Characterisation of cosmic ray induced noise events in AstroSat-CZT imager

Abstract

The Cadmium Zinc Telluride (CZT) Imager onboard AstroSat  consists of pixelated CZT detectors, which are sensitive to hard X-rays above 20 keV. The individual pixels are triggered by ionising events occurring in them, and the detectors operate in a self-triggered mode, recording each event separately with information about its time of incidence, detector co-ordinates, and channel that scales with the amount of ionisation. The detectors are sensitive not only to photons from astrophysical sources of interest, but also prone to a number of other events like background X-rays, cosmic rays, and noise in detectors or the electronics. In this work, a detailed analysis of the effect of cosmic rays on the detectors is made and it is found that cosmic rays can trigger multiple events which are closely packed in time (called ‘bunches’). Higher energy cosmic rays, however, can also generate delayed emissions, a signature previously seen in the PICsIT detector on-board INTEGRAL. An algorithm to automatically detect them based on their spatial clustering properties is presented. Residual noise events are examined using examples of Gamma Ray Bursts as target sources.

Appendix A: Algorithm for detecting ‘DPHstructures’

Figure A1

Histograms of (a) $N_\mathrm{{points}}$, (b) $M_\mathrm{{sum}}$, and (c) $N_\mathrm{{pairs}}$ with different values of ‘threshold’. Since most of the pairs are non-identical, $N_\mathrm{{points}}$ is more likely to be even than odd, hence it shows regular dips at odd integers (as can be seen as slight dips in (a)). It is observed that these parameters are insensitive to the value of ‘threshold’ chosen. Hence, the ‘threshold’ is fixed it at its most conservative upper limit throughout the work.

Figure A2

(a) Histogram of the parameter ${M_\mathrm{{sum}}}/{N_\mathrm{{points}}}$ for the DPHs which are not flagged. This ratio rarely goes close to 3, which is the value of ‘allowable’ used for flagging. (b) Same for the ones that are flagged. Note that although the total number of flagged DPHs in a typical dataset is much smaller than the number of DPHs that are flagged, most of them do not have any hot pairs, hence both $M_\mathrm{{sum}}$ and $N_\mathrm{{points}}$ are zero. Figure (a) includes only those within finite values of $M_\mathrm{{sum}}$ and $N_\mathrm{{points}}$, explaining why the total number is smaller than in Fig. (b). The sharp increase at values close to 4 in (a), compared to the rarity of those in (b) below 3, demonstrates that the distinction is real. The reality of this distinction is also verified by manual examination of each DPH for long stretches of data which preferentially include weak as well as bright GRBs, examples of which are given in Fig. A4.

Figure A3

Random DPHs are simulated with the event-rate as input. The parameter ‘allowable’ is allowed to vary, and flagging is carried out on the random DPHs based on these variable values. The plot show the resulting number of DPHs flagged as a percentage of the total number of DPHs simulated (5400), as a function of the variable. An average count-rate of 150 per second, and a high count-rate during bright GRBs, of 1500 per second, are considered. The flagged percentage is 0 for $M_\mathrm{{sum}}/ N_\mathrm{{points}}> 3$, proving the robustness of the algorithm for both the average data and during GRBs. In fact, it is more robust when the count-rates are high as seen during GRBs, i.e. DPHs during bright GRBs have $\sim$0 probability of getting flagged.

Figure A4

Instructive examples of Detector Plane Histograms (DPH), plots of counts shown at positions $\mathrm{det}\,x$ vs. $\mathrm{det}\,y$. Top: On the left is a DPH which shows clustering (the color-bar is of counts), with the identified clustered events shown in the right. Bottom: On the left is a DPH that does not show clustering. The pairs that are used to test the clustering are explicitly shown in the right to demonstrate that the presence of such random pairs are not enough to flag this DPH.

The aim of such an algorithm is to consider a DPH, and numerically decide whether the DPH shows any spatial clustering or not. This algorithm will output a flag 0 if clustering is detected or 1 if it is not. A requirement of such an algorithm is that it should be independent of the total number of events in the DPH, since it is to be run on DPHs made during average count-rates as well as during GRBs. The basic assumption made here is that genuine X-ray photons (from the astrophysical sources of interest as well as background X-ray photons extraneous to the instrument) are independent events and are randomly distributed in the detector plane, whereas the ‘noise’ events, ether induced by cosmic rays or from local electronic effects, would be spatially clustered in the detector plane.

The algorithm is detailed below:

• Consider only those pixels in the DPH which register non-zero counts. If there are n such pixels, there are $^{n}C_{2}$ pairs. For each pair, calculate a measure of ‘hotness’,

  $$\begin{aligned} m{}_{ij} = \dfrac{c{}_{i}\times c{}_{j}}{D_{ij}}, \end{aligned}$$

  where $c_{i}$ is the count in the i-th pixel and $D_{ij}$ is the distance between the pixels (in units of detx/dety, which is unity). This quantity is large if count in either pixel is large and/or if the distance between the pixels constituting the pair is small.

