X-ray Emission Line Profile Diagnostics of Hot Star Win by aku11392


									    X-ray Emission Line Profile
   Diagnostics of Hot Star Winds:
Constraints on Kinematics, Geometry, and Opacity

                              David H. Cohen
                               Dept. of Physics and
                               Swarthmore College

                           much of this work was performed by
                          Swarthmore seniors Roban Kramer and
                                  Stephanie Tonnesen
What are the x-rays we see?
What do the observations look like?
What trends emerge, and how can the properties of the individual stars and of
the trends among lines and among stars be explained by the physical effects we expect
might be present?

     z Pup: wind x-rays, but less absorption than expected
     z Ori and d Ori: similar situation, very little wind absorption; but wind-
     shock parameters are otherwise satisfactory
     Magnetic O stars and B stars are a different story: q1 Ori C, t Sco, b Cru
X-rays from normal stars are traditionally assumed to obey the
coronal approximation:
They’re thermal line emission from a low-density, optically thin, steady-state
plasma in which the ionization balance is governed by collisional ionization and
radiative and dielectronic recombination. Collisional excitation and spontaneous
emission are the only important atomic processes between bound states.

                                              The line emission we see is from
                                              spontaneous emission following
                                              collisional excitation from the
                                              ground state (the x-ray emission is a
                                              cooling process)
                                              Some recombination and free-free
                                              continuum emission can be present
The coronal approximation paradigm was inspired by the Sun and
solar-type cool stars
But, it’s assumed to also apply to hot stars
Potential difficulties include
   - Lines that may be optically thick to scattering
   - Non-equilibrium ionization (seen in the sun, locally-flares) may be a
   bigger issue in wind-shock sources, where the plasma is moving
   rapidly…recombination and cooling times are of order 103 to 104 seconds,
   as are flow times.
   - Excitation out of excited states can be important for metastable levels
   (e.g. forbidden lines in helium-like ions)
   - The X-ray radiation field can have important effects on the bulk cool
   wind component in hot stars
      In the coronal approximation, line strengths are a function
      almost exclusively of plasma temperature1,2 (density-dependence
      of collisional ionization and radiative recombination is the same, so density
      effects cancel out for the most part)

      We see,
      characteristically, the
      Lyman series and He-
      like lines of abundant
      elements: nitrogen
      through sulfur (Z=7 -
      14), and L-shell3 lines
      of iron (between 11 and
      17 Å)

1Elemental    abundance plays an important role too
2Emissivities   of individual lines are fairly strongly peaked in temperature, with characteristic widths of 0.3 dex.
3L-shell   refers to transitions to the n=2 level (so Li-like to Ne-like ground states)
In OB stars, we see basically the same lines1 but the resolved
shapes of these lines provide information about the plasma
kinematics and, via continuum absorption by the cold bulk wind2,
about the spatial distribution of the plasma.
                                                                                 24 Å        12 Å

The wavelength dependence of
individual lines leads to the expectation
that different absorption characteristics
will be seen in different lines from a
given star.

The temperature dependence of
individual lines can potentially provide
information about the kinematics and
location of different plasma temperature
                                                                                     O K-shell
components.                                                                           edges

1Significant   continuum emission will only be seen in plasma with temperatures above about 20 X 10 6 K
2Photoelectric   absorption due to K-shell (“inner-shell”) photoionization is the dominant proces
 Chandra and XMM, launched in 1999, are the first
 instruments to allow for the measurement of resolved x-ray
 emission lines*

       The resolution of the Chandra medium energy grating
       (MEG) is .023 Å FWHM: l/Dl ~1000 at 23 Å (300 km s-1)
       The effective area is only a few square centimeters

*The   EUVE spectrometers measured emission lines from the B2 II star e CMa.
               The Chandra Archive of Hot Stars
     Because of the pathetically small effective area of the gratings, only a handful
     of single OB stars can produce high-quality spectra -- we will look at those
     single OB stars* that are publicly available (or have been published).

            Star              Sp. Ty.                Mdot                Vinf            comments
    z Pup                O4                  2.5 (-6)             2500
    z Ori                O9.5 II             1(-6)                1860
    d Ori                O9.7 I              1(-6)                2000
    q1 Ori C             O7 V                4(-7)                2500                1100 G dipole
                                                                                      magnetic field

    t Sco                B0 V                3(-8)                1500                Unusually X-ray
                                                                                      bright and hard

    g Cas                B0.5 Ve             5(-8)                1800                Same, but more so

    b Cru                B0.5 IV             ~5(-9)               1200                Beta Cep var.

