The characteristic curve of cool-core fractions from groups to massive clusters

Characteristic curve of cool-core fractions

In the paper "How the cool-core population transitions from galaxy groups to massive clusters" we unveil how the population of cool-core clusters changes from the scales of galaxy groups to massive clusters. The largest Magneticum simulation (Box2b/hr) shows a very characteristic curve, which peaks in the transition from galaxy groups to clusters (1e14 Msun) and decreases towards both sides, small galaxy groups and massive galaxy clusters. This trend is also followed by the observational data, but it does not decrease so sharply for the lower mass systems. A priori, this reminded me of the Gamow peak, where two factors with opposing trends (high energy tail of the Maxwell-Boltzmann distribution and tunnelling through a Coulomb barrier) combine to produce a range of energies where the probability of fusion is maximised.

This was a very inspiring idea, so we looked into the underlying trends of the two main factors known to affect the thermodynamical evolution of galaxy clusters: On one hand, we have the feedback from the supermassive black hole (SMBH) hosted in the central Brightest cluster galaxy (BCG), and on the other, the impact of thermal conductivity and recent merge activity. From the Magneticum simulations, it is possible to obtain in a straightforward way the energy injected by the central SMBH, and we can also obtain the Spitzer coefficient for thermal conductivity and the number of mergers undergone by the BCG as a proxy for the merger activity. As I suspected, the relative impact (w.r.t. the bolometric luminosity) on the central SMBH decreases towards the most massive galaxy clusters, but on the other hand, the Spitzer coefficient increases sharply due to the T^(5/2) dependency, and the number of mergers increases since the most massive clusters typically had more mergers to assemble. These factors combined in a similar way as in the Gamow peak to produce the characteristic curve of cool-core fractions.

Left: Relative impact of central black hole, Center: Number of merges, Right: Spitzer coefficient normalized to 1keV

Concept of the driving factors behind the characteristic curve of cool-core fractions

The question was: How can we quantify the dynamical state of groups and clusters of galaxies to verify that they are imprinted with energy from recent merge activity? In the realm of observations, there are a lot of works based on the morphological parameters of galaxy clusters. For example, the X-Ray Morphological Analysis of the Planck ESZ Clusters by Lorenzo Lovisari and collaborators is a wonderful example, including images of the clusters to give you a visual idea of what disturbed and relaxed clusters look like. However, we were looking for a direct quantification rather than a tracer; in this sense, cosmological simulations provide a lot of insight since it is possible to recover all energy-related variables for each particle in a simulated galaxy cluster, including the internal and kinetic energy.

Total freedom ratio

Initially I considered the virial ratio (two times the total internal and kinetic energy over the gravitational energy), since this is expected to be 2 for relaxed systems according to the Virial Theorem. However, this result is only exact for closed systems, and in open systems (for example, the core region of a galaxy cluster), it is necessary to consider boundary conditions (the pressure and potential external to the core), which is cumbersome to obtain from a smooth particle hydrodynamics (SPH) simulation. However, if we don't consider the boundary conditions, the ratio between the total energy and the potential energy for each particle is analogous to the square of the ratio between a particle's velocity and the escape velocity. We called this ratio the 'freedom ratio' which as see on the left panel shows a clear increasing trend towards more massive galaxy clusters, indicating that they have been energised by recent merge activity.

Kinetic energy fraction

Now you can see that our cool-core clusters (shown in blue) and hot-core clusters (shown in orange) have similar trends and distributions, so why does the extra energy from merge activities turn only some clusters into hot-core clusters whereas others remain as hot-core clusters? The answer to this lies in the thermalisation of the energy introduced by the merge activity. We can quantify it as the ratio between the internal energy and the total (internal plus kinetic) energy of a galaxy cluster. This is a quantity that is also very difficult to measure observationally (we only have the estimations from Hitomi) but is easily accessible for cosmological simulations. As you can see on the right panel, the kinetic energy fraction for cool-core clusters is generally higher than for hot-core clusters, although in both cases it decreases towards the most massive clusters, indicating that the thermalisation process is more efficient in converting kinetic energy into internal energy at that scale, thus helping to reduce the cool-core fractions.