X-ray Emission Line Profile Diagnostics of Hot Star Winds:

Constraints on Kinematics, Geometry, and Opacity

David H. CohenDept. 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?

Pup: wind x-rays, but less absorption than expected

Ori and Ori: similar situation, very little wind absorption; but wind-shock parameters are otherwise satisfactory

Magnetic O stars and B stars are a different story: 1 Ori C, Sco, 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)

1Elemental abundance plays an important role too2Emissivities 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)

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)

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.

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

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.

24 Å 12 Å

O K-shell edges

Chandra and XMM, launched in 1999, are the first instruments to allow for the measurement of resolved x-ray emission lines*

*The EUVE spectrometers measured emission lines from the B2 II star CMa.

The resolution of the Chandra medium energy grating (MEG) is .023 Å FWHM: ~1000 at 23 Å (300 km s-1)

The effective area is only a few square centimeters

The Chandra Archive of Hot StarsBecause 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).

*HD206267 Ori, Cma, other stars in the1 Ori system, and several interacting binaries, 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.

Star Sp. Ty. Mdot Vinf comments

Pup O4 2.5 (-6) 2500

Ori O9.5 II 1(-6) 1860

Ori O9.7 I 1(-6) 2000

1 Ori C O7 V 4(-7) 2500 1100 G dipole magnetic field

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

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

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

Global appearance of spectra (Chandra MEG)

Pup(O4 I)

Ori(O9.5

II)

Ori(O9.7 I)

Ori C(O7 V)

Sco(B0 V)

Cru(B0.5 IV)

10 Å 10 Å20 Å 20 Å

Focus in on a characteristic portion of the spectrum

There is clearly a range of line profile morphologies from star to star

Ne X Ne XNe IX Ne IXFe XVII Fe XVII

Pup

(O4 I)

Ori

(O9.5 II)

Ori

(O9.7 I)

Ori C

(O7 V)

Sco

(B0 V)

Cru(B0.5 IV)

12Å 12Å

15Å

15Å

Differences in the line shapes become apparent when we look at a single line (here Ne X, Ly)

Pup

Ori

Ori

Ori C

Sco

Cru

Cas

AB Dor (K1 IIIp)

Capella (G2 III)

Now let’s focus on individual linesPup: 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:

: v(r) (1 R /r)

Ro,q : j 2r q

: ( p 0;z) dz'

r'2 (11

r')z

for r>Ro

The line profile is calculated from:

Increasing Ro makes lines broader; increasing * makes them more blueshifted and skewed.

Ro=1.5

Ro=3

Ro=10

=1,2,4

where

M

4Rv

L 8 2 je R

1

1 r2drd

We fit all the (8) unblended strong lines in the Chandra spectrum of Pup: all the fits are statistically good

Ne X

12.13 ÅFe XVII

15.01 ÅFe XVII

16.78 Å

Fe XVII 17.05 Å

O VIII 18.97 Å

N VII 24.78 Å

We place uncertainties on the derived model parameters

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 * values possible.

lowest * best * highest *

To find the parameter uncertainties, we calculate models on a grid in parameter

space.

Displayed grids are slices of constant *, 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 Pup spectrum.

*

q

Ro

Lines are well fit by our four parameter model ( is actually held constant at =1; so three free parameters): Pup’s x-ray lines are consistent with a spatially distributed, spherically symmetric, radially accelerating wind scenario, with reasonable parameters:

*~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)

Note: dotted line is interstellar.

Wind opacity for canonical B star abundances.

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 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.

N K-edge

Do the other O supergiants, Ori and Ori, fit into the wind-shock paradigm?

The Ne X line in Ori (left) is skewed and blueshifted (>1), though not as much as the same line in Pup (below)

The strong lines in these other O supergiants can also be fit by the simple spherically symmetric wind model

Ori Fe XVII 15.01 Å

Ori O VIII 18.97 Å

Though they are clearly less asymmetric and a little narrower

*=0 *=0.4

Best-fit * 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

Ori Ori

Ori 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

It’s these small Ro values that produce the relative narrowness of the lines (compared to Pup).

q, the power-law index describing the radial dependence of the x-ray emissivity, is more or less consistent with zero

Ori Ori

There are correlations among the model parameters

Ori Fe XVII 15.013 Å

Higher goes with lower Ro (right)

Bigger q goes with bigger Ro (left)

Ro=1

Ro=2

Ro=2 Ro=1

What about the stars with the harder X-rays and narrower lines: 1 Ori C and Sco?

Sco’s Ne X line overplotted with a delta function model. Capella

Sco

Pup

The lines in Sco look more like those in coronal sources…and the

lines in 1 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 ~2 to make lines in 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 1 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 1 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.

speed density temperature

We looked at some snapshots from these simulations and synthesized line profiles (and emission measure distributions and light curves)

Note: throughout, the speed is in terms of an assumed terminal speed of 2500 km s-1

This first snapshot of 1 Ori C is from a time when the hot plasma is relatively placid, filling the closed loop region

The geometry and viewing angle are relatively well established for this star.

There is a 45tilt 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 anglesHere 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

Observed range in 1 Ori C at four observed viewing angles

Line widths synthesized from MHD simulation

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).

This “minimum velocity” is 1/5 the FWHM resolution

Constellation-X will have better resolution than Chandra only at high energies…but its effective area will be 1000 times bigger

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

Cas

Line centroids from MHD agree well with observed values for 1 Ori C

Cas (B0.5 Ve): quite anomalous