Cosmic Ray Feedback
Cosmic rays produced or deposited at sites in hot cluster gas are thought to provide the pressure that forms X-ray cavities. While cavities have a net cooling effect on cluster gas, young, expanding cavities drive shocks that increase the local entropy. Cavities also produce radial filaments of thermal gas and are sources of cluster cosmic rays that diffuse through cavity walls, as in Virgo where a radio lobe surrounds a radial thermal filament. Cosmic rays also make the hot gas locally buoyant, allowing large masses of low entropy gas to be transported out beyond the cooling radius. Successive cavities maintain a buoyant outflow that preserves the cluster gas temperature and gas fraction profiles and dramatically reduces the cooling rate onto the central black hole.
address=Department of Astronomy and Astrophysics, UC Santa Cruz
When a relatively small mass of gas accrets onto massive black holes in the cores of cluster and group-centered elliptical galaxies, enough energy can be released to solve the cooling flow problem: Why does the hot cluster gas radiate X-rays but does not appear to cool? Mass cooling rates must be reduced by at least an order of magnitude below those predicted by traditional cooling flows. While sufficient accretion energy is available, there is no general consensus regarding the mechanisms by which energy is delivered from the black hole to the hot gas. One of the major obstacles has been the observation that the gas temperature typically has a minimum at the center of the cluster atmosphere, just adjacent to the energy source at the black hole.
Fortunately, X-ray observations of cavities in the hot gas in (a minority of) clusters suggest that energy from the black holes can be transmitted from the central source by jets to both near and distant regions in the cluster gas. Radio emission from young X-ray cavities suggest that all cavities are inflated and supported largely by the pressure of relativistic cosmic rays that are created or deposited by jets. Cavities are not formed explosively but in a subsonic fashion, driving outward propagating shocks that increase the entropy lost by radiation in the local cluster gas. It is usually assumed that the work done during cavity formation also compresses the ambient gas, helping to restore the thermal energy lost by radiation. However, while the entropy is increased by shocks around young cavities, most of the work is consumed in increasing the potential (not thermal) energy of cluster gas as gas moves out in the cluster potential to accommodate the cavity volume. As cluster gas moves nearly adiabatically outward, its density decreases and it cools. For most, perhaps all, cavities this global expansive cooling offsets the heating by the cavity-produced shock. Furthermore, as shocks move out into the cluster gas the deposition of dissipative heating in the shock transition is not distributed in the cluster in proportion to the local radiative cooling. Because the gas density profiles in clusters are generally flatter than , most wave energy is absorbed near the cluster centers. After a few Gyrs of heating by successive outward propagating waves, the gas temperature in the cluster core rises far above the temperatures observed and inflowing gas cooling from more distant regions of the cluster cools catastrophically just beyond the heated core. Since cluster density profiles are not tuned to receive wave energy that balances local radiative losses, cavity (or other) shocks cannot be the dominant means of shutting down cooling flows.
These difficulties have led us to consider an alternative solution to the cooling flow problem in which low entropy gas near the cluster center is circulated outward by cosmic ray buoyancy to distant regions in the cluster without much disturbing the observed gas temperature profile. For simplicity, we consider only the two most relevant cluster components, hot gas and (relativistic) cosmic rays. Since strong shocks are rare, as cavities evolve the combined pressure of thermal and cosmic ray gases must remain close to hydrostatic equilibrium in the cluster potential. We assume that cosmic rays are deposited (or created) by jets at sites that become X-ray visible cavities. For simplicity we ignore non-adiabatic direct heating of the hot gas by cosmic rays via Columb heating or Alfven dissipation.
Cosmic rays and hot gas exchange momentum by means of small, microgauss magnetic fields that are nearly frozen into the hot gas but which are too weak to influence the gas dynamics. Gradients in cosmic ray pressure cause X-ray cavities to form. In addition cosmic rays must be allowed to diffuse in the hot gas. Diffusion is expected in part because of the notorious difficulty in confining a relativistic plasmas with magnetic fields and also because we expect synchrotron emission from the electron component of the cosmic rays to eventually evolve into radio lobes that can be much larger than the cavities. For simplicity we do not define in detail the particle nature of the cosmic rays – electrons or protons – and consider only their (relativistic) energy density. Our main interest is to understand how cosmic rays inflate X-ray cavities and buoyantly transport hot gas far from the cluster cores. In summary, cosmic rays are injected at cavity sites, advected by the thermal gas, diffuse relative to the gas and have gradients that can act directly on the hot gas.
