On the influence of high energy electron populations on metal abundance estimates in galaxy groups and clusters
aa r X i v : . [ a s t r o - ph . C O ] O c t Astronomy&Astrophysicsmanuscript no. metal-arxiv c (cid:13)
ESO 2018November 13, 2018
On the influence of high energy electron populations on metalabundance estimates in galaxy groups and clusters.
D. A. Prokhorov , Institut d’Astrophysique de Paris, CNRS, UMR 7095, Universit´e Pierre et Marie Curie, 98bis Bd Arago, F-75014 Paris, France Moscow Institute of Physics and Technology, Institutskii lane, 141700 Moscow Region, Dolgoprudnii, RussiaAccepted . Received ; Draft printed: November 13, 2018
ABSTRACT
Aims.
Spectral line emissivities have usually been calculated for a Maxwellian electron distribution. But many theoretical works ongalaxy groups and clusters and on the solar corona suggest to consider modified Maxwellian electron distribution functions to fitobserved X-ray spectra. Here we examine the influence of high energy electron populations on measurements of metal abundances.
Methods.
A generalized approach which was proposed in the paper by Prokhorov et al. (2009) is used to calculate the line emissivitiesfor a modified Maxwellian distribution. We study metal abundances in galaxy groups and clusters where hard X-ray excess emissionwas observed.
Results.
We found that for modified Maxwellian distributions the argon abundance decreases for the HCG 62 group, the iron abun-dance decreases for the Centaurus cluster and the oxygen abundance decreases for the solar corona with respect to the case of aMaxwellian distribution. Therefore, metal abundance measurements are a promising tool to test the presence of high energy electronpopulations.
Key words.
Galaxies: clusters: general; Atomic processes; Radiation mechanisms: non-thermal
1. Introduction
Galaxy clusters are large structures in the Universe, with radii ofthe order of a megaparsec. Groups of galaxies are the poorestclass of galaxy clusters. The space between galaxies in clus-ters is filled with low-density ∼ − cm − high temperature( k B T ∼ −
10 keV) gas (for a review, e.g. Sarazin 1986). Thetemperatures of 1-10 keV are close to the values of the K-shellionization potentials ( I Z = Z Ry , where Z is the atomic numberand Ry is the Rydberg constant) of heavy elements with atomicnumbers in the range of Z = ff er from a Maxwellian distribution (e.g. Porquet etal. 2001).Hard X-ray tails reported from BeppoSAX observations inthe X-ray spectra of some galaxy clusters (Fusco-Femiano etal. 1999; Fusco-Femiano et al. 2004; Rossetti & Molendi 2004for the Coma cluster; Kaastra et al. 1999 for the Abell 2199;Molendi et al. 2002 for the Centaurus cluster) were interpreted asbremsstrahlung emission from non-thermal subrelativistic elec-trons (see e.g. Sarazin & Kempner 2000) or from thermal elec- Send o ff print requests to : D.A. Prokhorov e-mail: [email protected] trons with a Maxwellian spectrum distorted by a particle ac-celeration mechanism (Blasi 2000; Liang et al. 2002, Dogiel etal. 2007). The bremsstrahlung interpretation is associated witha huge energy output of emitting particles and faces energeticsproblems (e.g. Petrosian 2001). Evidence for a hard X-ray ex-cess above the thermal emission was also discovered in galaxygroups with ASCA (Fukazawa et al. 2001, Nakazawa et al.2007). The evidence for and the nature of hard X-ray spectraltails in these galaxy groups and clusters are discussed in the re-view by Rephaeli et al. (2008).The use of non-extensive thermo-statistics (Tsallis 1988; fora review, see Tsallis 1999), based on the natural generalizationof entropy for systems with long-range interactions, was pro-posed by Hansen (2005) to fit the X-ray spectrum observed nearNGC 4874 (near the center of the Coma cluster). We considernon-extensive thermo-statistics as another approach to explainhard X-ray excess in groups and clusters in the framework of thebremsstrahlung model.A more traditional interpretation of hard X-ray tails basedon the inverse Compton scattering (ICS) of relativistic electronson relic photons (Sarazin & Lieu 1998) faces a serious problem.The combination of hard X-ray and radio observations within theICS model implies a magnetic field much lower than the valuesderived from Faraday rotation measurements (e.g. Clarke et al.2001). Yet several arguments have been proposed to alleviate (atleast in part) the disagreement (for a review, see Brunetti 2003;Ferrari et al. 2008; Petrosian et al. 2008).The presence of high energy subrelativistic electrons (non-thermal subrelativistic electrons or thermal electrons with aMaxwellian spectrum distorted by the particle accelerationmechanism) or the use of non-extensive thermo-statistics mustbe probed using various observational methods in order to testinterpretations of X-ray tails from galaxy clusters. D.A. Prokhorov: Metal abundance estimates
