NASA’s X-ray Spectral Fitting Package lacks one of the key solar flare emission models, that of thick-target bremsstrahlung. In sswidl’s OSPEX, this model is implemented as thick2.pro. Using sunxspex’s emission module, the thick-target model can be adapted for use with XSPEC or PyXspec.
The current implementation of the model has not been optimized to take advantage of numpy, but is rather a direct translation from IDL. XSPEC-compatible models based on sunxspex can be found here.
Example
Full example code can be found here. A single STIX spectrum is fit with a thermal bremsstrahlung model (XSPEC’s apec) plus a thick-target model, in multiple stages. The reduced output is reproduced below.
1 spectrum in use
Spectral Data File: stx_spectrum_20210908_1712.fits{13} Spectrum 1
Net count rate (cts/s) for Spectrum:1 2.348e+04 +/- 2.074e+01
Assigned to Data Group 1 and Plot Group 1
Noticed Channels: 1-29
Telescope: Solar Orbiter Instrument: STIX Channel Type: PI
Exposure Time: 58.56 sec
Using fit statistic: chi
Using Response (RMF) File stx_srm_20210908_1712.fits for Source 1
Solar Abundance Vector set to file: User defined abundance vector / no description specified Fitting with single thermal model initially over range 2.0-10.0 keV
========================================================================
Model apec<1> Source No.: 1 Active/On
| Model | Model | Component | Parameter | Unit | Value | |
|---|---|---|---|---|---|---|
| par | comp | |||||
| 1 | 1 | apec | kT | keV | 1.00000 | +/- 0.0 |
| 2 | 1 | apec | Abundanc | 1.00000 | frozen | |
| 3 | 1 | apec | Redshift | 0.0 | frozen | |
| 4 | 1 | apec | norm | 1.00000 | +/- 0.0 |
Reading APEC data from 3.0.9
Fit statistic : Chi-Squared 1.328790e+06 using 29 bins.
Test statistic : Chi-Squared 1.328790e+06 using 29 bins.
Null hypothesis probability of 0.000000e+00 with 27 degrees of freedom
Current data and model not fit yet.
No channels ignored (no channels in specified range)
24 channels (6-29) ignored in spectrum # 1
Fit statistic : Chi-Squared 998363.0 using 5 bins.
Test statistic : Chi-Squared 998363.0 using 5 bins. Null hypothesis probability of 0.0e+00 with 3 degrees of freedom Current data and model not fit yet.
After first fit
Model apec<1> Source No.: 1 Active/On
| Model | Model | Component | Parameter | Unit | Value | |
|---|---|---|---|---|---|---|
| par | comp | |||||
| 1 | 1 | apec | kT | keV | 1.79174 | +/- 4.62000E-03 |
| 2 | 1 | apec | Abundanc | 1.00000 | frozen | |
| 3 | 1 | apec | Redshift | 0.0 | frozen | |
| 4 | 1 | apec | norm | 9.52623E+05 | +/- 7654.01 |
Fit statistic : Chi-Squared 561.79 using 5 bins.
Test statistic : Chi-Squared 561.79 using 5 bins.
Null hypothesis probability of 1.93e-121 with 3 degrees of freedom
Single thermal fit took 0.491 seconds
========================================================================
Model apec<1> + thick2<2> Source No.: 1 Active/On
| Model | Model | Component | Parameter | Unit | Value | |
|---|---|---|---|---|---|---|
| par | comp | |||||
| 1 | 1 | apec | kT | keV | 1.79000 | frozen |
| 2 | 1 | apec | Abundanc | 1.00000 | frozen | |
| 3 | 1 | apec | Redshift | 0.0 | frozen | |
| 4 | 1 | apec | norm | 9.52623E+05 | frozen | |
| 5 | 2 | thick2 | a0 | 1e-35 | 100.000 | +/- 0.0 |
| 6 | 2 | thick2 | p | 4.00000 | +/- 0.0 | |
| 7 | 2 | thick2 | eebrk | keV | 16.7000 | +/- 0.0 |
| 8 | 2 | thick2 | q | 6.00000 | +/- 0.0 | |
| 9 | 2 | thick2 | eelow | keV | 3.40000 | +/- 0.0 |
| 10 | 2 | thick2 | eehigh | keV | 3200.00 | +/- 0.0 |
| 11 | 2 | thick2 | norm | 1.00000 | +/- 0.0 |
New model: single thermal fit with previous fit parameters (kT=1.79, norm=952622.80) plus thick target model initially over range 10.0-30.0 keV
Fit statistic : Chi-Squared 5.996501e+07 using 11 bins.
