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Column Manipulations

Here are all the manipulations we'll need to be able to do for the AVO demo (all points refer to the Extragalactic Scenario):

• point 2: calculate the hardness ratio, defined as HR=(H-S)/(H+S), where here H is the "hard" X-ray count rate (2.0 - 8.0 keV) and S is the "soft" X-ray count rate (0.5 - 2.0 keV) in the X-ray catalogues (files paper13_table3.cat and paper13_tableA2.cat available on the Extragalactic Scenario page (by definition -1 <= HR <= 1). If necessary we can do this before hand and add an extra column. Absorbed sources are defined by HR >= -0.2. When H is an upper limit set HR equal to -1, when S is an upper limit set HR equal to 1.

• point 3.1.3 and 3.5: derive X-ray power from the flux (fx) and redshift (z); the usual relationship is Lx = 4 pi Dl(z)^2 fx, where Dl is the luminosity distance, which depends on the adopted cosmology. In the simple (but wrong) case of an empty Universe one gets
  • Lx ~ 8.778 10^57/(Ho/70)^2 fx (1+z-(1+z)^(1/2))^2 erg/s, where fx is in erg/cm^2/s; in the more realistic case of a cosmological constant one should perform an integral over redshift. An analytical fit is given in the Szokoly et al. paper as follows:
  • Lx ~ 2.195 10^57/(Ho/70)^2 fx Dl(z)^2 erg/s, where Dl = (1+z)*(3.308-3.651*(0.207+0.446*(1+z)+0.757*(1+z)^2-0.204*(1+z)^3+(1+z)^4)^(-1/8))

• point 3.2.3: derive ratio between X-ray flux and optical flux, the ACS I-band fluz, fx/fi. We will establish the source type (1 or 2) for the sources without spectra: if log(f_x/f_i) > -1.4 (equivalent to log(f_x/f_r) > -1 for (R - i) ~ 1, the typical value for our sources) AND HR is >= -0.2 then the object is a type 2; if log(f_x/f_i) > -1.4 AND HR is < -0.2 then the object is a type 1; the cut in f_x/f_i gets rid of the galaxies. Note that we need the ACS I-band fluxes, which can be derived from the ACS I magnitudes by converting first to Vega magnitudes (I_Vega = I_ACS - 0.42) and then using the following relationship (from Zombeck) to derive the I-band flux: I_flux = (10^(-0.4*I_Vega-9.080))*2400 or I_flux = (10^(-0.4*I_ACS-8.912))*2400

• point 3.2.4.2: estimate the X-ray power based on the fx/fi flux; we will use this relationship, as in this paper, namely log Lx = log(fx/fr) + 43.05 (Fig. 5). Since these sources have typically <(R - i)> ~ 1, log fr = log fi - 0.4*<(R - i)> = log fi - 0.4. Therefore log Lx = log(fx/fi) + 43.45. (All logs are log_10.)