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Subsections


7. Spatial-Spectral Mixing: Extended Sources and Crowded Fields

The non-dispersive high-resolution spectroscopy offered by the Resolve instrument onboard XRISM allows observation of extended sources (e.g., clusters of galaxies, supernova remnants) with an unprecedented spectral resolving power (Chapter 5). Xtend can be used for the imaging of these sources and for the spectral analysis, albeit at lower spectral resolution (Chapter 6). Given the spatial resolution permitted by the observatory, and Resolve pixel and field of view (FOV) size, the region of interest may be affected by leaked photons from elsewhere, causing Spatial-Spectral Mixing (SSM). Apart from extended sources, crowded fields with bright point sources in or near the field of view can also be affected by SSM. Therefore, caution is warranted for both the observation planning and the data analysis of extended sources and crowded fields.

In this chapter, we provide guidance on the observation planning and proposal preparation for extended sources and crowded fields that may warrant careful considerations regarding SSM, especially for Resolve. Firstly, we briefly describe SSM in Section 7.1. In Section 7.2, we provide a general guidance on which cases require careful simulations at a reasonable degree of confidence as well as strategies on how to mitigate the issue. In Section 7.3, we demonstrate how to conduct spatially-resolved feasibility studies.

In Section 7.4, we refer to tools to account for the background that becomes significant for weak sources, then in Section 7.5, we caution proposers on the accurate assessment of the pointing coordinates and branching ratios. We conclude the chapter with Section 7.6, providing considerations for observation planning that may help proposers configure their feasibility studies.

We leave theoretical and detailed practical considerations on SSM to Chapter 9.


7.1 Spatial-Spectral Mixing (SSM)

The Resolve FOV size ( $3'\times3'$) is comparable to the Point Spread Function (PSF) (HPD $\sim $1.3 ; Chapter 4), while pixel size ( $0.5'\times0.5'$) is sub-PSF. While Xtend FOV is much larger, the PSF size can still be large compared to regions of scientific interest. As a consequence, in both instruments, photons will be scattered by the PSF to and from regions of interest, resulting in angular distance and azimuth dependent “contamination". In the following, we refer to this process as “Spatial-Spectral Mixing" (SSM).

Source definition: Portion of the astrophysical source that is covered by the sky region of the Resolve FOV.

Internal SSM occurs when a source has spatially-resolved spectral features that lie within the field of view, which intermix across pixels.

External SSM occurs when emission from unwanted/“contamination" sources outside the sky region of the detector and/or the extension of the source beyond the Resolve sky region that end up inside the FOV.

Examples of the internal SSM can be e.g. a supernova remnant hosting clumps and/or hot spots with specific spectral features such as bright metal lines; a complex star-forming region with several spatially-resolved stars; or a galaxy cluster emission that varies with location across the FOV. In all these examples photons generated by different physical processes will end up contributing to pixels that do not correspond to their location in the sky.


7.2 Feasibility Recommendations for Assessing and Accounting for SSM

As shown in the Flow Chart, Figure 7.1, in case the proposers intend to observe a point source or a mainly uniformly distributed extended source whose extent is smaller than Resolve FOV, where the source is at/near Resolve aimpoint, a simple approach of spectral simulation using XSPEC tool FAKEIT may suffice, with case dependent caveats. For the extended source case above, a point source Ancillary Response File (ARF) is provided on the XRISM Website `Proposal Tools subpage”
(https://heasarc.gsfc.nasa.gov/docs/xrism/proposals/responses.html) can be used.

The website also provides an ARF for a circular region with a radius of r=5$'$ and with flat source distribution that is intended for spectral simulations of the sky background. If the source is marginally larger than the FOV, this flat ARF can be used by scaling it for the source at hand, i.e.; the model normalization has to be multiplied by ($\pi$$\times $5$^2$)/([area of source from which flux was derived in arcmin]$^2$).

