5.2 Photoionization Tabulated Grids

Table 4: Parameter ranges for XSTAR Photoionization Model Grids.

Parameter	Value	Interval Size
$L_{\rm ion}$ ($10^{38}$ ergs$^{-1}$)&dotfill#dotfill;	$1.587\times 10^{7}$	-
$T_{\rm init}$ ($10^{4}$ K)&dotfill#dotfill;	$100$	-
$\log n$ (cm$^{-3}$)&dotfill#dotfill;	$8 \cdots 14$	$1.0$
$\log N_{\rm H}$ (cm$^{-3}$)&dotfill#dotfill;	$18 \cdots 25$	$0.5$
$\log \xi$ (ergcms$^{-1}$)&dotfill#dotfill;	$-2 \cdots 5$	$0.25$
$v_{\rm turb}$ (kms$^{-1}$)&dotfill#dotfill;	$100 \cdots 500$	$100.0$
$A_{\rm Fe}$ &dotfill#dotfill;	$1.0$	-
$C_{f}=\Omega / 4 \pi$&dotfill#dotfill;	$0.5$	-

Figure: Chandra  HETGS spectrum for PG1211+143 fit with the XSTAR warmabs model (see Table 5). The lower panel plots the $\chi ^2$ residuals between the observation and the model.

We used the ionizing SED made in §5.1 to generate grids of XSTAR models. We utilized MPI_XSTAR ⁴ (Danehkar et al., 2018) that allows parallel execution of multiple XSTAR runs on a computer cluster (in this case, the ODYSSEY cluster at Harvard University). It employs the xstar2table script (v.1.0) to produce multiplicative tabulated model files: an absorption spectrum imprinted onto a continuum (xout_mtable.fits), a reflected emission spectrum in all directions (xout_ain.fits), and an emission spectrum in the transmitted direction of the absorption (xout_aout.fits). The first and second tabulated model files are used as absorption and emission components of the ionized outflows (or infalls) in spectroscopic analysis tools. Table 4 lists the parameters used for producing XSTAR model grids. To cover the possible range of physical conditions, we initially considered a large range of gas densities $n$ from $10^{8}$ to $10^{14}$cm$^{-3}$, column densities $N_{\rm H}$ from $10^{18}$ to $10^{25}$cm$^{-2}$, ionization parameters $\xi$ from $10^{-2}$ to $10^{5}$ ergcms$^{-1}$, and turbulent velocities of 100-500 kms$^{-1}$, for use in spectral fitting.

We computed a grid of $15 \times 29$ XSTAR models on the two-dimensional $N_{\rm H}$-$\xi$ plane, sampling the fundamental parameter space with 15 logarithmic intervals in the column density (from $\log N_{\rm H}=18$ to $25$cm$^{-2}$ with the interval size of $0.5$) and 29 logarithmic intervals in the ionization parameter (from $\log\xi=-2$ to $5$ ergcms$^{-1}$ with the interval size of $0.25$), assuming a gas density of $n=10^{12}$cm$^{-3}$. For diagnostic purposes, we have initially constructed some grids with the same $N_{\rm H}$-$\xi$ parameter space for $\log n=8$-$14$cm$^{-3}$ (interval size of $1$), and $v_{\rm turb}=100$-$500$kms$^{-1}$ (interval size of $100$). However, we found that results were indistinguishable for this wide range of the gas density in highly-ionized absorbers. Hereafter, all XSTAR models correspond to a gas density of $n=10^{12}$cm$^{-3}$.

The turbulent velocity is another important parameter in photoionization modeling. An increase in the turbulent velocity increases the equivalent width of an absorption line for a given column density of each ion. To estimate equivalent widths correctly, the velocity width, which is associated with line broadening, must be measured precisely. The high spectral resolution of MEG and HEG data allows for the possibility of determining the velocity width. However, due to insufficient counts, our HETGS observations pointed to a wide range of velocity widths with high uncertainties, so we could not measure the exact value of $v_{\rm turb}$ for each ion. From the line width measurements (see Table 3), we adopted a velocity turbulence of $v_{\rm turb}=200$kms$^{-1}$ for the warm absorber, which approximately corresponds to the HETGS optimal spectral resolution.

Figure: The 1-sigma (68%), 2-sigma (95%), and 3-sigma (99%) confidence contours of the logarithm of the ionization parameter ($\log \xi$) vs. the logarithm of the column density ( $\log N_{\rm H}$; left), the logarithm of the ionization parameter ($\log \xi$) vs. the turbulent velocity ( $v_{\rm turb}$; middle), and the logarithm of the column density ( $\log N_{\rm H}$) vs. the turbulent velocity ( $v_{\rm turb}$; right) of the ionized absorber with the best-fitting parameters listed in Table 5, respectively. The cross sign shows the best-fitting values in each panel.

We proceeded to fit the combined MEG and HEG data shown in Figure 5, multiplying our continuum model by the XSTAR tabulated grids produced from the ionizing SEDs in §5.1. There are a total of two free parameters in the tabulated grid fitting, namely, the ionization parameter $\xi$ and column density $N_{\rm H}$ of the ionized absorber. Using the base continuum model described in §4.1, the model for the spectra containing 1 ionized absorber and 4 Fe emission lines are implemented as follows: $\textsf{tbnew}~\times \textsf{highecut}~\times (\textsf{diskbb}~+ \textsf{zpowerlw}~+ \sum_{i=1}^{4} \textsf{zgauss}~(i)) \times \textsf{xstar\_absorber}~$. These models successfully described the data with an ionization parameter of $\log \xi=2.9\pm0.1$ and a column density of $N_{\rm H}=(2.4\pm0.6)\times10^{21}$ (90% confidence levels), with an observed redshift of $(0.0201\pm0.0005)c$. The model with these parameters has a goodness-of-fit of $\chi^{2}/{\rm d.o.f}=738/661$. These results allowed us to refine our parameter estimations in performing the warmabs model fitting described in the subsequent section.