Profiles

Different from X-ray spectra, which are usually presented without deconvolution. In imaging analysis, people always show ‘surface brightness’ profiles rather than ‘count’ profiles.

Channel and bin

Channel is the smallest unit of a profile. The width of the channel should be smaller than the PSF width. The surface brightness in the $i$th channel is

\[S_i = \frac{N_{\mathrm{total},i} - N_{\mathrm{NXB},i}} {A_\mathrm{pixel}\sum_{j}{t_{i,j}} }\]

To calculate the surface brightness in each channel, the package first calculate the total count number, scaled NXB count number, and the sum of exposure in each channel. When fitting a profile, the model is calculated in each channel as well.

In most cases, the count number in each channel is small. In other words, the raw profile is oversampled. Although the fit results will be the same when use the C-statistics, to better present the profile, rebinning is needed.

Column	Description
r	Bin radius
r_error_left	Left bin width
r_error_right	Right bin width
sb	Observed surface brightness
sb_error	Observed surface brightness uncertainty
bkg_sb	Subtracted NXB profile
bkg_sb_error	NXB profile uncertainty
model_sb	Model profile
total_cts	Total count number
bkg_cts	Scaled NXB count number

Profile types

There are two types of surface brightness profiles:

• Radial profile

• Azimuthal profile

Binning methods

The sbfit package supports three binning methods:

• Minimum total count

• Linear step

• Logarithmic step