aa r X i v : . [ a s t r o - ph ] A ug Emission Lines in X-ray Spectra of Clusters ofGalaxies
Paolo Tozzi
INAF – Osservatorio Astronomico di Trieste – via G.B. Tiepolo 11 – 34143 Trieste – ITALY
Abstract.
Emission lines in X–ray spectra of clusters of galaxies reveal the presence of heavyelements in the diffuse hot plasma (the Intra Cluster Medium, or ICM) in virial equilibrium in thedark matter potential well. The relatively simple physical state of the ICM allows us to estimate,with good accuracy, its thermodynamical properties and chemical abundances. These measures putstrong constraints on the interaction processes between the galaxies and the surrounding medium,and have significant impact on models of galaxy formation as well. This field is rapidly evolvingthanks to the X–ray satellites Chandra and XMM–Newton. Among the most relevant progresses inthe last years, we briefly discuss the nature of cool cores and the measure of the Iron abundance inhigh redshift clusters. Future X–ray missions with bolometers promise to provide a substantial stepforward to a more comprehensive understanding of the complex physics of the ICM.
Keywords:
X–ray Spectroscopy - Emission Lines – Clusters of Galaxies
PACS:
CONTINUUM X–RAY EMISSION FROM CLUSTERS OFGALAXIES
The 0.5-10 keV X-ray band is currently explored by the two X–ray satellites Chandraand XMM–Newton, both launched in 1999. Energies E > . T > × K. Therefore X–ray astronomy is an ideal observational windowsfor very hot astrophysical plasmas.At the beginning of the era of X–ray astronomy, R. Giacconi and collaborators de-tected X–ray emission from clusters of galaxies with the Uhuru satellite. This emissionwas identified as bremsstrahlung from hot diffuse plasma (the Intra Cluster Medium,from now on ICM), thanks to its extended distribution and the detection of higly ionizedFe lines in the X–ray spectra. Nowaday the imaging of bright X–ray clusters of galaxiesis possible up to redshifts as high as z ∼ .
3. As an example, in Figure 1 we show the dif-fuse X–ray emission (in red) from the massive cluster RXJ1252 at z ∼ . r ICM (cid:181) r − [5]. Typical total luminosities areobserved to be roughly in the range L X ∼ − f ew × erg/s.Clusters are bound objects formed via gravitational instability from the fluctuationsin the primordial density field [10]. The temperature of the diffuse baryons constitutingthe ICM is determined by the energy equipartition between the mass components:dark matter, ( ∼
80 %), diffuse baryons ( ∼ ∼ IGURE 1.
Left panel: the X–ray emission (in red) of the cluster RXJ1252 at z = .
235 (observed withthe Chandra satellite) on top of the optical image (from the VLT). Right panel: Chandra X–ray spectrumof the extended emission in RXJ1252 [14]. The Fe line clearly stands out at the rest–frame energy E ∼ . leading to the formation of the cluster. The dark matter, dynamicaly dominant, andthe baryons, rapidly adjust and reach a pressure balance with the gravitational forces.The velocities of particles become randomised, and the structure settles into the virialequilibrium. In its simplest form, the virial theorem writes as 2 T + U =
0, where T is theaverage kinetic energy per particle and U is the average potential energy. This impliesthat, when virialization can be applied, a measure of the temperature of the ICM givesa good estimate of the total mass of the cluster. Typical cluster masses are in the range10 − M ⊙ , corresponding to T ICM ∼ −
10 keV.The continuum emission from the plasma is almost entirely given by bremsstrahlungdue to the acceleration of electrons in the Coulomb field of positive ions (mainly Hy-drogen and Helium nuclei). The relevant case for clusters of galaxies is bremsstrahlungemission averaged over a thermal distribution of electron speeds. This emission can becomputed with a classical treatment [15] plus quantum effects (included in the Gauntfactor of order unity) while the relativistic corrections are often ignored (being few per-cent for kT ICM >
10 keV). The thermal bremsstrahlung emission simply scales as: dEdtdV (cid:181) n e T / ICM . (1)This implies that the continuum emission of the ICM is strongly dependent on its densitydistribution (through the electron density n e ) but only weakly on its temperature. X–RAY LINE EMISSION FROM CLUSTERS OF GALAXIES
