Results

ionized partial covering modelzxipcf(Reeves et al. 2008) leaving the redshift as free param-eter to simulate a ionized wind. High resolutionXMM observations of MCG–6-30-15 revealed that often several layers of ionizing regions are required to model the spectrum (Nandra et al.

2007), thus, we also test a model in which we multiply two independentcwa18components to model a two-zone ionized absorber.

We want to study three different scenarios to model the reflection component (see Table 4.2). In the first scenario, we assume the reflection component and the Fe Kα line are blurred by relativistic effects due to the proximity of the SMBH. We use the same model as the one used in Chapter 3 of this thesis, which is kerrconv(Brenneman & Reynolds 2006) with the same parameter constraints. For the second scenario, we represent the reflection from an ionized accretion disc with the model reflionx(Ross & Fabian 2005). In this model, the incoming hard X-ray photons photoionize the surface of the accretion disk to the extent that the main X-ray absorbers are significantly ionized. MCG-6-30-15 is a case of study for complex absorption and reflection features. For this reason, in contrast to Chapters 2 and 3, we do not fit the data with a simple absorbed power-law (zwabs*zpowerlw) as we know already that a power-law can not model adequately the complex spectrum of MCG-6-30-15.

Finally, we add two narrow absorption lines modeled withzgaussat 6.7 and 6.97 keV. We fix the sigma of these components at 0.01 keV, since this was the value found inNandra et al.

(2007) and we allow the norm of the components to vary between 10⁻¹⁰and 10.

4.4 Results 87

Table 4.5: Comparison of the total sample Bayesian evidence for the models zwabs * (zpowerlw + pexmon) and zwabs * (zpowerlw + pexmon + blur(pexmon)). We fit the models in the observed frame energy range 2.5 – 10 keV.

Model^a log10(Z)^b

zwabs*(zpowerlw+pexmon) -208.8

zwabs*(zpowerlw+pexmon+kerrconv(spin=1)(pexmon)) -3.3 zwabs*(zpowerlw+pexmon+kerrconv(spin=0)(pexmon)) 0

aModel components.

bLogarithm of the Bayes evidence of the full sample normalized to the largest evidence.

the latter from the rest of the analysis and we proceed to include onlycwa18in the next model fits.

In most of the spectra, two absorption lines at 6.7 keV and 6.97 keV are observable (Nandra et al. 2007). We decide to test the evidence with and without these features. The model we use for this purpose is zgauss(I will denote them as G in the following tables, for the sake of brevity) subtracted twice from the continuum plus reflection model. We fix the energy of the two absorption lines at 6.7 and 6.97 keV and we also fix the energy width at 0.01 keV as found byNandra et al.(2007). The only parameter we allow to vary in those components in the norm.

From Table 4.7 one can see that the models with the two absorption lines are in general preferred over the models without.

As a next step, we want to take into account different models for the reflection component to compare three different scenarios to explain the blurring of the Fe Kα line: 1) the broad-ening reflection component arises due to relativistic effects due to the proximity of the SMBH (kerrconv(pexmon)), 2) the Fe Kαline appears broadened because primary X-ray contin-uum is reflected by ionized matter and complex absorption (reflionx), 3) there is a contri-bution of both effects (relxill). For all three scenarios, we include apexmon component in the model to fit the narrow reflection from the torus. We model the primary continuum as a zpowerlawin the first and second model, but the third does not need such a component, since we allow the reflection fraction parameter of relxillto be positive and that already models the primary continuum (see Table 4.8).

Before comparing these three different reflection models, we need to choose a parameter configuration forrelxillto make the model as physical as possible but keeping the complex-ity given by extra free parameters to a minimum. The minimal number of the free parameter we can have is 7 by allowing the variation of the photon indexΓ, after linking it to the photon index of thepexmon, the norm, the reflection fraction, R, the inclination angle, the spin, a, and the logarithmic ionization fraction, log(ξ) (see Table 4.2). We chose a semi-physical parameter combination where the breaking angle R_bris fixed to 15, the Index 1 is free to vary and the Index 2 is frozen to 3.

The source count rate in the 2.5–10 keV and 4–7 keV is shown in Figure 4.3, the best fit model is shown in Figure 4.2 and the best fit parameters are reported in Figure 2.4. The values in Figure 2.4 are mean of the posterior distribution and the 68% confidence interval for the plotted

Table 4.6: Source by source comparison of the total sample Bayesian evidence for the models with absorption components cwa18 x 2, zwabs, swind1, zxipcf, and cwa18 and con-tinuum and reflection(zpowerlw + pexmon + blur(spin 0)(pexmon)). We fit the models in the observed frame energy range 2.5 – 10 keV.

