ζ Pup: XMM RGS lineprofile analysis
N VII at 20.910 A
There is almost no RGS2 data for this line, so we will use only the RGS1 data.
First we repeat the nonporous fit shown on the main page.
Nonporous: RGS1

[20.70:21.07]
v_{inf} = 2250
β = 1
powerlaw continuum, n = 2
norm = 9.05e4 +/ (7.33e4:1.13e3)
q = 0
h_{inf} = 0
taustar = 4.93 +/ (3.90:5.59)
R_{o} = 1.41 +/ (1.01:2.03)
shift = 0
norm = 1.66e4 +/ (1.56e4:1.73e3)
chisq = 40.52 for N = 36

The fit is quite good (though mostly, I assume, because these data are relatively low S/N). The taustar value is high, as would be expected.
Next, we'll fit models with anisotropic porosity assuming flattened, radially oriented clumps. We use the "stretch" porosity length distribution, h(r), parameterized by h_{inf}. We will fit first with h_{inf} a free parameter, and then at fixed values of h_{inf} = 0.5, 1, 2, and 5 R_{*}.
anisoporous: RGS1, h_{inf} free

[20.70:21.07]
v_{inf} = 2250
β = 1
powerlaw continuum, n = 2
norm = 9.26e4 +/ (:)
q = 0
h_{inf} = 0.00 +/ (0.00:0.03)
taustar = 4.88 +/ (4.00:5.89)
R_{o} = 1.32 +/ (1.01:2.03)
shift = 0
norm = 1.65e4 +/ (1.56e4:1.75e4)
chisq = 40.52 for N = 36

Note that despite the fact that the terminal porosity length's bestfit value is found to be zero (1e7 or so, actually), the bestfit model parameters are not identical to the nonporous fit. They are very close, of course, but the small differences are probably due to the numerical integration that's required in the aniso case. Note that the 68% upper confidence limit on h_{inf} is 0.03, and that enables slightly larger confidence limits on taustar.
Now, a sequence of fits with fixed h_{inf} values of 0.5, 1, 2, and 5.
anisoporous: RGS1, h_{inf} = 0.5

[20.70:21.07]
v_{inf} = 2250
β = 1
powerlaw continuum, n = 2
norm = 7.61e4 +/ (5.26e4:9.96e4)
q = 0
h_{inf} = 0.5
taustar = 7.96 +/ (6.15:10.16)
R_{o} = 1.60 +/ (1.24:2.01)
shift = 0
norm = 1.69e4 +/ (1.59e4:1.80e4)
chisq = 52.92 for N = 36

anisoporous: RGS1, h_{inf} = 1

[20.70:21.07]
v_{inf} = 2250
β = 1
powerlaw continuum, n = 2
norm = 6.20e4 +/ (3.75e4:8.79e4)
q = 0
h_{inf} = 1
taustar = 12.95 +/ (9.61:17.46)
R_{o} = 1.70 +/ (1.36:2.14)
shift = 0
norm = 1.75e4 +/ (1.63e4:1.86e4)
chisq = 62.38 for N = 36

anisoporous: RGS1, h_{inf} = 2

[20.70:21.07]
v_{inf} = 2250
β = 1
powerlaw continuum, n = 2
norm = 3.53e4 +/ (:)
q = 0
h_{inf} = 2
taustar = 34.11 +/ (:)
R_{o} = 1.62 +/ (:)
shift = 0
norm = 1.86e4 +/ (:)
chisq = 73.45 for N = 36

anisoporous: RGS1, h_{inf} = 5

[20.70:21.07]
v_{inf} = 2250
β = 1
powerlaw continuum, n = 2
norm = 3.53e4 +/ (:)
q = 0
h_{inf} = 5
taustar = 100 +/ (:)
R_{o} = 1.73 +/ (:)
shift = 0
norm = 1.91e4 +/ (:)
chisq =84.35 for N = 36

Summarizing
The effect of porosity and the tradeoff between porosity length and optical depth can be summarized by looking at the joint parameter confidence limits. We show the 68%, 95%, and 99% limits below. The bestfit model is the filled circle.
Now, we'll look at models with isotropic porosity.
isoporous: RGS1, h_{inf} free

[20.70:21.07]
v_{inf} = 2250
β = 1
powerlaw continuum, n = 2
norm = 9.11e4 +/ (6.94e4:1.14e3)
q = 0
h_{inf} = 0.22 +/ (0.00:1.34)
taustar = 5.55 +/ (3.90:9.18)
R_{o} = 1.49 +/ (1.01:2.08)
shift = 0
norm = 1.66e4 +/ (1.56e4:1.76e4)
chisq = 40.45 for N = 36

isoporous: RGS1, h_{inf} = 0.5

[20.70:21.07]
v_{inf} = 2250
β = 1
powerlaw continuum, n = 2
norm = 9.19e4 +/ (6.96e4:1.11e3)
q = 0
h_{inf} = 0.5
taustar = 6.18 +/ (4.72:8.07)
R_{o} = 1.65 +/ (1.14:2.11)
shift = 0
norm = 1.66e4 +/ (1.56e4:1.76e4)
chisq = 40.55 for N = 36

isoporous: RGS1, h_{inf} = 1

[20.70:21.07]
v_{inf} = 2250
β = 1
powerlaw continuum, n = 2
norm = 9.19e4 +/ (7.10e4:1.15e3)
q = 0
h_{inf} = 1
taustar = 7.42 +/ (5.51:10.09)
R_{o} = 1.79 +/ (1.43:2.15)
shift = 0
norm = 1.66e4 +/ (1.56e4:1.76e4)
chisq = 41.01 for N = 36

Note: with h_{inf} = 1, taustar has increased by 51 percent.
isoporous: RGS1, h_{inf} = 2

[20.70:21.07]
v_{inf} = 2250
β = 1
powerlaw continuum, n = 2
norm = 9.40e4 +/ (7.26e4:1.16e3)
q = 0
h_{inf} = 2
taustar = 10.16 +/ (7.40:14.42)
R_{o} = 1.95 +/ (1.65:2.28)
shift = 0
norm = 1.66e4 +/ (1.56e4:1.76e4)
chisq = 42.40 for N = 36

isoporous: RGS1, h_{inf} = 5

[20.70:21.07]
v_{inf} = 2250
β = 1
powerlaw continuum, n = 2
norm = 8.39e4 +/ (6.23e4:1.06e3)
q = 0
h_{inf} = 5
taustar = 26.09 +/ (18.13:38.53)
R_{o} = 2.14 +/ (1.85:2.52)
shift = 0
norm = 1.69e4 +/ (1.60e4:1.79e4)
chisq = 49.02 for N = 36

Summarizing
We show the 68%, 95%, and 99% limits below. The bestfit model is the filled circle.
And here is an extensive log of all these xspec fits.
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last modified: 18 May 2012