3. Changing Fitting Models

As explained in "Spectroscopy -- First Steps", there are many spectrum models available in SPEX. The default is the photon flux model named "f_vth_bpow". It is a combination of an isothermal function plus a double power-law. Let us try another model named "f_vth_thin".

Model "f_vth_thin" assumes a thin-target bremsstrahlung spectrum. By fitting with this model, we are able to get several parameters of the electron ensemble that produced the observed X-ray photon flux assuming thin-target interactions. This is in contrast to the parameters of the measured photon spectrum obtained using the "f_vth_bpow" model.

First, let us change the model to "f_vth_thin" to fit one interval (#8) of the above 37 intervals we selected.

SPEX> ifirst, 8
SPEX> ilast, 8
 

Current interval is set to one interval at 00:30:00 -- 00:30:19.999 UT. Then we change the fitting model to "f_vth_thin":

SPEX> f_model, f_vth_thin
SPEX> photon
 

Then we will need to input the initial guesses for the 8 parameters. Here is a brief explanation of those 8 parameters:

Since the computation of this model involves an integration, the fitting speed is much slow than that of "f_vth_bpow" model. One thing we can do it to decrease the high energy cutoff, i.e. a(7). The default is 32000 keV, for most spectrum (fitting energy range below 300 keV), we can cut down to 5000 keV without affecting the high energy flux.

As a rule of thumb, we should always obtain good starting parameters before we do any fitting. After changing the parameters, you can check the spectral window to compare the model spectrum and the data points. If there is not good agreement, the model parameters should be changed by typing the photon command. When the starting parameters give good agreement with the data points, then you can expect the fitting program to converge to good best-fit values. This is achieved with the fit command.

After we set fitting range and give a good initial values for those fitting parameters, we try a model with isothermal plus broken power law electron distribution:

SPEX> free, 1, 1, 1, 1, 1, 1, 0, 0
SPEX> fit
 

The following plot is produced for interval 8 in the spectrum window:

We can check the fitting parameters as follows:

SPEX> print, apar
4.25845 3.19432 17.1155 1.58129 131.000 2.47378 10.0000 5000.00

SPEX> print, chi
1.09850
 

There is another model called "f_vth_thick" that fits a thick-target bremsstrahlung spectrum. It also has 8 parameters with the same physical meaning as those of "f_vth_thin" except for the normalization factor, i.e. a(2). For the thick-target model, a(2) is electron flux, i.e. the nonthermal electron density * source area * electron velocity (in units of 1.0e35 electrons s-1). Since "f_vth_thick" involves two integrations, the fitting speed is much slower than for the other functions. It takes a few minutes to fit one interval. The fitting time depends on how many free parameter you set and the value of the high energy cut-off a(7). This should be at least a factor of 10 greater than the highest photon energy to be fit.

Let us use "f_vth_thick" to fit the same time interval as above:

SPEX> f_model, f_vth_thick
SPEX> erange, 15, 300 ;set fitting range
SPEX> free, 1, 1, 1, 1, 1, 1, 1, 1, 0 ;model with isothermal plus broken power law with free low energy cutoff
SPEX> fit
 

The following plot is the spectral fit with "f_vth_thick" we got:

SPEX> print, chi
1.11807

SPEX> print, apar
4.16548 3.21193 0.871608 3.67201 139.870 4.50256 37.9659 5000.00
 

After fitting the spectrum, we can compute the electron distribution using the "brm_distrn.pro" in SSW. Here are the details.

This page last updated: June 27, 2011