Simulations to test He-like forbidden-to-intercombination line ratio modeling for O, Ne, Mg, Si, S and Fe.
March, 2006
M. Walter-Range
Swarthmore College
107 108 109 1010 1011 1012 1013
-0.5
0.0
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1.0
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2.0
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3.0
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4.0 BDT (1972) PrismSPECT Porquet (2001)
I forb
idde
n/Iin
terc
ombi
nati
on
ne (cm-3)
Oxygen
109 1010 1011 1012 1013 1014 1015
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3.0 BDT (1972) PrismSPECT Porquet (2001)
I forb
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natio
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ne (cm-3)
Neon
1010
1011
1012
1013
1014
1015
1016
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2.0
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3.0 BDT (1972) PrismSPECT Porquet (2001)
I forb
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ne (cm-3)
Magnesium
1010 1011 1012 1013 1014 1015 1016
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1.0
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2.0
2.5 BDT (1972) PrismSPECT Porquet (2001)
I forb
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ne (cm-3)
Silicon
According to Equation 4 in Blumenthal, Drake, and Tucker 1972, .The values of nc are from BDT: Oxygen: nc=3.4E10, Neon: nc=6.4E11, Magnesium: nc=6.2E12, Silicon: nc=4.0E13.The PrismSPECT modeling uses ATBASE v4.3 beta, with the “most detailed” model chosen for the He-like atomic models. The workspaces and the associated ATM files can be found at: http://astro.swarthmore.edu/~mwalter1/lab_notes/ps_workspaces
)22()1(
)12(3
13
01
13
PSCF
SSAcn
Porquet’s group did not recalculate R0 for any elements heavier than Si, so the following two plots only contain the original BDT line and the PrismSPECT values. For Sulfur: nc=1.9E14, Iron: nc=4.7E16.
1013 1014 1015 1016 1017 1018 1019 1020
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BDT (1972) PrismSPECT
I forb
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ne (cm-3)
Iron
1010 1011 1012 1013 1014 1015 1016 1017
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2.0 BDT (1972) PrismSPECT
I forb
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ne (cm-3)
Sulfur
The largest disagreement between PrismSPECT and the BDT function occurs in the low-density limit for each of the elements shown above. However, the calculations do show agreement with the analytic expression in terms of overall shape. This includes the (effective) values for nc in PrismSPECT/ATBASE.
The following plots are the results from simulations in which the varying property was the radiation source drive temperature (and thus the UV mean intensity driving the 3S – 3P photoexcitation). I used a one-sided radiation field, and the planar option for the plasma geometry.
If you would like to see the exact settings I entered into PrismSPECT, there are PowerPoint documents with screenshots for all the simulations I ran, available at: http://astro.swarthmore.edu/~mwalter1/lab_notes
I have also uploaded several of the workspaces I was using. They can be found at: http://astro.swarthmore.edu/~mwalter1/lab_notes/ps_workspaces
The step-by-step procedure I used is available at: http://astro.swarthmore.edu/~mwalter1/lab_notes/procedure_for_plotting_R_vs_phi.pdf
This procedure is based on equations that can be found at: http://astro.swarthmore.edu/~mwalter1/lab_notes/phi_equations.pdf
For each ion, I have plotted the PrismSPECT results, the original BDT model, and a BDT curve using Porquet’s newer values for R 0.
Oxygen: the Dependence of f/i upon photoexcitation rate, φ
100 101 102 103 104 105 106 107
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3.0
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4.0
Fitting parameters: Chi^2/DoF = 0.00003R^2 = 0.99999 Ro 3.84719 ±0.00357phic 732.09002 ±3.48982
R vs. , O VIII fo
rbid
den/I
inte
rcom
bina
tion
(s-1)
BDT (1972) Porquet (2001) PrismSPECT R PrismSPECT fit
Note the excellent agreement between PrismSPECT and BDT for this element:
PrismSPECT BDT Porquet
R0 3.847 3.85 3.7
φc 732.09 732 N/A
The black dotted line corresponds to Blumenthal, Drake, and Tucker’s (1972) analytic model. Porquet’s results (2001) are shown as a solid black line.
The individual data points are the f/i ratio calculated by PrismSPECT for a particular value of φ.
The dashed blue line is a BDT-type function that fits the PrismSPECT points and determines the parameters R0 and φc.
