New Resonance Scattering Model in AtomDB: Application to Line Suppression in Galaxy Clusters and Elliptical Galaxies

In this paper, we present the simple, one-step, self-consistent, and fast resonance scattering model rsapec based on the AtomDB database. This model can be used as an alternative to the commonly used APEC model for fitting X-ray spectra with optically thick lines. The current model is intended, in general, for verifying the presence of the effect and for spectral modeling of galaxy clusters and elliptical galaxies under applicable assumptions. We test rsapec to derive the line suppression in the elliptical galaxy NGC 4636 and the Perseus cluster of galaxies and obtain resonance suppressions of ∼1.24 and ∼1.30, respectively.

X-ray spectral lines are subject to being distorted by resonant scattering (RS).Resonant scattering occurs when optically thick line photons are absorbed by ions with similar resonant transition energies and are immediately reemitted in another direction.This process redirects photons, suppressing resonance line emission in some areas with matching enhancements in others.For example, in galaxies and clusters of galaxies, the resonant line intensities are reduced towards their center and enhanced towards their outskirts.
Over the years, several studies reported the detection of the RS effect and demonstrated the importance of incorporating resonance scattering in modeling the X-ray spectra (Gilfanov et al. 1987;Shigeyama 1998;Churazov et al. 2004;Sanders & Fabian 2006;Nelson et al. 2023).RS is crucial for the accurate determination of the abundances of heavy elements in the intra-cluster medium (Akimoto et al. 2000;Sarkar et al. 2022a), measurements of velocity fields and anisotropy of gas motion (Churazov et al. 2010;Sarkar et al. 2022bSarkar et al. , 2023)), and the polarization of bright X-ray emission lines in galaxy clusters and elliptical galaxies (Zhuravleva et al. 2010).RS can be important for diagnostics of density or ionization state using He-like ions, Fe L shell ions, or the ratios of He-like to H-like ions (Schmelz et al. 1992).RS has also been suggested as an explanation for the weakness of O VII lines in the shell of the Cygnus Loop supernova remnant, which otherwise would imply a low oxygen abundance or charge transfer (Uchida et al. 2019).
Tackling the problem of RS is not straightforward.Monte Carlo radiative transfer simulations have been extensively used in the context of RS in galaxies and clusters of galaxies (Gilfanov et al. 1987;Sazonov et al. 2002;Molnar et al. 2006;Zhuravleva et al. 2011).Examples include the Geant4 toolkit used for simulating the passage of photons through matter with functionalities like complex geometries and tracking (Agostinelli et al. 2003;Hitomi Collaboration et al. 2018) and radiative Monte Carlo simulations used for the cluster ICM (Sazonov et al. 2002;Churazov et al. 2004;Zhuravleva et al. 2010).The above techniques are rigorous and time-consuming.
In this paper, we present a simple, one-step, and fast RS model for collisionally-ionized plasma for elliptical galaxies and galaxy clusters.Our new RS model, rsapec, can be used as an alternative to the commonly used APEC model for fitting the X-ray spectrum with optically thick lines.This model aims to verify the presence of the effect and for spectral modeling of galaxy clusters and elliptical galaxies under relevant assumptions outlined in Shigeyama (1998).Sections 2 and 3 elaborate on the theoretical background and the model parameters used for constructing the rsapec model.Section 4 shows the application of the rsapec model to the elliptical galaxy NGC 4636 and the Perseus cluster of galaxies.Section 5 discusses our results.

