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\title[X-ray Emission from O Stars] %% give here short title %%
{X-ray Emission from O Stars}

\author[David H. Cohen]   %% give here short author list %%
{David H. Cohen$^1$}

\affiliation{$^1$Swarthmore College, Department of Physics and Astronomy, 500 College Ave., Swarthmore, Pennsylvania 19081, USA}

\pubyear{2008}
\volume{250}  %% insert here IAU Symposium No.
% \pagerange{119--126}
% \date{?? and in revised form ??}
% \setcounter{page}{119}
\jname{Massive Stars as Cosmic Engines}
\editors{F. Bresolin, P.A. Crowther \& J. Puls, eds.}
\begin{document}

\maketitle

\begin{abstract}

  Young O stars are strong, hard, and variable X-ray sources,
  properties which strongly affect their circumstellar and galactic
  environments.  After $\approx 1$ Myr, these stars settle down to
  become steady sources of soft X-rays. I will use high-resolution
  X-ray spectroscopy and MHD modeling to show that young O stars like
  $\theta^1~{\rm Ori~C}$ are well explained by the magnetically
  channeled wind shock scenario.  After their magnetic fields
  dissipate, older O stars produce X-rays via shock heating in their
  unstable stellar winds.  Here too I will use X-ray spectroscopy and
  numerical modeling to confirm this scenario.  In addition to
  elucidating the nature and cause of the O star X-ray emission,
  modeling of the high-resolution X-ray spectra of O supergiants
  provides strong evidence that mass-loss rates of these O stars have
  been overestimated.

  \keywords{hydrodynamics, instabilities, line: profiles, magnetic
    fields, MHD, shock waves, stars: early type, stars: mass loss,
    stars: winds, outflows, x-rays: stars}
\end{abstract}


%\firstsection % if your document starts with a section,
              % remove some space above using this command.

%\section{Introduction}
%\section{Data comparison: high-resolution X-ray spectra}

O stars dominate the X-ray emission from young clusters, with X-ray
luminosities up to $L_{\rm x} = 10^{34}$ ergs s$^{-1}$ and emission
that is hard (typically several keV) and often variable.  This strong
X-ray emission has an effect on these O stars' environments, including
nearby sites of star formation and protoplanetary disks surrounding
nearby low-mass pre-main-sequence stars.  The X-ray emission is also
interesting in its own right, as it traces important high-energy
processes in the extended atmospheres of O stars. In this paper, I
will show how the spectral properties of the X-rays from the
prototypical young, magnetized O star, $\theta^1~{\rm Ori~C}$ are in
line with the predictions of the Magnetically Channeled Wind Shock
(MCWS) model, but how this process seems to dissipate as O stars age,
with weaker line-driven instability wind shocks explaining the X-ray
emission in older O stars.  I also will show how the X-ray emission
can be used as a probe of the conditions in the bulk stellar winds of
these objects.  Specifically, the resolved X-ray line profiles in
normal O supergiants provide an independent line of evidence for
reduced mass-loss rates.

Now, it is certainly the case that many young O stars do not show the
X-ray signatures of the MCWS mechanism.  And indeed, only a handful of
O and early B stars have had direct detections of magnetic fields.  Of
course, highly structured, non-dipole fields will be very difficult to
detect on hot stars, even if their local strength is quite high.  But
one should keep in mind that wind-wind interactions in close binaries
can also produce the hard, strong, and variable X-rays seen in many
young O stars.

Because $\theta^1~{\rm Ori~C}$ has a well established, predominantly
dipole field, and because many of its properties are explained by this
field, I treat it here as a potential prototype.  I also note that the
incidence of hard, strong X-ray emission from O stars diminishes
rapidly as one looks from young ($<1$ Myr) clusters to older (2 to 5
Myr) clusters.  This fact can be explained if the fossil fields in
young O stars dissipate as the stars age. If wind-wind binaries
account for many of these sources, then only the very earliest O stars
with very short lifetimes are involved.