Test statistic : Chi-Squared 5.996501e+07 using 11 bins. Null hypothesis probability of 0.000000e+00 with 4 degrees of freedom Current data and model not fit yet.
After second fit
========================================================================
Model apec<1> + thick2<2> Source No.: 1 Active/On
| Model | Model | Component | Parameter | Unit | Value | |
|---|---|---|---|---|---|---|
| par | comp | |||||
| 1 | 1 | apec | kT | keV | 1.79000 | frozen |
| 2 | 1 | apec | Abundanc | 1.00000 | frozen | |
| 3 | 1 | apec | Redshift | 0.0 | frozen | |
| 4 | 1 | apec | norm | 9.52623E+05 | frozen | |
| 5 | 2 | thick2 | a0 | 1e-35 | 95.0755 | +/- 7.76587E+06 |
| 6 | 2 | thick2 | p | 4.02057 | +/- 0.669320 | |
| 7 | 2 | thick2 | eebrk | keV | 17.9996 | +/- 1.47333 |
| 8 | 2 | thick2 | q | 5.88059 | +/- 5.66308E-02 | |
| 9 | 2 | thick2 | eelow | keV | 3.34427 | +/- 9.47710E+05 |
| 10 | 2 | thick2 | eehigh | keV | 5.09335E+05 | +/- 9.36953E+08 |
| 11 | 2 | thick2 | norm | 2.85250E-02 | +/- -1.00000 |
Fit statistic : Chi-Squared 1295.61 using 11 bins.
Test statistic : Chi-Squared 1295.61 using 11 bins. Null hypothesis probability of 2.98e-279 with 4 degrees of freedom
Thick target fit took 18.098 seconds
Single thermal plus thick target model fit over range 3.0-30.0 keV, all parameters free
After final fit
========================================================================
Model apec<1> + thick2<2> Source No.: 1 Active/On
| Model | Model | Component | Parameter | Unit | Value | |
|---|---|---|---|---|---|---|
| par | comp | |||||
| 1 | 1 | apec | kT | keV | 1.79000 | +/- 0.141548 |
| 2 | 1 | apec | Abundanc | 1.00000 | frozen | |
| 3 | 1 | apec | Redshift | 0.0 | frozen | |
| 4 | 1 | apec | norm | 9.37035E+05 | +/- 2.97826E+05 | |
| 5 | 2 | thick2 | a0 | 1e-35 | 95.0779 | +/- 2.64005E+07 |
| 6 | 2 | thick2 | p | 4.02055 | +/- 3.44348 | |
| 7 | 2 | thick2 | eebrk | keV | 18.4142 | +/- 5.73387 |
| 8 | 2 | thick2 | q | 5.88056 | +/- 0.173404 | |
| 9 | 2 | thick2 | eelow | keV | 3.34430 | +/- 3.03023E+05 |
| 10 | 2 | thick2 | eehigh | keV | 6.59341E+04 | +/- 6.31369E+06 |
| 11 | 2 | thick2 | norm | 2.80595E-02 | +/- 1.09979E+04 |
Fit statistic : Chi-Squared 1153.91 using 11 bins.
Test statistic : Chi-Squared 1153.91 using 11 bins. Null hypothesis probability of 2.70e-251 with 2 degrees of freedom
Thermal + thick target fit took 26.880 seconds
Chisq: 1153.914
Results
Remarks
- No background has been specified in this example.
- Fitting is still slow, on the order of 10s, which is comparable to OSPEX. Should this remain the case, the only major advantages of XSPEC over OSPEX (mulitple instruments, fit methods, error calculation MCMC) are likely to be important only for special cases.
- If the break energy eebrk is at any point less than the lower energy limit eelow, the original sunxspex code raises an exception. This behaviour will cause XSPEC to fail, so when this occurs the model instead makes no change to the calculated flux vector. This can cause long loops with no improvement, if XSPEC continues to vary the parameters in the space where eebrk < eelow. In the example, setPars() is used to ensure that eebrk is always greater than eelow. A better solution will need to be found for the future.
- This model has not yet been tested for the fitting of multiple spectra.
- This model does not make use of numpy’s module for dealing with Legendre series.
- Unlike sunxspex models, this model takes in unitless arrays. However, units are controlled by XSPEC - counts/s are converted to photons/s.
- Currently the correct behaviour of this model is partially dependent on an external file containing the coronal abundances, which are not native to XSPEC. In the future this should be changed to take advantage of sunxspex’s abundance calculations.