Probing the low-energy spectrum of non-thermal electrons in galaxy clusters with soft gamma ray observations
aa r X i v : . [ a s t r o - ph . H E ] M a r Probing the low-energy spectrum of non-thermal electronsin galaxy clusters with soft gamma ray observations
P. Marchegiani Abstract
In this paper we study the possibility ofprobing the low-energy part of the spectrum of non-thermal electrons in galaxy clusters by detecting theirnon-thermal bremsstrahlung (NTB) emission in the softgamma ray band, using instruments like e-ASTROGAM.Using the Coma cluster as a reference case, we findthat, for very low values of the minimum energy ofthe electrons, in principle the NTB is detectable, butthis situation is possible only for conditions that canbe maintained only for a short time compared to thecluster lifetime. The possibility of constraining the lowenergy spectrum of non-thermal electrons through NTBis therefore hard to achieve in next years.
Keywords gamma rays: galaxies: clusters; galaxies:clusters: general
Our knowledge of the properties of non-thermal elec-trons in galaxy clusters is based on the observation ofdiffuse radio emission like radio halos and relics, thatare produced by synchrotron emission of relativisticelectrons having energy of the order of GeV interact-ing with magnetic fields with intensity of the order of µ G (e.g. Feretti et al., 2012). The same electrons arealso expected to produce Inverse Compton Scattering(ICS) emission when interacting with the Cosmic Mi-crowave Background (CMB) photons (Perola & Rein-hardt, 1972); however, this emission has not yet beenfirmly detected even in nearby and rich clusters likeComa (e.g. Gastaldello et al., 2015).
P. Marchegiani School of Physics, University of the Witwatersrand, Pri-vate Bag 3, 2050-Johannesburg, South Africa. Email:[email protected]
While there are hints of a steepening of the electronsspectrum at high energies giving origin to an analogoussteepening in the integrated radio halo spectrum (seeThierbach et al., 2003 for the Coma case), the lowerenergy part of the electrons spectrum remains basicallyunconstrained, with the possible exception of the detec-tion in a few clusters of an excess in the Extreme Ul-traviolet band (EUV; see e.g. Lieu et al., 1996, Bowyeret al., 2004), that can be due to ICS of electrons withenergy of the order of 100–200 MeV (Sarazin & Lieu,1998), but also to thermal bremsstrahlung from gaswith low temperature (Lieu et al., 1996).Due to the steep spectra usually found for non-thermal electrons in galaxy clusters (see e.g. Ferettiet al., 2012), the low-energy part of the electrons spec-trum is expected to provide the largest contribution tothe total number and the total energy content of theseelectrons. Therefore it would be important to identify away to probe the electrons spectrum at low energies, inorder to estimate the ratio between the energy contentstored in non-thermal electrons and the other compo-nents of the Intra Cluster Medium (ICM), like thermalgas, magnetic field, and non-thermal protons (see, e.g.,Colafrancesco & Marchegiani, 2011 for an analogousdiscussion in radio galaxies).Electrons with energies lower than ∼
100 MeV areexpected to have a short lifetime compared with thecluster one because of the Coulomb interactions withthe thermal electrons, with the lifetime being shorterfor lower electrons energies (e.g. Sarazin, 1999). As aresults, non-thermal electrons spectra that are injectedwith an initial power-law shape are expected to flattenat low energies (e.g. Lieu et al., 1999); this fact can bephenomenologically parametrized through the value ofthe minimum Lorentz factor γ min for which the elec-trons spectrum can be described by a power law for γ > γ min (e.g. Colafrancesco & Marchegiani, 2011). The energy content stored in the non-thermal electronsis strongly depending on this value.A possible way to probe the low-energy part of non-thermal electrons spectrum in galaxy clusters is givenby the study of the non-thermal Sunyaev-Zel’dovich ef-fect (SZE), i.e. the distortion of the CMB spectrumby ICS produced in ionized media present in cosmicstructures (e.g. Colafrancesco, Marchegiani & Pal-ladino, 2003). A non-thermal contribution to the to-tal SZE has been possibly detected in the Bullet clus-ter (Colafrancesco, Marchegiani & Buonanno, 2011;Marchegiani & Colafrancesco, 2015), suggesting thepossibility of a very small value of the minimum energyof the electrons ( γ min ∼ . X ≡ P non − th /P th ≈ .
