## Instructions for PIMMS

PIMMS is a simple tool to estimate count rates that we have adapted to also calculate the sensitivity to polarization. If you have never used PIMMS before, you should start by reading the original help file at the HEASARC. PIMMS was designed to assist the calculation of the exposure time needed to detect an X-ray source to a certain sensitivity. Here we discuss how the pimms output can be used to calculate the sensitivity to polarization.

### Sensitivity to Polarization

The Minimum Detectable Polarization (MDP) is given by $$MDP = {\sqrt{-2 ln(1-CL)} \sqrt{2} {\sqrt{C_S+C_B}\over{C_S <\mu>}}}$$ Where $C_S$ are source counts, $C_B$ background counts, CL is the confidence level, and $<\mu>$ is the source-count-weighted modulation factor [see ref]. For CL=0.99 and when using an imaging detector $C_S≫C_B$ for most sources, we find: $$MDP_{99} = {4.292 \over{\sqrt{C_S} <\mu}>}$$ From this we see that sensitivity is linear in the modulation factor but goes as the square root of the source counts (or the exposure time).

### The Detector

The numbers used in pimms are based on the ground calibration of the flight detectors and mirrors.

Polarization is determined by analyzing photoelectron tracks created in the detector. If a track is highly elliptical it provides more information about the direction of the original electron than tracks that are more circular. We can get a statistically better measure of the polarization by weighing elliptical tracks more. This reduces the effective number of useful counts by a small amount. The ERxxxx rate tells you the effective number of counts that should be used in all sensitivity to polarization calculations.

### WebPIMMS Output

WebPIMMS calculates and outputs three IXPE count rates. These are (where xxxx denotes the current version number):

TRxxxx is the Total count rate. This cannot be in the polarization calculations, but can be used to calculate the sensitivity to variations in the energy spectrum or the light curve. Due to telemetry limitations, if you have a bright source (>0.1 Crab) then you must estimate the count rate in the full band. This will determine how long the observation can be before the on-board storage fills and the observation will need to be broken up.

ERxxxx is the Effective count rate useful for polarization. This is the number that should be used when determining the sensitivity polarization.

MRxxxx is the Modulated count rate. This can be used to calculate the modulation factor $<\mu>=$MRxxxx/ERxxxx.

WebPIMMS also calculates the modulation factor and $MDP_{99}$ for both a 10,000 and 100,000 sec observation. You can calculate $MDP_{99}$ for other integration times by scaling by the inverse of the square root of the integration time. Clearly, you will only be able measure polarizations larger than the minimum.

### Agree to terms

When you have read the above, click the following button to go to the IXPE Web PIMMS page.