Energy shift of Fe-K fluorescence lines due to low ionization demonstrated with XRISM in Centaurus X-3

TL;DR

This study demonstrates that low ionization of Fe in Cen X-3 induces a measurable differential shift between the Fe Kα and Kβ fluorescence lines. By combining XRISM/Resolve high-precision spectroscopy with atomic-structure calculations, the authors constrain the Fe ionization state to $q\approx5$ (Sc-like) and show that incorporating this ionization correction reconciles the Fe-based systemic velocity with optical measurements. The differential line shift serves as a robust diagnostic to decouple ionization effects from kinematic shifts, enabling refined constraints on the location of the fluorescing material near the L1 region. The method is broadly applicable to Fe Kα analyses in other systems and highlights the need to account for ionization when interpreting line energy shifts.

Abstract

The Fe K$α$ fluorescence line at 6.4 keV is a powerful probe of cold matter surrounding X-ray sources and has been widely used in various astrophysical contexts. The X-ray microcalorimeter spectrometer onboard XRISM can measure line shifts with unprecedented precision of $\sim$0.2 eV, equivalent to a line-of-sight velocity of $\sim$10 km s$^{-1}$. At this level of accuracy, however, several factors that influence the line energy must be carefully considered prior to astrophysical interpretation. One such important factor is the ionization degree, Fe$^{q+}$. The K$α$ line shifts redward by $\sim$4 eV as $q$ increases from 0 (neutral) to 8 (Ar-like). Additionally, the accompanying Fe K$β$ line at 7.06 keV shifts blueward by $\sim$30 eV from $q=0$ to 8. We demonstrate that this effect is actually observable in the XRISM data of the high-mass X-ray binary Centaurus X-3 (Cen X-3). We advocate that the differential energy shift between the K$α$ and K$β$ line provides a robust estimate of $q$ by decoupling from other effects that shift the two lines in the same direction. We derived $q \sim 5$ (Sc-like) for the fluorescing matter by comparing the observation with atomic structure calculations of our own and in the literature. By accounting for the derived charge state and the corresponding shift in the rest-frame line energy, we made corrections for this effect and reached a consistent residual shift among the K$α$, K$β$, and the optical measurement attributable to the systemic velocity of the system. Consequently, we obtained a new constraint on the location of the cold matter. This ionization effect needs to be assessed in all use cases of the Fe K$α$ line shift beyond Cen X-3, and the proposed metric is generally applicable to all of them.

Figures (6)

• Figure 1: (a) X-ray count rate, (b and c) RV curves of the Fe K$\alpha$ (magenta) and K$\beta$ (cyan) line before and after the ionization correction, and (d) their Gaussian width. The MJD is given at the bottom, while the orbital phase at the top. In panel (a), Hp events in the 1.6--12 keV are binned at every 128 s. The three phases ($\phi_\mathrm{I}$, $\phi_\mathrm{II}$, and $\phi_\mathrm{III}$) are defined with arrows. In panel (b) and (c), the green dashed-and-doted line is the systemic velocity of Cen X-3 Hutchings1979. Panel (b) assumes that the lines are from neutral Fe ($q=0$), while panel (c) is corrected for the ionization effect assuming that they are from Sc-like Fe ($q=5$). Alt text: Four stacked line graphs with a common x-axis showing MJD and orbital phase. The y-axis shows count rate in the top panel, line shift in the middle panels, and line width in the bottom panel.
• Figure 2: (a) Broadband spectra of Resolve in three different phases obtained during the orbital phases $\phi_\mathrm{I}$ (blue), $\phi_\mathrm{II}$ (red) and $\phi_\mathrm{III}$ (black). (b) Close-up view of each orbital-phase-resolved spectrum in the Fe K band, shown in the same color as panel a. The laboratory rest-frame energy of the Fe K lines are shown with the vertical magenta lines. Alt text: Two line graphs show count versus energy. The right panel is divided into three vertical sections.
• Figure 3: Fitting results of the Fe K$\alpha$ (left panels) and Fe K$\beta$ (right panels) lines for the three phases (top: $\phi_\mathrm{I}$, middle: $\phi_\mathrm{II}$, and bottom: $\phi_\mathrm{III}$). In each panel, the data (black) and the best-fit model (red) are shown at the top, while the fitting residual at the bottom. Panels (a)-(b), (c)-(d), and (e)-(f) show the K$\alpha$ and K$\beta$ lines at $\phi_\mathrm{I}$, $\phi_\mathrm{II}$, and $\phi_\mathrm{III}$, respectively. Alt text: Six line graphs for the K$\alpha$ and K$\beta$ lines in the three phases. Each panel shows the spectrum and residual to the best-fit model.
• Figure 4: Line energy shift of (a) K$\alpha_1$ and (b) K$\beta_1$ relative to the neutral value, and (c) their differences as a function of the ionization degree $q$. Two theoretical calculations, Palmeri2003 and this work (RLSDA/SIC), are shown in red and green, respectively. In the former, numerous lines in the unresolved transition array were averaged by weighting with the fluorescence yield and the results up to $q=8$ is available. In the latter calculation, a single Slater determinant was adopted without explicitly resolving angular-momentum coupling as in the configuration-interaction calculations. The resulting line energies therefore represent statistical-weighted averages over all allowed transitions, rather than those of any specific single transition. The energy difference of the initial and final orbitals are used up to $q=11$ (table \ref{['tab:rlsda_sic']}). The horizontal black line and gray region show the observed RV offset and its $1\sigma$ uncertainty. Alt text: Three line graphs with a common x-axis showing the ionization degree. The y-axis shows the energy difference in the top, middle, and bottom panels.
• Figure 5: Visualization of the atmosphere model calculation for the effective temperature of $3.5 \times 10^{4}$ K and the surface gravity of $10^{3.5}$ times of the solar value Lanz2003: (a) the Fe charge state distribution, (b) electron density, (c) temperature, and (d) the Fe K optical depth ($\tau_{\mathrm{Fe K}}$) are shown as a function of the Rosseland optical depth ($\tau_{\mathrm{Ross}}$) as a proxy for the geometrical depth ($z$) from the surface. Here, $\tau_{\rm Ross}$ is the Rosseland mean optical depth, increasing inward from the stellar surface ($\tau_{\rm Ross}=0$) toward deeper atmospheric layers. The data are available online at https://tlusty.oca.eu/tlusty/Tlusty2002/tlusty-frames-OS02.html. Alt text: Four line graphs for O star atmosphere model for the ion charge state distribution, electron density, temperature, and Fe K optical depth as a function of Rosseland optical depth.