5.3 Photoionization Analytic Modeling

We constrained the properties of potential ionized absorbers using the XSTAR analytic model warmabs , relying on all atomic level populations calculated by XSTAR using the same UV-X-ray ionizing SED from §5.1. Fitting the spectrum with the tabulated grids (see §5.2) is much quicker than the warmabs analytic modeling. However, parametric intervals used in the computation of the model grids (see interval sizes in Table 4) could add large uncertainties to derived parameters. Hence, we also used the analytic model to put more accurate constraints on the ionization state and column density of the warm absorbing gas, as well as to explore any variations in elemental abundances. As this approach is computationally expensive, we utilized the parameters determined from the XSTAR table model grids in §5.2 as initial values, and employed warmabs only to make finer estimations of the physical conditions.

For the soft excess, we again use an absorbed disk component. The high-ionization lines visible in the spectrum (c.f. Table 3) clearly require a highly ionized warmabs component. Given that the tbnew component in our phenomenological model (§4.2) shows more absorption than expected for foreground Milky Way absorption ( $N_{\rm H} = 2.6 \times 10^{20}$ cm$^{-2}$; Wakker et al., 2011), we have tried three different options for additional absorption in PG1211+143 . Specifically, we considered (1) a neutral absorber (tbnew ) at the PG1211+143  systemic redshift, (2) a mildly ionized warmabs model (also at the PG1211+143  systemic redshift), and (3) a low-ionization warmabs model at the same observed redshift as the high-ionization warmabs component.⁵For this third possibility we also tied the abundance and turbulent velocity parameters to those of the high-ionization warmabs component.

Table 5: Best-fitting parameters for the XSTAR warmabs model, the continuum model and iron lines obtained using the ISIS  emcee hammer routine.

Component	Parameter	Value
	$\chi^{2}/{\rm d.o.f}$ &dotfill#dotfill;	$610/614$
highecut	$E_{c}$(keV) &dotfill#dotfill;	$1.4^{+0.3}_{-0.4}$
	$E_{f}$(keV) &dotfill#dotfill;	$11.3^{+3.5}_{-0.8}$
diskbb	$T_{\rm in}$(keV) &dotfill#dotfill;	$0.096^{+0.002}_{-0.010}$
	Norm &dotfill#dotfill;	$1.2^{+1.5}_{-0.3}\times 10^{4}$
zpowerlw	$\Gamma$ &dotfill#dotfill;	$1.55^{+0.04}_{-0.07}$
	Norm ($\gamma$keV$^{-1}$cm$^{-2}$) &dotfill#dotfill;	$1.38^{+0.04}_{-0.09} \times 10^{-3}$
zgauss $_{\rm K\alpha}$	$E$(keV) &dotfill#dotfill;	$6.41^{+0.06}_{-0.05}$
(FeK$\alpha$)	$\sigma$(keV) &dotfill#dotfill;	$0.004^{+0.13}_{}$
	Norm ($\gamma$cm$^{-2}$s$^{-1}$) &dotfill#dotfill;	$3.6^{+3.2}_{-2.0}\times10^{-6}$
zgauss $_{\rm He\alpha}$	$E$(keV) &dotfill#dotfill;	$6.66^{+0.12}_{-0.09}$
(FeXXV)	$\sigma$(keV) &dotfill#dotfill;	$0.06^{+0.22}_{-0.02}$
	Norm ($\gamma$cm$^{-2}$s$^{-1}$) &dotfill#dotfill;	$5.2^{+6.6}_{-3.9}\times10^{-6}$
warmabs	$\log n$ (cm$^{-3}$) &dotfill#dotfill;	12.0
	$\log N_{\rm H}$ (cm$^{-2}$) &dotfill#dotfill;	$21.47^{+0.18}_{-0.58}$
	$\log \xi$ (ergcms$^{-1}$) &dotfill#dotfill;	$2.87^{+0.32}_{-0.10}$
	$v_{\rm out}$ (kms$^{-1}$) &dotfill#dotfill;	$-17300^{+100}_{-130}$
	$v_{\rm turb}$ (kms$^{-1}$) &dotfill#dotfill;	$90^{+210}_{-60}$
	$A_{\rm Ne}$ &dotfill#dotfill;	$0.6^{+2.0}_{-0.2}$
	$A_{\rm Mg}$ &dotfill#dotfill;	$1.5^{+3.2}_{-0.4}$
	$A_{\rm Si}$ &dotfill#dotfill;	$3.0^{+4.8}_{-1.1}$
	$A_{\rm S}$ &dotfill#dotfill;	$0.6^{+5.3}_{-0.4}$
	$A_{\rm Fe}$ &dotfill#dotfill;	$1.2^{+1.6}_{-0.6}$
warmabs	$\log N_{\rm H}$ (cm$^{-2}$) &dotfill#dotfill;	$21.08^{+0.10}_{-0.62}$
	$\log \xi$ (ergcms$^{-1}$) &dotfill#dotfill;	$1.29^{+0.34}_{-0.29}$

All three of these possibilities resulted in essentially identical parameters for the highly ionized absorber. None of the three possibilities produced identifiable spectral features, but rather affected the shape of the low-energy X-ray continuum. Differences among the fits were primarily restricted to the soft excess parameters, with subtler differences in the highest and zpowerlw parameters. In what follows, we only present results for option (3), the additional low-ionization component at the observed redshift of the high-ionization component. However, we consider the high-ionization component to be the only one with well-measured parameters, and we only discuss its physical implications.

In our fits, we used the solar abundances defined by Wilms et al. (2000), and adjusted the elemental abundances and the turbulent velocity to match the absorption lines. The best-fitting parameters derived from our model fits are listed in Table5. We determined the fit parameter confidence intervals by employing the ISIS emcee hammer routine, which is an implementation of the Markov Chain Monte Carlo (MCMC) Hammer algorithm of Foreman-Mackey et al. (2013), and now included in the Remeis ISISscripts⁶. The MCMC approach allowed us to improve the best-fitted values of the ionization parameter ($\xi$), the column density ($N_{\rm H}$), the turbulent velocity ( $v_{\rm turb}$), and the chemical composition of the warmabs model as well as other phenomenological model parameters (continuum and iron lines) listed in Table 5 (the fits, however, are not very sensitive to the chemical composition). Figure 6 shows the 1-sigma (68%), 2-sigma (95%), and 3-sigma (99%) confidence contours of $\log \xi$ versus $\log N_{\rm H}$, $\log \xi$ versus $v_{\rm turb}$, and $\log N_{\rm H}$ versus $v_{\rm turb}$. There is a slight anti-correlation between the absorber column and turbulent velocity (somewhat expected to fit the equivalent widths of the detected features). Overall, the main absorber parameters are well constrained.

Figure: Thermal stability curve for $n_{\rm H} = 10^{12}$cm$^{-3}$ produced using the XSTAR model associated with the UV-X-ray ionizing SED shown in Figure4. It shows the distribution of equilibrium temperature $\log T$ as a function of $\log (\xi/T)$. The thick solid lines in the curves correspond to the regions with the thermally stable gas. The best-fitting $\xi$ value of the ionized absorber component is labeled as PG1211 with its corresponding error bar at the 90% confidence level.