Transcript invited review of X-ray line profile diagnostics from hot stars

X-ray Emission Line Profile
Diagnostics of Hot Star Winds:
Constraints on Kinematics, Geometry, and Opacity
David H. Cohen
Dept. of Physics and
Astronomy
Swarthmore College
much of this work was performed by
Swarthmore seniors Roban Kramer and
Stephanie Tonnesen
Outline
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 windshock 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
too.
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 Helike 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
3L-shell
of individual lines are fairly strongly peaked in temperature, with characteristic widths of 0.3 dex.
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
components.
1Significant
O K-shell
edges
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)
q1 Ori C
z Pup
(O7 V)
(O4 I)
t Sco
z Ori
(B0 V)
(O9.5 II)
b Cru
d Ori
(B0.5 IV)
(O9.7 I)
10 Å
20 Å
10 Å
20 Å
Focus in on a characteristic portion of the spectrum
12Å
z Pup
15
Å
12
Å
15Å
q1 Ori C
(O7 V)
(O4 I)
t Sco
(B0 V)
z Ori
(O9.5 II)
d Ori
b Cru
(B0.5 IV)
(O9.7 I)
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
z Ori
t Sco
g Cas
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

dz'
t  : t ( p  0;z)  t   z

where t  
1 b
r' (1 )
r'
2
Ro=3
M
4 Rv
The line profile is calculated from:
Ll  8

2
 
1

1
R
jet r 2 drd
Increasing Ro makes lines
broader; increasing t*
makes them more
blueshifted and skewed.
Ro=10
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
12.13 Å
Fe XVII
17.05 Å
Fe XVII
15.01 Å
O VIII
18.97 Å
Fe XVII
16.78 Å
N VII
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
fit (black circles) and 95%
confidence limits (gray
triangles) on the three fitted
parameters for seven of the lines
in the z Pup spectrum.
q
Ro
t*
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
parameters:
t*~1
:4 to 15 times less than predicted
Ro~1.5
q~0
But, the level of wind absorption is significantly below what’s
expected.
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
wavelength dependence of the
cross sections (and thus of the
wind optical depth), BUT the
lines we fit cover only a
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
more.
OR perhaps clumping plays a
role. And clumping certainly
could play a role in the overall
reduction of wind optical
depth.
Wind opacity for canonical B
star abundances.
N K-edge
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
t*=0
z Ori O VIII 18.97 Å
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 xray 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=1
Ro=2
Ro=2
Bigger q goes with
bigger Ro (left)
Ro=1
Higher t goes with
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
seen.
y-component
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
them.
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
similarly
narrow in this
snapshot, with
the disk
infall…
The lines are narrow from all viewing angles…only
slightly exceeding the instrumental resolution.
Range of
vel. Widths
seen in
other O
stars
Line widths
synthesized
from MHD
simulation
Observed
range in q1
Ori C at four
observed
viewing
angles
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
Conclusions
• 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
adequately
• 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
Capella
g Cas
Line centroids from MHD agree well with observed values for
q1 Ori C
g Cas (B0.5 Ve): quite anomalous