55. Moreover, an in-terpretation of a stacked analysis of Planck HFI data ingalaxy clusters (Hurier, 2016) in terms of a non-thermalcontribution to the SZE (Marchegiani & Colafrancesco,2017) has indicated a low value of γ min in this sample,that corresponds to a possible pressure ratio of the or-der of X ∼ − −
6% (Huber et al., 2013,Prokhorov & Churazov, 2014); therefore, it would beuseful to identify another possible way to detect low-energy non-thermal electrons, in order to check the va-lidity of these results.Non-thermal electrons with
E <
100 MeV shouldemit by non-thermal bremsstrahlung (NTB) when in-teracting with the thermal gas nuclei (e.g., Enßlin, Lieu& Biermann, 1999); this radiation should be emitted inthe region of the electromagnetic spectrum under 100MeV, that is presently almost unexplored, but can be-come accessibile in the future thanks to proposed in-struments like e-ASTROGAM and AMEGO . There-fore in this paper we study the possibility to use NTBas a probe of low-energy non-thermal electrons at thelight of the properties of these instruments, using theComa cluster as a case of study. Coma is a rich andnearby cluster where a bright radio halo has been ob-served (e.g. Deiss et al., 1997), meaning that a highlevel of diffuse non-thermal activity is present; for thesereasons, it looks as one of the candidates where in prin-ciple the observation of non-thermal emissions is morefavored compared to other clusters. http://eastrogam.iaps.inaf.it/ https://asd.gsfc.nasa.gov/amego/ We adopt in this paper a simple phenomenologicalmodel, i.e. a power-law spectrum for non-thermal elec-trons for γ > γ min , and explore the consequences onthe produced NTB by varying the values of γ min . Sincethe angular resolution of the proposed instruments (deAngelis et al., 2018) is larger than the Coma cluster an-gular size, we consider the emission integrated on thewhole cluster as a point-like source.The outline of the paper is the following: in Section 2we describe the theoretical methods used in this paper.In Section 3 we present the results, and summarize anddiscuss our results in Section 4. Throughout the paper,we use a flat, vacuum–dominated cosmological modelfollowing the results of Planck, with Ω m = 0 . Λ =0 .
692 and H = 67 . − Mpc − (Ade et al., 2016). NTB is produced by interactions of non-thermal elec-trons with thermal nuclei. For an electrons spectrumgiving the particle density per unit of energy and vol-ume N e ( E, r ), the NTB emissivity is given by: j B ( E γ , r ) = Z dEN e ( E, r ) P B ( E γ , E, r ) (1)(e.g. Schlickeiser, 2002), where E γ is the energy of theemitted photon, and P B ( E γ , E, r ) = βcE γ n th ( r ) σ ( E γ , E ) , (2)where n th ( r ) is the thermal gas density, and where thecross section for relativistic electrons is given by: σ ( E γ , E ) = 1 E γ π ασ T "" (cid:18) − E γ E (cid:19) φ + − (cid:18) − E γ E (cid:19) φ (cid:21) , (3)being α = 1 / .
036 the fine-structure constant and σ T = 6 . × − cm the Thomson cross section. Forunshielded target nuclei (like in the case of the ionizedintra cluster medium) we can assume φ = φ = Z φ u ,with Z = 1 and φ u = 4 (cid:20) ln (cid:20) Em e c (cid:18) E − E γ E γ (cid:19)(cid:21) − (cid:21) . (4)In the following we assume for the non-thermal elec-trons spectrum a simplified phenomenological model,assuming that they have a radial profile proportionalto the thermal gas one g th ( r ), and a power-law spec-trum with a low-energy cut-off: N e ( γ, r ) = k γ − s e g th ( r ) for γ ≥ γ min , (5) with a typical value of the spectral index in galaxy clus-ters s e = 3 .
7, and where the parameter k provides thenormalization of the non-thermal electrons density.The thermal gas density profile in the Coma clusteris derived from X-ray measures: n th ( r ) = n g th ( r ) = n " (cid:18) rr c (cid:19) − q th (6)with parameters n = 3 . × − h / cm − , r c =300 h − kpc and q th = 1 .
