X-ray spectral fitting

To better understand the nature of the X-ray detected massive galaxies a variety of models were fitted to the X-ray spectra. The Chandra ACIS-I instrument can detect photons over a range of 0.2-10 keV but the detector response drops off markedly at the highest and lowest energies, especially for sources at a large OAA, so the energy range was limited to 0.5-8 keV. The goodness of fit was determined using a maximum likelihood statistic (C-statistic; Cash 1979) because it is well suited to analysing sources with a low number of

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Table 4.2: Description of how parameters for spectral fitting of massive galaxies. Columns (4) to (7) describe the potentially free parameters of the various models used. Free parameters are labeled as such, otherwise the parameter has been fixed to the value quoted. Solar abundance values were assumed for elements heavier than He (including Fe). Column (1): model ID; column (2): number of free parameters in the model; column (3): photon index of power-law emission from the central source; column (4): normalisa- tion factor for power-law emission from the central source; column (5): column density of obscuring material; column (6): photon index of central scattered power-law emission; column (7): normalisation factor for scattered power-law emission.

Model ID Nf ree Γsrc Normsrc NH Γscat Normscat

(1) (2) (3) (4) (5) (6) (7)

A 1 1.9 Free ... ... ...

B 2 1.9 Free Free ... ...

C 3 1.9 Free Free 1.9 Free

D 2 1.9 Free ... 1.9 Free

counts (see Section 2.4.4). The spectra were grouped according to energy channel, with 8 raw channels per bin producing 63 bins for each spectrum over the 0.5-8 keV range. This preserves the spectral resolution even with very low numbers of counts (compared, e.g. to binning by counts).

The parameters for each model used in this analysis are presented in Table 4.2. The photon index has been fixed at Γ = 1.9 for all of the models. This is because leaving the photon index free does not reduce the C-statistic sufficiently to warrant the inclusion of an additional free parameter.The following models have been chosen for use in the spectral fitting:

A) Simple unobscured power-law emission, POWERLAW, from the XSPEC (Arnaud, 1996) model library. A fixed local galactic absorption of NH = 9 × 1019cm−2 (Dickey

and Lockman, 1990) was also applied. This is the simplest of the models used in this analysis with only 1 free parameter; the power-law normalisation.

B) Brightman and Nandra (2011a) model of power-law emission obscured by material configured in a spherical geometry. This model is preferred to the neutral absorption model, ZWABS, of XSPEC because it includes line emission and Compton scattering, which can be important for the most heavily obscured objects. This model has 2 free parameters; the power-law normalisation and the NH of the spherical obscurer.

C) Brightman and Nandra (2011a) model of power-law emission obscured by material configured in a toroidal geometry with an additional scattered power-law component. This model features self-consistent iron Kα line emission along with a Compton hump generated by reflection off the obscuring torus. The opening angle of the torus has been fixed at 30 degrees because the spectra are rather insensitive to the opening angle. The torus is always assumed to be observed with an almost edge-on orientation (fixed

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at 80 degrees) assuming the power-law emission is undergoing maximum obscuration. This model has 3 free parameters; the power-law normalisation, the torus NH and the

scattered power-law normalisation.

D) Model of neutral reflection from a Compton thick obscurer, PEXMON, devised by Nandra et al. (2007b) with an illuminating power-law component. Derived from the PEXRAV model (Magdziarz and Zdziarski, 1995) it features self-consistent iron Kα line emission with a Compton hump and iron Kβ line emission (George and Fabian, 1991). This model has 2 free parameters; the power-law normalisation and the illumi- nating power-law normalisation.

For models with the same number of free parameters, the model with lowest C-statistic is adopted as the best-fitting model. If, however, the models have differing amounts of free parameters then selecting the best fit is non-trivial. In this case a critical threshold is defined, ∆cstatAB, for a more complex model (B) to be preferred over a model with fewer

free parameters (A), ie cstatA− cstatB > ∆cstatAB must be satisfied to prefer model

B to model A. Threshold ∆cstat values for comparing models with differing numbers of free parameters were calculated following the method described in Section 2.4.3. The spectral fitting analysis presented in this chapter (and in similar analyses presented in this thesis) uses a 99% ∆cstat threshold is used because it will provide the most conservative estimate. As stated previously, the ∆cstat threshold is dependent on the number of counts in a spectrum as brighter spectra have more well defined emission features. Thus critical ∆cstat values were calculated for 3 different ranges of counts; < 100 counts (low), 100 ≤counts< 500 (medium) and > 500 counts (high). The results of this ∆cstat analysis are given in Table 4.3.

The best fitting model was determined by following the logic tree/flow chart shown in Figure 4.2. The process is designed to compare iteratively models of increasing numbers of free parameters to one another until either additional free parameters cannot be justified by their C-statistic values or the model with the maximum number of free parameters is chosen (model C). Initially the C-statistic value of the simplest model (model A) is com- pared to all the more complex models. By measuring ∆cstatAB, ∆cstatAC and ∆cstatAD

it is determined whether or not model A is the best fit. If not, then the ∆cstatBC and

∆cstatDC are calculated to determine whether model C is the best fit. If model C is not

suitable then whichever model has the lowest C-statistic between B and D is chosen as the best fit. The absorbed and unabsorbed 2-10 keV luminosities were calculated following the methods described in Section 2.4.5.

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Table 4.3: The 90%, 95% and 99% threshold values of ∆cstat required to justify the inclusion of additional free parameters when selecting the best-fitting models using C- statistic in CDFS 4Ms data. Column (1): the pairing of models to which the threshold values correspond i.e. ∆cstatXY is value required to prefer model Y to model X; column

(2): 90% certainty threshold for low count source; column (3): 95% certainty threshold for low count source; column (4): 99% certainty threshold for low count source; column (5): 90% certainty threshold for medium count source; column (6): 95% certainty threshold for medium count source; column (7): 99% certainty threshold for medium count source; column (8): 90% certainty threshold for high count source; column (9): 95% certainty threshold for high count source; column (10): 99% certainty threshold for high count source.

< 100 counts _{100 ≤counts< 500 ≥ 500 counts} Threshold 90% 95% 99% 90% 95% 99% 90% 95% 99% (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) ∆cstatAB 1.94 3.16 7.00 1.79 2.80 5.24 1.56 2.93 5.66 ∆cstatAC 2.25 3.80 6.90 2.23 3.59 6.65 1.96 3.35 5.76 ∆cstatAD 1.86 2.86 7.19 1.75 3.07 5.88 1.67 2.72 5.30 ∆cstatBC 1.62 2.72 5.89 1.38 2.68 5.50 1.39 2.68 5.82 ∆cstatDC 3.01 3.72 6.45 2.51 3.09 4.67 1.72 4.53 7.52

Figure 4.2: Logic tree outlining the process used to select the best-fitting X-ray emission model using the C-statistic values from spectral fitting.

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4.4

Results

4.4.1 X-ray detected massive galaxies