Non-Equilibrium Ionization State and Two-Temperature Structure in the Linked Region of Abell 399/401
aa r X i v : . [ a s t r o - ph ] J un PASJ:
Publ. Astron. Soc. Japan , 1– ?? , c (cid:13) Non-Equilibrium Ionization State and Two-Temperature Structurein the Linked Region of Abell 399/401
Takuya
Akahori and Kohji
Yoshikawa
Center for Computational Sciences, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki [email protected], [email protected] (Received 2008 May 16; accepted 2008 June 2)
Abstract
We investigate a non-equilibrium ionization state and two-temperature structure of the intraclustermedium in the linked region of Abell 399/401, using a series of N-body + SPH simulations, and find thatthere exist significant shock layers at the edge of the linked region, and that the ionization state of irondeparts from the ionization equilibrium state at the shock layers and around the center of the linked region.As for the two-temperature structure, an obvious difference of temperature between electrons and ions isfound in the edge of the linked regions. K α line emissions of Fe xxiv and Fe xxv are not severely affected bythe deviation from the ionization equilibrium state around the center of the linked region, suggesting thatthe detection of relatively high metallicity in this area cannot be ascribed to the non-equilibrium ionizationstate of the intracluster medium. On the other hand, the K α emissions are significantly deviated fromthe equilibrium values at the shock layers, and the intensity ratio of K α lines between Fe xxiv–xxv andFe xxvi is found to be significantly altered from that in the ionization equilibrium state. Key words: galaxies: intergalactic medium — X-rays: galaxies: clusters — X-rays: individual (A 399,A 401)
1. Introduction
According to a standard scenario of hierarchical struc-ture formation in the universe, galaxy clusters are formedthrough successive merging of galaxies, galaxy groups, andclusters. About a half of observed clusters have irregularX-ray morphology (e.g., Akahori, Masai 2005 referencestherein), and a part of such irregularities thought to becaused by such merging events.Abell 399/401 is well-known as merging clusters onan early stage of the merging. Fujita et al. (1996) andSakelliou, Ponman (2004) found that the intraclustermedium (ICM) at the linked region of the two clustersis compressed based on the ASCA and XMM-Newton ob-servations, respectively. Recently, Fujita et al. (2008) re-ported the detection of Fe K emission lines near the centerof the linked region based on the Suzaku XIS observation,and the metallicity in that regions is estimated to be 0.2times the solar metallicity, which seems relatively highcompared with theoretical predictions based on numericalsimulations (e.g., Tornatore et al. 2007).The estimation of physical properties of ICM in X-rayobservations is usually based on the assumptions that ICMis in the ionization equilibrium state and that electronsand ions share the same thermal temperature. Such as-sumptions can be justified around central regions of galaxyclusters by the fact that ICM density is high enough toquickly achieve ionization equilibrium and thermal equili-bration between electrons and ions. As for the ionizationequilibrium, the timescale required to reach collisional ion-ization equilibrium for an ionizing plasma, is estimated as n e t > ∼ cm − s (see e.g., Masai 1984), where n e is the number density of electrons. Therefore, for n e ∼ − cm − in the linked region (Sakelliou, Ponman 2004;Fujita et al. 2008), t ∼ Gyr is comparable to or longer thanthe merger timescale, so that the ionization equilibrium isno longer a reasonable assumption. Actually, in the warm-hot intergalactic medium (WHIM), where the density ismuch lower, the deviation from the ionization equilibriumhave been pointed out by Yoshikawa, Sasaki (2006). In ad-dition, the thermal equilibration in merging clusters hasbeen studied by Takizawa (1999) based on N-body/SPHsimulations, and the two-temperature structure of ICM,i.e. the difference in temperature between electrons andions, is reported especially at low-density regions. Thetwo-temperature structure of WHIM has been also sug-gested by Yoshida et al. (2005).Therefore, there exists sufficient reasons to suspect thatthese assumptions are not valid in the linked region ofAbell 399/401. In this paper, we investigate an ionizationstate and temperature structure of ICM in the linked re-gion by relaxing the assumptions of ionization equilibriumand thermal equipartition between electrons and ions, andverify to what extent such a non-equilibrium state affectthe interpretations of the observational data.