125 taken from Briel, Henry& B¨ohringer (1992).As effect of NTB, it is expected that an electron withenergy E has the maximum of its emission at approxi-mately E γ ∼ E/
2, and that, for an electrons spectrumas in eq.(5), the NTB has a flux spectrum F B ∝ E − s e +1 γ (e.g. Longair, 1994). As a consequence, we expect theNTB has a steep photon spectrum, with a sudden low-energy break at an energy E γ ∼ γ min m e c /
2, underwhich the photons spectrum should strongly decrease.Non-thermal electrons emit also by ICS with theCMB photons in a frequency range going from EUVto gamma rays, if the electrons spectrum does notsteepen at high energies, with a spectral index α ICS = − ( s e − /
2, i.e. flatter than the NTB one. The combi-nation of NTB and ICS therefore has a flatter compo-nent, given by ICS, with a peak produced by NTB atan energy around E γ ∼ γ min m e c /
2; the detection ofsuch a peak can in principle allow to derive the valueof γ min .Non-thermal electrons emit also by synchrotron inthe radio band when interacting with the intra-clustermagnetic field. The intensity and the spatial profile ofthe magnetic field can be derived from Faraday Rota-tion measures, that in the case of Coma provide as abest fit a central value of B = 4 . µ G and a radialprofile proportional to g / th ( r ) (Bonafede et al., 2010).In the following we normalize the electrons density k by requiring that the radio flux produced at 1.4 GHzfor these properties of the magnetic field is equal tothe observed value of 640 mJy (Deiss et al., 1997); wechoose this frequency because it is the highest frequencywhere the spectrum of the Coma radio halo has a power-law shape (Thierbach et al., 2003). We also note thatthis simple model does not take into account the pos-sible effect of re-acceleration of electrons that can beprovided by turbulences, that can boost the electronsspectrum only for electrons that emit in the radio band,i.e. with γ ∼ − (e.g. Brunetti et al., 2001). Asa consequence, in presence of this boosting producedby turbulences, the ratio between the number of elec-trons emitting in radio and the ones with lower energieswould be higher, and the flux produced by NTB would be reduced compared to the radio one. For this reason,in our simplified model the resulting NTB should beconsidered as an upper limit.The low-part of the electrons spectrum is basicallyunconstrained; at low energies the electrons loose theirenergy mainly because of the Coulomb interactionswith the thermal gas, and for low energies the elec-trons lifetime can be smaller than 10 yrs (e.g. Sarazin,1999); low energy electrons therefore should be presentonly for a short time after being accelerated. Electronswith γ ∼ −
200 should instead have a longer life-time, even comparable with the cluster one (e.g. Enßlinet al., 1999, Brunetti et al., 2001), so it is reasonable tothink that a low-energy cutoff in the electrons spectrumshould not be higher than these values.In the following, we normalize the density of non-thermal electrons to the radio flux at 1.4 GHz as de-scribed, and for several values of γ min we calculate theICS and NTB emissions in the soft gamma ray band,comparing the results with the expected sensitivity ofe-ASTROGAM; we also calculate the energy contentstored in non-thermal electrons compared to the ther-mal one, and the heating rate provided by non-thermalelectrons compared with the cooling rate due to thermalbremsstrahlung, in order to check if the physical config-urations associated to these assumptions are problem-atic for the stability of the ICM.The energy content stored in the non-thermal elec-trons is given by: U e = Z ∞ γ min dγN e ( γ )( γ − m e c , (7)that can be compared with the energy stored in thethermal gas, U th = 3 n th k B T e , that is ∼ . × − ergcm − at the center of the Coma cluster.Non-thermal electrons can also heat the ICM be-cause of Coulomb interactions. The heating rate in-duced by the electrons having the spectrum assumed inEq.(5) is given by:˙ ǫ h ≡ dǫdt (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) heat = Z ∞ E min N e ( E ) (cid:18) dEdt (cid:19) dE . (8)For a relativistic electron with velocity v = βc andLorentz factor γ , the heating rate on thermal gas dueto Coulomb interactions is: dEdt ≈ K Z β (cid:20) ln 2 m e c β γ I p − β (cid:21) , (9)where Z is the (suitably averaged) squared chargeof the plasma’s nuclei, K = 4 π n th r m e c and r e = e /m e c ≃ .
