r ) The wind velocity is assumed to have the form: The optical depth of the wind along a ray with impact parameter p is given by: 2 t p, z t z b R dz' b r' 2 1 R r' 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: (r) ~ o 1 v cf (r) ~ r q The delta function picks out the resonance velocity, mapping into . which dictates the density of the wind as well. where r' M t 4v R p 2 z' 2 for r Ro q parameterizes the radial fall-off of the emissivity. Ro parameterizes the lower radius of X-ray emission