Measuring the shock-heating rate in the winds of O stars using X-ray line spectra

Abstract

We present a new method for using measured X-ray emission line fluxes from O stars to determine the shock-heating rate due to instabilities in their radiation-driven winds. The high densities of these winds means that their embedded shocks quickly cool by local radiative emission, while cooling by expansion should be negligible. Ignoring for simplicity any non-radiative mixing or conductive cooling, the method presented here exploits the idea that the cooling post-shock plasma systematically passes through the temperature characteristic of distinct emission lines in the X-ray spectrum. In this way, the observed flux distribution among these X-ray lines can be used to construct the cumulative probability distribution of shock strengths that a typical wind parcel encounters as it advects through the wind. We apply this new method to Chandra grating spectra from five O stars with X-ray emission indicative of embedded wind shocks in effectively single massive stars. The results for all the stars are quite similar: the average wind mass element passes through roughly one shock that heats it to at least 10 6 K as it advects through the wind, and the cumulative distribution of shock strengths is a strongly decreasing function of temperature, consistent with a negative power-law of index n ≈ 3, implying a marginal distribution of shock strengths that scales as T −4 , and with hints of an even steeper decline or cut-off above 10 7 K.

An ‘analytic dynamical magnetosphere’ formalism for X-ray and optical emission from slowly rotating magnetic massive stars

“…The bound-free X-ray opacity in the wind and cool magnetospheric plasma is expected to more or less monotonically increase with wavelength through most of the X-ray bandpass, as shown in, e.g., figure 2 of Cohen et al (2014). This is because for each ion that contributes to the bound-free opacity, the opacity is strongest closest to the threshold set by the ionization potential and decreases strongly toward higher energies.…”

“…The biggest uncertainty and potential cause of star-to-star variation in the Xray opacity is likely due to helium, which may be singly ionized in some cases -and would thus contribute significant opacity at longer wavelengths -and may be fully ionized -and thus contribute no bound-free opacity -in other cases. The size of this helium ionization effect can be seen in figure 3 of Cohen et al (2014). Note that the wind opacity at a fiducial photon energy of 1 keV (12Å) corresponds to a cross section per hydrogen atom of roughly 10 −22 cm 2 .…”

“…Moreover, for embedded wind shocks arising from the line deshadowing instability of radiative driving, Cohen et al (2014) has recently presented an analysis of X-ray line emission that infers a power-law form for the cumulative distribution p(Ts) for the mass fraction undergoing a shock with temperature Ts.…”

Chandra X-ray observation of the young stellar cluster NGC 3293 in the Carina Nebula Complex

“…It is well established that most of the hottest B-type stars (spectral types B0 to ≈ B2) are rather strong X-ray sources; their X-ray emission is thought to be related to their strong stellar winds, similar to the case of O-type stars (e.g., Zhekov & Palla 2007;Cohen et al 2014). Most B-type stars with spectral types later than ≈ B2 remain undetected in X-ray observations; this is in good agreement with the theoretical expectations, since these stars only have relatively weak winds that are incapable of producing strong X-ray emission, and at the same time the B-type stars (and also the A-type stars) have no outer convection zones, and thus no magnetic dynamo action is expected, which is the prerequisite for the X-ray emission due to coronal magnetic activity (as in the late-type stars).…”

The magnetic field ofζ Orionis A

“…We then recalculated η * but this time using the mass-loss rate ofṀ = 3.4 × 10 −7 M yr −1 and V ∞ = 1850 km s −1 determined by Cohen et al (2014). This gives η * = 4.2.…”