*HD206267,   i Ori, t Cma, other stars in the q1 Ori system, and several interacting binaries, h Carina, and WR
stars have been observed too, and there are a few more hot stars recently observed or proposed for observation
with the Chandra gratings (Cyg OB2 no.8). But the total number ofeffectively single OB stars for which
Chandra will produce high-quality grating spectra is probably less than a dozen.
 Global appearance of spectra (Chandra MEG)

             z Pup                            q1 Ori C
               (O4 I)                             (O7 V)

             z Ori                              t Sco
              (O9.5 II)                           (B0 V)

             d Ori                               b Cru
              (O9.7 I)                          (B0.5 IV)

10 Å       20 Å                10 Å            20 Å
   Focus in on a characteristic portion of the spectrum
    12Å                           15            12                           15Å
                                  Å             Å
                       z Pup                                      q1 Ori C
                       (O4 I)                                      (O7 V)

                         z Ori                                      t Sco
                      (O9.5 II)                                    (B0 V)

                         d Ori                                       b Cru
                      (O9.7 I)                                    (B0.5 IV)

   Ne X       Ne IX          Fe XVII           Ne X       Ne IX          Fe XVII

There is clearly a range of line profile morphologies from star to star
Differences in the line shapes become apparent when
      we look at a single line (here Ne X, Lya)

      z Pup                 q1 Ori C                   g Cas

       z Ori                 t Sco                AB Dor
                                                      (K1 IIIp)

       d Ori                 b Cru                    Capella
                                                        (G2 III)
                  Now let’s focus on individual lines
                 zPup: prototypical O supergiant wind
  We can look at the line profiles non-parametrically: are they blueshifted? asymmetric?

We calculate the first four moments of each line profile: the first
moment is proportional to the wavelength shift while the third
     moment, the skewness, is an indicator of asymmetry.
  Our idea: fit lines with the simplest model that can do the job, and
  use one that, while based in physics, is general in the sense that
  any number of physical models can be tested or constrained based
  on the model fits.
  From Owocki & Cohen (2001): spherically symmetric, two-fluid (hot plasma is
  interspersed in the cold, x-ray absorbing bulk wind); beta velocity law.

Visualizations of the wind use hue to indicate line-of-sight velocity and saturation to indicate emissivity;
corresponding profiles are plotted vs. scaled velocity where x = -1,1 correspond to the terminal velocity.
The model has four parameters:                            Ro=1.5
 b : v(r)  (1 R /r) b
 Ro,q : j   2 rq          for r>Ro
 t  : t ( p  0;z)  t   z

                                    2    1 b
                                   r' (1 )                Ro=3
     where t  
 The line profile is calculated from:

                   
                  1     
   Ll  8    2
                             jet r 2 drd                Ro=10
                 1    R

  Increasing Ro makes lines
  broader; increasing t*
  makes them more
  blueshifted and skewed.                      t=1,2,4
We fit all the (8) unblended strong lines in the Chandra
 spectrum of z Pup: all the fits are statistically good

         Ne X                   Fe XVII                    Fe XVII
       12.13 Å                  15.01 Å                    16.78 Å

       Fe XVII                    O VIII                     N VII
       17.05 Å                  18.97 Å                    24.78 Å
     We place uncertainties on the derived model parameters

                                  lowest t*      best t*    highest t*

Here we show the best-fit model to the O VIII line and two models
that are marginally (at the 95% limit) consistent with the data; they
   are the models with the highest and lowest t* values possible.
  To find the parameter uncertainties, we calculate models on a grid in parameter space.

Displayed grids are slices of constant t*, with the best fit line profile in each slice
                shown to the right. Note the parameter uo =1/Ro
Graphical depiction of the best     q
fit (black circles) and 95%
confidence limits (gray
triangles) on the three fitted
parameters for seven of the lines
in the z Pup spectrum.

Lines are well fit by our four parameter model (b is actually
held constant at b=1; so three free parameters): z Pup’s x-ray
lines are consistent with a spatially distributed, spherically
symmetric, radially accelerating wind scenario, with reasonable
   t*~1      :4 to 15 times less than predicted
But, the level of wind absorption is significantly below what’s
And, there’s no significant wavelength dependence of the optical
depth (or any parameters).
Ro of several tenths of a stellar radius is expected based on
numerical simulations of the line-force instability (self-excited on the
left; sound wave purturbations at the base of the wind on the right)
We do expect some                  Wind opacity for canonical B
wavelength dependence of the            star abundances.
cross sections (and thus of the
wind optical depth), BUT the
lines we fit cover only a                             N K-edge
modest range of wavelengths.
And in the case of z Pup,
nitrogen overabundance (not
in calculation shown at right)
could flatten out the
wavelength dependence even
OR perhaps clumping plays a
role. And clumping certainly
could play a role in the overall
reduction of wind optical
                                    Note: dotted line is interstellar.
Do the other O supergiants, z Ori and d Ori, fit into the
                wind-shock paradigm?

