Astron. Astrophys. 324, 449-456 (1997)

1. Introduction

The short cooling times (less than a Hubble time) of the central intracluster medium (ICM) of X-ray emitting clusters of galaxies points to gas sinking towards the center of the cluster in a "cooling flow" (for reviews, see Fabian et al. 1984, 1991 and Fabian 1994). A sizeable proportion of the cooling flows also contains extended (from kpc to tens of kpc) optical emission line filaments around the central dominant galaxy of the cluster, which is always at the center of the flow (Heckman 1981; Cowie et al. 1983; Hu et al 1985; Johnstone et al. 1987; Heckman et al. 1989; Baum 1992). These extended optical filaments systems are seen only in cooling flows and are thought to be a phase of the evolution of thermal instabilities arising in the cooling flow. The line emission flux ratio [NII] 6583/H allowed Heckman et al. (1989) to divide the filaments into two distinct classes, class I with an average [NII]/H , and class II with [NII]/H . Also, the class II filament systems tend to have higher H luminosity and to belong to cooling flows with greater mass accretion rates. More recently, however, the discovery of filaments in cooling flows whose line ratios are intermediate between those typical of class I and II systems (Crawford & Fabian 1992; Allen et al. 1992; Crawford et al. 1995) called for a continuous distribution instead of a clear split into two classes. In addition, there are some H -luminous class I (i.e. with high [NII]/H ) systems (e.g., A1068, A2146, RX J0439.0+0520) departing from the trend of class I systems having low H luminosities.

One of the major problems associated with the optical filaments is their high luminosities (typically H luminosities are to ergs s^-1). Quiescently cooling gas that recombines only once at the X-ray determined mass accretion rate would not be detectable as emission line nebulae. The fact that the central regions of cooling flows often do show optical emission requires some source of energy to repeatedly reionize the gas. Several models, considering different mechanisms for ionization and heating of the gas, - shocks (David et al. 1988, David & Bregman 1989), thermal conduction (Böhringer & Fabian 1989), and photoionization by soft X-rays and EUV produced in the cooling gas (Voit & Donahue 1990; Donahue & Voit 1991; Voit et al. 1994) -, have met difficulties in explaining the observed line ratios and luminosities. It is possible that some combination of photoionization and shock models could explain the observations. One example of these hybrid models involves the combination of self-absorbed irradiating mixing layers of cold clouds embedded in the hot cooling gas and emission from shocks generated in collisions between these clouds (Crawford & Fabian 1992).

Jafelice and Friaça (1996) have investigated magnetic reconnection as a heating mechanism and concluded that magnetic reconnection cannot be invoked as the sole mechanism powering the optical line emission in cooling flows. However, it could be an important ingredient to explain the emission coming from low ionization lines. The models with high magnetic reconnection efficiencies exhibit a strong [OI] 6300 emission, and, therefore, magnetic reconnection could be an additional component together with other mechanisms producing most of the emission in H and higher ionization lines (as [NII] 6583). The existence of magnetic fields in the ICM has suggested magnetic reconnection as a heating mechanism. In this paper we investigate another heating mechanism expected to be at work in the presence of magnetic fields: Alfvén heating (AH). Here we explore the importance of AH not only as a dominant energy source for optical filaments in cooling flows but also as an ingredient contributing to the emission of some optical lines.

The Alfvén heating comes from the dissipation (damping) of Alfvén waves. These waves are easily generated in many cosmic plasmas, but they possess no linear damping mechanism since they are not compressive. Nonlinear damping of these waves occurs when one Alfvén wave decays into another plus a slow magnetosonic wave, or two Alfvén waves combine into one fast magnetosonic wave; the resulting magnetosonic waves can then be dissipated. The dissipation of these waves may contribute to heat the solar corona, to influence the interplanetary wave spectrum, and to determine the wave spectrum available to scatter cosmic rays. As they are not compressive, the nonlinear decay occurs due to second order effects in the wave amplitude. Interacting Alfvén waves are compressive and thus generate a new compressive wave (see Chin and Wentzel 1972). The resulting heating - at least in terms of nonlinear, resonance surface and turbulent damping mechanisms - has been applied to study the thermal stability in the broad line region of quasars and in the basis of the wind in hot stars, in a successful way (Gonçalves et al. 1993a, 1996a, b).

Alfvén waves are created by perturbed magnetic fields. In view of this, two conditions that are fulfilled by the core of a cooling flow make it a favorable site for the generation of Alfvén waves: it contains magnetic fields, and it is turbulent.

The lack of any strong hard X-ray emission due to inverse Compton from the relativistic electrons in a few clusters (generally not cooling flows) that have halo radio sources imposes a lower limit for the magnetic field of 0.1 µG over scales of up to 500 kpc (Rephaeli & Gruber 1988). At the smaller ( kpc) scales of cooling flows, magnetic fields of typically 1-3 µG are derived corresponding to a magnetic pressure of about 1% of the thermal pressure. At the center of a cooling flow still more intense magnetic fields must be present since the field is amplified by compression as the gas flows inward (Soker & Sarazin 1990). As a matter of fact, Faraday rotation and depolarization of the radio emission of extended radio sources (Ge & Owen 1993; Taylor et al. 1994) residing in cooling flows have revealed that the magnetic field increases inward and that it can reach 20-100 µG depending on the degree of ordering of the field. In this way, at the very center of the flow, the magnetic pressure can supersede the thermal pressure.

One kinematic signature of the filament systems is the lack of organized velocity patterns (e.g., rotation or shear or infall) (Heckman et al. 1989; Baum 1992). The filaments typically have very small rotational velocities and are turbulently, and not rotationally, supported. A small number of filament systems do show apparent rotation with rotational velocities of km s^-1 within a few kpc. However, these same systems show disordered velocity patterns at larger scales (Hu et al. 1985). Lines are broad throughout the filamentary region, but line widths decrease from 500-100 km s^-1 in or near the galactic nucleus to 100-300 km s^-1 at the largest radii (typically 5-15 kpc). This suggests that the inner ICM is highly turbulent, with the amplitude of random velocities increasing inward. In fact, the core of a cluster is expected to be turbulent not only due to the frequent crossing of galaxies through it but also due to relics of merging of subclusters. In addition, the absence of rotation in the center of cooling flows requires rotational breaking of the gas flowing inward, and turbulent viscosity is the most likely transport process of angular momentum in a cooling flow (Nulsen et al. 1984).

The possibility of using the turbulent energy to heat the plasma in the core of cooling flows was also considered by Loewenstein and Fabian (1990), in order to explain the kinematics of the cooling flow clouds. They assume a magnetic viscous heating process (' plasma slip') where the magnetic field that passes from the clouds to the hot gas can be forced to oscillate by the noise and so cause the ionized particles within the cloud to oscillate and collide with neutral particles. This process can efficiently transport Alfvén wave energy to length scales of cm.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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