THEORETICAL BACKGROUND:
priyanka.chakraborty@cfa.harvard.eduarXiv:2310.03892v1[astro-ph.HE] 5 Oct 2023 2.1.What drives intensity change in resonance lines?Line intensities in observed spectra is suppressed if line photons are scattered or destroyed.In resonance scattering, photons in the lines considered are not destroyed but just scattered out of the line of sight, effectively causing a migration of photons from the dense to the more diffuse regions of astrophysical objects.This model does not include photons scattered into the line of sight, which is only important in the outer parts of a cluster and can even enhance the resonance line strength (Gilfanov et al. 1987).Resonance enhancement will be addressed in a future paper.
Photons can also be scattered due to electron scattering escape, as a result of photons scattering off high-speed electrons, and receiving large Doppler-shifts from their line-center (Chakraborty et al. 2021(Chakraborty et al. , 2022)).In addition, photons can be destroyed due to processes like Case A (optically thin) to Case B (optically thick) transfer and resonant Auger destruction (Ross et al. 1996;Chakraborty et al. 2020a,b,c).While the above processes become important at large hydrogen column densities (N H ∼ 10 23 −10 24 cm −2 ), RS effects can noticeably alter line intensities at the much smaller hydrogen column densities (N H ∼ 10 20 −10 21 cm −2 ) typically found in galaxy clusters and elliptical galaxies considered in this paper.

Calculating the RS factor
Optical depth at a line's center (τ 0 ) is defined as: where h is the Planck constant, c is the speed of light, r e is the classical electron radius, f is the oscillator strength for the given transition, n p is the proton number density, Z is the elemental abundance, δ i is the ion fraction at the given temperature, ∆E is the Doppler velocity width described by the following equation: where E 0 is the energy of the transition, A is the atomic weight of the element, m p is the proton mass, and V 1,turb is the the line of sight velocity dispersion (Gu et al. 2018).
We adopt a similar approach as used by Shigeyama (1998) for calculating the emergence of resonance lines of line-center optical depth τ 0 from optically thick plasma.Shigeyama (1998) investigated the effect of resonance line scattering in altering the surface brightness profile of resonance line emissions by numerically solving radiative transfer equations for an isotropically emitting radiation source by Λ-iteration method , and estimated the RS factor (f , spectral intensity ratio with and without resonance scattering) at the line-center (see figure 4 in their paper).
We use their reported f values and interpolated for the optical depths which didn't have the information for the RS factor.For computational efficiency, we exclude lines with τ < 0.05 with negligible line scattering (< 2%) from the RS calculation.The fraction of photons scattered away due to RS at the line-center is therefore f scattered = 1-f .Line optical depths vary along the line profile following a Voigt profile distribution.Line photons are absorbed and re-emitted, diffusing slowly in space until they reach the wings of the line with small optical depth and freely escape the cloud (Osterbrock 1962).For simplicity, it can be assumed that the scattered photons follow the Doppler line profile α(x)= exp(-x 2 ), where x =(E -E 0 )/∆ E (Pozdnyakov et al. 1983).This Gaussian approximation is sufficient given the resolving power and signal-to-noise of the current and near-future X-ray observatories.We construct a Gaussian line profile G(x) = I 0 f scattered exp(-x 2 ) to account for the photons scattered away from our line of sight, where I 0 is the maximum intensity of the unscattered default AtomDB line profile.We further subtract G(x) from the default AtomDB line profiles to produce the RS-corrected line profiles.

MODEL PARAMETERS:
The new resonant scattering model rsapec presented in this paper has been designed based on the modified version of apec, which models X-ray emission from collisionally ionized, optically-thin astrophysical plasmas (Smith et al. 2001;Foster et al. 2012).The apec model calculates the line emissivities using three external model parameters-electron temperature, metal abundances, and redshift.However, solving for equations 1 and 2 is a prerequisite for accurately synthesizing the spectrum for an optically thick plasma subject to resonance scattering.For constructing rsapec, we added two additional model parameters to apec -line of sight velocity broadening in one dimension (V 1,turb ) and nL, Figure 2. Left: X-ray spectrum of the Perseus cluster core (outer region) fitted with m1(=tbabs*bapec, blue line) and m2 (=tbabs*rsapec, red line) within the energy range 6.0-7.0 keV.Right: The same spectrum fitted with m1 and m2 within a narrower energy range (6.5-6.6 keV) around the Fe Kα complex.where nL is the electron density (n e ) integrated over line-of-sight: We chose nL as a free parameter in rsapec as n p (and therefore n e1 ) is the only direct r-dependent quantity in equation 1.The quantity δ i depends on the temperature, which in galaxy clusters is only slightly dependent on radius (Russell et al. 2008), at least up to 100 kpc after which resonance suppression usually becomes unimportant.We, therefore, neglect the radial dependence of δ i for simplicity.
We also introduced rsvapec and rsvvapec, equivalent to vapec and vvapec, respectively.rsvapec has 14 extra model parameters with the option to change abundances of the elements: H, He, C, N, O, Ne, Mg, Al, Si, S, Ar, Ca, Fe, Ni. rsvvapec has 30 extra model parameters with the option to vary the abundances of all the elements between H and Zn.
We also adjusted the above models to be compatible with pyXSPEC (Arnaud 1996).Equations 1-2 are simultaneously solved along with the f factor and fitted with the observed spectrum within the AtomDB database to determine best-fit parameters for galaxies and clusters of galaxies with optically thick emission lines.Utilizing the fitted nL value, abundances, and ionization fraction2 , it is also possible to get constraints on turbulent velocities.

