Weight tables
We use a full-sky catalog analysis model, currently pointlike, see source_weights, to evaluate the predicted flux from a source of interest with respect to the background, the combined fluxes from all other sources.
We choose the following binning:
- energy: 4/decade from 100 MeV to 1 TeV (but only upto 10 GeV really used)
- event types: Front/Back
- Angular position: HEALPix, nside from 64 to 512 depending on the PSF
In the tables, the energy index and event type are packed into a 1-byte band index, and the HEALPix index is in NEST order.
The table output also includes the predicted flux for each band, and the spectral model used.
@ipynb_doc
def weight_table_plots():
"""
### Plots of weight vs. radius
These plots, of a strong source with little background, and a weak one, show the
value of the weight vs. the radius of the pixels in the table. These is a
plot for each energy/event type band. The top row has energies 100 MeV to 1 GeV,
the bottom row 1 GeV to 10 GeV, Front, in green, and Back in orange.
{img}
Note the absense of Back for energies below {Emid} MeV. The pointlike model does not
compute these to avoid the larger PSF and Earth limb background. The maximum radius
per band is determined by the PSF.
"""
Emid = round(10**2.5)
img = image('weight_table_plots.png', width=500, caption=None)
return locals()
weight_table_plots()
Plots of weight vs. radius
These plots, of a strong source with little background, and a weak one, show the value of the weight vs. the radius of the pixels in the table. These is a plot for each energy/event type band. The top row has energies 100 MeV to 1 GeV, the bottom row 1 GeV to 10 GeV, Front, in green, and Back in orange.
The local code used to do the unpacking is in the class WeightMan
This table is used with the data, as a simple lookup: A weight is assigned to each photon according to which energy, event type or HEALPix pixel it lands in.
Accounting for variations from neighboring sources
Consider the case where sources $S_1$ and $S_2$ have overlapping pixels. For a given pixel and band, the corresponding weights are $w_1$ and $w_2$, and we investigate the effect on $S_1$ from a fractional variation $\alpha_2 \ne 0$ of $S_2$, such that its flux for that pixel, $s_2$, becomes $(1+\alpha )\ s_2$. With the background $b$, the flux of all sources besides $S_1$ and $S_2$, we have for the $S_1$ weight,
$$ w_1 = \frac{s_1}{s_1+s_2+b}\ \ ,$$
and similarly for $S_2$. Replacing $s_2$ with $(1+\alpha ) s_2$, we have for the modified weight $w_1'$ that we should use for $S_1$, $$w'_1 = \frac{w_1}{1+\alpha_2\ w_2}\ \ . $$