Figure 7.1: A Flow Chart guiding the proposers on how to assess the significance of SSM and recommendations on how to proceed with proposal feasibility studies.
\includegraphics[width=0.8\textwidth]{.././Figures_Extended_sources/SSM_FlowChart.pdf}

In cases where there are multiple sources within FOV, and/or Resolve FOV is surrounded by sources whose emission has non-negligible SSM contribution, and/or sub array analysis is intended, and/or spatially-resolved analysis with the prospective data is intended, spatially-resolved simulations, e.g.; HEASIM, will yield the most accurate errors on the model parameters of interest.

7.2.1 Demonstration of SSM Contamination

In this section, we illustrate the SSM contamination and provide a spatially-resolved spectral simulation walk-through. In the light of information given, proposers may then decide whether their science goals would be affected by the contamination or not, and if so, learn how they can perform tailored simulations.

The external and internal SSM are illustrated in Figure 7.2 for the simple case of photons from a single point-like source spreading over the detector.

Resolved point sources within and outside Resolve FOV may require careful feasibility analysis. In Figure 7.2, the fraction of the XMA PSF that falls onto Resolve FOV is visualized for a point source like emission at 1.5 keV and 6.0 keV, and at various angular distances from the aimpoint, i.e.; panel corresponding to 2$'$ then represents the case of a point-like source that lies just outside/near the FOV, an example of external SSM. This simulation puts the optical axis at the aimpoint. Resolve optical axis is tilted about 15$''$ with respect to the nominal aimpoint direction (Section 4.2.1), hence an observation of a standard point source at the aimpoint will have an off-axis angle of $\sim $0.2$'$.

Figure 7.2: XRTRAYTRACE simulation images of Resolve FOV from a point-like source emission at various distances from aimpoint for energies 1.5 keV and 6.0 keV.
\includegraphics[width=0.98\linewidth]{Figures_Extended_sources/SSM_Frac_Image.pdf}

Figure 7.3: Raytracing simulation results on the PSF fraction on Resolve for a point-like source at various distances from aimpoint for energies 1.5 keV and 6.0 keV.
\includegraphics[width=0.6\linewidth]{Figures_Extended_sources/SSM_Frac.pdf}


Table 7.1: Raytracing simulation results on the PSF fraction on Resolve for a point-like source at various distances from aimpoint for energies 1.5 keV and 6.0 keV.
  PSF Fraction on Resolve (%)
Distance from aimpoint (arcmin) 1.5 keV 6.0 keV
0 (aimpoint) 91.2 86.5
1 87.9 83.3
2 63.2 59.8
2.5 24.2 23.0
3 9.3 8.9
3.5 4.4 4.4
4 2.5 2.6
5 $<$1 1.1
6 $<$1 $<$1

These raytracing simulations are conducted using XRTRAYTRACE tool with source parameter set to “point", and various off-axis angles are set by offaxis keyword. We illustrate the fraction for azimuthal angle (roll parameter) at 0 degrees We emphasize that azimuthal dependence on the PSF fraction is strong and non-linear. For some roll angles (one of them being 3.0$'$), the scattered PSF fraction may reach fractions as high as factor of three of the reported values in Table 7.1 by extension in Figure 7.3. The user may estimate the fraction by setting the roll angle to their desired setting and run XRTRAYTRACE.

We present the results of the PSF fraction falling on the detector with respect to the full PSF in Table 7.1 and in Figure 7.3. These fractions are obtained by diving the photons within the Resolve FOV by the total number of focal-plane photons (NRESPLN keyword of the output event file). As stated earlier, the PSF does not have azimuthal symmetry and the simulations presented here use only “roll=0.0". As demonstrated in Figure 7.3 the energy dependence of the PSF fraction is expected to be weak. With this information, the proposers can decide whether SSM affects their science case or not.


7.3 Multiple extended and point sources of interest within FOV; a spatially-resolved spectral simulation walk-through with HEASIM

One of the most comprehensive tools for observation simulations that bay be affected by the SSM is HEASIM (part of HEASoft). This software can simulated cases where e.g. the extended source has multiple sources with distinct emission features within FOV, the region of interest is a fainter portion of the source, the full extend of the source does not fit in the Resolve FOV and/or subarray Resolve analysis is intended. Simplifying assumptions are typically made regarding source geometry and spectral properties. The responses and auxilary files, i.e; specfiles_v003.tar.gz, as well as tailored HEASIM Hitomi guide and HEASIM XRISM quick start guide can be obtained from XRISM Proposal Tools Webpage.