2. Model and Calculation
We carry out N-body/SPH simulations of two merg-ing galaxy clusters, in which a non-equilibrium ioniza-tion state and two-temperature structure of ICM are bothtaken into account. Radiative cooling and electron heat T. Akahori and K. Yoshikawa [Vol. ,conduction are both ignored in these simulations.The time evolution of two-temperature structure is fol-lowed with the same way as Takizawa (1999). We as-sume that the electrons and ions always reach Maxwelliandistributions with temperatures, T e and T i , respectively,and the two temperatures are equalized through Coulombscattering on a timescale of t ei = 2 × yr ( T e / K) / ( n i / − cm − ) · (cid:18) (cid:19) , (1)where n i is the number density of ions, and ln Λ isthe Coulomb logarithm. By introducing the dimension-less temperatures of electrons and ions, ˜ T e ≡ T e /T and˜ T i ≡ T i /T , respectively, normalized by the mean tempera-ture of electrons and ions, T ≡ ( n e T e + n i T i ) / ( n e + n i ), theevolution of two-temperature structure is described by d ˜ T e dt = ˜ T i − ˜ T e t ei − ˜ T e u Q sh , (2)where u and Q sh are the specific thermal energy and theshock heating rate per unit mass, respectively. The firstterm of the r.h.s. denotes the thermal relaxation ratebetween ions and electrons. Note that recent studies onsupernova remnants showed that T e /T i ∼ < df j dt = j − X k =1 S j − k,k f k − Z +1 X i = j +1 S i − j,j f j − α j f j + α j +1 f j +1 , (3)where j is the index of a particular ionization stage con-sidered, Z the atomic number, f j the ionization fractionof an ion j , S i,j the ionization rate of an ion j with theejection of i electrons, and α j is the recombination rate ofan ion j . Ionization processes include collisional, Auger,charge-transfer, and photo-ionizations, and recombinationprocesses are composed of radiative and dielectronic re-combinations. Ionization and recombination rates are cal-culated by utilizing the SPEX ver 1.10 software package .Actual calculations are carried out in essentially the sameway as Yoshikawa, Sasaki (2006), except that the reactionrates are computed using the electron temperature, T e ,rather than the mean temperature, T , in order to incor-porate the effect of two-temperature structure. We solvethe time evolution of each ionization fraction of H, He, C,N, O, Ne, Mg, Si, S, and Fe, but we focus only on iron.To reproduce the situation of Abell 399/401, the ini-tial condition of the two clusters is set up as follows. Weconsider a head-on merger (Oegerle, Hill 1994), and as-sume that their collision axis is perpendicular to the line of sight. Each cluster has the same shape for simplicitysince the differences of the two clusters in shape and sizeare slight (Sakelliou, Ponman 2004). We adopt the Kingprofile for the initial dark matter distribution, in which theradial velocity dispersion, σ ∗ r , satisfies σ ∗ r = k B T vir /µm ,where k B is the Boltzmann constant and T vir is the virialtemperature (the virial radius is r vir = 3 . M ( r vir ) ≃ . × M ⊙ ). For the initialICM distribution, we first assume the temperature pro-file, T ( r ) = ( T vir /β ) exp( − r/r vir ), with β = 0 .
6, and thedensity profile is obtained by assuming hydrostatic equi-librium. The above parameters are chosen so that X-raysurface brightness satisfies the β -model best-fit (Sakelliou,Ponman 2004), and that the spectroscopic-like tempera-ture, T sl (Mazzotta et al. 2004), reproduces the observedtemperature at the unperturbed regions by Markevitch etal. (1998). The number of particles of each galaxy clus-ter is set to a half million each for dark matter and ICM.The initial relative velocity of the two clusters is set to1050 km / s to reproduce the observed temperature of thelinked region in terms of T sl , and the initial separationis ∼ Z , is very in-sensitive to the resulting ionization state of ions as longas Z ≪
1. We also assume ˜ T e = ˜ T i = 1 and an ionizationequilibrium state at the start of the simulation.
3. Result
In the rest of this paper, we present the results of asnapshot of the simulation in which the separation be-tween the centers of the two clusters is ∼ n (= n e + n i ) ∼ × − cm − (figure 1a), and T sl = 6 .