The Sunyaev-Zel’dovich (SZ) e ff ect can be used to constrainthe electron distribution in galaxy clusters. The study of the in-fluence of high energy subrelativistic electrons on the SZ ef-fect was done for the Coma and Abell 2199 clusters by Blasiet al. (2000) and Shimon & Rephaeli (2002). A method basedon the measurement of the spectral slope around the crossoverfrequency of the SZ e ff ect was proposed by Colafrancesco et al.(2009) to analyse the high energy electron populations in galaxyclusters.A new probe to study the electron distribution in galaxy clus-ters, namely the flux ratio of the emission lines due to FeK α transitions (FeXXV and FeXXVI) was considered by Prokhorovet al. (2009). This flux ratio is very sensitive to the populationof electrons with energies higher than the ionization potentialof a FeXXV ion (which is ≈ ffi cient sensitivity to measure the iron line flux ratio.Kaastra et al. (2009) have shown that relative intensities ofthe satellite lines are sensitive to the presence of supra-thermalelectrons in galaxy clusters and that the instruments on futuremissions like Astro-H and IXO will be able to demonstrate thepresence or absence of these supra-thermal electrons.In this paper we study the influence of high energy electronpopulations on metal abundance estimates in galaxy groups andclusters and show that the e ff ect of high energy particles can besignificant. This e ff ect is a promising test to the presence of highenergy subrelativitic electrons in galaxy groups and clusters be-cause of substantial changes in abundance estimates for modifiedMaxwellian distributions. We also consider the e ff ect of high en-ergy electrons on abundance estimates in the solar corona wherethe presence of modified Maxwellian electron distributions hasbeen proposed.The paper is organized as follows. In Sect. 2.1 we choosea galaxy group and a galaxy cluster where high energy sub-relativistic electron populations have been proposed and de-rive values of the electron distribution parameters. We calcu-late the changes in metal abundances with respect to the val-ues for a Maxwellian distribution in Sect. 2.2. We discuss thebremsstrahlung model of hard X-ray emission from galaxy clus-ters in Sect. 3 and present our conclusions in Sect. 4. We calcu-late an oxygen abundance drop for the solar corona in AppendixA.
2. Metal abundances in groups and clusters with ahigh energy electron population.
Usually metal abundances are derived under the assumption of aMaxwellian electron distribution. Let us consider here the influ-ence of high energy subrelativistic electron populations on metalabundance determinations.
Since we want to analyse the influence of a high energy subrel-ativistic electron population on abundance estimates of chemi-cal elements with atomic numbers Z
26, we must consider cool clusters where the influence of high energy subrelativistic elec-trons on impact excitation and ionization is more important.The two objects which will be considered below are the HCG62 group and the Centaurus cluster, with respective tempera-tures of 1 keV and 3.5 keV. These objects are interesting becauseof hard X-ray excess detections by Fukazawa et al. (2001) andMolendi et al. (2002), suggesting a possible high energy sub-relativistic electron component if these hard X-ray excesses areinterpreted via bremsstrahlung emission.The HCG 62 group is a bright group of galaxies at a redshiftz = = . ± .
03 keV in theenergy band below 2.5 keV (Nakazawa et al. 2007). A hard X-ray excess from this galaxy group was discovered by Fukazawaet al. (2001). The highly significant hard X-ray signal in the en-ergy band 4.0-8.0 keV, of which only ∼
25% can be accountedfor by thermal IGM (intragalactic medium) emission, was recon-firmed by Nakazawa et al. (2007). Abundances of Mg, Si, S andFe were obtained with Suzaku by Tokoi et al. (2008).The Centaurus cluster (Abell 3526) is amongst the nearest(z = = . ± . σ level and concluded that it is impossible from the Beppo-SAXPDS data alone to establish the origin of this emission. The abun-dances of chemical elements in the Centaurus cluster were stud-ied by Molendi et al. (2002) and Fabian et al. (2005).To interpret hard X-ray spectral tails in the framework of thebremsstrahlung model, di ff erent electron distributions were pro-posed (e.g. Dogiel 2000; Sarazin & Kempner 2000; Dogiel et al.2007). In the paper by Sarazin & Kempner (2000) it is assumedthat the supra-thermal electron populations start at an electronkinetic energy 3kT, where T is the temperature of the intraclus-ter medium (ICM). This electron distribution was considered byShimon & Rephaeli (2002) for an analysis of the influence ofsupra-thermal electrons on the SZ e ff ect and by Prokhorov etal. (2009) for an analysis of electron distributions by means ofthe flux ratio of iron lines FeXXV and FeXXVI. In this case theelectron distribution function is given by: f ( x ) = f M ( x ) , x < f ( x ) = f M ( x ) + λ x − ( µ + / , x ≥ = E / kT, f M ( x ) is a Maxwellian function, µ = .
