ζ Pup: XMM RGS line-profile analysis

The results presented here (August 2011) are preliminary. Initially, we're exploring issues related to the model fitting and looking at some rudimentary results for taustar trends among the strong lines and the taustar vs. porosity-length tradeoff.

The data shown here were reduced by Maurice in 2010, and include all GO and GTO observations. A set of brief emails from him describing the reduction are available [14 June 2010 and 21 June 2010]. The effective exposure times are 767 ks for RGS1 and 763 ks for RGS2.

Comparisons can be made to these older, and extensive, fits to the Chandra data. New: and now there's a corresponding page of Chandra fit results analogous to the RGS fits shown on this page.

The entire RGS spectrum

RGS1

RGS2

Line-by-line results

15.014 Angstroms: Fe XVII

We did some preliminary tests first, exploring the background, continuum fitting, optimal statistic and error weighting, and wavelength range over which to fit.

Below are the systematic fits of different model cases.

Non-porous

[14.80:15.07]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 3.23e-3
q = 0
h_inf = 0
taustar = 1.84 +/- (1.69:1.99)
R_o = 1.57 +/- (1.47:1.66)
norm = 6.41e-4 +/- (6.28e-4:6.51e-4)
chisq = 110.34 for N = 52

Note that the uncertainties on taustar and h_inf assume delta chi square = 1, with the errors scaled up by 2.3 (so, in effect, we're using delta chi square = 2.3).

Compare these results to the analogous model fit to the same line in the Chandra spectrum.

Anisotropic porosity

We test several values of h_inf, using anisotropic porosity, employing the Rosseland bridging law (and with the numerical switch on). 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
[14.80:15.07]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 2.99e-3
q = 0
h_inf = 0.5 (frozen)
taustar = 3.41
R_o = 1.44
norm = 6.49e-4
chisq = 157.87 for N = 52

h_inf = 1
[14.80:15.07]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 2.88e-3
q = 0
h_inf = 1.0 (frozen)
taustar = 4.89
R_o = 1.49
norm = 6.54e-4
chisq = 222.34 for N = 52

h_inf = 5
[14.80:15.07]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 2.43e-3
q = 0
h_inf = 5.0 (frozen)
taustar = 33.40
R_o = 1.53
norm = 6.69e-4
chisq = 521.61 for N = 52

All three of these anisotropic porosity models (h_inf = 0.5, 1, 5) produce poor fits from a formal statistical point of view (though the situation is ambiguous, quantitatively, because the best-fit model does not produce a formally good chi square) and qualitatively, visually, the venetian blind bump is apparent in the model at a level greater than what is seen in the data.

Isotropic porosity

Here we fit models with isotropic porosity (and still using the Rosseland bridging law), 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, though as can be seen below, for small porosity lengths, the quality of the model fits is roughly the same as for the non-porous model.

h_inf = 0.5
[14.80:15.07]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 3.21e-3
q = 0
h_inf = 0.5 (frozen)
taustar = 2.11 +/- (1.93:2.31)
R_o = 1.58 +/- (1.50:1.67)
norm = 6.41e-4 +/- (6.32e-4:6.51e-4)
chisq = 111.89 for N = 52

h_inf = 1
[14.80:15.07]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 3.19e-3
q = 0
h_inf = 1.0 (frozen)
taustar = 2.44 +/- (2.21:2.71)
R_o = 1.59 +/- (1.52:1.66)
norm = 6.42e-4 +/- (6.32e-4:6.51e-4)
chisq = 113.75 for N = 52

h_inf = 5
[14.80:15.07]
v_inf = 2250
β = 1
powerlaw continuum, n = 2; norm = 2.94e-3
q = 0
h_inf = 5.0 (frozen)
taustar = 10.63 +/- (8.85:13.20)
R_o = 1.62 +/- (1.56:1.67)
norm = 6.46e-4 +/- (6.37e-4:6.55e-4)
chisq = 152.05 for N = 52

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. 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 (and a rather high value of taustar).

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. The global best-fit model is denoted by the filled circle and the contours represent the formal 68%, 90%, and 95% confidence limits (with a scaling of 2.3 to correct for the formally poor fit of the best-fit model, as we have done above when evaluating confidence limits on individual parameters). The fourth, outermost contour is arbitrarily set at twice the value of the 95% contour, and its purpose is simply to trace out the quantitative tradeoff between the two parameters in the fit. (Note that R_o, along with the normalizations, is still a free parameter here even though it is not shown in this parameter space).

Here too, there is good agreement with the corresponding Chandra result.

18.969 Angstroms: O VIII

Note that we're treating the closely spaced Ly-alpha doublet as a single line, centered at the emissivity-weighted mean of the wavelengths of the two components.

Below are the systematic fits of different model cases. Same as above for the Fe XVII line at 15.014 A.