1 Introduction↩︎

Blueshifted absorption lines imprinted by accretion disk winds are some of the most distinct spectral features of X-ray binaries. First discovered using the ASCA observatory [1], [2], our understanding of disk winds and their observational signatures has significantly improved over the last \(\sim2\) decades thanks to Chandraand XMM-Newton[3], [4]. More recently, signatures of disk winds in X-ray binaries were also discovered in the UV, optical and infrared energy bands [5]–[7].

Typically, disk winds in X-ray binaries reach velocities up to 1000 km/s [8], much lower than certain types of wide-angle outflows observed in accreting supermassive black holes [9] and ultraluminous X-ray sources [10], [11] that can exhibit velocities in excess of \(10\%\) of the speed of the light. Nevertheless, the X-ray binary disk wind mass outflow rates can be of the same order as the mass accretion rates onto the compact object [12], [13]. Therefore, by transporting this significant mass as well as angular momentum outside the binary system, they can affect the long-term evolution of X-ray binaries [14], [15].

Despite being known for over 2 decades, much is still unknown about these phenomena in X-ray binaries, including their exact physical launching mechanism. It is also challenging to accurately quantify their mass outflow rates, and thus constrain the actual impact on their binary systems and neighborhoods. One of the reasons why this is difficult is because disk winds are mainly studied through their X-ray absorption lines, and thus are only sampled along a single line of sight towards the compact X-ray source. X-ray absorption line spectroscopy is the most straightforward way to understand the wind properties such as its column density, ionization parameter and velocity, but it gives us a limited view of the complex 3D structure of the outflow. Statistical studies of samples of X-ray binaries [16], [17] suggest that the vertical wind structure is not spherical but equatorial (with a \(\sim10^{\circ}\) half-opening angle), but this parameter cannot typically be constrained in any individual source.

Hercules X-1 (hereafter Her X-1) is an X-ray pulsar, an X-ray binary powered by a highly magnetized neutron star rotating every 1.2 seconds [18]. It is famous for its 35-day cycle of high and low flux states, introduced by a warped, precessing accretion disk that is seen almost edge-on [19], [20]. This warped disk precession changes our line-of-sight through the accretion flow, and at certain times of the 35-day precession cycle, outer parts of the disk obscure our view of the inner accretion flow (which produces most of the X-rays). At other times, the inner accretion flow is uncovered, resulting in two high-flux periods during each 35-day cycle named the Main High and the Short High states.

The disk precession offers a unique and powerful tool to study the 3D properties of the disk wind of Her X-1, as our time-variable sightline intersects the wind streamlines at different locations over the 35-day precession cycle, specifically at different heights above the accretion disk. A schematic showing this situation is shown in Fig. 1 of [21]. According to the model of the Her X-1 warped disk precession by [22], the inner and outer rings of the accretion disk precess by 11\(^{\circ}\) and 20\(^{\circ}\), respectively, over the 35-day precession cycle [22]. A significant part of the wind structure then crosses our line of sight during the 35-day cycle, assuming that the structure is equatorial with a relatively small opening angle [16].

Thus, we can explore the wind vertical structure through its X-ray absorption lines by sampling the wind properties over a range of precession phases. The disk wind is present in X-ray absorption during both the Main and Short High states [13], [23] and has a velocity of \(250-1000\) km/s and an ionization parameter of \(\log (\xi\)/erg cm s\(^{-1})\)of \(3-4\), consistent with typical X-ray binary disk winds. [13] and [21] performed a detailed study of the wind during the Main High state and leveraged the disk precession to produce a 2D map of this outflow, and estimated the mass outflow rate to be as high as \(70\%\) of the mass transfer rate from the secondary star.

Typical accretion disk winds detected in X-ray binaries are highly ionized, with ionization parameters around \(\log (\xi\)/erg cm s\(^{-1})\)of 4. Some of their strongest observational signatures are therefore in the Fe K energy band, with particularly strong transitions of Fe XXV (at 6.7 keV) and Fe XXVI (at 6.96 keV). The recently launched XRISMobservatory [24] offers a generational leap in our spectral capability in this energy band. The microcalorimeter Resolve instrument onboard XRISMachieves a spectral resolution of 4.5 eV at 6 keV [25], which is roughly \(\sim10\times\) the spectral resolution of ChandraHETG gratings (first order) and \(\sim30\times\) the spectral resolution of typical X-ray CCDs such as EPIC onboard XMM-Newtonat these energies. Therefore, XRISMis an outstanding instrument to study the physics of accretion disk winds in X-ray binaries, providing a precision and detail much greater than has previously been possible.

In September 2024, we carried out a large observational campaign on Her X-1 led by XRISM. The aim of the campaign is to study and understand the 3D structure of the Her X-1 disk wind with unprecedented precision [26]. To achieve this goal, we observed a significant fraction of a single Main High state of Her X-1 for a duration of \(\sim400\) ks (resulting in a \(\sim200\) ks clean exposure time after accounting for XRISM’s low-earth orbit). In addition to this XRISMobservation, we also obtained simultaneous observations with Chandra(50 ks), XMM-Newton(80 ks) and NuSTAR(40 ks), each covering part of the long XRISMexposure.