33 is takenfrom Sarazin & Kempner (2000) and the normalization coe ffi -cient λ is calculated from observational data. For the calcula-tions of the ionization, excitation and recombination rates theelectrons with very high energies ( ≥
20 kT) have negligible ef-fect (Porquet et al. 2001), therefore we can place the cut-o ff atany energy above that of 20 kT without changing line emissivi-ties.Another approach to fit the X-ray spectra of galaxy clustersin the framework of the bremsstrahlung model was proposedby Hansen (2005). He considered the ICM in thermodynamicalequilibrium, but with an electron distribution function which isdefined through non-extensive thermo-statistics (Tsallis 1988).Reasons for using Tsallis statistics in galaxy clusters are dis-cussed in Sect. 4 of Hansen (2005). The equilibrium distribu-tion function in non-extensive thermo-statistics (e.g. Silva et al.1998) is: f ( x ) = C √ x (1 − ( q − x ) / ( q − (2)where C is the normalization constant, and q is the parameterquantifying the degree of non-extensivity. .A. Prokhorov: Metal abundance estimates 3 The electron distribution f ( x ) has the same form as a Kappa-distribution which is frequently interpreted as a consequence ofacceleration mechanisms in the solar corona (Leubner 2004).Let us find values of the distribution parameters λ (see Eq. 1)and q (see Eq. 2) from the ASCA data for the HCG 62 group andfrom the Beppo-SAX data for the Centaurus cluster:1. The HCG 62 group. Fukazawa et al. (2001) using the ob-served luminosity ratio of the non-thermal and thermal X-raycontinuum components, and the non-thermal bremsstrahlungmodel (Kempner & Sarazin 2000) estimated that the non-thermal electron population is 6% of the thermal electronpopulation (the non-thermal electron energy density is 25%of the thermal electron energy density). We obtain the valuesof λ = .
28 and q = .
97 by integrating over the electronspectra f ( x ) and f ( x ) respectively.2. The Centaurus cluster. The total luminosity of the non-thermal component in the 20-200 keV band was calculatedby Molendi et al. (2002) from a Beppo-SAX observation.Molendi et al. (2002) considered the bremsstrahlung modelas one of the possibilities to explain the hard X-ray ex-cess. The luminosity in the 2-10 keV band was calculated byFabian et al. (2005). From the observational data we derivethat the non-thermal electron population is 5% of the thermalelectron population (the non-thermal electron energy densityis 21% of the thermal electron energy density) and obtainthe values of λ = .
25 and q = .
975 by integrating over theelectron spectra f ( x ) and f ( x ) respectively.Note that supra-thermal electron populations that are 4% and8% of the thermal electrons were also proposed by Sarazin &Kempner (2000) for the Coma and Abell 2199 clusters.Evidence for non-thermal X-rays in galaxy clusters is stillcontroversial (e.g. Rossetti & Molendi 2004; Kitaguchi et al.2007). The Suzaku observation of the Coma cluster does not pro-vide evidence for non-thermal excess in the central region of theComa cluster (Wik et al. 2009). An analysis of Suzaku XIS andHXD measurements of HCG 62 resulted in an upper limit onnon-thermal emission (Tokoi et al. 2008), but at a level whichdoes not exclude the ASCA result.The influence of the derived high subrelativistic electronpopulations on the metal abundance estimates will be consideredin Sect. 2.2. We now show that the e ff ect of high energy subrelativistic elec-trons on hydrogen-like and helium-like emission lines can besignificant. A generalized approach to calculate the emissivityin hydrogen-like and helium-like spectral (iron) lines for a mod-ified Maxwellian electron distribution was given by Prokhorovet al. (2009). In this section we propose to study the sum of theH-like and He-like line volume emissivities (in units of photonscm − s − ) instead of the line volume emissivity ratio.The sum of the H-like and He-like line volume emissivitiesfor a chemical element of atomic number Z can be written as ε Z = n e n H A Z × ( ξ Z − Q Z − + ξ Z − Q Z − + ξ Z − α Z − + ξ Z α Z − ) (3)where n e is the electron number density, n H is the H ionic num-ber density, A Z is the abundance of the considered chemical ele-ment, ξ Z − and ξ Z − are the ionic fractions of He-like and H-likeions respectively, Q Z − and Q Z − are the impact excitation ratecoe ffi cients, and α Z − and α Z − are the rate coe ffi cients for the contribution from radiative recombination to the spectral lines:He-like triplet and H-like doublet.Let U denote the reduced expression for the sum of emissiv-ities ε Z defined as: U = ξ Z − Q Z − + ξ Z − Q Z − + ξ Z − α Z − + ξ Z α Z − Γ (4)where Γ = Z − π a √ I Z / m e corresponds to the characteristic ratecoe ffi cient value, m e is the electron mass, a is the Bohr radius,and I Z is the K-shell ionization potential.For the sake of clarity, we consider in more detail the elec-tron distribution f ( x ) because of the distinct non-thermal power-law component at x ≥
3. In this case the non-thermal electronshave energies higher than 3kT, which corresponds to the energies E HCG62 = E A3526 = . I Z , therefore ions of argon I Z = = . I Z = = . ffi cients to calculate the direct ionization crosssections are taken from Arnaud & Rothenflug (1985), the ra-diative recombination rates are taken from Verner & Ferland(1996), and the dielectronic recombination rates are taken fromMazzotta et al. (1998). Note that the fraction of Li-like ions ofAr at temperatures kT ≥ ≥ f ( x ), with a fraction of highenergy subrelativistic electrons equal to 6% as in the HCG 62group. Fig. 1.