Obs. Id^a log(Z_cwa18×2)^a log(Z_zwabs)^b log(Z_Rswind1)^c log(Z_zxipcf)^d log(Z_cwa18)^e

0111570201 -4.4 -1.5 -0.1 -0.8 0

0111570101 -1.4 -0.6 -2.2 -1.1 0

0029740801 -14.8 -4.5 -2.7 0 -0.6

0029740701 -11.2 -3.2 -0.2 -0.1 0

0029740101 -5 -2.2 -0.5 -0.1 0

0693781401 -3.6 -0.5 0 -0.8 -0.5

0693781301 -21.5 -1.6 0 -0.4 -1.1

0693781201 -18.5 -4.3 -1.5 -0.7 0

Total -78.2 -16.2 -5 -1.7 0

aXMM-Newtonobservation Id.

bLogaritmic Bayesian evidence for the modelcwa18 * (zpowerlw + pexmon + reflionx).

cLogaritmic Bayesian evidence for the modelcwa18 * (zpowerlw + pexmon + blur(pexmon)).

dLogaritmic Bayesian evidence for the modelcwa18 * ( pexmon + relxill).

Table 4.7: Comparison of the total sample Bayesian evidence for the models cwa18 * (zpowerlw + pexmon) and cwa18 * (zpowerlw + pexmon + blur(pexmon)) with and without two absorption Gaussians component at energies 6.7 and 6.97 keV. We use twice the componentzgaussto model the lines and in the table we write that in short asG × 2. We fit the models in the observed frame energy range 2.5 – 10 keV.

Model^a log10(Z)^b

cwa18*(zpowerlw+pexmon) -182.5

cwa18*(zpowerlw+pexmon - G × 2) -181.9

cwa18*(zpowerlw+pexmon+kerrconv(spin=1)(pexmon)) -10.4 cwa18*(zpowerlw+pexmon+kerrconv(spin=1)(pexmon) - G × 2) -10.1 cwa18*(zpowerlw+pexmon+kerrconv(spin=0)(pexmon)) -2.3 cwa18*(zpowerlw+pexmon+kerrconv(spin=0)(pexmon) - G × 2) 0

aModel components.

bLogarithm of the Bayes evidence of the full sample normalized to the largest evidence.

4.4 Results 89

Table 4.8: Comparison of the total sample Bayesian evidence for the models cwa18

* (zpowerlw + pexmon + reflionx), cwa18 * (pexmon + relxill) and cwa18 * (zpowerlw + pexmon + blur(pexmon)). We fit the models in the ob-served frame energy range 2.5 – 10 keV.

Obs. Id^a log(Zreflionx)^b log(ZRkerrconv)^c log(Zrelxill)^d

0111570201 -5.7 -0.6 0

0111570101 -3.3 -0.8 0

0029740801 -20.5 -0.4 0

0029740701 -2.6 0 -0.7

0029740101 -14.8 -1.7 0

0693781401 -1.6 0 -1.2

0693781301 -4.8 -1.5 0

0693781201 -9.6 -0.1 0

Total -60.3 -1.6 0

aXMM-Newtonobservation Id.

bLogaritmic Bayesian evidence for the modelcwa18 * (zpowerlw + pexmon + reflionx).

cLogaritmic Bayesian evidence for the modelcwa18 * (zpowerlw + pexmon + blur(pexmon)).

dLogaritmic Bayesian evidence for the modelcwa18 * ( pexmon + relxill).

quantities.

We find that this model describes the data better than any other model combination we chose (see Figure 4.2) and fits the spin and inclination parameters consistently over the eight observa-tions (see Figure 2.4).

As a test, we compare the model withrelxilland two negative Gaussian at 6.7 and 6.97 keV with the same model but only one of the two lines at the time (see Table 4.9).

Even after a visual inspection, the model seems to fit the data well. However, we can still observe a positive residuum at 8 keV that might mirror the behavior of the background.

Finally, we apply the hierarchical Bayesian model (HBM) similarly as described in the pre-vious chapter to calculate the mean and sigma of the disc inclination (see Figure ??). We parametrize the posterior distributions of inclination and spin by modelling them with a beta distribution, as shown in Figure 4.5 and 4.6. We find that the mean of the inclination angle is 43.79^+0.86_−0.98while the mean spin is 0.29^0.11_−0.12(see Figure 4.7). The standard deviation of the popula-tion of both parameters is an upper limit. This shows that the method does not detect significant variation among the eight posterior distributions.