48 keV are in good agreement with the observa-tions (Sakelliou, Ponman 2004; Fujita et al. 2008).We find that the shock heating rate is typically a fewpercent of the adiabatic heating rate inside the linked re-gion. This means that both the electrons and ions aremainly heated by the adiabatic compression in almost thesame rate with no significant shocks there. Accordingly,as can be seen in figure 1c, the electron temperature isonly a few percent lower than the mean temperature inthis region. On the other hand, at the edge of the linkedregion (the white-dashed rectangles), there exist signifi-cant shock layers with mach number of 1.5–2. In theselayers, we can see that the electron temperature is typi-cally 10–20 % lower than the mean temperature, and evenlower toward outer regions.Figure 1d and 1e show the ionization fraction of Fe xxv and the ratio of the fraction relative to that in the ioniza-tion equilibrium state, respectively. Here, the ionizationequilibrium state is calculated assuming that T e = T i . Ino. ] Non-Equilibrium Ionization State and Two-Temperature Structure in Abell 399/401 3 Fig. 1.
Maps of (a) the ICM density in units of log cm − , (b) the mean temperature in keV, (c) the ratio of the electron temperaturerelative to the mean temperature, (d) the ionization fraction of Fe xxv , (e) the ratio of the Fe xxv fraction relative to that in theionization equilibrium state, and (f) the ratio of the line intensity in 6.6–6.7 keV band integrated along the line of sight relative tothat in the equilibrium state. The white-solid squares and white-dashed rectangles indicate the regions corresponding to the Suzakuobservation by Fujita et al. (2008) and the shock layers, respectively. the center of the linked region, the Fe xxv fraction is typ-ically 30–60 %, the largest among other ionization states,and is 10–20 % larger than that in the equilibrium state.In the shock layers at the edge of the linked region, theFe xxv fraction is nearly 80 % and 30–40 % larger thanthat in the ionization equilibrium state.The excess of the Fe xxv fraction can be understoodas follows. In the linked region, the electron tempera-ture is increasing from ∼ ∼ xxv fraction is decreasing in time becausean Fe xxv fraction peaks at ∼ xxv to higher ion-ization states is not quick enough to catch up with theionization equilibrium state, leaving the Fe xxv fractionlarger than that in the equilibrium state.Deviations from the ionization equilibrium state can beseen also for Fe xxiv . Its fraction is ≃ ∼ xxiv and Fe xxv fractions, the fractionsof Fe xxvi and Fe xxvii are ∼ ∼ α linesof Fe xxiv and Fe xxv in a rest-frame energy band of 6.6–6.7 keV is larger than those in the ionization equilibriumstate, primarily because of the excess of Fe xxv fraction.On the other hand, since the Fe xxvi fraction is smallerthan that in the equilibrium state, K α lines of Fe xxvi in 6.9–7.0 keV band in rest frame are dimmer. It shouldbe noted that the iron line emission detected in Fujitaet al. (2008) corresponds to the K α lines of Fe xxiv andFe xxv in the 6.6–6.7 keV energy band. Figure 1f depictsthe ratio of the intensity in 6.6–6.7 keV band projectedalong the line of sight relative to that in the ionizationequilibrium state, and it can be seen that the intensitychanges are significant (typically ∼
15 %) at the shocklayers, while the intensity is only a few percent enhancedaround the area of the Suzaku observation by Fujita etal. (2008), despite the excess of the Fe xxv fraction by10–20 % (figure 1e). This is because the deviation fromthe ionization equilibrium is significant only at the centerof the linked region, and its effect is diluted in integratingalong the line of sight. This suggests that the iron lineemission detected by Fujita et al. (2008) is not severelyaffected by the deviation from the ionization equilibrium.Here, let us define the ratio of the X-ray intensity betweenthe two energy bands as R = F (6 . − . F (6 . − . . (4)Figure 2 shows the map of the ratio R/R eq , where R eq isthe intensity ratio defined above but in the ionization equi-librium state, and clearly indicates that the intensity ratiodeparts from the one in the ionization equilibrium statewithin the shock layers. Note that this intensity ratio isindependent of the local abundance of iron, but primarilydepends on its ionization state. Therefore, such excess ofthe intensity ratio, R , can be used as a stringent observa-tional tracer of the non-equilibrium ionization state. T. Akahori and K. Yoshikawa [Vol. , R / R eq y [ M p c ] x [Mpc]10 2 3 1.51.41.31.11.00.90.70.81.2 Fig. 2.
