As most of the astrophysical processes include phenomena that lead to particle accelera- tion and energy ejection (radiation), of great importance in astrophysics is the creation of shocks. In general, a shock wave can be described as a disturbance that propagates through a medium, carrying energy faster than its signal speed, causing the compression, heating and acceleration of the medium. The properties of the medium are therefore completely altered by the passage of the shock front, but one has the ability to measure the sudden change in pressure, temperature and density of the flow (McKee & Hollenbach, 1980).
The most common sources of shock generation in astrophysics are those where super- sonic compressive disturbances occur. Shocks can therefore be found in both galactic and extragalactic environments, span over a variety of processes and are divided into: a) non- relativistic shocks, such as Supernovae remnants, accretion onto hydrostatic intracluster medium (ICM, galaxy clusters), and b) relativistic shocks, such as pulsar winds, Gamma- Ray Bursts (GRBs) and radio AGN jets (Bykov & Treumann, 2011).
tion of the supersonic propagating jet -compared to the X-ray-emitting interstellar medium (ISM)- with the intragroup/intracluster medium, gives rise to shock fronts. As the jet ter- minates at the radio hotspots (jet head) its fluid goes through a powerful shock in order to inflate a layer (cocoon) of radio-emitting plasma. The jet flow momentum and energy are usually keen to drive a bow shock into the surrounding medium in front of the area of the jet termination shock that heats the ambient gas as it passes through the termination shock fill- ing an area around the lobe of radio-emitting plasma. Observations of such processes show a jet (extending several kpc) that emits in radio, inflating lobes that exhibit bright edges.
The sound speed in the gas of temperature T is cs=
s γ kT µ mH
(1.1) where γ = 5/3 is the ratio of the specific heats, kB is the Boltzmann constant and µmH =
0.6mH is the mass per particle with mH being the mass of the hydrogen atom. Taking into
consideration the above, the sound speed can be calculated by
cs≈ 516(kBT/KeV )1/2kms−1 (1.2)
or,
cs≈ 0.54(kBT/KeV )1/2kpc Myr−1 (1.3) The general description of the Mach number of the advance speed, υadv of the bow
appropriate units by
M ≈ 580(υadv/cs)(kBT/KeV)−1/2 (1.4)
where c is the speed of light and υadvis not as fast as the bulk jet speed.
The hot, X-ray emitting intracluster/intragroup gas is related to the jets of an active galaxy. Provided that the ambient gas is in hydrostatic equilibrium, its density and tempera- ture profile will depend on its thermal history, been largely affected by the source dynamics. In the case of a bow shock propagation from a jet, rims of shocked gas are expected to be seen surrounding the radio lobe along with the ambient gas X-ray emission (Worrall & Birkinshaw, 2006).
Applying the Rankine-Hugoniot conditions for a strong shock (Spitzer, 1978) we are able to get a relation for density, temperature and pressure respectively
ρ2/ρ1= 4M2/(M2+ 3) (1.5)
T2/T1= (5M2− 1)(M2+ 3)/16M2 (1.6)
P2/P1= (5M2− 1)/4 (1.7)
where ρ1, T1, P1 represent the unshocked gas and ρ2, T2, P2 the shocked gas areas at
the tip of the bow shock, for a monoatomic gas. From the above equations, as an example, in the energy band 0.8-2 keV, aM = 4 shock, will create a contrast in the X-ray emissivity between shocked and unshocked gas a factor of 3 higher, provided that the ambient gas in the ISM of the galaxy is at a galaxy temperature of ∼0.3 keV (using equation 1.5 and
converting density into X-ray emissivity, Worrall & Birkinshaw 2006).
Despite the fact that low-power FR-I jets transfer a great amount of their energy without evolving a proper beam head, as they are in good contact with the external medium in which they are embedded, the above equations can also be applied to them (Worrall & Birkinshaw, 2006). A nice example is the low-power radio galaxy Cen A (Croston et al., 2009; Kraft et al., 2007, 2003), that shows such shell of X-ray emitting gas that has the geometry of a shocked ambient gas. The Mach number of the shock in the gas is calculated by assuming a temperature and density such that the combined thermal and ram pressure is in pressure equilibrium.
In addition, apart from the temperature jump seen in the ambient X-ray gas, the Mach number of a shock that a radio jet creates in the ambient gas can also be constrained from the radio observations. By using a radiative age model (Jaffe & Perola, 1973, e.g.,) the age of the source can be estimated and from the knowledge of the extend of the radio lobes (or the extend of the rim of compressed gas from the core of the galaxy) the supersonic expansion speed of the lobes can be calculated (Kolokythas et al. 2015, also see Chapter 3), resulting in an estimate of the Mach number of the shock in the medium.
In clusters of galaxies shocks could be generated from the motion of the galaxies in the cluster medium (heating of the intracluster gas through friction; Ruderman & Spiegel 1971; Hunt 1971), through gravitational infall (Miniati et al., 2000), cluster mergers with other groups or clusters (cold fronts; e.g. A3667, Vikhlinin et al. 2001), or from double radio AGN relics (Roettiger et al., 1999). Such shocks are effective in causing a sharp increase of both their temperature and density. The calculation of the density jump in the X-ray surface brightness discontinuity across the shock edge, allows a measurement of the shock’s Mach number (Markevitch, 2006). Recently, X-ray surface brightness discontinuities were
discovered at the place that some radio relics exist, with the most probable explanation being that these discontinuites are shocks with Mach numbers of 2 (Finoguenov et al., 2010; Macario et al., 2011).