Energy (keV) 0.10

1.00

Counts/sec/keV

relxill_OF_cGx2N Id: 0029740101

2 × 10⁰ 3 × 10⁰ 4 × 10⁰ 6 × 10⁰ 10.0 Energy (keV) 0.75

1.00 1.25

Counts/sec/keV

Energy (keV) 0.10

1.00

Counts/sec/keV

relxill_OF_cGx2N Id: 0029740701

2 × 10⁰ 3 × 10⁰ 4 × 10⁰ 6 × 10⁰ 10.0 Energy (keV) 0.75

1.00

Counts/sec/keV

Energy (keV) 0.10

1.00

Counts/sec/keV

relxill_OF_cGx2N Id: 0029740801

10.0 2 × 10⁰ 3 × 10⁰ 4 × 10⁰ 6 × 10⁰

Energy (keV) 0.8

1.0 1.2

Counts/sec/keV

Energy (keV) 0.10

1.00

Counts/sec/keV

relxill_OF_cGx2N Id: 0111570101

10.0 2 × 10⁰ 3 × 10⁰ 4 × 10⁰ 6 × 10⁰

Energy (keV) 0.75

1.00 1.25

Counts/sec/keV

4.4 Results 91

Energy (keV) 0.10

1.00

Counts/sec/keV

relxill_OF_cGx2N Id: 0111570201

2 × 10⁰ 3 × 10⁰ 4 × 10⁰ 6 × 10⁰ 10.0 Energy (keV) 0.75

1.00 1.25

Counts/sec/keV

Energy (keV) 0.10

1.00

Counts/sec/keV

relxill_OF_cGx2N Id: 0693781201

2 × 10⁰ 3 × 10⁰ 4 × 10⁰ 6 × 10⁰ 10.0 Energy (keV) 1.0

1.2

Counts/sec/keV

Energy (keV) 0.10

1.00

Counts/sec/keV

relxill_OF_cGx2N Id: 0693781301

2 × 10⁰ 3 × 10⁰ 4 × 10⁰ 6 × 10⁰ 10.0 Energy (keV) 0.9

1.0 1.1

Counts/sec/keV

Energy (keV) 0.10

1.00

Counts/sec/keV

relxill_OF_cGx2N Id: 0693781401

2 × 10⁰ 3 × 10⁰ 4 × 10⁰ 6 × 10⁰ 10.0 Energy (keV) 0.5

1.0

Counts/sec/keV

Figure 4.2: Best fit model with residua. The model here represented is cwa18*(pexmon + relxill - 2 × G) (in red). The values shown here represent the mean and the 68%

confidence interval.

0029740101

0029740701

0029740801

0111570101

0111570201

0693781201

0693781301

0693781401 0.5

1.0 1.5 2.0 2.5

Countsrate[counts/sec]

Source counts, 2.5-10 keV Source counts, 4-7 keV

Figure 4.3: Source count rate in the 2.5–10 keV and 4–7 keV energy range for all eight observa-tions.

4.4 Results 93

2.1 2.2 2.3 2.4 2.5

Photonindex

1 2 3 4 5 6 7 8

Reflectionfraction

30 35 40 45 50

Inclinationangle

0.5 1.0 1.5 2.0 2.5 3.0

Ionizationparameter

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Spin

−3

−2

−1 0 1 2

Ionizationparameterofcwa18

0029740101 0029740701

0029740801 0111570101

0111570201 0693781201

0693781301 0693781401

−7.5

−5.0

−2.5 0.0 2.5 5.0 7.5 10.0

Index1

0029740101 0029740701

0029740801 0111570101

0111570201 0693781201

0693781301 0693781401 21.5

21.6 21.7 21.8 21.9 22.0 22.1

Columndensityofcwa18

Figure 4.4: Best fit parameters for the modelcwa18*(pexmon + relxill - 2G)for all eight observations. The value reported here are the mean of the posterior distribution and the 68%

confidence interval for the most relevant free parameters of the model for every observation.

Inclination angle 0

100 200 300 400 500 600 700

Posterior distribution

34 36 38 40 42 44 46

X 0

1 2 3 4 5 6 7 8

Beta distribution

Beta distr. ⁰ Inclination angle 200

400 600 800 1000 1200 1400

Posterior distribution

35.0 37.5 40.0 42.5 45.0 47.5 50.0 X

0 1 2 3 4 5 6 7 8

Beta distribution

Beta distr. ⁰ Inclination angle 200

400 600 800 1000 1200 1400 1600

Posterior distribution

40 41 42 43 44 45 46 47

X 0

1 2 3 4 5 6

Beta distribution

Beta distr. ⁰ Inclination angle

100 200 300 400 500 600 700 800

Posterior distribution

36 38 40 42 44 46 48 50 52 X

0 1 2 3 4 5 6 7

Beta distribution

Beta distr.