Instructions for downloading and installing HEASIM can be found at
https://heasarc.gsfc.nasa.gov/docs/software/lheasoft/help/heasim.html

Other tools for simulating SSM in Resolve include “SIXTE”
https://www.sternwarte.uni-erlangen.de/sixte/ and “simx”
https://hea-www.harvard.edu/simx/

HEASIM allows simulation of multiple distinct emission sources within and outside the Resolve FOV as well as subarray analysis to account for the potential internal and external SSM. An example can be Resolve pointing to a galaxy cluster center with multi temperature intracluster medium plasma (extended source) as well as an AGN (point source). Below, we briefly describe the process using HEASIM and HEASoft tools.

HEASIM calculates simulated events for each input source in the “source definition file". This event file contains spatial, spectral, and temporal characteristics of the source. The spectral model of the spectrum in photons cm$^2$ s keV as a .qdp file, sky position coordinates, sky distribution; either as an image/sub-image input obtained from an instrument that has better angular resolution (Chandra, XMM-Newton), or with available analytical models should be provided for the HEASIM run. Note that HEASIM will include the non-X-ray background in its simulations, by default. You can configure this setting, as discussed later in the text.

After the simulation is complete, a spectra can be extracted from the event file for a specific region of interest, which should be fitted with the responses specific to HEASIM, i.e.; specfiles_v003.tar.gz and not the canned responses that are generated for XSPEC FAKEIT simulations.

Figure 7.4: A cartoon of the set-up for the HEASIM walk-through. The gray square with the red frame indicates the Resolve FOV. The star represents the central AGN. Blue (/orange circle) depicts a plasma at 1keV (/4 keV) with spatial extent of radius 1$'$ (/8$'$) representing galaxy cluster Cool-core(CC) (/intracluster medium(ICM)), respectively.
\includegraphics[width=0.5\linewidth]{Figures_Extended_sources/heasimCartoon.pdf}

In the following, we describe HEASIM steps for a case study of a circular extended source (r=8$'$, thermal plasma kT=4 keV intracluster medium; ICM) with another concentric plasma distribution (r=1$'$, thermal plasma kT=1 keV Cool-core: CC) where there is also a point source (AGN) at the center. Consider investigating the velocity broadening in the r=1$'$ plasma, a cool core as illustrated in the cartoon presented in Figure 7.4.

STEP 1 - Construct spectral models for each source and save them as a QDP file.
To do so; in XSPEC use the model that best describes your source (e.g.; TBabs*apec for ICM) with the norm parameter adjusted to value that yields correct flux, then convert them into models, i.e; 

XSPEC>model TBabs*apec
Set model parameter values and rescale the norm to a value such that the model flux is what is expected from the source, then: 

XSPEC>data none
XSPEC>energ 0.1 27.1 27000
XSPEC>cpd /xs
XSPEC>setplot comm wdata cluster-icm-mod.qdp
XSPEC>plot model

In our case study, there will be two more models for an AGN and a cool-core. Most simply, TBabs*powerlaw for the AGN and TBabs*bvapec, to study line broadening of the cool-core. If the models are obtained from .qdp files as demostrated above, the spec_mod parameter in the source definition file (STEP 2) will be set to “user". For the case at hand, one will define two more models for these sources: i.e.; cluster-agn-mod.qdp, cluster-CC-mod.qdp.

Alternative STEP 1- HEASIM can also be run using spectral definition keywords (spec_mod, spec_par, flux, and bandpass) directly in the source definition file where spec_mod parameter will be set to the desired model allowed by HEASIM, which are quite limited, instead of using user option.

STEP 2 - Make source definition files.

Make a “.dat" file, e.g CC-Cluster-AGN.dat that describes all source position in the sky, and source characteristics. This file enables the definition of multiple sources.