This is the first manuscript describing the 2024 XRISMobservations of Her X-1. Here we focus on the evolution of the wind properties with Her X-1 precession phase. Thanks to the excellent spectral capabilities of XRISM, we are for the first time able to track the kinematics of the wind and their variations with precession phase. The manuscript is structured as follows. In section 2, we describe the September 2024 observational campaign on Her X-1, and the preparation and reduction procedures for all datasets. In section 3, we present the results of this study using phenomenological as well as physically motivated spectral fitting approaches. In section 4, we discuss the results and in section 5 we summarize the conclusions of this paper. Throughout the paper, we assume a distance of 6.1 kpc for Her X-1 [27].

2 Observations and Data Preparation↩︎

2.1 2024 observations of Hercules X-1↩︎

The XRISMHer X-1 observation began on September 10 2024 with a gross duration of 380 ks, resulting in a clean exposure of 210 ks. A raw XRISMlightcurve of the observation is shown in Fig. 1. The aim of the campaign was to begin observing as close as possible to the Turn-on of the Main High state, when our line of sight samples the disk wind at low heights above the disk (just after the disk itself uncovered our line of sight towards the X-ray source), and continue observing for a significant fraction of the High state as our sightline rises to greater heights above the disk. Thanks to an accurate Turn-on ephemeris prediction using the method of [28], we were able to observe the transition from the Low into the Main High state roughly 30 ks after the beginning of the XRISMexposure. By using XRISMand Chandralighcurves and finding the time when Her X-1 reached for the first time \(\sim50\)% of the typical X-ray flux during the high-flux state, we determined that the Turn-on occurred at MJD=60563.46. With XRISMwe observed 3 nearly complete High state binary orbital periods [18]. Hereafter, these orbits are denoted Orbit 1, Orbit 2 and Orbit 3, respectively. In addition to the high flux intervals, we also observed several periods of absorption dips and two complete and one partial eclipses. We note that this paper only focuses on high flux intervals, and all eclipse, Low state and absorption dip state data were excluded.

As the XRISMgate valve was closed, we also requested Director’s Discretionary Time from XMM-Newton[29] to capture the soft X-rays of Her X-1, primarily using the Reflection Grating Spectrometers (RGS). XMM-Newtonperformed one observation which overlapped with Orbit 1, and one observation during Orbit 3 (80 ks total exposure time). We further triggered our Guaranteed Time observations with Chandra[30] and performed two simultaneous observations with the ChandraHETG gratings during Orbits 1 and 2, with a total exposure of 50 ks. Finally, to capture the hard X-rays above 17 keV, we triggered our Guest Observer program with NuSTAR[31] and observed Her X-1 for \(\sim40\) ks in two snapshots during Orbits 2 and 3. The approximate timings of all simultaneous observations are shown alongside the XRISMlightcurve in Fig. 1.

Further details of all observations taken during the 2024 campaign on Her X-1 are listed in Table 2 in Appendix 6.

2.2 XRISMdata reduction↩︎

We reduced all XRISMdata using heasoft v6.35.1 with the caldb version 20250315. We followed standard data reduction routines described in the XRISM ABC Data Reduction Guide¹. We extracted events from the full Resolve array except the calibration pixel (12) and pixel 27, which is known to show abnormal gain behavior. We only used High and Medium quality primary events (Hp and Mp events), which were extracted into separate spectral files and fitted simultaneously without stacking. Typically, Mp event count rates were \(10-20\)% of the Hp count rates during Her X-1 high flux periods analyzed in this paper. We generated the response matrix files and ancillary response files using rslmkrmf and xaarfgen, respectively. The data were binned according to the optimal binning scheme [32] using the ftool routine ftgrppha. Finally, the data were converted from ogip format into spex format using the trafo routine. Since Her X-1 is a very bright source during its high flux periods, we did not use any generated XRISMbackground spectra. As the gate valve was closed during the Her X-1 observation, no source counts are registered below 1.8 keV. We therefore used the Resolve data between 1.8 and 12 keV. Data in the range between 12 and 17.5 keV were excluded as no atomic features are expected in this energy range and the higher statistics NuSTARspectra are available. The XRISMdata were separated into multiple intervals in order to perform a time-resolved wind study. Further details of the time-resolved XRISMdata slices are listed in Appendix 6. We did not use any data from the Xtend instrument in this study, as its spectral resolution is not sufficient for a detailed disk wind analysis performed here.

2.3 XMM-Newtondata reduction↩︎

XMM-Newtondata were reduced using the XMM-NewtonScientific Analysis System (SAS) package version 21.0.0. We processed the raw RGS [33] data with rgsproc using default source and background extraction regions. Considering the brightness of Her X-1, we did not exclude any periods of high background. The default background regions were strongly contaminated by source counts and hence we used blank field background spectra instead, following the same approach as [21]. The final RGS spectral files were converted into spex format using the trafo routine, and binned by a factor of 3 directly within spex to achieve an oversampling of the instrumental resolution by roughly a factor of 3. RGS 1 and 2 data were always fitted simultaneously without any stacking. For spectral fitting, we used the 7.2 Å(1.7 keV) to 36 Å(0.35 keV) wavelength range.

We also used data from the European Photon Imaging Camera (EPIC) pn [34]. The EPIC-pn camera was operated in Timing mode and the data were processed with the epproc routine and extracted using evselect. Only events of pattern \(\leq4\) (single and double) were accepted as valid events. No periods of background flaring had to be excluded for these observations. The source region was a rectangle centered on Her X-1 (RAWX coordinates between 15 and 56), and the background region was a narrow rectangle as far away on the chip from the source as possible (RAWX coordinates between 2 and 5). To mitigate pile-up, we also excluded a single central pixel column for observation 0953011401 and the central two pixel columns for observation 0953011501. The data were grouped using specgroup to oversample the spectral resolution of EPIC-pn by a factor of at most three and also to achieve Gaussian statistics, and finally converted into spex format using trafo. They were used in the energy range from 2 to 10 keV only for a comparison with the XRISMResolve data and not for wind parameter estimates.

