temperature in Sect. 4.3.2. Also other works, such as e.g. Yu et al. (2011), found an underestimation of the true ICM temperature. This systematic bias in the temperature estimates, which arose from the simulation of the event files and the extraction of the cluster spectra, asked for a further investigation of the simulation software and procedures. Several of these aspects are discussed in Sects. 5.6.3 & 5.6.5.
For the bias in the temperature uncertainties, the results by Borm et al. (2014) were mainly reproduced (comp. Sect. 4.3.3) with an average value of unity and a slightly increased scatter of±15%. Also and similarly in both approaches, a tendency of an underestimation of the true statistical uncertainty by the error-command was observed as well as no general trend with neither the cluster mass nor the cluster redshift. In general, the little deterioration for the event file ansatz, which was especially observed for those clusters with the lowest number of detected photons, was expected due to the additionally per-formed simulation steps.
In summary, the slight decrease in the temperature precision as well as in the accuracy of the uncertain-ties was predicted and suggested no significant systematics to be present in the event simulation or the spectral extraction. However, the strongly increased bias in the temperature estimates required a further investigation of possible systematics in the two procedures.
5.6 Discussion
5.6.1 Understanding the Simulation Results
To explain the above described trends of the development of the relative temperature uncertainties and the biases, we summarised the guidelines for the spectral fit (comp. also Sect. 4.5.1). The fitting process was especially influenced by the spectral line emission complexes, which are dominant for ICM temperatures of kBT 2.5 keV, as well as by the exponential cut-offat large energies (comp.
Fig. 2.8). The line complexes in general present the main constraining power for the different cluster characteristics.
In the above simulations, the cluster mass defined the ICM temperature through the applied scaling relations, where the temperature increased with the cluster mass for a fixed redshift (comp. Eq. 5.1). As the emission lines in the cluster spectra faded with increasing temperature, the fit results were degraded.
At the same time, with increasing ICM temperatures, the exponential cut-offshifted to higher energies and thus out of the peak of the instrumental effective area, which is located at energies between (0.5−2.0) keV (comp. Fig. 2.11). These aspects explained the influence of the cluster mass on the observed temperature precisions and on the biases. However, an increased cluster mass also resulted in a raised luminosity and accordingly in a larger number of detected photons, which reduced the statistical scatter in the spectrum and thus supported the spectral fit (comp. Fig. 5.4). Following the simulation results, this improvement in the statistical scatter could not compensate for the effect of the fading emission lines and the shifting cut-off.
On the other hand, an increase in the redshifts yielded a reduction in the number of observed photon events, which decreased as∝1/D2L with the luminosity distanceDL. Additionally, the energy stamp of the spectral features shifted with redshift as∝1/(1+z).
As a whole, the computed relative temperature uncertainties as well as the biases were dependent on the complex interplay between different cluster characteristics, but especially on the cluster mass and the corresponding ICM temperature, and on the cluster redshift.
5 Investigating Systematic Biases in theeROSITAEvent Files and their Analysis
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
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Ratio of Photon Counts in Dependence on the Redshift
M=1013.6Msun M=1013.9Msun M=1014.2Msun M=1014.5Msun
Figure 5.6:Ratio of the extracted number of cluster photon counts and the model photon numbers for all 19 distinct galaxy clusters in dependence on the redshift. The extracted number of counts is taken as the median value of the distribution of the analysis results of the (M,z)-combinations. Credit: Data taken from Wenzel (2014)
5.6.2 Choice of Spectral Regions
As theeSASStasks for the source detection were still under investigation and their systematics were not completely quantified, yet, the source and the background regions were defined manually. This procedure also allowed us to focus only on the possible systematics in the event simulations and in the spectral extraction software. According to the observational power of the current X-ray instruments and the general definition of the cluster scaling relations (comp. Sect. 5.3.1), we described the source extent asα500. In addition to the above argumentation, this choice of the cluster region was tested based on the number of included cluster photon counts.