MODEL APPLICATIONS:
We apply our new RS model to model the resonance line suppression in NGC 4636 observed by RGS onboard XMM-Newton and the outer core of the Perseus cluster observed by Hitomi.The observational log of the above observations is listed in Table 1.In both cases, best-fit results were obtained by minimizing C-statistic (Cash 1979).The parameter errors were measured with 1σ confidence.The velocity listed in tables 4 and 5 is only the one-dimensional turbulent velocity, which dominates over thermal broadening in clusters and galaxies.The widths of the emission lines within AtomDB is calculated considering both thermal and turbulent broadening.

NGC 4636
NGC 4636 is a giant elliptical galaxy shining brightly in the X-rays.High-resolution XMM-Newton observations of NGC 4636 revealed a wealth of characteristic soft X-ray emission lines from various ion stages of nitrogen, oxygen, neon, magnesium, and iron (Xu et al. 2002).We use the 64 ksec first-order RGS spectrum of NGC 4636 as a test case of the RS model on elliptical galaxies.We used the XMM-Newton tool rgsproc for RGS data reduction for a cross-dispersion region of 3.5' width.The first-order spectra from RGS1 and RGS2 was combined using the tool rgscombine.Table 1 lists the observational log of the spectra.Several detected has τ > 0.1, Fe XVII 15.015 Å (0.8258 keV) line being the only transition with significant optical depth (τ ∼ 0.93).Refer to table 2 for the list of optical depths with more than τ > 0.1.
Firstly, we attempted to fit the observed spectrum within the energy range 0.33-2.5 keV, including most of the line and continuum emission with a single-temperature bapec model multiplied with the pyXSPEC routine tbabs to account for the galactic absorption.The absorbing hydrogen column density is set to 2.0×10 20 cm −2 using the measurement of the galactic atomic hydrogen column density by HI4PI Collaboration et al. (2016).The pyXSPEC routine rgsxsrc was used to account for the spatial distribution of the X-ray emission along with the MOS1 image as done by Fukushima et al. (2022).The boresight required in the rgsxsrc routine was set to the X-ray brightest point of the image.Using the model m 1 (=tbabs*bapec) modified by rgsxsrc we obtained a best-fit temperature of ∼ 0.64 keV, and reduced χ 2 = 3847.43/3222.Next, we fit the observed spectrum within the same energy range with the rsapec model multiplied with tbabs (m 2 =tbabs*rsapec) and convoluted with rgsxsrc .The fit to the spectrum was improved, with χ 2 = 3798.39/3221and a best-fit temperature of ∼ 0.65 keV was obtained.The measured value of the one-dimensional turbulent velocity was 153.35 +62.06  −45.69 km/s and 165.01 +57.29  −49.23 km/s for m 1 and m 2 respectively, consistent with the turbulence measurement in NGC 4636 by Ogorzalek et al. (2017) (121 +51 −35 km/s).Table 4 lists the best-fit parameters for m 1 and m 2 in 0.33-2.5 keV energy range.The measured value of nL was 8.12 × 10 20 cm −2 , which agrees well with the estimate of nL for NGC4636 as shown in the appendix.
The left panel of Figure 1 compares the fit of m 1 and m 2 within the same energy range.The emissivity of the 15.015 Å Fe XVII line with optical depth close to unity is significantly affected, and the emissivities of the other lines listed in table 2 are partially affected by resonance scattering.As a result, we get a slightly better fit with m 2 compared to m 1 .The right panel of Figure 1 compares the two models within a narrow energy range (0.80-0.85 keV) around the 15.015 Å Fe XVII line.Within the narrow range, the fit of m 2 (χ 2 = 120.97/85 is noticeably better compared to that of m 1 (χ 2 = 146.23/86)with an F-test probability << 0.01.We estimate the line suppression in Fe XVII due to RS to be ∼ 1.24.Two-temperature/multi-temperature models showed no noticeable improvement in the fit to the spectrum.