The rate that cosmic rays diffuse through the gas increases with cosmic ray particle energy, so the diffusion coefficient we seek is a mean over the particle energy spectrum. While is difficult to derive, an approximate value can be determined from dimensional considerations, length/time. For example, spallation rates in the Milky Way indicate that cosmic rays reside in the disk plane having a scale height kpc for about yrs, i.e. cm/s, and this is very close to the values considered in detailed models of cosmic ray diffusion in the Milky Way. Similarly, cosmic rays must remain trapped in cavities for a typical cluster buoyancy time yrs, but the appropriate scale length is not the radius of the cavity but the thickness of the cavity wall, kpc, for which cm/s. It is also useful to explore larger rates, cm/s, to follow the progress of more energetic cosmic rays. For spherical cavities forming in a uniform thermal gas, the strength of circum-cavity shocks varies inversely with and with the efficiency that cosmic rays diffuse through the cavity walls into the ambient gas. Also is likely to decrease in high density gas where the magnetic fields may be larger.
A major inspiration for the long term evolution of X-ray cavities has been the recent discovery of a narrow ( kpc) kpc-long radial filament of cooler, slightly overdense thermal gas in the Virgo cluster. Such radial features arise naturally from the “splash” following the formation of cavities in a gaseous atmosphere. Radial thermal filaments are driven by the confluence of gas flowing toward the bottom of buoyant cavities, which is relieved as gas squirts up through the cavity center and far beyond. (Cavitations following undersea explosions also produce intense, vertically directed flows above the sea surface.) The past history of Virgo is revealed in two very similar timescales: the dynamical time for the thermal filament to flow out from the cluster core, yrs, and the synchrotron age yrs of cosmic ray electrons in the large southern radio lobe which extends out to 30-40 kpc. Since the thermal filament lies right along the central diameter of the radio lobe, it is natural to conclude that they were formed by the same cavity event yrs ago. The relevant diffusion coefficient for energetic cosmic rays that diffuse away from the cavity site, cm/s, is reasonable. Evolutionary models of a cavity inflated by diffusing cosmic rays at radius 10 kpc from the center of Virgo show that these two features could indeed have formed at the same time from a cavity that is no longer visible. This is the first calculation that establishes a dynamical relationship between these large-scale cluster features observed at both X-ray and radio frequencies.
But the most important contribution of cosmic rays to cluster dynamics is not the short-term fireworks – cavities, filaments, radio lobes, etc. – but the long-lasting buoyant outflow of cluster gas to large radii. As cosmic rays diffuse into cluster gas, their pressure provides a small fraction of the total pressure required to maintain approximate local hydrostatic equilibrium. In such regions the gas pressure and density are slightly lowered and the cluster gas becomes naturally buoyant. The local buoyant outflow velocity can easily exceed the (very small) cooling inflow velocity due to radiative losses. By this means very large masses of low entropy gas can be slowly transported far from the galactic center before catastrophic radiative cooling occurs[5,4].
To illustrate this effect we explore how the 2D evolution of the Virgo cluster is affected by the presence of cosmic rays. Consider first the response of the cluster without cosmic rays as it evolves by radiative losses away from its presently observed density and temperature profiles, becoming a traditional cooling flow. The left column in Figure 1 shows the initial configuration (solid lines) assumed to be in hydrostatic equilibrium and its density, temperature and pressure profiles after 3 Gyrs (long dashed lines). The dotted line shows the ratio of local gas entropy to its initial value . After 3 Gyrs the central temperature and entropy have dropped due to radiative losses and the gas density has adopted a central peak characteristic of traditional cooling flows. The large central cooling rate at this time, 85 yr, is incompatible with the absence of cooled gas in the cluster core.
However, the 2D flow is radically different in the presence of cosmic rays. Assume that successive cavities form every 200 Myrs at 10 kpc from the cluster center. Each identical cavity is inflated in 20 Myrs by diffusing cosmic rays of total energy ergs. Two cosmic ray diffusion is given by with (low ) or (high ). The evolution of Virgo with cosmic rays after 3 Gyrs is shown in Figure 1 for each . Regardless of , it is seen that the gas density and temperature distributions are maintained close to the original profiles. The entropy is enhanced locally near the cavity site (10 kpc), but is generally negative. Most of the low entropy gas near and within 10 kpc has been buoyantly transported out to 20-70 kpc (where is much longer), but the cosmic ray pressure (short dashed lines) is generally small.
Most importantly, the central radiative cooling rates after 3 Gyrs have been reduced to 0.1 - 1 yr, very far below the cooling flow value. Low entropy gas that would have otherwise cooled has been made buoyant by cosmic rays that diffused through the cavity walls. The time-averaged cosmic ray luminosity erg s is modest, only equal to the observed X-ray luminosity within kpc. Most of the energy that drives the buoyant outflow comes from the gravitational potential energy of the cluster.
This simple exploratory calculation suggests that the feedback deposition of cosmic rays into galaxy clusters provides a robust means of shutting down cooling flows. Moreover, the low central gas fraction observed in galaxy cluster cores can be created and maintained by cosmic ray feedback. Finally, the transport of low-entropy gas to distant regions in the cluster is consistent with recent Suzaku observations showing that the entropy in the outer regions of clusters is much lower than previously expected.
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