2.4 NuSTARdata reduction↩︎

The NuSTARdata were reduced using standard procedures with the NuSTAR Data Analysis Software. The data were first processed using the nupipeline routine, and the spectral files were extracted using the nuproducts routine. The source regions were circles centered on Her X-1 with a radius of 90 arcsec, and the background regions were larger circles away from the source with a radius of 140 arcsec. FPMA and FPMB data were extracted separately and fitted simultaneously without stacking. The spectra were binned with ftgrppha according to the optimal binning scheme and used in the energy range between 10 and 75 keV. The data below 10 keV were not needed as higher-resolution XRISMResolve spectra were available. The \(10-12\) keV region was used for cross-calibration between XRISMand NuSTAR.

3 Results↩︎

All data were fitted in the spex fitting package [35] version 3.07.03 by minimizing the Cash statistic [36]. All uncertainties are provided at \(1\sigma\) significance.

Thanks to the excellent spectral resolution of XRISM/Resolve, we are able for the first time to separate the various spectral features in the complex Fe K band of Her X-1. With previous XMM-Newtonand Chandraspectra, we were able to determine the presence of the strongest emission lines [37], and the disk wind absorption [21] in this band, but much uncertainty remained due to crowding of spectral features at these energies. The time-averaged high-flux XRISM/Resolve spectrum (from all 3 orbits combined), alongside a simultaneous XMM-NewtonEPIC-pn spectrum, is shown in Fig. 2.

XRISMclearly resolves several spectral components in the Fe K band. A narrow Fe I K\(\alpha\) line is strongly detected and the K\(\alpha\)​1 and K\(\alpha\)​2 components are partially resolved. Blueshifted absorption from the accretion disk wind is also present. The strongest feature is the absorption line of Fe XXVI (Ly\(\alpha\)​1 and Ly\(\alpha\)​2 components are observed), but Fe XXV absorption is also present, although much weaker than Fe XXVI. The ratio of these two transitions indicates a high ionization degree of the wind. For the first time, we also detect a narrow Fe I K\(\beta\) emission line. Finally, all of this narrow spectral structure is super-imposed on a highly broadened Fe K complex known from previous Her X-1 studies [37].

All narrow components are broadened beyond the instrumental resolution of XRISM. This is expected considering the orbital motion of Her X-1 with a projected orbital velocity of 170 km/s [38], which smooths all orbital-averaged spectra by this velocity width. Additionally, the narrow Fe I K\(\alpha\) line is consistent with having at least 2 kinematic components, a very narrow one (with a width of \(\sim100\) km/s) and a slightly broadened one (with a width of \(\sim1000\) km/s). The origin of the components of the Fe I line will be explored in detail by Narita et al. (in prep.).

Thanks to the very long exposure with XRISM, we are able to probe how the wind varies with time (and Her X-1 precession phase). To show this visually, we extracted data from the 3 Her X-1 orbits into separate spectra, and focused specifically on the Fe XXVI absorption line energy region. This is shown in Fig. 3. The Fe XXVI doublet clearly varies from orbit to orbit. Its strength decreases over time from Orbit 1 to 2 to 3, as the 35-day cycle precession phase increases, in agreement with previous Her X-1 observations [21]. For the first time, thanks to XRISM, we are also able to see shifts in its centroid energy and width over time. The line appears to broaden with time, and consistently shifts to higher energies. Therefore, the optical depth of the outflow in Fe XXVI decreases, and its projected velocity increases, as well as its velocity width.

In the following sections we perform a more detailed, quantitative analysis of these variations. We perform a time-resolved analysis, where the interval sizes are defined adaptively depending on the strength of the wind absorption features. In subsection 3.1 we describe the setup of the spectral fitting model. In subsection 3.2 we model the wind absorption features with a phenomenological spectral model which allows us to assess the absorption lines in the most model-independent manner. Finally, in subsection 3.3 we apply a photoionization model to determine the physical parameters of the disk wind.

3.1 Spectral model setup↩︎

We use a phenomenological spectral model to describe the continuum and line emission from Her X-1 before modeling the disk wind absorption. Each time interval of the time-resolved analysis is fitted independently. We fit the XRISMHp and Mp data in two separate spectra using a cross-calibration constant. Its value is in all cases within 1% of unity. The XRISMdata are fitted simultaneously with NuSTARdata to obtain a coverage from 1.8 keV to 75 keV which encompasses most of the X-ray emission of Her X-1 (more than 90% of its X-ray luminosity is in this range). The inclusion of the NuSTARdata is needed for correct spectral energy distribution (SED) modeling, necessary to apply a photoionization spectral model in subsection 3.3, and also to correctly describe the primary continuum across a broad band. Incorrect primary continuum modeling could have consequences for the inference of best-fitting parameters of the highly broadened Fe K emission lines as well as of the absorption lines. As we did not observe any significant variability in the count rate (which agrees within 5%, Table 2) and spectral shape between the two NuSTARobservations taken during Orbit 2 and Orbit 3, for each time interval analyzed we use the full NuSTARspectrum from the appropriate observation. We introduce a cross-calibration constant between the XRISMand NuSTARdata to account for any calibration differences and to account for possible residual variability from interval to interval in the hard X-ray (\(>12\) keV) flux during individual XRISMintervals. The value of the cross-calibration constant varies by less than 10% for all analyzed intervals during Orbits 2 and 3 indicating weak, if any (pulse-averaged) variability in the hard X-rays.