While the continuum emission is relatively simple to model, the total emission mustalso include lines associated to the ions of heavy elements distributed in the diffuseICM. First, it is important to understand the kind of equilibrium which applies to theCM . In general, equilibrium is given by a balance between competing processes. Inthe case of strict thermodynamic equilibrium, every atomic process is as frequent asits inverse process (principle of detailed balance). The classic example is the blackbody. The detailed balance does not apply to the ICM, nevertheless, it appears to be inthe so called collisional (or coronal) equilibrium. To understand what is the collisionalequilibrium, we first recall the three main “actors”: • the kinetic distribution of electrons and ions; • the atomic level populations; • the radiation field.Since the radiation field does not participate to the equilibrium, we consider only theequilibrium between the electron and ion population and the atomic levels. The four keyelectron–ion collisional processes (and their inverse) are: • Collisional excitation (Collisional deexcitation); • Collisional ionization (Three body recombination); • Radiative recombination (Photoionization); • Dielectronic Capture (Autoionization).Only few of these processes are relevant in the collisional ionization equilibrium. Infact, thanks to the very low density of the ICM, atoms are always in their ground state,and collisional deexcitations and three body recombinations are negligible. Since themedium is optically thin, photoionization, photo excitation and scattering are neglected,so that excitation and ionization are dominated by electron ion collisions. Deexcitationis dominated by spontaneous radiative decay, and ions will recombine by radiative or di-electronic recombination. It follows that the equilibrium is given by the balance betweenimpact ionization (and excitation autoionization) and radiative and dielectronic recom-bination. The interpretation of the resulting spectrum will require a detailed knowledgeof the ionization, recombination and excitation rates of several transitions, in particularof K–shell transitions of C, N, O, Ne, Mg, Si and Fe, and L–shell transitions of Si, S,Ar, Ca, Ni and Fe.To compute the collisional excitation rates we also assumes a Maxwellian energydistribution of the electron energies, and a cooling time longer than relaxation time(necessary to achieve equilibrium, condition satisfied thanks to the low density of theICM except sometimes in the very inner regions). Thus in a steady state the rate ofchange of the population density n j of the j th ionization state of a given element isgiven by: 0 = dn j dt = S j − n j − − S j n j − a j n J + a j + n j + , (2)where S j is the ionization rate for ion j with ejection of one electrons (direct ionizationand autoionization), while a j is the recombination rate of ion j (radiative and dielec-tronic). The ionization structure is derived by solving for each element with atomic The following description follows Kahn 2005[8].
IGURE 2.
Upper panel: ion concentration of some elements as a function of T ICM . Lower panel: Feions concentration as a function of the ICM temperature (from [12]). number Z a set of Z+1 coupled rate equations. In the steady state the equation reducesto: n j + n j = S j ( T ICM ) a j + ( T ICM ) . (3)Thus the ratio of two adiacent ionization states of a given element depends only on T ICM and not on the electron density n e as long as stepwise ionization (more than onecollision) in S j and three body recombination in a j + can be neglected. The fraction ofions at the stage z of a given element, h z , can be expressed directly as a function of theratio of adiacent states.The emissivity of a given emission line (which is proportional to the EquivalentWidth, EW , of a line) is given by e = n e n i g ( T ICM ) E where g is the collisionalexcitation rate for transition E and n i = A Z h z ( T ICM ) n H is the density of the ion in theground state. Once the coefficient a and S are known from fundamental atomic physics,the concentration of each ion of a given element can be straightforwardly computedfrom the measure of the equivalent width. An example of the ion concentration ofsome elements as a function of T ICM is shown in Figure 2. The equivalent width canbe measured directly through X–ray spectroscopy and it is defined as: EW ≡ Z ( I n − I n I n ) dh n , (4)where I n is the spectrum, I is the continuum component, and the integral is over