                                     The Ne X line in z Ori (left) is
                                     skewed and blueshifted (>1s),
                                     though not as much as the same
                                     line in z Pup (below)
  The strong lines in these other O supergiants can also
  be fit by the simple spherically symmetric wind model

d Ori Fe XVII 15.01 Å                z Ori O VIII 18.97 Å

                   t*=0                              t*=0.4

Though they are clearly less asymmetric and a little narrower
 Best-fit t* values are a few tenths, although a value of zero can be
ruled out at the 95% confidence limit in all but one line…however,
   values above 0.5 or even 1 cannot be ruled out in most cases

              d Ori                                z Ori
 Ro, the radius of the onset of X-ray emission is within the first
 stellar radius above the photosphere; and consistent with a height of
 3/10 R* or less at the 95% confidence level for all the lines

                  d Ori                                          z Ori

It’s these small Ro values that produce the relative narrowness of
the lines (compared to z Pup).
q, the power-law index describing the radial dependence of the x-
        ray emissivity, is more or less consistent with zero

             d Ori                               z Ori
            There are correlations among the model parameters
                            z Ori Fe XVII 15.013 Å


                                                     Ro=2             Ro=1

       Bigger q goes with                             Higher t goes with
       bigger Ro (left)                                  lower Ro (right)
     What about the stars with the harder X-rays and narrower
                    lines: q1 Ori C and t Sco?

t Sco’s Ne X line overplotted
 with a delta function model.                             Capella

                                                            t Sco

                                                            z Pup

                                  The lines in t Sco look more like
                                 those in coronal sources…and the
                                   lines in q1 Ori C aren’t a whole
                                              lot broader.
Narrow(ish) and symmetric lines…due to line scattering?

                                    The symmetrizing and
                                    narrowing effects of
                                    line scattering are really
                                    only significant for
                                    constant velocity winds
                                    (here, reproduced by
                                    large Ro)
Can narrow(ish) lines be explained by slow wind acceleration?

  You only need b~2 to make lines in z Pup as narrow as the
                   Chandra resolution.
Small Ro values also produce narrow lines.
But the large x-ray luminosities and hard x-ray spectra
already argue against instability-generated shocks…
…and suggest that a hybrid wind-magnetic model might
be appropriate, especially on q1 Ori C, on which an 1100 G
dipole field has been discovered

 ud-Doula and Owocki (2001)
 have performed MHD
 simulations of magnetically
 channelled winds: Equatorward
 flow inside closed field lines and
 associated strong shocks are
                                             of velocity
ud-Doula has made models specific to q1 Ori C, and included radiative
 cooling for the first time: This is a movie of density, evolving from an initial spherically
                                 symmetric steady-state wind.
    We looked at some snapshots from these simulations and
synthesized line profiles (and emission measure distributions and light curves)
     This first snapshot of q1 Ori C is from a time when the hot plasma is
                 relatively placid, filling the closed loop region
        speed                          density                     temperature

Note: throughout, the speed is in terms of an assumed terminal speed of 2500 km s-1
The geometry and viewing angle are relatively well established
for this star.

There is a 45tilt
between the rotation
axis and both the
magnetic axis and the
direction of the Earth:
we see a full range of
viewing angles of the
magnetosphere, and
have Chandra
observations for four of
 We thus synthesize line profiles for a range of viewing angles
                Here we show 0, looking down the magnetic axis
   Color contours are now line-of-sight velocity; and the black contours enclose
                             plasma with T > 106 K

The profile is very narrow
Two other viewing angles from the same hydro snapshot (45, 90 )
Snapshots from another time in the MHD simulations --
 one with material falling back onto the star from the
  closed field region -- shows similarly narrow lines

 speed                 density              temperature
             Line profiles and Line-of-Sight Velocities

The lines are
narrow in this
snapshot, with
the disk
        The lines are narrow from all viewing angles…only
          slightly exceeding the instrumental resolution.

                                                     Range of
                                                     vel. Widths
                                                     seen in
                                                     other O

Line widths
synthesized                                          Observed
from MHD                                             range in q1
simulation                                           Ori C at four
 Overall x-ray modulation with rotation phase (alternately,
 viewing angle of magnetic axis) is well reproduced by the
MHD models (solid line; data are colored symbols, with longer
 wavelength lines purple and short wavelength lines green).
Constellation-X will have better resolution than Chandra only at
 high energies…but its effective area will be 1000 times bigger

      This “minimum velocity” is 1/5 the FWHM resolution
• There is a relatively wide variety of line profile morphologies
seen in Chandra observations of OB stars
• Spherically symmetric, wind-shock models fit most O stars
• But mean wind optical depths are low
• There are some anomalous stars with narrow lines and/or very
hard spectra…hybrid wind-magnetic models are promising
• B stars have narrow lines; but still might be consistent with the
wind-shock scenario if the wind acceleration is slow or the onset
radius of x-rays is close to the photosphere
Supplemental Slides
     AB Dor   g Cas

Line centroids from MHD agree well with observed values for
                        q1 Ori C
g Cas (B0.5 Ve): quite anomalous

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