• If

  $$\begin{aligned} m{}_{ij} > \mathrm{threshold}, \end{aligned}$$

  call it a ‘hot pair’. It is to be noted that the maximum allowable value for threshold is

  $$\begin{aligned} \mathrm{threshold}_{\mathrm {max}} = \dfrac{1\times 1}{\sqrt{2}} \simeq 0.707, \end{aligned}$$

  which is the case for two diagonally-located neighbouring pixels registering 1 count each. If ‘threshold’ is larger than this, we will miss these hot pairs, thus defeating the purpose.

• Construct the set of all pixels which contribute to any such hot pair.

• Modify the choice of hot pairs: If a pair is such that it consists of two neighbouring pixels only, each registering one count, and there is no hot pixel in its immediate neighbourhood, then do not consider the pair for the following steps. This ensures that actual double events are not considered whereas neighbouring pixels with one count each in the neighbourhood of a cluster are retained.

• Calculate the ‘gross’ parameters:

  • (1) total number of non-identical points contributing to the identified hot pairs: $N_\mathrm{{points}}$;

  • (2) the sum of the measures of the hotness for each such hot pairs:

    $$\begin{aligned} M_\mathrm{{sum}}= \sum _{\{\mathrm {all\, pairs}\}}m_{ij}\,; \end{aligned}$$

  • (3) the number of hot pairs detected (note that even if one pixel contributes to two/more hot pairs, all these pairs are counted): $N_\mathrm{{pairs}}$.

• Construct a parameter based on these gross parameters as a proxy for the randomness in the DPH. When the value of this proxy exceeds a certain cutoff, parametrized by ‘allowable’, then the DPH is flagged, i.e. deemed to show clustering; otherwise not.

• If the DPH shows clustering, identify only those events in it that contribute to this flagging. Particularly, remove any lingering isolated single or double event that may have correlated with a pixel registering multiple counts, owing only to their proximity.

To optimize the values of ‘threshold’ and ‘allowable’, we resort to simulations of random DPHs, with mean count-rate of single and double events as inputs. The mean count-rate is typically 90 events s$^{-1}$ for single and 60 events s$^{-1}$ for double events, so in a 100 ms timescale, they are 9 and 6 events respectively. First, the number of single and double events to be chosen for a particular DPH to be simulated are drawn from Poisson distributions with the given means. Then, these many values of detx and dety are drawn from a uniform random distribution of all possible detx and dety values (0 to 63). For double events, one of the neighbouring events is first chosen randomly and the other is drawn randomly from the neighbouring coordinates, taking due care of corners and edges. For the case of GRBs, the mean count-rates input into the simulation process are increased, as discussed below (see Fig. A3).

For each such simulated DPH, the gross parameters $N_\mathrm{{points}}$, $M_\mathrm{{sum}}$, and $N_\mathrm{{pairs}}$ are calculated, and this is done on multiple DPHs (typically 5400 for one full orbit) with different inputs to the parameter ‘threshold’. The identification of hot pairs based on ‘threshold’ is insensitive to the value of this parameter, as demonstrated in Fig. A1. Hence it is safe to keep it fixed at its most conservative maximum value, i.e. 0.70, which will detect diagonally-placed neighbouring pixels each registering a count.

Next, we experiment the construction of ‘allowable’ based on the three gross parameters, and flag random DPHs based on the different experimental values of these parameters. It turns out that both $\mathrm{allowable} = M_\mathrm{{sum}}= 8$ and $\mathrm{allowable} = N_\mathrm{{pairs}}= 8$ flag less than $1\%$ random DPHs, but this conclusion is seen to break down in the presence of bright GRBs like GRB160802A, since the number of photons in the DPH are $\sim$10 times greater than the usual, resulting in random pixels getting paired and marked as hot pairs. Normalizing any of the parameters by the total number of photons does not help because extremely bright DPHstructures have total number of counts comparable to the total counts in random DPHs during GRBs, simply because the clustering illuminates its neighbourhood very brightly. Hence, we define $\mathrm{allowable} = M_\mathrm{{sum}}/ N_\mathrm{{points}}$, which normalizes for the additional $M_\mathrm{{sum}}$ contribution from the pairs that are created due to chance co-incidence of a larger number of random events during GRBs. This simple modification fantastically discriminates clustered DPHs from random ones, as shown in Fig. A2. The reason is that, although the total number of counts in a clustered DPH is large, the clustering is spread over a few pixels, and the same pixels register many events; on the other hand, random DPHs with increased total counts, where the $M_\mathrm{{sum}}$ is increased by co-incidental pairing of random events, have many such pairs which are themselves randomly distributed over the entire quadrant. In comparison, $\mathrm{allowable} = M_\mathrm{{sum}}/ N_\mathrm{{pairs}}$ does not do a better job because the small number of neighbouring pixels in a cluster tend to pair up with most of the other pixels in the cluster.

Random DPHs from GRBs and during average count-rates are examined along with DPHs that show clustering: it is seen that $\mathrm{allowable} = M_\mathrm{{sum}}/ N_\mathrm{{points}}= 3$ distinctly separates clustered DPHs from random ones, whether they are during a GRB or otherwise. This is verified first visually by looking at a significant number of DPHs manually, and also demonstrated in Figures A2 and A3. Examples of detected DPHstructures and DPHs with non-detections are shown in Fig. A4.