82 fm. Here I p = ~ ω p , with ω p = Table 1
Values of γ min and corresponding values of theratio of the energy content stored in non-thermal electronsand in the thermal gas, of the heating rate, and of the ratiobetween heating and cooling rates. γ min U e /U th ˙ ǫ h ˙ ǫ h / ˙ ǫ c erg cm − s − .
7% 1 . × −
725 3 .
3% 2 . × − .
2% 4 . × − .
20% 2 . × − . . × − . × −
200 0 . . × − . × − [4 π n th e /m e ] / being the plasma frequency (e.g. Co-lafrancesco & Marchegiani, 2008). The heating rate canbe compared with the cooling rate of the thermal gas,given by˙ ǫ c ≡ dǫdt (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) cool = r π e √ m e h m c ¯ G ¯ z n √ kT (10)(e.g. Longair, 1994), where ¯ z is an average charge ofthe IC plasma and ¯ G is the Gaunt factor; the coolingrate at the center of the Coma cluster is ˙ ǫ c ∼ . × − erg cm − s − . The values of the heating rateare dependent on the value of the normalization of theelectrons spectrum and the electrons minimum energy(see eq.8), and for the models we are using are reportedin Table 1. The normalization of the electrons spectrum requiredto not produce a radio emission in excess compared tothe observed one is k = 1 . × − cm − ; since the ra-dio emission is not sensible to the low-energy spectrumof electrons, this value does not depend on γ min . Weconsider several value of γ min between 3 and 200, andcalculate the energy content stored in the relativisticelectrons and the heating rate provided by them. Theresults are in Table 1.The high-energy emission provided by relativisticelectrons by NTB and ICS for different values of γ min isshown in Fig.1, where it is compared with the expectedsensitivity of e-ASTROGAM for an effective exposureof one year (de Angelis et al., 2018). From this figure,it is possible to see that the expected soft gamma rayemission from diffuse relativistic electrons is below thee-ASTROGAM sensitivity for γ min > γ min ≤ Fig. 1
High energy emission in the Coma cluster producedvia ICS and NTB by non-thermal electrons with spectrumas in Eq.(5) with s e = 3 . γ min = 200 (solid line),100 (dashed), 30 (dot-dashed), 10 (three dots-dashed), 5(long dashed), and 3 (dotted). Plotted are also the upperlimits in the hard X-ray band from NuSTAR (Gastaldelloet al., 2015) and in the gamma ray from Fermi-LAT(Ackermann et al., 2010), the thermal emission fromthe Intra Cluster Medium (blue line), the Astro-H (HXIand SGD) sensitivity for 100 ks of time integration (fromhttp://astro-h.isas.jaxa.jp/researchers/sim/sensitivity.html;black thick line), and the sensitivity of e-ASTROGAM foran effective exposure of one year (de Angelis et al., 2018;red solid thick line). For reference also the e-ASTROGAMsensitivity divided by a factor of 10 (red dashed thick line)and 100 (red dot-dashed thick line) is plotted. conditions in this case are problematic: first, the result-ing energy content stored in the relativistic electrons isbigger than 3%, i.e. of the order of the upper limitson the cosmic ray protons derived from Fermi-LAT up-per limits (Huber et al., 2013; Prokhorov & Churazov,2014), while it is expected that non-thermal electronsshould contain only a fraction of the energy stored incosmic ray protons of the order of 10 − or smaller (e.g.Vazza & Br¨uggen, 2014). Second, electrons with such alow value of minimum energy should have a very smalllifetime, of the order of 10 − yrs because of theCoulomb losses (e.g. Sarazin, 1999), and therefore theyshould be present only for a small fraction of the clusterlifetime, if no steady sources of acceleration are present.Finally, as it is possible to see from Table 1, where wealso show the values of the ratio between the heatingand the cooling rates, the heating rate provided by elec-trons with low γ min is much higher than the cooling rateof the gas, and this can be a problem for the stability ofthe ICM. However, this last problem is not too seriousif the electrons have a short lifetime: for example, inthe case γ min = 3 the heating rate at the center of the Coma cluster is ˙ ǫ h ∼ . × − erg cm − s − . Assum-ing the lifetime of these electrons to be of the order of10 yrs (really it is probably smaller, see Sarazin, 1999),the energy density provided at the center of the clusterduring this lifetime is ∼ . × − erg cm − . Thisnumber is smaller than the energy density of the ther-mal gas at the center of the cluster, ∼ . × − ergcm − , therefore the heating provided by non-thermalelectrons during their lifetime is not sufficient to over-heat the ICM. Obviously, this fact excludes the possi-bility of a steady source for acceleration of electrons,and puts a limit on the time for which NTB from low-energy electrons is in principle observable.In Fig.1, we also show for reference the sensitivityof hypothetical instruments with sensitivities 10 and100 times better than e-ASTROGAM. In the first case,NTB emission would be detectable for values up to γ min ∼ >