For Orbit 1 intervals, which lack simultaneous NuSTARcoverage (due to a spacecraft tracker visibility violation at that time period), we use the NuSTARobservation from Orbit 2. The cross-calibration constant for the analyzed time intervals during Orbit 1 is on average 30% off the typical value during Orbits 2 and 3, indicating variability in the hard band. Nevertheless, inclusion of this (even if approximate) hard X-ray tail is much preferred to ignoring it completely. Assuming that the spectral shape in the hard X-ray band (\(>12\) keV) remains consistent, the \(\sim30\%\) flux variability is taken into account for SED modeling by applying the cross-calibration constant.

The primary continuum is described with a Comptonization component, using the comt model. This model was found to be insufficient alone to describe the entire \(1.8-75\) keV energy band. A satisfactory fit was found when an additional hard exponential cutoff was applied using the etau component. The primary continuum is further affected by cyclotron resonance scattering at \(\sim35-40\) keV [39], which we reproduce using a line component. This is a strictly phenomenological description of the primary X-ray pulsar emission which allows us to focus on the interpretation of the spectral features in the Fe K band. A physical interpretation of the broadband continuum emission will be discussed in future work.

We then focus on the Fe K band, which is shown in Fig. 4. In agreement with our previous results from XMM-Newton[37], we require two highly broadened emission lines to accurately describe the broad Fe K structure on which the narrow emission and absorption lines are imprinted. These lines are modeled with simple Gaussians, which describe the spectral shape required by the XRISMdata surprisingly well. Their origin and variability will be discussed in future work (Kosec et al. in prep), but one of the lines has a \(1\sigma\) width of about 1 keV and its centroid is consistent with Fe I at 6.4 keV, while the second line has a \(1\sigma\) width of \(0.2-0.3\) keV and its centroid is instead consistent with the position of Fe XXV at 6.67 keV.

To describe the narrow Fe I K\(\alpha\) and K\(\beta\) lines, we also use single Gaussians. We note that we do not use 2 kinematic components to describe Fe I K\(\alpha\) and K\(\beta\) in this work, as doing so would further increase the complexity of our model with very little effect on the absorber properties. The Fe I K\(\alpha\) and K\(\beta\) kinematic structure will be addressed in Narita et al. (in prep.). As the origin of the two narrow lines is likely the same and the K\(\beta\) line is relatively weak, we couple its velocity width to that of the K\(\alpha\) component, and couple its energy to that of the K\(\alpha\) component times the ratio of neutral K\(\beta\) and K\(\alpha\) rest-frame positions. The origin of these features will be studied in detail in Narita et al. (in prep.). Nevertheless, it is important to (at least crudely) model these features here for an accurate description of the emission continuum. Furthermore, the Fe I K\(\beta\) component is located at \(\sim7.07\) keV, close to the Fe XXVI transition at 6.96 keV, and so omitting the K\(\beta\) model could have consequences for our description of the wind absorption through the Fe XXVI line. The time-averaged high-flux Her X-1 XRISMspectrum is shown in Fig. 4 and shows how the final spectral model consists of different model components.

Finally, the entire Her X-1 emission spectrum is subjected to Galactic absorption. This is included within the model with a hot component, which describes absorption by almost neutral gas [40]. The column density of this absorber is set to \(1\times10^{20}\) cm\(^{-2}\)based on our previous study of Her X-1 [37], [41]. This Galactic absorption model is applied as the last effect, only after the ionized disk wind absorber is applied.

3.2 Phenomenological wind modeling↩︎

The aim of this study is to probe how the disk wind varies with precession phase of Her X-1, as our sightline changes due to the warped disk precession. Therefore, we perform a detailed time-resolved study of the XRISMdataset. We chose a range of time-resolved intervals guided by the strength of the wind absorption lines and the statistics (and clean XRISM exposure) required to constrain them. As the first step, we perform phenomenological modeling of the wind absorption. We use the slab model [42] in spex, which can determine the ionic column density in any specific ion by simultaneously fitting the optical depth of all the absorption lines which such ion produces. At the same time, the ratios of the different ion column densities are not constrained, and as such this spectral model gives us the most model-independent understanding of how the wind absorption lines behave over time.

The strongest features of the disk wind in the \(2-10\) keV XRISMbandpass are the absorption lines of Fe XXV and Fe XXVI. In this first step, we simply use slab to fit for the column density of Fe XXV and XXVI ions. The slab model has two further variables - the absorber velocity (determined from the blueshift of the component) and the velocity width (determined from the line widths). This basic setup allows us to investigate any variation in the wind kinematics and in the strength of its wind absorption signatures.

XRISMhas the capability to track the kinematics of the wind of Her X-1 and its variations despite the low wind velocity of just hundreds of km/s. We observe that the wind velocity evolves in a range between 150 and 800 km/s. This is consistent with previous X-ray grating measurements in Her X-1 using ChandraHETG and XMM-NewtonRGS [13], [21], [23]. In fact, the XRISMdata quality is so good that we can now observe binary orbital motion in the evolution of the wind velocity with precession phase. This is shown in Fig. 5 by using the densest time-resolved sampling attempted in this study, where we split the high-flux XRISMexposure from all 3 orbits into 19 time intervals. Clear sinusoidal motion is observed on the timescale of the orbital period, which is expected because the wind is launched by the accretion disk orbiting the neutron star, and the neutron star is in orbital motion with the secondary star. On top of the orbital evolution, we also see systematic evolution in wind outflow velocity with precession phase.

