Bpow - Broken Power Law
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==Broken Power Law== | ==Broken Power Law== | ||
===Introduction=== | ===Introduction=== | ||
- | The broken power law | + | The broken power-law function can be used to model the non-thermal portion of the spectrum for a selected time interval during a flare. It is usually used with a thermal function to model the spectrum at lower energies. |
+ | |||
===Parameters=== | ===Parameters=== | ||
Revision as of 23:00, 9 September 2009
Contents |
Broken Power Law
Introduction
The broken power-law function can be used to model the non-thermal portion of the spectrum for a selected time interval during a flare. It is usually used with a thermal function to model the spectrum at lower energies.
Parameters
- a[0] - normalization at epivot (50 keV by default)
- a[1] - negative power-law index below break
- a[2] - break energy (keV)
- a[3] - negative power-law index above break
Fitting with Bpow
There are four free parameters that are allowed to vary when using Bpow to fit the non-thermal portion of a spectrum (see parameters above). In practice, a[1], the negative power law index below the break energy is set to 1.5 and fixed. This is done because the broken power law is a phenomenological fit component. The non-thermal photon spectrum is due to the bremsstralung interaction of energetic electrons with plasma. The model of this interaction (thick target or thin target) supposes that their is a low energy cutoff in the electron distribution function. This is necessary because the energy in the electrons becomes infinite otherwise. This cutoff means that there is a rollover in the resulting photon spectrum. In the broken power-law model, this rollover is represented by the sharp change in slope at the break energy. The negative power-law index of 1.5 below the break energy was arrived at by checking the calculated slope of the photon spectrum below the electron cutoff energy. This value is not definitive. A better approximation of the photon spectrum from an electron spectrum with a low energy cutoff can be obtained using the thick or thin target function available in OSPEX.
The plot below shows an example of the broken power law in count flux (top panel) and photon flux (lower panel):
In this case the break energy (a[2]) is ~15keV with a negative power law index above the break (a[3]) of 6.25. The normalization value (a[0]) of 2.51 photons cm^(-2) s^(-1) keV^(-1) is the flux at 50keV obtained from the low energy power-law component alone. The count-flux model is the photon model convolved with the detector response matrix (DRM). The DRM accounts for instrumental effects on the incident photon spectrum.
- The broken power law is an approximation to the non-thermal photon spectrum
- The negative power law index below the break, a[1], is usually fixed at 1.5, but this is not strictly necessary
- The negative power law index above the break, a[3], gives the hardness of the X-Ray spectrum, the smaller the value the harder the spectrum.