anenergy range close to the line. Since EW is directly proportional to the ion concentration n i / n H , it depends only on temperature and abundance.There are of course sources of uncertainties. The first one is due to the accuracy ofatomic physics. Both ionization and recombination rates can be uncertain by a factor 2-4.Fortunately, ionization and recombination rates for H–like and He–like ions, which emitlines that are among the strongest in astrophysical plasmas, are known more accurately.he second critical aspect is given by the spectral resolution. X–ray spectra may beobtained directly with CCD imagers or with reflection gratings spectrometers. In thefirst case, the spectral resolution is limited and several lines often blend with each other.Only few bright sources can be analyzed with grating spectroscopy, due to the highS/N required. Therefore, in some cases, the abundance of several elements cannot berecovered accurately.Finally, a source of uncertainty comes from an aspect intrinsic to the physics ofclusters: in general the ICM may have different temperatures at different radii, withsignificant gradients in the central regions. This aspect can be modelled, or can bemitigated in bright clusters thanks to spatially resolved spectroscopy and deprojectiontechniques. In any case, the presence of different temperatures along the line of sightsignificantly affects abundance measures. IRON ABUNDANCE AT HIGH REDSHIFT
Temperatures and abundances are measured at the same time (from line ratios and shapeof the continuum) with the use of fitting packages which implement atomic physics andthe collisional equilibrium equations. Heavy elements (generally called metals), amongwhich Iron is the most prominent, are always found in the ICM. Over a wide range of T ICM , the EW of the Fe K–shell line (mostly from Fe + 24 and Fe +25) is several orders ofmagnitudes larger than any other spectral feature. At lower energies O, Si, S, and L–shelltransition in lower Fe ions show significant EW. Their abundance is consistent with beingproduced by the elliptical cluster galaxies [9]. In general, Fe abundance is observed tobe about Z ∼ . Z ⊙ (where the Iron solar abundance is [1]) at least for T ICM > T ICM ≤ a elements over Fe is very relevant to understand the relative contribution of TypeII andTypeIa SNe. However, here we will discuss only some results on the Fe abundance athigh redshift.We recall that the Fe line can be measured in the highest redshift clusters selectedin X–rays, as shown in the right panel of Figure 1. In a recent work, Balestra et al.(2007) used the Chandra archive for clusters at redshift z ≥ . ∼ . R vir )is changing by a factor of about 2 between now and z ∼ . ∼ z >
1, in line with the expectation that the bulkof star formation in massive spheroids, responsible for the large majority of the metals,occurs at z ≥
2. On the other hand, we do not expect much star formation responsible forIron production after z ∼ .
5. Therefore, the most likely interpretation of the increase ofthe average Iron abundance in the inner 0 . R vir of clusters, may be due to deposition ofpreviously enriched gas towards the center. Currently, several approaches can be used. Aphenomenological model based on detailed chemical galactic evolution, shows that the IGURE 3.
Left: solid squares and circles show Fe abundance in the inner regions of hot clusters( kT > Z Fe evolution of the form ∼ ( + z ) − . . Right: the two top panels shows the model(blue) and the data from the Reflection Grating Spectrometer of XMM–Newton for the cool–core clusterAbell 1835. In the bottom panel the gas colder than 2.7 keV has been removed in the model, which nowshows a good agreement with the data [12]. Fe increase is consistent with the transformation of gas–rich spirals into S0 galaxies,with the consequent deposition of highly enriched gas in the central regions wherethe ram pressure stripping is more efficient [4]. N–body Hydrodynamic simulations,on the other hand, show that high abundance, low entropy gas, previously associatedto galaxies or group–size halos, may sink to the center during the mass growth ofthe cluster (see Cora et al. in preparation). These models favour a dynamical originof the observed evolution, but they must also explain the abundance profiles and thetemperature gradients in cluster cores observed in spatially resolved spectral analysis(see [17] and [2]).