In the following analysis, we correct any wind outflow velocity measurements for the orbital motion of the neutron star and its accretion disk. We use the velocity correction formula from [13], based on the measurement of the projected orbital velocity of \(169.049 \pm 0.004\) km/s by [38] and the systemic velocity of Her X-1 of \(-65 \pm 2\) km/s by [43]. The orbital phase was calculated using the ephemeris of [28], which specifies an orbital period of 1.700167590 days, an eclipse midpoint on MJD 46359.871940, and a change of the orbital period of \(-(4.85 \pm 0.13) \times 10^{-11}\) s s\(^{-1}\).

We experimented with a range of time interval splitting which would maximize the time resolution while minimizing the uncertainties on the relevant parameters. In the end, a compromise was achieved by splitting the high-flux XRISMexposure into 14 intervals, where the exposure of each interval varied adaptively depending on the strength of the Fe XXV and XXVI wind absorption during each interval. The slab component free parameters were measured for each analyzed interval. The results are shown in Fig. 6 and listed in Table [Slab95table]. We find that the wind is strongly variable, in agreement with previous studies and that all four slab parameters vary significantly over the sampled precession phase range. Additionally, the observed variations are not monotonic in most of the parameters, but show jumps just after Her X-1 emerges from eclipses by the secondary. We discuss these results in section 4.

3.3 Photoionization wind modeling↩︎

In the second part of the analysis, we replace the phenomenological slab model with the photoionization model pion [44] while keeping the other (continuum) spectral components the same. pion takes into account the SED of the currently loaded emission spectral model to calculate the ionization balance of all elements and produce their transmission function when subjected to the input SED, assuming photoionization equilibrium. Therefore, with pion we can take into account all of the wind absorption lines across the XRISMenergy range, but at much higher computational cost. In return, we are able to determine physical parameters of the outflow such as its column density and ionization parameter, required to determine the outflow energetics and mass outflow rate. This is also naturally a more model-dependent approach to analysing the wind properties than using the phenomenological slab model which does not make assumptions on the conditions of the wind (e.g. single ionization phase versus multiphase), which is why we describe the results from both approaches in this manuscript.

pion requires correct SED modeling to accurately determine the physical quantities. This is one of the main reasons why we add NuSTARdata to any XRISMtime interval spectral fit. To also model the soft X-rays (0.35-1.8 keV) accurately, we perform a spectral fit of the RGS data from XMM-Newton  which was taken simultaneously with Orbits 1 and 3. For this step, the RGS data are used solely to determine the shape of the SED and not to constrain any of the wind absorption lines in the RGS band, considering we only have partial time coverage of the XRISMobservations with XMM-Newton. The RGS data are fitted with a simplified model from Appendix 7 containing a simple blackbody (bb), a blackbody modified by coherent scattering (mbb) and one Gaussian line describing the broad 1 keV feature [37]. This simplified model accounts for more than 99% of the soft X-ray flux. The model is added to each fitted XRISMtime interval, and its best-fitting parameters (from the RGS analysis) are fixed. For all time intervals during Orbit 1, we use the results from the XMM-Newtonobservation taken during that orbit. For all time intervals during Orbits 2 and 3, we use results from the XMM-Newtonobservation taken concurrently with Orbit 3, considering that Orbits 2 and 3 show comparable count rates across the XRISMenergy band (while Orbit 1 is somewhat fainter, Fig. 1). An example of the final, full-band SED (from Orbit 1) is shown in Fig. 8.

Additionally, pion assumes elemental abundances during the spectral fit. These could in principle be left to the default (Solar) values. However, there is strong evidence suggesting that elemental ratios in Her X-1 are in fact not Solar [21], [23], [45], [46]. Therefore, before proceeding with the time-resolved pion analysis, we perform the best-quality analysis of the wind elemental abundances given our simultaneous coverage with XMM-Newtonand XRISMthat cover a wide energy band (0.35-12 keV), containing a broad range of elemental transitions. This elemental abundance analysis is described in further detail in Appendix 7. In the pion analysis described below, we fix the abundances to the values listed in Table 3.

The derived SEDs and elemental abundances are applied in a spectral fit to each of the time intervals independently. For this analysis, we had to reduce the number of time intervals to just 10. This was needed because pion requires multiple ionic transitions to accurately determine the column density and the ionization parameter - specifically, both Fe XXV and XXVI absorption lines are required, and the Fe XXV line is much weaker than the Fe XXVI line. Increasing the number of time intervals significantly expanded the uncertainty ranges on the column density and ionization parameter. The results of the pion analysis are shown in Fig 7. As in the phenomenological analysis with the slab model, all parameters strongly vary with Her X-1 precession phase. The results are discussed in the following section.