%\section{Data comparison: high-resolution X-ray spectra}

We begin the comparison of young and old O stars and their X-rays by
showing in Fig.\ \ref{fig:spectra} the {\it Chandra} MEG spectra of
two representative stars: $\theta^1~{\rm Ori~C}$ (O4-7 V), with an age
of $\approx 1$ Myr, and $\zeta$ Pup (O4 If), with an age of several
Myr, and already evolved well off the main sequence. The $\zeta$ Pup
X-ray spectrum is typical of those measured for most O stars.

\begin{figure}[h]
\begin{center}
 \includegraphics[scale=0.15]{figs/spectra_v4converted.eps} 
 \caption{{\it Chandra} MEG spectra of $\theta^1~{\rm Ori~C}$ (top)
   and $\zeta$ Pup (bottom). The hydrogen-like Lyman alpha lines of Si
   and Mg are indicated in black, while the helium-like
   resonance-intercombination-forbidden complexes of the same elements
   are indicated in gray. }
   \label{fig:spectra}
\end{center}
\end{figure}

Two obvious differences between these spectra are the hardness of the
X-ray emission from $\theta^1~{\rm Ori~C}$ and the small line widths
in that star's spectrum.  The hardness implies a much higher plasma
temperature in the young O star, and this is best seen in the data
when one compares resonance lines of hydrogen-like and helium-like
ionization states of abundant elements.  In Fig.\ \ref{fig:spectra} I
have labeled these lines for silicon and magnesium.  In $\theta^1~{\rm
  Ori~C}$ the hydrogen-like lines are much stronger, whereas in
$\zeta$ Pup the helium-like lines are stronger.  This reflects a
significantly different ionization balance in these two stars which is
a direct effect of their different plasma temperatures.  The plasma
temperature distribution, based on the analysis of high-resolution
{\it Chandra} spectra of several O stars, has been determined by
Wojdowski \& Schulz (2005).  These authors assume a continuous
Differential Emission Measure (DEM), which can be thought of as a
density-squared weighting of the plasma temperature distribution.
Their results are shown in Fig.\ \ref{fig:dem}, where it can easily be
seen that the DEM for $\theta^1~{\rm Ori~C}$ is the only one (of seven
O stars) with a positive slope.  Its peak is near $T=30$ million K,
whereas the DEMs of the more evolved O stars (including $\zeta$ Pup)
all peak near one or two million K.

\begin{figure}[h]
\begin{center}
 \includegraphics[scale=0.23]{figs/wojdowski_schulz_2005_fig5_converted.eps} 
 \includegraphics[scale=0.30]{figs/f6mod_converted.eps} 
 \caption{Differential emission measures of seven O stars and two B
   stars, derived from thermal spectral model fits to {\it Chandra}
   spectra (left; taken from \cite[Wojdowski \& Schulz,
   2005]{ws2005}). $\theta^1~{\rm Ori~C}$ is the only star whose DEM
   has a positive slope. The panel on the right shows a DEM predicted
   by the MHD simulations of $\theta^1~{\rm Ori~C}$ (taken from
   \cite[Gagn\'{e} et al., 2005]{Gagne2005}). }
   \label{fig:dem}
\end{center}
\end{figure}

We also show in Fig.\ \ref{fig:dem} the DEM from a snapshot of an MHD
simulation of the magnetically confined wind of $\theta^1~{\rm
  Ori~C}$.  The agreement is quite good, both in terms of the overall
emission measure and the shape of the DEM.  The simulation shows a
peak at 15 to 20 million K, modestly lower than that seen in the data,
but the main property -- a rising DEM up to and beyond 10 million K --
matches the data well. These MHD simulations confirm the predictions
of \cite{bm1997} that strong shock fronts near the magnetic equator
where the wind from the northern and southern hemispheres meets can
heat a significant amount of wind plasma to the observed high
temperatures.  Snapshots of temperature and emission measure from an
MHD simulation are shown in Fig.\ \ref{fig:mhd}. It can be seen that
the bulk of the shock-heated plasma is in the magnetically confined
region near $r \approx 2~{\mathrm {R_{\ast}}}$.  Due to this
confinement, the speed and line-of-sight velocity of this material is
low, and thus the emission lines from the thermal X-ray emission are
relatively narrow.

