5.4 Thermal Stability

The photoionization model fitting yielded the ionized absorber with the physical conditions listed in Table 5, hydrogen-equivalent column density $ N_{\rm H}$ (in cm$ ^{-2}$) and ionization parameter $ \log \xi$ (in ergcms$ ^{-1}$), which are required to reproduce the blueshifted absorption features in the spectrum of PG1211+143 .

Figure: The distribution of temperature $ \log T$ (top panel) and the ion fraction distributions of the neutral hydrogen (HI), the He-like (black line) and H-like (gray line) ions of the relevant elements (Ne, Mg, Si and Fe) as a function of ionization parameter $ \log \xi$ produced using the XSTAR model with the ionizing UV-X-ray SED shown in Figure4. The thick solid lines in the curves correspond to the regions with the thermally stable gas. The vertical dot line (labeled as PG1211) is associated with the XSTAR warm absorber with parameters listed in Table 5. We note that while FeXXV is included here, it was not detected with any significance in this Chandra observation. The gas density is chosen to be $ n_{\rm H} = 10^{12}$cm$ ^{-3}$. As can be seen, H I can exist even at the high ionization required by the detected X-ray lines, lending extra credence to our findings that the $ \rm \sim 16980 \,km \, s^{-1}$ outflow we detect with Chandra and HST are likely associated.
\includegraphics[width=3.2in, trim = 50 30 0 0, clip, angle=0]{figures/fig7_ion_fraction_xi.ps}

The stability curve, in which temperatures ($ T$) of clouds are plotted against their pressures ($ \xi/T$), is an effective theoretical tool to illustrate the thermal stability of ionized absorbing clouds (Chakravorty et al., 2013; Reynolds & Fabian, 1995; Krolik et al., 1981; Krolik & Kriss, 2001; Chakravorty et al., 2009). The absorber is thermally stable where the slope of the stability curve is positive and where the heating and cooling mechanisms are in equilibrium. Figure 7 shows the stability curve generated using the XSTAR model for a gas density $ n_{\rm H} = 10^{12}$cm$ ^{-3}$ and the corresponding parameters specified in §5.3. As can be seen, the ionized absorber is just at the edge of the thermally stable region. Interestingly, in the prior XMM-Newton observation in 2014, when PG1211+143 was twice as bright, the ionization parameter $ \xi $=3.4 (Pounds et al., 2016b), consistent with the increased brightness, and lying on the next-highest stable portion of the curve.

Figure 8 shows the distribution of temperature $ \log T$, the neutral hydrogen (HI), and ion fractions of the He-like and H-like ions of the relevant elements (Ne, Mg, Si and Fe) with respect to the ionization parameter $ \log \xi$, from our XSTAR  model. The distribution of temperature and ion fractions typically depend on the ionization parameter, the gas density, and the ionizing SED (Kallman & Bautista, 2001). The thick solid lines correspond to the range where the absorbing gas is thermally stable. This figure further shows that both the X-ray detected ions and the UV absorber detected in HI can all coexist in a single ionization zone at the same velocity.

Ashkbiz Danehkar