10, and in the second case it would be de-tectable also for γ min ∼ γ min ,that in principle can be observed with an instrumentlike Astro-H, even if in this band this emission is lowerthan the thermal one, so it would be necessary to dis-entangle thermal and non-thermal emissions.We also calculated the flux in the EUV and SoftX-ray (SXR) bands produced by the non-thermal elec-trons by ICS of the CMB photons, and compared theresults with the flux measured with EUVE in the 0.13–0.18 keV band, F EUV ∼ . × − erg cm − s − (Bowyer et al., 2004), and with the flux measured byROSAT in the 0.2–0.4 keV band, F SXR ∼ . × − erg cm − s − (Bonamente et al., 2002). The ICS fluxcalculated in our model, that does not depend on thevalue of γ min because it is produced by electrons with γ > F ICS ∼ . × − erg cm − s − in theEUV band, and F ICS ∼ . × − erg cm − s − inthe SXR band. Both these values are much lower thanthe observed ones, suggesting that the observed emis-sions in these bands should have a different origin, likea thermal origin from a low-temperature component ofthe ICM (e.g. Lieu et al., 1996).Finally, NTB does not appear to be observable inthe Fermi-LAT band, where instead the emission ofhadronic origin, not considered in this paper, shouldbe dominant (e.g. Colafrancesco & Blasi, 1998). The study of the low-energy part of the spectrum of rel-ativistic electrons in galaxy clusters by detecting theirNTB appears to be a hard task with the next gener-ation of instruments operating in the soft gamma rayband.As pointed out by Petrosian (2001), NTB is ineffi-cient compared with the Coulomb losses rate: the con-sequence is that the electrons with low energy have avery short lifetime compared to the cluster one, andthat the heating rate provided by these electrons is veryhigh, while the NTB emission is not very strong.We have found that in principle there is a narrowregion of the parameters space (with γ min ≤
5) wherethe NTB in the Coma cluster can be observed with e-ASTROGAM. However, these electrons can be presentonly for a short fraction of the cluster lifetime because oftheir short lifetime, and because otherwise they wouldoverheat the cluster gas. Also, the energy content ofthese electrons should be of the order of the upper lim-its on cosmic ray protons energy content in galaxy clus-ters: this can be a problem because, on the basis of ourpresent understanding of mechanisms of particles accel-eration in galaxy clusters, one should expect that theenergy content of the electrons should be lower thanthe one of protons (e.g. Vazza & Br¨uggen, 2014), evenif some attempt to identify some acceleration mecha-nism efficient on electrons but not on protons in galaxyclusters has been done (e.g. Wittor, Vazza & Br¨uggen,2016).On the other hand, since several studies of non-thermal SZE in galaxy clusters (Colafrancesco et al.,2011, 2014; Marchegiani & Colafrancesco, 2017) indi-cate a possible low value of γ min and a high energy con-tent stored in non-thermal electrons, it still appears use-ful to try to detect galaxy clusters with e-ASTROGAMin order to check these results.It is also necessary to point out that, even if a clusterwould be in principle observable, other issues could bepresent in order to establish if the observed emissionwould be really produced by diffuse electrons. In fact,the expected angular resolution of e-ASTROGAM, al-though improved compared to previous gamma ray in-struments, in the energy range 30–100 MeV is of theorder of 1.5 degrees (de Angelis et al., 2018), there-fore basically all cluster core regions (including Coma)should appear as point-like sources; therefore, the pres-ence of other sources with a soft gamma ray emission(e.g. AGNs) in the field of view of the instrument wouldbe difficult to remove from the cluster one.Another possible problem can be the gamma rayemission produced by decay of neutral pions produced in hadronic interactions between cosmic ray protonsand thermal gas nuclei (e.g. Colafrancesco & Blasi,1998). Although still not firmly detected in galaxy clus-ters (e.g. Ackermann et al., 2016), this emission shouldbe dominant at energies of the order of 70 MeV or more,and this is another factor that limits the possibility todetect the NTB in galaxy clusters only to the case oflow values of γ min .In order to improve the situation, it would be neces-sary an instrument with a sensitivity at least 10 times(or preferably more) better than e-ASTROGAM. How-ever, considering that this instrument adopts very ad-vanced technological solutions for the present day, it isdifficult to think that these improved sensitivity levelscan be reached in next years. We also note that, sincemost of other rich clusters are more distant than Coma,the situation is not expected to be easier in other clus-ters, especially in clusters that do not host a radio halo,suggesting that the non-thermal activity in these clus-ters can be lower than in the Coma case. Acknowledgments
This work is based on the research supported by theSouth African Research Chairs Initiative of the De-partment of Science and Technology and National Re-search Foundation of South Africa (Grant No 77948).PM acknowledges support from the Department ofScience and Technology/National Research Founda-tion (DST/NRF) Square Kilometre Array (SKA) post-graduate bursary initiative under the same Grant. Ithank the Referee for useful comments and suggestions.
