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16 2. The X-ray environment of radio galaxies
where r is the projected radial distance from the centroid of the X-ray surface brightness
distribution, S (0) is the central surface brightness, r c is the X-ray core radius andβ= µm pσ 2 r
k B T
. Here,
µ is the mean molecular weight, m p is the proton mass, andσ r is the radial velocity dispersion of
the galaxies.
The model of Eq. 2.2 has the advantage that its shape is uniquely described by only two
parameters: the core radius and the slopeβ. The latter determines the sharpness of the turnover
beyond the core radius and the asymptotic slope of the scaling. Physically,β represents the ratio
between the specific kinetic energy of the gravitationally bound galaxies and the specific thermal
energy of the hot gas. Fits to the X-ray surface brightness profiles generally giveβ∼0.4-0.7,
indicating that the energy per unit mass is higher in the hot gas than in the galaxies. The core
radius r c is highly correlated with the parameterβ, in the sense that larger r c corresponds to higher
β: indeed, a given X-ray surface brightness can be reproduced by a concentrated distribution with
a rapid decline (small r c and highβ), or by a more diffuse one with a flatter decline (large r c and
lowβ). Typical ranges for the fitted X-ray parameters are summarized in Table 2.1.
Assuming that the gas-density distribution is isothermal and hydrostatic, the surface
brightness profile of Eq. 2.2 corresponds to the density profile called aβmodel and given by
(Cavaliere & Fusco-Femiano 1976):
where n e (0) is the central electron density.
] − 3
n e (r)=n e (0)
[1+ r2 2 β
. (2.3)
Theβmodel adequately describes the surface brightness profiles of regular X-ray emission
over a wide range of radii. However, it fails in reproducing the strongly peaked X-ray surface
brightness distributions observed in some systems. This peak might be interpreted as emission due
to the ISM of the central elliptical galaxy, superimposed on that from the intergalactic medium, or
as an indication of the presence of a cooling flow (e.g. Trinchieri, Fabbiano & Kim 1997; Helsdon
& Ponman 2000; Croston et al. 2008). In both cases, the fit to the X-ray surface brightness is
significantly improved by using two distinctβmodels, one for each component (e.g. Croston et al.
2008). Analogously, fits to the temperature profile often require two-temperature models. Fig. 2.1
shows an example of X-ray emission from a relaxed galaxy cluster and the best fitting doubleβ
model describing the surface brightness profile.
Models of this type are used later in the thesis (Chapters 4 and 5) to parametrize the density
distributions of hot gas around radio galaxies.
r 2 c
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