The parameters are: ra, dec, NH, spec_mod, spec_par, flux, bandpass, filename, format, units, source_spec. First line corresponds to, a 8’-circular beta-model surface brightness distribution isothermal temperature
Second line to, a 1’-circular beta-model surface brightness distribution w/ isothermal temperature, velocity broadening
Third line to the AGN
49.95,41.51,0.0,user,0.,0.,0.-0.,cluster-icm-mod.qdp,2,2,extmod(beta,0.53,1.26,0.0,0.0,0.0,8.0)
49.95,41.51,0.0,user,0.,0.,0.-0.,cluster-CC-mod.qdp,2,2,extmod(beta,0.53,0.3,0.0,0.0,0.0,1.0)
49.95,41.51,0.0,user,0.,0.,0.-0.,cluster-agn-mod.qdp,2,2

For definitions of the keywords and how they are used, please read HEASIM help file.

While selecting ra and dec keywords as the center of the astrophysical sources, check Section 7.5 for possible pitfalls about source center coordinates.

Alternative STEP 2 - Use an input image from existing X-ray data from a telescope with smaller PSF than XRISM (Chandra, XMM-Newton) instead of a spatial distribution model with keyword “extmode”.

STEP 3 - Create mock event lists and spectra with HEASIM (and Xselect)

Below, we are putting the Resolve at the center of this cluster indicated by rapoint and decpoint paremeters, for 200ks exposure time, with roll angle 0. 

heasim mission=xrism instrume=rsl rapoint=49.95 decpoint=41.51
roll=0.00 exposure=200000. insrcdeffile=CC-cluster-AGN.dat
outfile=CC-cluster-AGN.fits
psffile=sxs_psfimage_20140618.fits
vigfile=SXT_VIG_140618.txt
rmffile=resolve_h5ev_2019a.rmf
arffile=resolve_pnt_heasim_withGV_20190701.arf
intbackfile=resolve_h5ev_2019a_rslnxb.pha
flagsubex=no seed=1234567890 clobber=yes

One may set intbackfile=NONE if NXB is negligible (a bright source case).

Important note: The responses used here are HEASIM responses and not the canned responses prepared for XSPEC. In addition, while running HEASIM simulation as well as fitting the spectra extracted from the HEASIM events, one should use the point source ARF, i.e: resolve_pnt_heasim_withGV_20190701.arf regardless of the source spatial distribution, unless the user can make a tailored ARF specific to their source's spatial distribution. STEP 4 discusses the implications of using the point source ARF on the estimated flux.

Alternative STEP 3 - Shift and roll Resolve FOV.
Proposers may need to shift and roll the instrument to avoid a bright point source right on the edge of Resolve, or distinct temprature clumps within FOV that require special orientation. In which case rapoint decpoint, roll, parameters should be adjusted accordingly.

To extract spectrum from the output event file, whole FOV, one may use XSELECT tool: 

xsel:HITOMI-SXS-PX_NORMAL > read events CC-cluster-AGN.fits
xsel:HITOMI-SXS-PX_NORMAL > extract spectrum
xsel:HITOMI-SXS-PX_NORMAL > save spectrum CC-cluster-AGN.pi
One can alternatively select a subarray region using filter column before extracting spectra: 

xsel:HITOMI-SXS-PX_NORMAL > filter column "PIXEL=28:35"

STEP 4 - Calculate branching ratios.
XRISM's superiority lies in the excellent spectral resolution. In most cases, the scientific goal of XRISM proposals will be constraining line features, which require high resolution primary (Hp) events and maybe in combination with the medium resolution primary (Mp) events.

If ct/sec/pixel is larger than 1 (rule of thumb) one should check branching ratios that can be done with SXSBRANCH tool. If not, most of the events are expected to be Hp events and the proposers can skip to STEP 5.