4 Discussion↩︎

We perform a comprehensive time-resolved analysis of the disk wind of Her X-1 by analyzing a long observation by XRISM. The total duration of \(\sim380\) ks allows us to probe the wind properties for a significant fraction of the Main High state, spanning roughly 12% of the entire 35-day precession period. The disk precession during this time shifts our line of sight across the wind vertical structure, resulting in a range of X-ray absorption spectra which give us a unique insight into the vertical properties of this structure. The observational campaign led by XRISM(and supported by coordinated observations with XMM-Newton, NuSTARand Chandra) also spanned almost 3 full high-flux (Main High state) orbital periods of Her X-1 and additionally captured 3 eclipses, 3 periods of absorption dips and a brief period of Low state. While this manuscript focuses on the time-resolved wind properties, our future publications will study many other aspects of this datasets including the pulse-resolved wind behavior, Her X-1 emission lines and other flux states.

For the first time, thanks to the spectral resolving power of XRISM  we are able to completely resolve the complex Fe K band of Her X-1. [37] correctly identified several features in this energy band including the disk wind absorption lines (strongest being the Fe XXV and Fe XXVI lines), a narrow Fe K\(\alpha\) line, a broadened Fe XXV line, and a highly broadened Fe K line. However, only now it is possible to measure the properties of these individual features with confidence.

The time-resolved analysis shows that all parameters of the wind are strongly variable. We clearly observe the imprint of the Her X-1 orbital motion on the overall wind velocity (Fig. 5). Even after correcting for this effect, the outflow velocity increases over time, as the precession phase increases and our line of sight samples greater heights of the wind above the warped disk of Her X-1. The observation of an increasing velocity could indicate that the total wind velocity increases as the wind rises above the disk - in other words, the wind is still within the acceleration zone as it is sampled by our sightlines. Alternatively, at least its projected velocity must increase, i.e. as it rises higher above the disk, its velocity vector aligns more with our line of sight. In reality, both of these possibilities may be at play.

In addition to the outflow velocity, we also observe a monotonic increase in the velocity width of the wind absorption lines. This is unlikely to be due to an increase of thermal turbulent velocity (as the wind ionization parameter and temperature do not greatly increase over time), but instead is plausibly due to a range of streamlines crossing our line of sight, which all have a slightly different projected outflow velocity from our line of sight. If the velocity vectors of these streamlines diverge going upwards in the flow, the line velocity width will increase as our sightline moves to greater heights. Additionally, as each time interval has a definite exposure time, the Her X-1 orbital velocity change over this duration will also contribute to the velocity width of the observed (time-integrated) wind features. However, this effect should not form the majority of the line velocity width, as the slab and pion analyses use different time interval samplings, and still show consistent velocity widths.

The column density of the wind, either in the individual lines (Fig. 6) or in the overall N\(_{\rm H}\) (Fig. 7) is seen to decrease significantly over time. Particularly, the Fe XXVI transition appears to decrease almost linearly over time, with two exceptions (discussed below). However, the change in N\(_{\rm H}\) is not as sharp as in [21] where a variation of as much as 3 orders of magnitude was found. Here, the change appears to be much lower, by about a factor of 3. This is because the behavior of the ionization parameter is very different compared with the previous analysis using XMM-Newtondata. Instead of strongly decreasing over time as seen in [21], \(\log (\xi\)/erg cm s\(^{-1})\)is relatively stable in Orbit 1 at around a value of \(3.65-3.7\), and increases in Orbit 2 and 3 to values consistent with \(3.8-3.9\). This difference is likely due to the enormous improvement in the dataset quality in the Fe K energy band thanks to the spectral resolution of XRISM(Fig. 2). At these ionization parameters, \(\log (\xi\)/erg cm s\(^{-1})\)is strongly constrained by the ratio of the Fe XXV and Fe XXVI transitions, and now for the first time the individual transitions are fully resolved. Previous measurements using XMM-NewtonEPIC-pn data were affected by a degeneracy between the strength of the broadened Fe XXV emission line at 6.67 keV, and the optical depths of the Fe XXV and Fe XXVI wind absorption lines (see also Appendix 7 for a further discussion of this effect). ChandraHETG spectra offered better spectral resolution, but more limited statistics in this energy range [23]. Now, finally, the ionization parameter can be confidently measured and indicates that as the wind rises to greater height above the disk, its ionization increases, and potentially stagnates. This is consistent with the wind freezing out at a constant \(\log (\xi\)/erg cm s\(^{-1})\)as it rises and expands into 3D space.

The different \(\log (\xi\)/erg cm s\(^{-1})\)variation with precession phase inferred here has implications for the 2D map of the wind produced in our previous work [21]. We will explore these consequences in more detail in a follow-up paper, where we will also directly compare the wind parameter measurements and their evolution with precession phase (and height above the disk) with a range of hydrodynamical simulations assuming various disk wind driving mechanisms. Qualitatively, this change in the ionization parameter evolution will push the wind location estimates (at certain phases/heights) with respect to the wind base closer to the neutron star. Hence, the wind streamline will be oriented more vertically than shown in Fig. 4 of [21].

We note that the significant uncertainties on the values of the column density are due to a degeneracy between N\(_{\rm H}\)and \(\log (\xi\)/erg cm s\(^{-1})\). The uncertainties on \(\log (\xi\)/erg cm s\(^{-1})\)are introduced because of the weakness of the Fe XXV transition, particularly in the second half of our campaign. This does not mean that the wind is detected weakly in these time segments, as it is still strongly detected through the Fe XXVI transition (Fig. 6). In each of the individual segments, the statistical improvement upon adding the disk wind is at least \(\Delta\)C-statof 90, but typically reaches \(200-500\).