\begin{figure}[h]
\begin{center}
 \includegraphics[scale=0.38,angle=0]{figs/f5b.eps} 
 \includegraphics[scale=0.38,angle=0]{figs/f5a.eps} 
% \includegraphics[scale=0.38,angle=0]{figs/f5b-color_converted.eps} 
% \includegraphics[scale=0.38,angle=0]{figs/f5a-color_converted.eps} 
 \caption{Contour plots of temperature (left) and emission measure per
   unit volume (right) from a 2-D MHD simulation of the magnetically
   confined wind of $\theta^1~{\rm Ori~C}$ (taken from \cite[Gagn\'{e}
   et al., 2005]{Gagne2005}).  Magnetic field lines are displayed as
   contours.  The wind flow up each closed field line encounters a
   strong shock due to the ram pressure of the wind flow from the
   opposite hemisphere, which heats the plasma according to
   $T_{\mathrm {shock}} \approx 10^7(v_{\mathrm {shock}}/1000~{\mathrm
     {km~ s^{-1}}})^2$ K. The head-on nature of the wind shocks leads
   to high shock velocities and temperatures.  In these MHD models,
   the field configuration is self-consistently solved for along with
   the wind dynamics. Note that another difference between the MHD
   simulations of the MCWS model and the initial analysis of
   \cite[Babel \& Montmerle (1997)]{bm1997} is the dynamical infall of
   material from the magnetic equator. Evidence of this can be seen in
   the snake-like structure visible in the emission measure panel,
   just above the star's surface, slightly below the equator. }
   \label{fig:mhd}
\end{center}
\end{figure}

In contrast, the X-ray emission lines of mature O stars, like $\zeta$
Pup, are quite broad, as can be seen in Fig.\ \ref{fig:line_profiles},
where I show the neon Ly$\alpha$ lines for the two stars. The X-ray
spectrum of $\zeta$ Pup is also soft, as I have already shown. The
X-ray emission from these older, presumably non-magnetized, O stars is
thought to arise in much milder wind shocks, embedded in the
outflowing, highly supersonic line-driven winds.  The Line-Driven
Instability (LDI) is generally thought to produce these shocks,
although models have difficulty reproducing the overall level of X-ray
emission unless the instability is seeded, perhaps by sound waves
injected at the base of the wind (\cite[Feldmeier et al.,
1997]{fpp1997}).  The softness of the X-ray spectra, along with the
large line widths from the high velocity of the shock-heated wind, is
well explained by this LDI wind-shock scenario, as I show in Fig.\
\ref{fig:vh1}. This figure shows a snapshot from a 1-D radiation
hydrodynamics simulation of the wind of an O supergiant like $\zeta$
Pup, accounting for non-local line radiation transport.  The
instability grows rapidly beyond about half a stellar radius (in
height; $r=1.5~{\mathrm {R_{\ast}}}$).  Shock fronts can be seen in
this snapshot, but they typically have velocities of only a few
hundred km s$^{-1}$, leading to heating of only a few million K.  The
soft spectra seen in Fig.\ \ref{fig:spectra} and the DEMs weighted to
low plasma temperatures, shown in the left-hand panel of Fig.\
\ref{fig:dem}, are in line with the results of this simulation.

\begin{figure}[h]
\begin{center}
 \includegraphics[scale=0.27,angle=90]{figs/toriC_NeX.ps} 
 \includegraphics[scale=0.27,angle=90]{figs/zpup_NeX.ps} 
 \caption{Ne X Lyman-alpha lines in the {\it Chandra} MEG spectra of
   $\theta^1~{\rm Ori~C}$ (left) and $\zeta$ Pup (right). The vertical
   dashed line represents the laboratory rest wavelength of this
   transition, and the vertical dotted lines represent the blue and
   red shifts associated with the UV wind terminal velocity in each
   star.  Note that the profile in the $\zeta$ Pup spectrum is shifted
   and skewed as well as being broadened. Error bars are from Poisson
   photon-counting statistics. }
   \label{fig:line_profiles}
\end{center}
\end{figure}


