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Appendix A: X-Ray data and ISM properties of the four radio-faint VCC galaxies

The Chandra Archive information for the four VCC galaxies analyzed here are reported in Table A.1. For the X-ray data reduction and analysis we followed the same procedures and software packages as in BBC08. To account for the possible contamination from the active nucleus, we excluded the innermost region from the analysis, adopting a minimum radius of 15. This is rather conservative, because a faint X-ray central point source is seen only in NGC 4365 (Sivakoff et al. 2003).

Since the diffuse emission in these targets is on average much fainter than in those discussed in BBC08, the contamination from stellar sources must be taken into account. These sources mainly belong to two classes: low-mass X-ray binaries (LMXB) and stars of old populations with hot coronae, mainly cataclysmic variables (CVs) and active binaries (ABs).

The brightest LMXB appear in the X-ray images as discrete sources superimposed to the diffuse coronal emission: they have been localized and removed from the event files through the wavedetect command. However, less luminous, unresolved LMXB can still have a non negligible contribution to the extended luminosity. As their emission is well described by a power-law model, they can be separated from the hot gas thermal emission through a spectral decomposition.

For this purpose we performed a two-components spectral fit, Mekal + Pow Law, adopting the galactic values for the column densities N_H. For the thermal model the metalicity is fixed to half the solar abundances, while for the power-law the spectral index has been fixed to the value found from the discrete sources for each galaxy. The resulting power-law photon indices are in the range Γ ≈ 1.3 − 1.6, in good agreement with the measurements of Irwin et al. (2003). We repeated this procedure considering four annuli for each galaxy. In three objects the integrated contribution of the unresolved LMXB is at a similar level of the thermal emission from the ISM, while it is negligible in NGC 4526. As an example we show in Fig. A.1 the results obtained for NGC 4365.

The second contaminating component originates from the stellar coronae of CVs and ABs; their contribution cannot be separated through a spectral analysis as for LMXB, because their thermal X-ray emission is similar to that of the ISM (e.g. Revnivtsev et al. 2007). We exploit conversely the result obtained by Revnivtsev et al. (2008): they show that the old stars contribution to the X-ray emission of early-type galaxies (per unit stellar luminosity in the K band) displays a small scatter (less than a factor of 2) around the value they measured for NGC 3379,

We then retrieved the K band surface brightness profiles of the four galaxies of interest from the 2MASS Large Galaxy Atlas. Assuming that the IR-to-X-ray scaling relationship also holds in our sources, we compared them with the X-ray brightness profiles obtained from our analysis. In Fig. A.2 we show as an example the case of NGC 4365. This is the galaxy where we measured the largest (possible) contribution from old stars that amounts to  ~ 30% of the total counts. We conclude that the diffuse soft X-ray light is dominated by the genuine emission from the galaxies hot coronae. Nonetheless, we corrected the observed profiles for this marginal contamination.

After removing the contribution from stellar sources, we followed the same procedure to derive the deprojected profiles of temperature and density as in BBC08, to which we refer the reader for further details. Very briefly, to measure the dependence of temperature with radius, we de-project the spectra assuming spherical symmetry using the PROJECT model in XSPEC, considering four annuli. The results are graphically reported in Fig. A.3. Concerning the density, we first of all determined the X-ray surface brightness profile (SBP) extracting the counts in a series of circular annuli. The next step is to de-project the observed SBP, i.e. obtaining the number of counts emitted per unit volume as a function of radius. Assuming spherical symmetry, the count contribution provided by each spherical shell to the inner ones were determined following the calculation by Kriss et al. (1983). From the deprojected SBP we obtained n(r) assuming thermal emission and inverting the normalization coefficient of the spectral model.

As the Bondi radius is well inside the innermost annulus (by a factor between 3 and 20), the value of the density was

extrapolated down to r_B through a fit across the profile, assuming a power-law in the form n(r) ∝ r ^− α. To limit systematic errors related to the arbitrary choice of the range of radii to be included in the fit, we performed the analysis twice by using four and six of the innermost density points. For each case we estimated the uncertainty related to the accuracy of the parameters of the fit describing the density behavior. We forced the density at r_B to be higher (or equal) than its measured value at the innermost annulus. We finally adopted for n_B the average of the values found in these two extrapolations and for its uncertainty the full range given by the overlap of the two individual error bars.

© ESO, 2010