We also use this combined X-ray dataset to measure the elemental abundances in the disk wind of Her X-1. This is discussed in further detail in Appendix 7 and the best-fitting abundances are listed in Table 3. In summary, the abundances of elements primarily in the RGS band (N and Ne) are over-abundant compared with O and consistent with previous studies [21]. However, the Fe/O ratio is significantly different from the previously measured value of 2.3 due to our improved spectral resolution in the Fe K band and is \(0.70_{-0.10}^{+0.08}\).

Most of the wind parameter evolution (after accounting for orbital motion) appears relatively smooth and monotonic, with two major systematic exceptions. After each eclipse by the secondary, most wind parameters significantly jump. This is seen particularly in the Fe XXV and XXVI line column densities in Fig. 6, which strongly increase for a single time segment. As a result, the overall wind ionization parameter decreases immediately after the first eclipse in the pion analysis (Fig. 7). A similar shift is observed also in the outflow velocity (in both the slab and pion analyses). Surprisingly, no similar variability is seen in the velocity width, which remains consistent across the eclipses. At the same time, no similar jumps in any wind parameters are seen just before the eclipses. However, we note that we lack coverage immediately preceding the eclipses, as these intervals are affected by absorption dips (not analyzed in this study), which offer limited information on the wind properties (Fig. 1).

These jumps indicate a more complex nature of the disk wind than previously considered. The jumps clearly show dependence on the orbital phase, and the large changes seem to only occur immediately following an eclipse, when our line of sight passes close to the secondary star. This may indicate multiphase nature of the wind, with one component originating from the Her X-1 accretion disk and following a smooth evolution (seen particularly in the Fe XXVI line column density), and a second component, plausibly originating from the secondary star, considering the orbital phase dependence. One of the possible launching mechanisms for this outflow could be the strong X-ray illumination of the secondary by Her X-1, which could launch a thermal wind from the stellar surface. The existence of such a wind was previously hypothesized by [47] based on the detection of P-Cygni profiles in the UV band. However, we note that these UV line detections in Her X-1 predate most X-ray binary disk wind confirmations (in the X-rays) and particularly the disk wind detection in this source [13]. It is thus possible that the UV lines are imprinted instead by the accretion disk wind. Alternatively, there could be a single disk wind component with its streamlines focused by the secondary star’s gravity, however the previous estimates of the wind’s location all place the wind location within the outer accretion disk radius, far away from the stellar influence. A more complex spectral analysis containing multiple absorption zones is required. This will be explored in follow-up work.

In addition to modeling the wind ionized absorption, we also searched for re-emission from the regions of the outflow that are not along our line of sight. The detection of emitting wind plasma would help constrain its solid angle and the wind 3D structure in even more detail. This re-emission is very weak, even in the high-quality XRISMdata. It is completely absent in the time-averaged high-flux spectrum (Fig. 2). There is evidence for weak re-emission in the orbit-resolved XRISMdata, but only in Orbit 1 (Fig. 3). This indicates that the outflow is being launched into a small solid angle, consistent with X-ray binary disk wind population studies [16], [17]. A follow-up study will model this weak re-emission signature in Her X-1 with a combined absorption-emission wind model.

The large coordinated observational campaign on Her X-1 led by XRISMand supported by XMM-Newton, NuSTARand Chandrareveals the structure of its accretion disk wind in unprecedented detail. This first study of the 2024 dataset where we performed a time-resolved, pulse-averaged study of the wind shows how the structure changes upwards along the wind streamlines, as the precessing disk moves our sightline to consecutively greater heights above the disk. At the same time, the depth of this study only scratches the surface that the XRISMdata provide, and opens many new questions discussed above. A follow-up study (Kosec et al. in prep) will explore the pulse-resolved variability of the wind properties, which has the power to constrain the wind number density, and precisely locate it along our line of sight to the neutron star.

The projected wind outflow velocity is seen to increase along the wind streamlines, from 250 km/s to 600 km/s. The question is - how much more can it increase further up the flow? If the wind is indeed thermally driven, a terminal velocity exceeding 1000 km/s would require very high Compton temperatures to accelerate the outflow to such speeds, or alternatively a contribution from radiation pressure would be needed. Future Her X-1 observations with XRISMat even later Her X-1 precession phases would help to answer this question and allow us to understand the wind properties even further along the streamlines, as the wind continues expanding into 3D space.

5 Conclusions↩︎

We present the first results from a large coordinated campaign on Hercules X-1 led by XRISM(210 ks exposure) and supported by XMM-Newton(80 ks), NuSTAR(40 ks) and Chandra(50 ks). This work focuses on the properties of the vertical structure of the disk wind of Her X-1, which we measured by performing a time-resolved analysis of the observations. We applied both phenomenological as well as physical spectral models to describe the ionized absorption imprinted by the outflow. Our conclusions are as follows:

• For the first time, thanks to the excellent spectral resolution of XRISM, we are able to fully resolve the complex Fe K energy band of Her X-1, and accurately measure the properties of the individual components. In particular, the absorption lines of Fe XXV and Fe XXVI from the accretion disk wind are resolved and allow us to accurately measure the ionization parameter of the wind.

• We directly observe the orbital motion of Her X-1 in the evolution of the wind outflow velocity. After correcting for this motion, the wind velocity is seen to increase with rising precession phase from 250 km/s to 600 km/s, as our sightline progressively samples the wind streamlines at greater heights above the disk. This indicates that either the wind is still within the acceleration zone at these heights, or that its velocity vector progressively aligns with our line of sight with increasing height above the disk. Additionally, we also observe a rise in the wind velocity width with increasing precession phase, from 200 to 400 km/s.