The map of the ratio,
R/R eq , in the same regionas figure 1. The contours from outside to inside indicate R/R eq = 1 .
4. Conclusion and Discussion
The ionization state of iron and two-temperature struc-ture in the linked region of Abell 399/401 is investigatedby using N-body + SPH simulations by relaxing the as-sumptions of ionization equilibrium and thermal equili-bration between electrons and ions.It is found that, around the center of the linked region,the Fe xxv fraction is 10–20 % larger than that in the ion-ization equilibrium state, and the electron temperature isonly a few percent smaller than the mean temperature ofelectrons and ions, because the ICM is mainly adiabati-cally heated inside the linked region. On the other hand,we find that there exist shock layers at the edge of thelinked region, and that the Fe xxv fraction is larger thanthat in the ionization equilibrium state by 30–40 %, andthe electron temperature is typically 10–20 % lower thanthe mean temperature around these layers.Our simulation indicates that the intensity of Fe K α emission lines is affected by such deviation from the ioniza-tion equilibrium state of iron in the linked region. Whilethe deviation from the ionization equilibrium state is re-markable around the center and the edge of the linkedregion, we find that the emission line intensity is stronglyaffected preferentially at the edge of the linked region.The area of the Suzaku XIS observation by Fujita etal. (2008), in which fairly high metallicity is reported, islocated at the central portion of the linked region. Our re-sults imply that X-ray emission in this area is not stronglyaffected by the effects of a non-equilibrium ionization stateand two-temperature structure. Therefore, the fact thathigh metallicity is detected in this area cannot be ascribedto the non-equilibrium ionization state of the ICM, andmust be explained by other physical processes.It is interesting to discuss the detectability of thenon-equilibrium ionization state and the two-temperaturestructure of ICM in Abell 399/401. According to our sim-ulations, it is expected that shock layers with a machnumber of 1.5–2 are located at the edge of the linkedregion, and that the ratio between K α emission lines of Fe xxiv – xxv and Fe xxvi are significantly different fromthat in the ionization equilibrium state. Observationally,such an intensity ratio of iron emission lines could beimportant clues for the detection of the deviation fromthe ionization equilibrium in these layers. In principle,the indication of the two-temperature structure can bealso obtained by the difference between electron and iontemperatures inferred from X-ray thermal continuum andthermal width of emission lines, respectively. Of course,the detections of the non-equilibrium ionization state andthe two-temperature structure are not very feasible withthe current observational facilities, but could be achievedby the X-ray spectroscopy with a high energy resolutionusing X-ray calorimeters in near future.Finally, we should discuss several caveats on the as-sumptions adopted in this work. The slope of the den-sity profile, i.e. β , is a sensitive parameter to the non-equilibrium ionization state and two-temperature struc-ture. If we adopt β = 0 .
5, the resultant departure fromthe ionization equilibrium is suppressed because the ICMdensity at the outskirts is relatively denser and the equili-bration timescales become shorter. In addition, we assumethat the encounter is taking place on the plane of the sky.If it is not the case, the effect of the non-equilibrium ion-ization state on the observed X-ray intensity at the shocklayers would be blurred to some extent in integrating alongthe line of sight, depending on the viewing angle.The authors would like to thank an anonymous ref-eree for useful comments and suggestions. This work iscarried out with computational facilities at Center forComputational Sciences in University of Tsukuba, andsupported in part by Grant-in-Aid for Specially PromotedResearch (16002003) from MEXT of Japan, and by Grant-in-Aid for Scientific Research (S) (20224002) and forYoung Scientists (Start-up) (19840008) from JSPS.