Neon: the Dependence of f/i upon photoexcitation rate, φ
PrismSPECT BDT Porquet
R0 3.02 3.17 3.1
φc 7712 7730 N/A
101 102 103 104 105 106 107 108
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0.5
1.0
1.5
2.0
2.5
3.0
Fitting parameters: Chi^2/DoF = 0.00029R^2 = 0.99985 Ro 3.01835 ±0.00972phic 7711.66073 ±173.14961
R vs. , Ne IXI fo
rbid
den/I
inte
rcom
bina
tion
(s-1)
BDT (1972) Porquet (2001) PrismSPECT R PrismSPECT fit
The black dotted line corresponds to Blumenthal, Drake, and Tucker’s (1972) analytic model. Porquet’s results (2001) are shown as a solid black line.
The individual data points are the f/i ratio calculated by PrismSPECT for a particular value of φ.
The dashed blue line is a BDT-type function that fits the PrismSPECT points and determines the parameters R0 and φc.
100 101 102 103 104 105 106 107 108
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1.0
1.5
2.0
2.5
3.0
Fitting parameters: Chi^2/DoF = 1.7497E-7R^2 = 1 Ro 3.20511 ±0.00019phic 43720.14526 ±16.97773
R vs. , Mg XI
I forb
idde
n/Iin
terc
ombi
natio
n
(s-1)
BDT (1972) Porquet (2001) PrismSPECT R PrismSPECT fit
Magnesium: the Dependence of f/i upon photoexcitation rate, φ
PrismSPECT BDT Porquet
R0 3.21 3.03 2.7
φc 4.37E4 4.86E4 N/A
The black dotted line corresponds to Blumenthal, Drake, and Tucker’s (1972) analytic model. Porquet’s results (2001) are shown as a solid black line.
The individual data points are the f/i ratio calculated by PrismSPECT for a particular value of φ.
The dashed blue line is a BDT-type function that fits the PrismSPECT points and determines the parameters R0 and φc.
Silicon: the Dependence of f/i upon photoexcitation rate, φ
102 103 104 105 106 107 108 109
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1.0
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Fitting parameters: Chi^2/DoF = 7.6328E-8R^2 = 1 Ro 2.45316 ±0.00013phic 207980.17872 ±56.20532
R vs. , Si XIIII fo
rbid
den/I
inte
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tion
(s-1)
BDT (1972) Porquet (2001) PrismSPECT R PrismSPECT fit
PrismSPECT BDT Porquet
R0 2.45 2.51 2.3
φc 2.08E5 2.39E5 N/A
The black dotted line corresponds to Blumenthal, Drake, and Tucker’s (1972) analytic model. Porquet’s results (2001) are shown as a solid black line.
The individual data points are the f/i ratio calculated by PrismSPECT for a particular value of φ.
The dashed blue line is a BDT-type function that fits the PrismSPECT points and determines the parameters R0 and φc.
Sulfur: the Dependence of f/i upon photoexcitation rate, φ
100 101 102 103 104 105 106 107 108 109
0.0
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2.0
Fitting parameters: Chi^2/DoF = 7.5329E-6R^2 = 0.99998 Ro 1.74493 ±0.00088phic 814464.48063 ±4163.06098
R vs. , S XV
I forb
idde
n/Iin
terc
ombi
natio
n
(s-1)
BDT (1972) PrismSPECT R PrismSPECT fit
PrismSPECT BDT Porquet
R0 1.75 2.04 N/A
φc 8.15E5 9.16E5 N/A
The black dotted line corresponds to Blumenthal, Drake, and Tucker’s (1972) analytic model.
The individual data points are the f/i ratio calculated by PrismSPECT for a particular value of φ.
The dashed blue line is a BDT-type function that fits the PrismSPECT points and determines the parameters R0 and φc.
Summary
We recalculate the O VII, Ne IX, Mg XI, Si XIII, and S XV forbidden-to-intercombination ratios, using the latest atomic model (ATBASE), in conjunction with PrismSPECT.
Comparisons with the old analytic model of Blumenthal, Drake, and Tucker (1972) are made,as well as comparisons with the model resulting from Porquet’s newer (2001) values for R0.
One significant difference is the inclusion of both of the 2 3P1,2 – 1 1S0 transitions.
Note also that there is some dependence in the ‘low density limit’ (Ro) on the plasma temperature. Our simulations use a temperature that produces an ionization fraction of the He-like state that is in excess of 50% (95% for O, 97% for Ne, 55% for Mg, 89% for Si, 89% for S). Blumenthal, Drake,
and Tucker do not include this effect in their model.
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