To exclude any systematics in the total abundance of cluster photons, generated during the simulation of the event files, we simulated test clusters as single sources in the centre of the event files, while ne-glecting any background emission. In these cases,∼ 100% of the expected model photon events were distributed in the simulated sky area. However, since the consideredβ-profiles for the surface bright-ness of the clusters showed no defined boundaries, several of the computed photon events were located outside our considered source region ofα500. Additionally, during the realistic simulations, the back-ground emission had to be subtracted from the spectrum of the source region to yield only the cluster photon events. The close position of the background region to the source, which was required to allow for larger cluster catalogues to be simulated in the same survey field-of-view, resulted in few cluster photons of the order of∼ 1% to be considered as background emission. Accordingly, the subtraction of the slightly overpredicted background from the source spectrum lead to a further reduction of the extracted cluster events. Despite these two aspects, for the majority of our simulated clusters,∼90% of the expected cluster photon events were located within the definedα500-region (Wenzel 2014), where this trend was observed independently of the cluster mass and of the cluster redshift (Fig. 5.6). For sev-eral (M,z)-combinations, higher numbers of the extracted photon counts were observed when compared
5.6 Discussion
to the model number of photon events. A statistical scatter in the ratio between extracted and expected photon counts was expected since the generation of cluster as well as of background counts, of their energetic and their spatial distribution, was a random processes withinSIXTE. However, averaging over 108 realisations of the same cluster observation did not compensate for this scatter, yet.
This is one of the origins for the observed increase in the uncertainties of the re-constructed cluster temperatures and is commonly encountered in the reduction of observed data. A possible small bias in the number of extracted counts, which originated from the spectral extraction softwareSRCTOOLis further investigated in the following section.
5.6.3 Bias in the Simulated Spectra?
To directly test whether the application ofSIXTEandSRCTOOLresulted in systematics in the simulated cluster data, the shape of the extracted spectrum was compared to the model spectrum generated within xspec (comp. Figs. 5.7 & 5.8), where for this analysis several test cluster event files without any background emission were generated. Initially, the extracted spectrum showed a strong depletion of the photon events for energies below E ≈ 0.7 keV with a complete depletion forE 0.3 keV. These findings initiated a discussion on the value of the over-all energy threshold as well as on the treatment of split events for the futureeROSITAdata.
The energy threshold is defined based on the telemetry of the instrument, since the limited band width and communication time of the instrument ask for a restriction to transfer the data of only those photon events above a certain energy value. As a second influence on the event file spectra, split events need to be corrected for, which describe those detections for which the photon energy is distributed amongst different detector pixels. If these events are not considered, the spectrum is overestimated at the lower energies and underestimated at the higher energy end. They are commonly identified by their pattern and all involved pixels are flagged for this event and are neglected for the subsequent data analysis. To correct for these systematics, the occurrences of these events and their patterns need to be simulated thoroughly and accounted for in the instrumental response. Both aspects, the energy threshold as well as the treatment of the split events, may induce the observed bias in the cluster spectra.
Initially, the energy treshold value was set toE =0.3 keV, which explained the observed total depletion of the extracted spectrum below these energies. In discussion with the involved software developers, this threshold was then shifted toE = 0.1 keV in order to reduce the bias in the spectra. The resulting extracted spectra with the adapted threshold is displayed in Fig. 5.8. Still, an underestimation of the extracted spectrum was visible for energies below E ≈ 0.4 keV and also a further decrease in this threshold did not improve the observed bias. The software set-up with the implemented small spectral bias observed in Fig. 5.7 was then applied for the simulation and analysis of our cluster data, while the origin of this bias and its impact on the analysis results was further investigated.
Eventually, one systematic effect was discovered to originate from the conversion between the photon energy given in detector channels and in units of keV in the spectral extraction. In the observations, the energy of the detected photons is in general first listed in terms of detector channels and is later-on converted to values in units of keV. In the our appliedSRCTOOLversion, this conversion was defined based on the average energy resolution of the eROSITA channels. However, each of these individual channels shows slightly different resolutions, which are stored in theresponse matrix file(RMF)(comp.
Sect. 3.1.2). Updating the SRCTOOLto account for the information of the RMF (version 08/2014), the bias in the spectra could almost be resolved completely (Fig. 5.8), and it was debated whether the remaining slight deviations were only a statistical artifact. Additionally, the influence of the split events treatment needs to be studied in further detail and has not been improved, yet.
5 Investigating Systematic Biases in theeROSITAEvent Files and their Analysis
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normalized counts s−1 keV−1
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Comparison between Model Spectrum and Extracted Spectrum
Figure 5.7:Comparison between the spectrum simulated withinxspecin black and the corresponding extracted spectrum in red for a cluster of M = 1015 Mat z = 0.02. The normalisation of the spectrum is artificially increased to reduce the statistical scatter in the photon counts and to allow for a clear inspection of the bias between the spectra. The extracted spectrum was generated with theSRCTOOLversion of April 2014, which was also applied during our data reduction.