This task computes branching ratios for each event resolution grade – for each pixel, and over the entire array. It statistically estimates these quantities using Poisson statistics, based on some count distribution in pixels and produces a more realistic version of the event file by populating the PIXEL, and ITYPE columns with the grade (ITYPE = 0:HP, 1:MP, 2:MS, 3:LP, 4:LS). 

sxsbranch infile=CC-cluster-AGN.fits filetype=sim
outfile=CC-cluster-AGN_branch.out 
pixfrac=pixfrac.txt pixmask=none 
ctelpixfile=pixmap.fits 
ctphafrac1=0.0 ctphafrac2=0.0

The new event file will then have a secondary extension .out, appended to the input event file, e.g.; CC-cluster-AGN.fits.out. To make pixel and/or grade selections, in XSELECT 

xsel:HITOMI-SXS-PX_NORMAL > read events CC-cluster-AGN.fits.out 
xsel:HITOMI-SXS-PX_NORMAL > filter column "PIXEL=28:35”
xsel:HITOMI-SXS-PX_NORMAL > filter ITYPE "0:0”
xsel:HITOMI-SXS-PX_NORMAL > extract spectrum
xsel:HITOMI-SXS-PX_NORMAL > save spectrum CC-cluster-AGN_branch.pi

Above, the spectrum extracted from only the Hp events.

STEP 5- Fitting the mock spectra with XSPEC
While fitting the spectrum and deriving errors, each source spectrum will be convolved with separate responses and will be fit with respective models: 

XSPEC12>data 1:1  CC-cluster-AGN_branch.pi 
XSPEC12>response 1:1 resolve_h5ev_2019a.rmf (For the r=8 arcmin ICM)
XSPEC12>response 2:1 resolve_h5ev_2019a.rmf (For the r=1 arcmin CC)
XSPEC12>response 3:1 resolve_h5ev_2019a.rmf (For the AGN)
XSPEC12>arf 1:1 resolve_pnt_spec_noGV_20190701.arf 
XSPEC12>arf 2:1 resolve_pnt_spec_noGV_20190701.arf 
XSPEC12>arf 3:1 resolve_pnt_spec_noGV_20190701.arf

Important note: The point-source ARF used above will end in wrong flux estimates but with the right count-rate which will enable correct statistics on the models parameters except for the normalization. If the objective of the proposal is to report fluxes, a rigorous tailored ARF generation is required. 

XSPEC12>model TBabs*apec (for ICM)
XSPEC12>... specify params
XSPEC12>model 2:CC TBabs*bvapec (for CC)
XSPEC12>... specify params
XSPEC12>model 3:AGN TBabs*powerlaw (for AGN)
XSPEC12>... specify params
XSPEC12>... fit, derive errors, etc.


7.4 Estimating the Background

In case of faint sources (e.g. galaxy cluster), the sky background should be accounted for. Additional important consideration for simulating emission from extended sources is the Non X-ray Background (NXB; Section 5.7), which has a count rate of about $\sim $6.6$\times $10$^{-4}$ counts s$^{-1}$ keV$^{-1}$ over 1-12 keV. Weak extended sources, such as outskirts of galaxy clusters, may have lower count rates, making it challenging to observe with Resolve. Proposers should take special care to simulate the NXB, which can be included in HEASIM simulation or directly as a model provided on a XRISM Proposal Planning subpage: https://heasarc.gsfc.nasa.gov/docs/xrism/proposals/responses.html


7.5 Caution: Pointing Coordinates and Branching Ratios

For the extended sources coordinates, using an existing X-ray image, if available, is highly recommended. A coordinate resolver (such as SIMBAD and NED) provides a single location for an extended object. The original source may have reported the peak position of the optical emission, for example, which may or may not be what a XRISM proposal needs. For an extended source without an X-ray image, a comparison of multiple sources (preferably including original reports) is strongly recommended.
In the ARK/RPS form, proposers should pay attention to report the correct branching ratio for Hp events that is obtained from the WebPIMMS. Note that WebPIMMS calculation is appropriate for an on-axis point source, and for spatially-resolved analysis, the branching ratio can be inferred from the SXSBRANCH tool (Section 7.3. Given that, if WebPIMMS show high Hp fraction for an extended source, it is valid to be used in the ARK/RPS form. If Hp fraction is well below 90%, then a detailed simulation is necessary for a quantitative assessment.


7.6 Considerations for Observation Planning

Most extended sources and crowded fields are affected by SSM. The best way to asses its impact is from existing X-ray data. Below we list a few things to consider while investigating whether SSM is important.

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