The Perseus cluster
Possible suppression in the 6.7 keV line of the He-like iron in the X-ray spectrum of Perseus cluster has long been a topic of interest (Gilfanov et al. 1987;Akimoto et al. 1999;Churazov et al. 2004;Gastaldello & Molendi 2004;Sanders & Fabian 2006;Russell et al. 2008;Zhuravleva et al. 2013).However, given that the Fe Kα spectral lines were unresolved, no compelling evidence of RS was detected in the observed spectra.For the first time, the Soft X-ray Spectrometer (SXS) onboard Hitomi separated the resonance line in the Fe Kα complex from other line components, detecting a suppression in the Fe XXV resonance (w) by a factor of ∼ 1.3 at the core of Perseus cluster.An ad hoc technique using a negative Gaussian to compensate for the RS suppresion was used to estimate this factor alongside an optically thin APEC model.
Our newly formulated models use theoretical scattering probability calculations to estimate the RS factor for the emergence of the Fe XXV resonance (w) line from a collisionally-ionized plasma as described in section 2. Optical depths were generated using the APED database (version 3.0.9).Table 3 shows the list of transitions with τ > 0.1 for the best-fit parameters at Perseus core.The model details for estimating best-fit parameters are discussed below.
We extracted the spectra for the outer region of Perseus core (30-60 kpc) using HEAsoft3 for observations with observation IDs listed in table 1.The observations' event files were merged and filtered using Xselect.Four distinct NXB spectra were derived from the four event files using sxsnxbgen and then averaged via mathpha.RMF, exposure map, and ARF are produced using sxsmkrmf, ahexpmap, and aharfgen, respectively.
We fitted the extracted without and with RS models: bapec and rsapec around the Fe Kα complex.The multiplicative pyXSPEC routine tbabs was included in each fit to account for the galactic absorption, with the absorbing hydrogen column density set to 1.38×10 21 cm −2 (Kalberla et al. 2005) towards the direction of the Perseus cluster.
Table 5 compares the best-fit model parameters fitting the observed spectrum between m 1 (=tbabs*bapec), and m 2 (=tbabs*rsapec) within the energy range 6.0-7.0 keV.Using m 1 , we obtained a best-fit temperature of 4.07 keV with a Cstat/d.o.f of 2390.51/1995.The model m 2 improved the fit to the observed spectrum with a best-fit temperature of 4.08 keV and a Cstat/d.o.f of 2314.05 /1994.The improvement to the fit is prompted by inclusion of the RS effect in the w line in m 2 , the only optically thick line observed in the spectrum.The emissivity for the w line is noticeably suppressed by RS.The measured value of nL was 1.2 × 10 22 cm −2 , which agrees well with the estimate of nL for the Perseus cluster as shown in the appendix.The turbulent velocity was measured at 167.80 ± 9.83 km/s for m 1 and 172.12 ± 9.11 km/s for m 2 , consistent with the value previously reported by Hitomi Collaboration et al. (2018) (164 ± 10 km/s).
The left panel of Figure 1 shows the spectrum of the Perseus outer core within 6.0-7.0 keV fitted with m 1 (Cstat/d.o.f = 2390.51/1995) and m 2 (Cstat/d.o.f = 2314.05/1994).The right panel compares the two models within a narrower energy range immediately around the Fe Kα complex (6.5-6.6 keV).The fit of m 2 (Cstat/d.o.f = 225.57/195) is significantly better than that of m 1 (Cstat/d.o.f = 280.18/196)with the F-test probability of << 0.01, especially the fit to the w line.Comparing m 1 with m 2 we find a RS line suppression factor of ∼ 1.30 in w.