THE NATURE OF COOL CORES
The total emission due to bremsstrahlung and lines can be expressed as L (cid:181) n e L ( T ICM ) where L is the cooling function including all the transitions for a given T ICM . The coolingtime t cool is defined as the ratio of the total internal energy of the ICM divided by thebolometric ICM emission. It turns out that t cool (cid:181) T ICM L − n − e (see [16]).If t cool << t H the baryons are expected to cool out of the hot phase and eventuallyrecombine and form stars or clouds of cold gas. In many local clusters it is possible tocompute the cooling time down to very small scales (about few kpc). In several cases aclear decrease of the temperature is observed towards the center, and the cooling timewithin 10 kpc can be significantly less than 1 Gyr (see [12]). It seems unavoidable topredict that baryons are flowing to the cold phase at a rate of the order of 100, sometimes1000 M ⊙ yr − in more than half of local clusters. The simplest model based on isobaricooling, predicts a spectrum rich in emission lines, which are strongly increasing atlow T ICM due to the higher number of ion species. However, grating spectroscopy ofthe brightest central regions of clusters, with the XMM–Newton satellite, provided asurprising result. Many of the lines expected in cooling flows were missing from theobserved spectra [11], as shown in the example of Figure 3 (right panels). It can beshown that the lowest temperature in the center is of the order of 1/3 of the virial one.This discovery has a strong impact: it implies that the ICM is kept above a temperaturefloor (not too far from the virial one) by some heating mechanism. It follows that thereare no more cooling flows, at least not as strong as previously thought, but only coolingcores. On one hand, this explains why we never observed the cooled gas resulting fromthe cooling process, neither in form of stars nor of cool gas. On the other hand, there isno consensus on the sources which constantly heat the ICM. This is an open problem,relevant not only for ICM, but also for general framework of galaxy formation andevolutionIn fact, this problem reminds us of the cooling catastrophe (also known as coolingcrisis). In the standard galactic formation scenario, baryons in CDM halos cool via ther-mal bremsstrahlung and line emission. Baryons are assumed to turn into stars when t cool < H − [18]. But the blind application of this criterion would result in the largemajority of the baryons locked into stars. This is a consequence of the high power atlow mass scales in the CDM power spectrum. The low fraction of baryons turned intostars, observed to be around 10% everywhere in the Universe, requires an ubiquitousmechanism which hampers the baryons from cooling. It would be nice if the same heat-ing process might explain the cooling core problem and solve the cooling catastropheat the same time. This still unknown process, or better, these class of processes, areknown under the name of feedback, a key ingredient in every model of cosmic structureformation.The main problem with feedback, is that any process we may think of, scales withvolume (and then with density), while cooling is a runaway process proportional to r . Therefore there is not an obvious, mechanism for self–regulation. Understandingfeedback is nowaday the most compelling goal for structure formation models. Maincandidates are SNe explosions and stellar winds (as confirmed by the presence of heavyelements in the ICM) and the much more energetic output from AGN. A spectacularexample that favours AGN as the best candidates as the main heating sources, is theX–ray mage of the Persues cluster [6], where hot bubbles created by the jets are pushingthe ICM apart, with a total mechanical energy sufficient to heat significantly the diffusebaryons. Still, how and on which time scale the energy is thermalized into the ICM isstill a matter of debate. PROSPECTS FOR THE FUTURE AND CONCLUSIONS
The results discussed so far are based on X–ray spectra from CCD, with a modestenergy resolution, and from reflection grating spectrometers, with high energy resolutionbut suitable only for very bright sources. Given the complex spatial structure of thethermodynamical properties of the ICM, an ideal instrument should attain at the sametime good spatial and spectral resolution. This can be achieved with X–ray bolometers inhe soft band, where most of the lines are. The bolometer that is expected to be onboardof the proposed EDGE satellite [13] will be able to detect absorption and emission linesfrom the Warm Hot Intergalactic Medium (WHIM) which includes the majority of thebaryons in the Universe [7]. With a nominal resolution of few eV, it will be able toresolve most of the X–ray lines, and to measure the thermal broadening and possiblythe bulk motions of the ICM in the inner regions of clusters, directly addressing aspectslike viscosity and turbulence. In addition, it will be possible to detect the low surfacebrightness ICM in the outskirts of clusters and in filaments.In the meanwhile, we still have to exploit the full potential of the Chandra and XMM–Newton satellites, which are still operating, and which already provided many archivalcluster observations. The results (among many others) presented in these Proceedings,show that line emission diagnostic in X–ray spectra of clusters of galaxies are an un-valuable tool to study the chemical and the thermodynamical state of the ICM. Anotheraspect I wanted to stress, is that studies of the chemical enrichment of the ICM andof the temperature structure in cool cores are extremely important for the entire field ofgalaxy and structure formation. For example, the mechanism responsible for the temper-ature floor in cool cores of clusters may be tightly related to the one responsible for thequenching of the star formation in massive spheroids at z ≥
2. Therefore, the technolog-ical challenge toward spatially resolved, high resolution X–ray spectroscopy, will be theway to achieve important steps forward in many aspects of extragalactic astrophysics.
ACKNOWLEDGMENTS
We would like to thank the organizers of this conference for providing a stimulatingscientific environment. We acknowledge financial contribution from contract ASI–INAFI/023/05/0 and from the PD51 INFN grant.