\begin{figure}[h]
\begin{center}
 \includegraphics[scale=0.35,angle=0]{figs/velden_converted.eps} 
 \caption{A snapshot showing the velocity (increasing with
   height; left-hand axis) and density (decreasing with height;
   right-hand axis) as a function of height above the photosphere in a
   radiation hydrodynamics simulation of the wind of $\zeta$ Pup.
   Shock-heated plasma cools rapidly; the bulk of the wind in any
   given snapshot is cold. }
   \label{fig:vh1}
\end{center}
\end{figure}


The predictions of this model can be further tested by examining the
X-ray emission line profiles, which have a characteristic asymmetric,
skewed shape, as can be seen in the right-hand panel of Fig.\
\ref{fig:line_profiles}. This shape, with a deficit of red-shifted
photons, arises in a spherically expanding wind with hot,
line-emitting material intermixed with warm, continuum-absorbing
material, as motivated by the global structure seen in Fig.\
\ref{fig:vh1}.  If the wind is optically thick (in the continuum;
$\kappa \approx$ constant across a line), then there is significantly
more attenuation of emission from the back of the wind, which is the
red shifted portion.  And there is comparatively more emission from
the front, blue shifted, less attenuated, side.

I fit an empirical model (\cite[Owocki \& Cohen, 2001]{oc2001}) to
emission lines in the spectrum of $\zeta$ Pup and get good fits by
adjusting only three parameters: the normalization, the inner radius
below which there is assumed to be no emission ($R_{\rm o}$), and the
wind optical depth (parameterized by the quantity $\tau_{\rm \ast}
\equiv {\dot{M} \kappa} / {4 \pi R_{\rm \ast} v_{\rm \infty}}$). The
fit to the Fe\, {\sc xvii} line at 15.014 \AA\ is typical and is shown
in Fig.\ \ref{fig:2fits} as the dashed histogram. The fit is
formally good, and the best-fit values with joint 68\% parameter
confidence limits are $R_{\rm o} = 1.53^{+0.12}_{-0.15} ~{\rm
  R_{\ast}}$ and $\tau_{\rm \ast} = 2.0 \pm 0.4$.

\begin{figure}[h]
\begin{center}
 \includegraphics[scale=0.3,angle=90]{figs/zpup_fexvii_15014_kauai_2mods.ps} 
 \caption{Best-fit wind profile model, for a non-porous wind, (dashed
   histogram) fit to the Fe\, {\sc xvii} line in the {\it Chandra}
   spectrum of $\zeta$ Pup. The solid histogram is the best-fit
   non-porous model for which the optical depth parameter is fixed at
   the value implied by the literature mass-loss rate ($\tau_{\mathrm
     {\ast}}=8$). Fit residuals for the two models are shown in the
   lower panel, with the circles corresponding to the low optical
   depth model represented by the dashed histogram, and the squares
   corresponding to the higher optical depth model.}
   \label{fig:2fits}
\end{center}
\end{figure}

%\section{Evidence for a lowered mass-loss rate}

The $R_{\rm o}$ derived from the profile is consistent with the onset
of the self-excited instability seen in the hydrodynamics simulation
shown in Fig.\ \ref{fig:vh1}. The optical depth consistent with the
data is actually quite small, which can be seen qualitatively in the
relatively modest asymmetry.  The mass-loss rate of $6 \times 10^{-6}~
{\mathrm {M_{\odot}~yr^{-1}}}$ derived from H$\alpha$ emission
(\cite[Puls et al., 1996]{Puls1996}) implies $\tau_{\rm \ast} = 8$.
The best-fit model with that value fixed is shown in Fig.\
\ref{fig:2fits} as the solid histogram. The fit is formally very poor.
Thus it would appear that the X-ray line profiles provide independent
evidence that mass-loss rates of O stars must be revised downward by a
factor of several; a factor of 4 for this star, according to this
particular line ($\tau_{\mathrm {\ast}}=2.0 \pm 0.4$ vs.\
$\tau_{\mathrm {\ast}}=8$).