DISCUSSION
We note that Sanders & Fabian (2006) constructed an xspec model for fitting spectra from clusters including resonance scattering.Their model calculated the emission spectrum from N annuli divided into multiple subannuli in the sky using the APED atomic database (version 1.3.1) to generate a list of resonance lines.
Our RS model rsapec is self-consistently built into the AtomDB databse where the emission spectrum is estimated solving thousands of atomic rates, just like apec/bapec but inclusive of the RS effects.rsapec is almost as fast as apec, and can be used to model resonance scattering in both elliptical galaxies and clusters of galaxies.In the current version of rsapec, scattering effects are estimeted based on a spherical geometry as described in Shigeyama (1998), which used a gas density profile with a 1D-β model with β = 0.5.In clusters, rsapec will model resonance scattering for the inner 100 kpc radius, beyond which resonance enhancement due to scattering into the line of sight becomes important.In future, we plan to extend the model to include a full radiative transfer treatment of the resonance scattering, which will include the flexibility to adjust the β values, resonance enhancement at radial distances larger than 100 kpc, and non-spherical geometries.The current model will also be used as a template for modeling RS processes in sources like cataclysmic variables for which the geometry or spatial resolution might differ but the approach to RS is the same.
We applied rsapec to fit the spectrum of the elliptical galaxy NGC 4636 and the Perseus clusters of galaxies.In perseus cluster, we estimated a suppression of ∼ 1.30 in the optically thick line Fe XXV Kα w (6.7004 keV) line, which compares well with the previously measured RS factor (∼ 1.28) by Hitomi Collaboration et al. (2018).For NGC4636, we estimated a suppression factor of ∼ 1.24 in the Fe XVII (0.8258 keV) line, without any prior studies available.We ignored all lines with τ < 0.05 from our resonance scattering treatment.
The XRISM mission, scheduled to launch in the next few months, will observe a sample of galaxies and clusters with optically thick lines.The rsapec model will be a self-consistent and one-step tool for extracting the best-fit parameters from the observed XRISM spectrum fitting the optically thin and optically thick lines simultaneously in place of the previously applied ad-hoc technique of using negative Gaussians alongside optically thin apec model to account for the RS suppression.

APPENDIX
A. ESTIMATE FOR nL -NGC 4636 Voit et al. (2015) estimated the radial profiles of electron density (n e ) of a sample of elliptical galaxies, including NGC 4636.Within the central 1 kpc region, n e is approximately constant in NGC 4636 (n e ∼ 0.12 cm −3 , refer to figure 1 in their paper), whereas within 1-10 kpc, the density profile steeply declines.The density profile integrated over the inner 10 kpc is: The rsapec model is now available at the main AtomDB website: http://www.atomdb.org/.

Table 1 .
Archival RGS/XMM-Newton observation of NGC 4636 and SXS/Hitomi observation of Perseus cluster.The SXS data for 4 observations (observation id: 100040020-100040050) were combined for a total exposure time of 243.53 ksec.

Table 2 .
List of lines with τ > 0.1 in NGC 4636 using best-fit parameters from Table4.

Table 3 .
List of lines with τ > 0.1 scattering in Perseus using best-fit parameters from Table5.

Table 4 .
Smith et al. (2000) for for m1(=TBabs × bapec)) and m2(=TBabs × rsapec) fitting the summed first-order RGS spectrum of NGC 4636 within the energy range 0.33-2.5 keV.The XSPEC convolution model rgsxsrc has been used to account for the spectral broadening of the extended source.The redshift is taken fromSmith et al. (2000)and has been frozen.

Table 5 .
Sanders et al. (2020)or m1(TBabs × bapec)and m2(TBabs × rsapec) fitting the Fe Kα complex of Perseus core observed by Hitomi.Fits are done for the energy range 6.0 to 7.0 keV for the outer region of Perseus core.The redshift is taken fromSanders et al. (2020)and has been frozen.