## 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 sensensivity. Here we discuss how the count rate impacts the sensitivity to polarization. We also mention how the detector impacts this number.

### 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

No actual flight hardware exists at this time. However, we have very good test versions of the detector and the mirrors, thus our effective area curve is based on a quantity known as the Current Best Estimate (CBE).

Polarization is determined by analyzing photoelectron tracks created in the detector. Only tracks that have significant extent provide directional information. Tracks that appear roughly circular effectivily decrease the modulation and since the sensitivity is linear in this factor but related to the square root of the counts, discarding these events will increase the sensitivity to polarization. Currently we obtain the best sensitivity by discarding 20% of the most circular events.

### WebPIMMS Output

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

EAxxxx the total count rate in the detector. This is useful when calculating sensitivity to variations in the energy spectrum or the light curve.

ELxxxx the count rate useful for polarization. Currently this is 0.80 times the EAxxxx rate but could change.

MAxxxx the modulated count rate. This can be used to calculate the modulation factor $<\mu>=$MAxxxx/ELxxxx.

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.