References
Ackermann, M., et al., 2010, ApJL, 717, L71Ackermann, M., et al., 2016, ApJ, 819, 149Ade, P. A. R., et al., 2016, A&A, 594, A13Bonafede, A., Feretti, L., Murgia, M., et al., 2010, A&A,513, A30Bonamente, M., Lieu, R., Joy, M. K., & Nevalainen, J. H.,2002, ApJ, 576, 688Bowyer, S., Korpela, E. J., Lampton, M., & Jones, T. W.,2004, ApJ, 605, 168Briel, U. G., Henry, J. P., & B¨ohringer, H., 1992, A&A, 259,L31Brunetti, G., Setti, G., Feretti, L., & Giovannini, G., 2001,MNRAS, 320, 365Colafrancesco, S., & Blasi, P., 1998, Astroparticle Physics,9, 227Colafrancesco, S., & Marchegiani, P., 2008, A&A, 484, 51Colafrancesco, S., & Marchegiani, P., 2011, A&A, 535, A108Colafrancesco, S., Marchegiani, P., & Palladino, E., 2003,A&A, 397, 27Colafrancesco, S., Marchegiani, P., & Buonanno, R., 2011,A&A, 527, L1Colafrancesco, S., Emritte, M. S., Mhlahlo, N., & Marche-giani, P., 2014, A&A, 566, A42de Angelis, A., et al., 2018, Journal of High Energy Astro-physics, 19, 1Deiss, B. M., Reich, W., Lesch, H., & Wielebinski, R., 1997,A&A, 321, 55Enßlin, T. A., Lieu, R., & Biermann, P. L., 1999, A&A, 344,409Feretti, L., Giovannini, G., Govoni, F., & Murgia, M., 2012,A&ARv, 20, 54Gastaldello, F., et al., 2015, ApJ, 800, 139Huber, B., Tchernin, C., Eckert, et al., 2013, A&A, 560,A64Hurier, G., 2016, A&A, 596, A61Lieu, R., Mittaz, J., Bowyer, S., et al., 1996, Science, 274,1335Lieu, R., Ip, W.-H., Axford, W. I., & Bonamente, M., 1999,ApJ, 510, L25Longair, M., 1994,
High Energy Astrophysics , CambridgeUniversity PressMarchegiani, P., & Colafrancesco, S., 2015, MNRAS, 452,1328Marchegiani, P., & Colafrancesco, S., 2017, MNRAS, 469,4644Perola, G. C., & Reinhardt, M., 1972, A&A, 17, 432Petrosian, V., 2001, ApJ, 557, 560Prokhorov, D. A., & Churazov, E. M., 2014, A&A, 567, A93Sarazin, C. L., 1999, ApJ, 520, 529Sarazin, C. L., & Lieu, R., 1998, ApJ, 494, L177Schlickeiser, R., 2002,
Cosmic Ray Astrophysics , Springer-Verlag, BerlinThierbach, M., Klein, U., & Wielebinski, R. 2003, A&A,397, 53Vazza, F., & Br¨uggen, M., 2014, MNRAS, 437, 2291Wittor, D., Vazza, F., & Br¨uggen, M. 2016, Galaxies, 4, 71