7. Choosing and Evaluating a Background Model

There are lots of useful hints and explanations about background subtraction in "RHESSI Spectroscopy - First Steps". Since a reasonable background subtraction is a fundamental pre-requisite for RHESSI hard X-ray spectroscopy, here is something more about it.

When you analyze the flare of interest, be sure to first check it's the long-term variation of the background from the quicklook observing summary plots, not only during the time of the flare but also for at least one RHESSI orbit before and after the flare. Here we will concentrate on the event that occurred on June 1, 2002 that peaked at 03:56 UT. The following window shows the observing summary from 01:00 to 07:00 UT, revealing a sinusoidal variation of the background emission due to changes in the magnetic latitude of the RHESSI spacecraft along its orbit (for details on the RHESSI background components see David Smith's "Problems, Pecularities and Phenomena in RHESSI Spectroscopy" document). The flare occurs around the maximum of the background emission when the spacecraft was at high geomagnetic latitudes. This makes the background subtraction a rather subtle issue.

For the analysis, set the observation time interval in the GUI to 1-Jun-03:20:00 - 1-Jun-04:15:00:

Then go to "Retrieve/Process Data -> Spectrum...". Choose all front detectors except 2 and 7 (the peculiarities of individual detectors are described in the "Problems, Pecularities and Phenomena in RHESSI Spectroscopy" document by David Smith). Set the time resolution to 4.0 s and choose bin code 6 (197 bins, 1-keV bands covering 3 to 100 keV, then 5-keV bands to 600 keV - check the button "Show Binning Codes" to see what choices you have). This is the best choice for this flare since there is emission detectable above 100 keV.

Click the "Plot Spectrum" button to accumulate the spectra and display them for all the intervals. Once the spectra have been obtained, click the button "Write output file..." to save the spectral data. Select the full response matrix ("0-Full calculation of diagonal, off-diagonal terms") -> "Write FITS file". Your window should look like:

Then call SPEX from an IDL session with the command "spex_proc". Read the spectral data and the spectrometer response (srm) matrix into SPEX and plot the count rates as follows:

SPEX> data,hessi,front
SPEX> _1file,hsi_spectrum_20020601_032000.fits
SPEX> dfile,hsi_srm_20020601_032000.fits
SPEX> graph
SPEX> energy_bands,6,12,12,25,25,50,50,300
SPEX> scale_bands,1,2,6,8
SPEX> th_ytype, 1
SPEX> graph
 

The sinusoidal background behavior tends to show up more prominently at high energies. So, you might try to use a higher-order polynomial fit at these energies. Let us apply a linear fit for the global energy range as well as for the energy band 6-12 keV, and a 3rd order polynomial fit for the higher energy bands (12-25, 25-50, 50-300 keV).

SPEX> back_order, 1,1,3,3,3
 

Now, starting with the first band we have to choose reasonable intervals before and after the flare during which the background is calculated.

SPEX> use_band= -1
SPEX> background ; select graphically the interval to be used for background determination
 

The same for the other energy bands. And you probably want to change the y-range.

SPEX> th_yrange,1e-3,10
SPEX> use_band=0
SPEX> back ; select background intervals
SPEX> use_band=1
SPEX> back ; select background intervals
SPEX> use_band=2
SPEX> back ; select background intervals
SPEX> use_band=3
SPEX> back ; select background intervals
 

The two images illustrate possible background selections for use_band=0 (3-12 keV band, chosen background model order=1) and use_band=2 (25-50 keV, chosen background model order=3).

There is no easy way within SPEX to plot the original count rates together with the modeled background. However, as always in SPEX you can execute every IDL-command from the SPEX prompt by typing "idl, command". Let us use this method to get a basic idea whether the derived background model is reasonable. The count rates before background subtraction are stored in the two-dimensional variable "flux" and the background data in "back":

SPEX> help, flux, back
 

The first index refers to energy bins, the second to time bins. See the help_spex.txt document by Richard Schwartz for a description of parameters used within SPEX.

Let us first check the energy band 6-12 keV where the chosen model is a 1st order polynomial (and remember that our data start at 3 keV).

SPEX> idl, plot, total( flux [ 6-3:12-3-1, * ], 1 ), /ylog, /xst
SPEX> idl, oplot, total ( back [ 6-3:12-3-1, * ], 1 )
 

Probably you'd prefer to plot the count rates as function of time, so let us do this for the 25-50 keV band:

SPEX> idl, utplot, ut [0, * ], total( flux [ 25-3:50-3-1, * ] , 1 ), /ylog, /xst,col=170
SPEX> idl, outplot, ut [0, *], total( back[ 25-3:50-3-1, * ],1)
 

In this case, the 3rd order plynomial fit yields a very good result. After evaluating the background model for the other energy bands, you may apply a 3rd order fit also to the first energy interval. To do this, set "back_order, 1, 3, 3, 3, 3", and redo the background subtraction for use_band = 0.

If your background estimates turn out to be rather bad, then you may wish to start from scratch. To undefine any background you have already subtracted, use the command "background, clear" (sets the background to zero everywhere). Afterwards, don't forget to start with "use_band=-1".

Sometimes you may find that you don't have a long enough continuous observation interval before and/or after the flare (due to RHESSI night times or the spacecraft passing through the South Atlantic Anomaly) to choose a background model of an order as high as 3 (by the way: 3 is the highest order SPEX allows). In these cases, it's probably the most safe solution to choose for each energy band individually a short interval before and after the flare (1 min or so, depending on the actual context) and apply a linear fit, i.e. use "backorder, 1, 1, 1, 1, 1". In particular, in short events 1st order models give reasonable results also when the flare is located on top of a high-latitude variation. When evaluating your chosen background model, keep in mind that inaccuracies in the background subtraction have a relatively stronger effect at high energies where the flare count rates are low. For alternative approaches to the background determination (e.g., using the data of one RHESSI orbit before/after the flare) see the suggestion in David Smith's "Behind, Beneath and Before HESSI Spectroscopy" or "BBB". You can also use data from 15 orbits before and/or after the flare to try and duplicate the same range of geomagnetic parameters as for the flare observation itself.

Finally, select a time interval around the maximum of the 25-50 keV emission and plot the count spectrum.

SPEX> select ; select graphically a time range
SPEX> count
 

Comparing the background subtracted count spectrum (yellow) with the background spectrum (orange) you see that at the chosen time interval your flare spectrum is reliable up to about 200 keV. Above, the measured count spectrum becomes dominated by the background spectrum.

This page last updated: June 27, 2011