Reduced argon emissivity U for a Maxwellian electrondistribution (solid line) and for a modified Maxwellian distribu-tion f ( x ) (dashed line) for the HCG 62 group.For the HCG 62 group (kT = U for a modified Maxwellian distribution f ( x ) increases by ≈ D.A. Prokhorov: Metal abundance estimates
Fig. 2.
Reduced iron emissivity U for a Maxwellian electron dis-tribution (solid line) and for a modified Maxwellian distribution f ( x ) (dashed line) for the Centaurus cluster.with respect to the case of a Maxwellian distribution. Such anincrease of the reduced emissivity U corresponds to a decreaseof the argon abundance A Z = for a constant value of ε Z = (seeEq. 3). For a modified Maxwellian distribution f ( x ) the argonabundance decreases by ≈
33% with respect to the case of aMaxwellian distribution. The decrement of the argon abundancefor a modified Maxwellian distribution f ( x ) is 27%.Abundances of Mg, Si, S and Fe in the HCG 62 group werecalculated from Suzaku data by Tokoi et al. (2008), but the ex-pected Ar abundance is 4.5 times smaller than the S abundance(Anders & Grevesse 1989) and it is more di ffi cult to detect Arlines. The predicted Ar abundance decrease is a tool to test thebremsstrahlung interpretation of the hard X-ray tail in HCG 62.The Centaurus cluster is another interesting object to study.In Fig. 2 we compare the reduced iron emissivity for aMaxwellian electron distribution and for a modified Maxwellianelectron distribution f ( x ) with a fraction of high energy subrel-ativistic electrons equal to 5%, as in the Centaurus cluster.We found that the iron abundance for the modifiedMaxwellian distributions f ( x ) and f ( x ) decreases by ≈ ≈
13% respectively with respect to the case of a Maxwelliandistribution.We also calculated changes in the abundance estimates forthe chemical elements closest in atomic numbers to Ar and Feand found that: 1) for HCG 62, the Si abundance increases by3%, and the S abundance decreases by 14%; 2) for the Centauruscluster, the Ar abundance increases by 2%, and the Ca abun-dance increases by 0.5%.High energy subrelativistic electrons lead to a higher appar-ent temperature. If the gas temperature is smaller than the tem-perature at which the reduced emissivity U of the chemical el-ement has a maximum value, then the abundance estimate de-creases because of an increase of the reduced emissivity with thetemperature at these temperatures. However, if the gas tempera-ture is higher than the temperature at which the reduced emissiv-ity U of the chemical element has its maximum value, then theabundance estimate increases.We now demonstrate how the argon and iron abundances in-ferred from X-ray observations yield important constraints onthe fraction of high energy electrons. For this purpose, syntheticclusters with temperatures of 1 and 3.5 keV (as in the HCG 62group and in the Centaurus cluster) and an electron distributionfunction f ( x ) are considered. The dependences of both argon and iron abundance ratios for a modified Maxwellian distribu-tion and for a Maxwellian distribution on the fraction of highenergy subrelativistic electrons are shown in Fig. 3. Fig. 3.
The solid (dashed) line shows dependence of the ratio ofthe argon (iron) abundances for a modified Maxwellian distri-bution and for a Maxwellian distribution on the fraction of highenergy electrons.We conclude that high energy electron populations can af-fect derived metal abundances for the HCG 62 group and theCentaurus cluster.