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Comparison between Model Spectrum and Extracted Spectrum
5.6 Discussion
As our presented simulation results were based on the previous version ofSRCTOOL, the effect of the updated task on our results was tested based on a selection of different clusters. In a first comparison, the reduced spectral bias showed only a negligible effect on our presented results and especially the bias in the estimated temperatures was not improved.
5.6.4 Catastrophic Failures
To improve the reliability of the analysis results and to approach the reduction of truly observed data, two types of catastrophic failures were defined for the spectral fit results (Borm et al. 2014, comp. also Sect. 4.2.4). The first type addressed those results for which the uncertainty region defined by the error-command was not set around the best-fit value. In this case, the data set was removed for the subsequent analysis steps as would be the procedure for real observed data with equivalent fit results.
The second type of catastrophic failures described best-fit temperatures, which were positioned outside the 3×1σ-region in the distribution of best-fit values for the 108 repeated simulations of the same cluster.
Those fit results were flagged, but still included in the analysis since these failures are not identifiable in observed data.
In the above presented results, no catastrophic failures of the first type were detected and the second type of failures occurred for only few of the 19 considered (M,z)-combinations. In those latter cases, less than 5% of the 108 realisations of the same cluster were affected by these failures (Wenzel 2014).
Accordingly, the presented simulation results were only negligibly influenced by catastrophic failures.
An equivalent finding was also discovered for the spectra-only simulations, where for clusters with available redshifts catastrophic failures of the first type did not arise and the second type of failures was detected only to an insignificant percentage (Sects. 4.3.1 & 4.5.3).
5.6.5 Discussing the Temperature Bias
As expressed in detail in Sect. 5.5, the ratio between the best-fit and the model ICM temperature, esti-mated in this extended set of simulations, was significantly increased in comparison to the spectra-only analysis (comp. Sect. 4.3.2). Several possible explanations of this bias have been investigated in the pre-vious sections. Accordingly, we excluded the influence of catastrophic failures (Sect. 5.6.4) and of the spectral bias (Sect. 5.6.3) for generating the temperature bias. The scatter and the bias in the extracted number of cluster photon counts mainly remained within ±10% and thus altered the normalisation of the spectrum only marginally. A small increase in the uncertainty of the best-fit values was expected due to this effect. What is more, the ratios of the numbers of extracted photons were almost randomly distributed around unity and were thus not able to account for a systematic and general overestimation of the cluster temperature.
Another possible origin for the temperature bias is the application of different instrumental responses for the simulation and the analysis of the spectra. For the steps withinSIXTEandSRCTOOL, the RSP for a pointed observation was convolved with an estimated vignetting to account for a more realistic instrumental effective area. In the spectral analysis, on the other hand, we manually assigned the survey response to the spectra, where both the spectra and the response were stacked for the seven telescopes.
This may have resulted in an inconsistent definition of the instrumental effective area in the different steps. A possible overestimation of the effective area during the spectral analysis would results in the assumption of reduced amplitudes of the emission lines and thus in biased-high temperature estimates.
Following these considerations, an extended, thorough inspection of the simulation set-ups within SIXTE as well as within SRCTOOLneeds to be supported. Unfortunately, the steps within the two different programmes could not easily be disentangled and the simulated spectrum was only studied
5 Investigating Systematic Biases in theeROSITAEvent Files and their Analysis
after a full simulation run, which impeded the difficulty of identifying the origin of the systematics.
Additionally, an additional bias, arising from the general treatment of the raw data independent of the applied analysis tools, needs to be considered and disentangled from the systematics in the software.
However, new updates for both softwares have been released since the work on this project. These in-cluded e.g., the option to extract the instrumental response in addition to the spectrum when applying SRCTOOL, which allows to study any systematics arising from manually assigning theeROSITAsurvey RSP to the extracted spectra. Additionally,eSASSnow includes a task to compute the exact exposure time from the event file and alsoSIXTEhas been extended by further simulation options. In conclusion, a repetition of the above simulations while applying the updated software tasks presents a potential option to solve and characterise the observed bias in the temperature estimates.