ζ Pup: Chandra HETGS line-profile analysis

These fits: non-porous, aniso-, and iso- porous (with hinf fixed at 0.5, 1, & 5) complement the initial work we did on the RGS spectrum.

The data shown here were reduced by David, several years ago, for the analysis that was published in Cohen et al. (2010). We use the wavelength ranges and continuum levels determined in that analysis. The effective exposure time is 68 ks; much shorter than the RGS effective exposure time. But the background is much lower, the spectral resolution is higher. The wavelength coverage overlaps, but there are some differences -- Chandra better at short wavelengths, XMM at long wavelengths. The two datasets are complementary.

The entire HETGS spectra

MEG

HEG

Line-by-line results

Below are the systematic fits of different model cases, presented in the same order and format as for the RGS data. Note that here, there are two plots for most lines: the Medium Energy Grating (MEG) data and the High Energy Grating (HEG) data. They were fit simultaneously (i.e. the model shown on each is the same -- with parameters listed to the right of the plots -- though they may look different because of the different spectral responses, binning, and effective area of the two different gratings). Also, here we fit the continuum separately from the line and use the C statistic (as described in Cohen et al. 2010).

The lines we fit and present here are:

Fe XVII @ 15.014 A
O VIII (Ly-alpha) @ 18.969 A
Ne X (Ly-alpha) @ 12.134 A
Fe XVII @ 16.780 A
Mg XII (Ly-alpha) @ 8.421 A

None of the other lines are strong enough and unblended enough to provide meaningful constraints on porosity (though 11 other lines and line complexes were fit and presented in Cohen et al. 2010 because there we were only looking at non-porous models). These same lines, with the exception of Mg XII (too weak), were fit in the RGS data and results are presented on the RGS results page. Several other lines in the RGS spectrum are fit, too.

15.014 Angstroms: Fe XVII

Non-porous

MEG

HEG

[14.87:15.13]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 1.71e-3
q = 0
h_inf = 0
taustar = 1.94 +/- (1.61:2.26)
R_o = 1.55 +/- (1.43:1.67)
norm = 5.24e-4 +/- (5.07e-4:5.48e-4)
C = 280.83 for N = 308

Compare these results to the analogous model fit to the same line in the XMM RGS spectrum. The agreement is very good. (Comparing the confidence limits as well as the best-fit parameter values is interesting. Though, note the continuum normalizations do not agree all that well.)

Anisotropic porosity

We test several values of h_inf, using anisotropic porosity, employing the Rosseland (inverse) bridging law. When the porosity length is treated as a free parameter, h_inf=0 was preferred, with the non-porous fit parameters recovered (i.e. the data do not favor anisotropic porosity).

h_inf = 0.5
MEG

HEG

[14.87:15.13]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 1.71e-3
q = 0
h_inf = 0.5 (frozen)
taustar = 2.51 +/- (2.11:3.19)
R_o = 1.61 +/- (1.47:1.69)
norm = 5.23e-4 +/- (5.05e-4:5.46e-4)
C = 293.94 for N = 308

h_inf = 1
MEG

HEG

[14.87:15.13]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 1.71e-3
q = 0
h_inf = 1.0 (frozen)
taustar = 3.02 +/- (2.37:3.86)
R_o = 1.65 +/- (1.55:1.75)
norm = 5.22e-4 +/- (5.04e-4:5.45e-4)
C = 303.80 for N = 308

h_inf = 2
MEG

HEG

[14.87:15.13]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 1.71e-3
q = 0
h_inf = 2.0 (frozen)
taustar = 3.76 +/- (2.76:5.32)
R_o = 1.74 +/- (1.63:1.83)
norm = 5.22e-4 +/- (5.04e-4:5.45e-4)
C = 317.39 for N = 308

h_inf = 5
MEG

HEG

[14.87:15.13]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 1.71e-3
q = 0
h_inf = 5.0 (frozen)
taustar = 6.95 +/- (3.94:12.27)
R_o = 1.84 +/- (1.73:1.95)
norm = 5.21e-4 +/- (5.03e-4:5.44e-4)
C = 338.35 for N = 308

All four of these anisotropic porosity models (h_inf = 0.5, 1, 2, 5) produce poor fits from a formal statistical point of view; though the h_inf = 0.5 model is only rejected at something like the 99.9% level, with Delta C ~ 13.

Confidence limits in taustar-h_inf parameter space

Isotropic porosity

Here we fit models with isotropic porosity, for the same set of fixed terminal porosity length values. Again, when h_inf is allowed to be free, a best-fit value of zero is found, indicating the non-porous models are favored.

h_inf = 0.5
MEG

HEG

[14.87:15.13]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 1.71e-3
q = 0
h_inf = 0.5 (frozen)
taustar = 2.18 +/- (1.79:2.60)
R_o = 1.58 +/- (1.48:1.69)
norm = 5.24e-4 +/- (5.07e-4:5.48e-4)
C = 282.01 for N = 308

h_inf = 1
MEG

HEG

[14.87:15.13]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 1.71e-3
q = 0
h_inf = 1.0 (frozen)
taustar = 2.46 +/- (1.99:3.00)
R_o = 1.61 +/- (1.48:1.69)
norm = 5.24e-4 +/- (5.07e-4:5.48e-4)
C = 283.35 for N = 308

Note: with h_inf = 1, taustar has increased by 27 percent.

h_inf = 2
MEG

HEG

[14.87:15.13]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 1.71e-3
q = 0
h_inf = 2.0 (frozen)
taustar = 3.09 +/- (2.43:3.98)
R_o = 1.65 +/- (1.56:1.73)
norm = 5.24e-4 +/- (5.06e-4:5.48e-4)
C = 286.44 for N = 308

h_inf = 5
MEG

HEG

[14.87:15.13]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 1.71e-3
q = 0
h_inf = 5.0 (frozen)
taustar = 5.70 +/- (4.04:8.45)
R_o = 1.74 +/- (1.65:1.81)
norm = 5.23e-4 +/- (5.05e-4:5.46e-4)
C = 297.17 for N = 308

Here, for the isotropic porosity models, the first two models (with h_inf = 0.5 and 1.0) are only very slightly worse than the non-porous model fit. Statistically, they are indistinguishable (the h_inf = 1 model, with Delta C ~ 3 is only rejected with about 90% confidence). Note that the actual taustar values found for these models tell us something -- they are only slightly higher than the non-porous best-fit model, implying that isotropic porosity has very little effect on the line profiles for porosity lengths less than unity. But, the high porosity model, with (h_inf = 5) does produce a substantially worse fit -- rejection probability >99.9% (and a rather high value of taustar).

Note that qualitatively, the RGS results for this line and these seven different models are similar. The best-fit taustar values for the anisotropic porosity models tend be higher in the RGS data fitting than in Chandra.

Confidence limits in taustar-h_inf parameter space

Given the isotropic porosity model, and allowing h_inf now to be a free parameter, along with the others, we can examine a 2-D grid of chi square values (or in this case, C values). The global best-fit model is denoted by the filled circle and the contours represent the formal 68%, 95%, and 99% confidence limits. (Note that R_o, along with the normalizations, is still a free parameter here even though it is not shown in this parameter space).

Details of the fitting are in the xspec log.

18.969 Angstroms: O VIII

The HEG count rate is so low at these long wavelengths, that we only fit the MEG spectrum for this line. Even the MEG doesn't have the greatest signal-to-noise.