3. Discussion
It can be supposed that, in addition to the bremsstrahlung-emitting thermal ICM and synchrotron-emitting, relativistic,non-thermal electrons, a high energy subrelativistic popula-tion of electrons exists which emits the hard X-ray excess asbremsstrahlung.There are three possible origins for high energy subrelativis-tic populations: non-thermal (Sarazin & Kempner 2000), quasi-thermal (Blasi 2000; Dogiel 2000; Liang et al. 2002; Dogiel etal. 2007; Wolfe & Melia 2008), and thermal in the frameworkof the non-extensive thermo-statistics (Hansen 2005). Since lineemissivities depend on the fraction of high energy electrons (e.g.Prokhorov et al. 2009) and do not depend on the origin of theseelectrons, we can use the electron distribution f ( x ) to calcu-late line emissivities in the cases of the non-thermal and quasi-thermal electron origins.Petrosian (2001) estimated the yield in non-thermalbremsstrahlung photons Y ∼ ( dE / dt ) br / ( dE / dt ) c ∼ − . Here( dE / dt ) br / ( dE / dt ) c is the ratio of bremsstrahlung to Coulomblosses of non-thermal electrons. Then for a hard X-ray flux F x ∼ erg / s a large amount of energy of the non-thermalelectrons F e ∼ F x / Y ∼ erg / s is transmitted to the back-ground plasma. As a result the ICM should be heated aboveits observable temperature in less than 10 Myr (Petrosian 2001,Wolfe & Melia 2006).It was, however, shown by Liang et al. (2002) and Dogiel etal. (2007) that a quasi-thermal electron population might over-come this di ffi culty via a higher radiative e ffi ciency (and there-fore a longer overheating time, but see Petrosian & East 2008).The energy supply necessary to produce the observed hard X-ray flux by quasi-thermal electrons is at least one or two orders .A. Prokhorov: Metal abundance estimates 5 of magnitude smaller (Dogiel et al. 2007) than derived form theassumption of non-thermal origin of emitting electrons. Wolfe& Melia (2008) have also considered a quasi-thermal electrondistribution to fit hard X-ray emission, but rather than requiringa second-order Fermi acceleration to produce the quasi-thermalelectrons, they assumed quasi-thermal electrons are producedvia collisions with non-thermal protons.
4. Conclusions
We have shown in this paper that the metal abundance estimatesdepend on the presence of high energy subrelativistic electronsproposed to account for measurements of hard X-ray excessemission from galaxy groups and clusters. Due to the impactof these energetic electron populations, the Ar abundance esti-mate in the HCG 62 group and the Fe abundance estimate in theCentaurus cluster significantly decrease by ≈
30 and ≈ ffi cient for de-tecting the high energy subrelativistic electron populations thanthat based on the Doppler broadening of the spectral lines pro-posed by Hansen (2005), which requires very high energy reso-lution, or than that based on the flux ratio of the emission lines(Prokhorov et al. 2009), which requires higher sensitivity instru-ments.Other possibilities to produce the change in the metal abun-dance estimates in galaxy clusters are the e ff ect of resonant scat-tering (Gilfanov et al. 1987) and the presence of multiphasehot gas - two temperature model (Buote & Fabian 1998, Buote2000).The e ff ect of resonant scattering causes the decrement of theFeXXV line at 6.7 keV, and, therefore, the decrement of the fluxratio of the iron lines FeXXV / FeXXVI. A decrement of the Feabundance is then produced, as in the case of a high energy sub-relativistic electron population. To separate the e ff ects of res-onant scattering and the high energy subrelativistic populationinfluence, the SZ e ff ect from a high energy subrelativistic popu-lation can be analyzed. Following the method of Colafrancescoet al. (2009), we calculated the value of the slope of the SZ ef-fect in the Centaurus cluster. We obtained the value of the slope S ≈ .
033 for both electron distributions f ( x ) and f ( x ) and thevalue of the slope S ≈ .
028 for a Maxwellian spectrum. Sincethe slope is equal to S ≈ . × kT / ( m e c ) for a Maxwellianelectron spectrum without a high energy subrelativistic electronpopulation (Colafrancesco et al. 2009), the value of the slopeof S = .
033 corresponds to that at an e ff ective temperature kT = . kT = . kT = . kT = . ∼ ∼ . Acknowledgements.
I am grateful to Florence Durret, Joseph Silk, WilliamForman, Vladimir Dogiel and Eugene Churazov for valuable suggestions anddiscussions and thank the referee for very useful comments.
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Appendix A: Oxygen abundance drop in the solarcorona