Inclination angle 0

100 200 300 400 500 600

Posterior distribution

36 38 40 42 44 46

X 0.0

0.2 0.4 0.6 0.8 1.0 1.2 1.4

Beta distribution

Beta distr. ⁰ Inclination angle

200 400 600 800

Posterior distribution

40 42 44 46 48 50 52

X 0

1 2 3 4 5 6

Beta distribution

Beta distr. ⁰ Inclination angle 100

200 300 400 500 600 700 800

Posterior distribution

34 36 38 40 42 44 46

X 0.0

0.5 1.0 1.5 2.0

Beta distribution

Beta distr. ⁰ Inclination angle 200

400 600 800 1000 1200

Posterior distribution

35.0 37.5 40.0 42.5 45.0 47.5 50.0 52.5 55.0 X

0 5 10 15 20 25

Beta distribution

Beta distr.

Figure 4.5:Top: Posterior distribution of the inclination angle of the eight observations of MCG-6-30-15Bottom: their respective fit with a beta distribution. The inclination parameter for these high quality spectra is very well constrained.

4.4 Results 95

0 Spin 200 400 600 800 1000

Posterior distribution

0.0 0.2 0.4 0.6 0.8

X 0.0

0.5 1.0 1.5 2.0

Beta distribution

Beta distr. ⁰ Spin

200 400 600 800 1000

Posterior distribution

0.0 0.2 0.4 0.6 0.8

X 0.0

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Beta distribution

Beta distr. ⁰ Spin

200 400 600 800 1000 1200

Posterior distribution

0.0 0.2 0.4 0.6 0.8

X 0

2 4 6 8

Beta distribution

Beta distr. ⁰ Spin

100 200 300 400 500 600

Posterior distribution

0.0 0.2 0.4 0.6 0.8

X 0.0

0.2 0.4 0.6 0.8 1.0 1.2 1.4

Beta distribution

Beta distr.

0 Spin 50 100 150 200 250 300 350 400

Posterior distribution

0.0 0.2 0.4 0.6 0.8

X 0.0

0.2 0.4 0.6 0.8 1.0 1.2 1.4

Beta distribution

Beta distr. ⁰ Spin

100 200 300 400 500 600 700 800

Posterior distribution

0.0 0.2 0.4 0.6 0.8

X 0

1 2 3 4 5

Beta distribution

Beta distr. ⁰ Spin

100 200 300 400 500 600

Posterior distribution

0.0 0.2 0.4 0.6 0.8

X 0.0

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Beta distribution

Beta distr. ⁰ Spin

100 200 300 400

Posterior distribution

0.0 0.2 0.4 0.6 0.8

X 0.0

0.5 1.0 1.5 2.0 2.5

Beta distribution

Beta distr.

Figure 4.6: Top: Posterior distribution of the spin of the eight observations of MCG-6-30-15 Bottom: their respective fit with a beta distribution. The spin parameter is not constrained very well.

Table 4.9: Comparison of the total sample Bayesian evidence for the models cwa18 * (pexmon + relxill - 2xG), cwa18 * (pexmon + relxill-G(6.7keV)) and cwa18 * (pexmon + relxill-G(6.97keV)). We fit the models in the observed frame energy range 2.5 – 10 keV.

Obs. Id^a log(Z2G)^b log(ZRG−6.7keV)^c log(ZG−6.97keV)^d

0111570201 -1.1 0 -2.5

0111570101 -0.6 0 -1.8

0029740801 -1 0 -0.5

0029740701 -2.1 -0.5 0

0029740101 -0.3 -0.1 0

0693781401 -0.3 0 0

0693781301 -0.3 0 -0.1

0693781201 0 -0.1 0

Total -5 0 -4.4

aXMM-Newtonobservation Id.

bLogaritmic Bayesian evidence for the modelcwa18 * ( pexmon + relxill).

cLogaritmic Bayesian evidence for the modelcwa18 * ( pexmon + relxill - gauss).

dLogaritmic Bayesian evidence for the modelcwa18 * ( pexmon + relxill +gauss).

Mean = 43.79

^+0.860.98

40.5 42.0 43.5 45.0 46.5

Mean

0.02 0.04 0.06 0.08 0.10

Sig m a

0.02 0.04 0.06 0.08 0.10

Sigma Disc Inclination

Sigma = 0.04

^+0.04_0.02

Mean = 0.29

^+0.110.12

0.15 0.30 0.45 0.60

Mean

0.1 0.2 0.3 0.4

Sig m a

0.1 0.2 0.3 0.4

Sigma Spin

Sigma = 0.06

^+0.08_0.03

Figure 4.7: Left: Average inclination angle for MCG–6-30-15 calculated with the hierarchical Bayesian model. Right: Average spin found with the same method. We find a mean inclination angle of 43.79⁺_−0.98^0.86degrees and a mean spin of 0.29⁺_−0.12^0.11.

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