It has been suggested that porosity associated with large-scale
clumping -- rather than reduced mass-loss rates -- can account for the
surprisingly small degree of asymmetry in the observed X-ray emission
line profiles in O stars (\cite[Oskinova et al., 2006]{ofh2006}).  By
fitting the line profile model, modified for the effects of porosity
produced by spherical clumps (\cite[Owocki \& Cohen, 2006]{oc2006}), I
can quantify the trade-off between atomic opacity and porosity (see
also \cite[Cohen et al., 2008]{Cohen2008}).  In Fig.\
\ref{fig:2fits_porous} I show the best-fit porous model with
$\tau_{\rm \ast} = 8$, the value implied by the literature mass-loss
rate, and with the porosity length, $h \equiv \ell/f$, free to vary.
Here $\ell$ is the clump size and $f$ is the volume filling factor of
the clumps.  The porosity length, $h$, completely describes the
effects of porosity on line profiles and in the limit of small clumps
it is equivalent to the interclump spacing.  The best-fit porous model
with the literature mass-loss rate is nearly indistinguishable from
the best-fit non-porous model, although the fit quality is formally
not as good.  More importantly, it requires a terminal porosity length
(the value of $h$ in the outer portion of the wind) of at least
$h_{\mathrm {\infty}} = 2.5$ R$_{\rm \ast}$ (68\% confidence), as
shown in the right-hand panel of Fig.\ \ref{fig:2fits_porous}. Even
ignoring the worse quality of the porous model fits, the very high
values of the porosity length required to fit the data are vastly
larger than the porosity lengths seen in state-of-the-art 2-D
radiation hydrodynamics simulations, which show LDI-induced structure
down to the grid scale (\cite[Dessart \& Owocki,
2005]{do2005}).Therefore, I conclude that there is no compelling
evidence that porosity explains the modestly asymmetric X-ray
line profiles in $\zeta$ Pup. Rather, these profiles provide
independent evidence for a reduced mass-loss rate.


\begin{figure}[h]
\begin{center}
 \includegraphics[scale=0.315,angle=90]{figs/zpup_fexvii_15014_kauai_2porousmods.ps} 
 \includegraphics[scale=0.31,angle=0]{figs/potsdam_fig5_converted.eps} 
 \caption{Best-fit wind profile model, for a non-porous wind (dashed
   histogram), fit to the Fe\, {\sc xvii} line in the {\it Chandra}
   spectrum of $\zeta$ Pup (left). The solid histogram is the best-fit
   porous model for which the optical depth parameter is fixed at the
   value implied by the literature mass-loss rate ($\tau_{\rm \ast} =
   8$). We also show confidence limits (68, 90, 95\%) in $h_{\mathrm
     {\infty}} {\rm {vs.}}~\tau_{\mathrm {\ast}}$ parameter space
   (right). The global best-fit model is indicated by the star at
   $h_{\mathrm {\infty}} = 0, \tau_{\mathrm {\ast}} = 2$.  The star at
   $h_{\mathrm {\infty}} = 3.3, \tau_{\mathrm {\ast}} = 8$ represents
   the best-fit model with the wind optical depth fixed at the value
   implied by the literature mass-loss rate.  The horizontal bar
   centered on it represents the 68\% confidence limit on the value of
   $h_{\mathrm {\infty}}$, given $\tau_{\mathrm {\ast}} = 8$ ($2.5 <
   h_{\mathrm {\infty}}/{\mathrm R_{\ast}} < 4.0$).  The vertical line
   at $h_{\mathrm {\ast}} = 1$ emphasizes that even that large
   porosity length cannot bring the optical depth close to the value
   associated with the literature mass-loss rate. }
   \label{fig:2fits_porous}
\end{center}
\end{figure}

\noindent
I acknowledge support from NASA/CXC grant AR7-8002X and from the
Swarthmore College Provost's Hungerford fund.

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\end{thebibliography}


\end{document}