• The column density of the wind decreases with increasing height above the disk, in agreement with previous observations, from \(20\times10^{22}\) cm\(^{-2}\)to \(7\times10^{22}\) cm\(^{-2}\). This decrease is also observed in the individual Fe XXV and XXVI absorption lines. In contrast to previous results, the ionization parameter \(\log (\xi\)/erg cm s\(^{-1})\)increases with the precession phase, from a value of 3.65 to \(3.8-3.9\). The wind ionization evolution is consistent with freezing out as it expands into 3D space.

• The wind parameter evolution is relatively smooth throughout the observation, except immediately after each eclipse, when a significant increase in ionized absorption is observed. We also detect a jump in the wind velocity at these phases. This suggests that the ionized absorption is multiphase, and a second component appears only briefly after eclipses. The second component may originate from the secondary star and could be driven thermally by the strong illumination of the secondary by the intense X-ray radiation from Her X-1.

• The improved spectral data quality allows us to perform a thorough study of elemental abundances within the disk wind. We are able to constrain the abundances of C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe and Ni. Their best-fitting values are listed in Table 3.

6 Further details of individual observations and time-resolved data intervals↩︎

Table 1 contains further information about the segmenting of high flux XRISMtime intervals. We explored a range of segmenting approaches by splitting the dataset into 10 intervals (used in the pion analysis in section 3.3), 14 intervals (used in slab analysis in section 3.2) and 19 intervals (used for the velocity evolution Fig. 5). The details in Table 1 are given for the 14 interval approach and include the clean exposure and the mean Hp and Mp quality event count rate of each segment. Table 2 contains details about the all coordinated observations during the 2024 campaign on Her X-1.

7 Elemental abundance analysis↩︎

We leverage the simultaneous XRISM, XMM-Newtonand NuSTARdata to perform the most detailed elemental abundance analysis of the disk wind of Her X-1 to date. We previously analysed the wind abundances in [21] and [23] using XMM-Newtonand Chandradata separately. However, the spectral resolution of XRISMin the Fe K band allows us to perform a much more robust analysis by resolving the complex structure in this energy band, and accurately measuring the wind ionization parameter. XMM-NewtonRGS data inform us about the abundances of lighter elements such as C, N, O, Ne and Mg with transitions in the \(0.35-1.75\) keV band. On the other hand, the energy band of XRISM(\(1.8-12\) keV) contains transitions of heavier elements including Si, S, Ar, Ca, Fe and Ni. Therefore, to extract the maximum amount of information, we combine both datasets. Since the disk wind is highly ionized and its signatures are the metallic lines of these elements (with no H lines within this X-ray range), we cannot extract the elemental abundances with respect to the abundance of hydrogen. Instead, we must compare the abundance with respect to one reference metal. Following our previous work [21], we primarily choose O to be the reference, and fix its abundance to 1. This choice is used in the pion spectral analysis in section 3.3. For completeness, we also list the best-fitting abundance values assuming Fe as the reference element. This choice allows a direct comparison with the abundance study of disk winds in 4 low-mass X-ray binaries by [48].

To leverage as much information as possible, we use all data from the 2024 campaign on Her X-1. However, as the disk wind is strongly variable, the data must be split and care must be taken in any simultaneous fitting. The XMM-Newtonobservations occurred during XRISMOrbit 1 and 3 but covered only parts of those orbits (compared with XRISM, which covered full orbits). For this reason, we split the XRISMdata from those orbits into two spectral data groups - one spectrum simultaneous with the XMM-Newtonpointing, and one spectrum non-simultaneous with XMM-Newton. There was no XMM-Newtonobservation during Orbit 2, and so those XRISMdata form their own data group. We also add the NuSTARobservations in each data group for accurate SED modeling (required by the pion wind model) - the NuSTARobservation which occurred during Orbit 2 for all data taken during Orbit 1 and 2, and the NuSTARobservation taken during Orbit 3 for all data from Orbit 3. Then we fit all these 5 data groups simultaneously, without any stacking - Orbit 1 (no XMM), Orbit 1 (with XMM), Orbit 2 (no XMM), Orbit 3 (XMM), Orbit 3 (no XMM). Cross-calibration constants are used to account for calibration differences between the different instruments, as well as to account for variability in the hard energy band covered by the NuSTARdata.

The spectral model used is similar to the one in section 3.2, but the phenomenological slab absorber model is replaced with a pion component. Moreover, we add several extra spectral components to describe the RGS data, and accurately describe the entire SED of Her X-1 from 0.35 keV to 75 keV. These spectral components are taken from [37]. The RGS spectrum is described with a combination of a regular blackbody (0.05 keV temperature, likely from direct disk emission), a blackbody modified with coherent Compton scattering (reprocessing of primary accretion column radiation with a temperature of \(0.1-0.2\) keV), a broad Gaussian line near 1 keV (Fe L emission), two medium-width emission lines (O VIII and N VII emission) and 2 narrow emission lines (O VII and N VI emission). For those data groups with no XMM coverage, we link the RGS component parameters to the best-fitting values from the nearby data groups with XMM coverage. Considering the evolution of the XRISMlightcurve (Fig. 1), Orbit 1 (no XMM) has its RGS component parameters fixed to those from Orbit 1 (with XMM). Orbit 2 and Orbit 3 (no XMM) data groups have the RGS component parameters fixed to those from Orbit 3 (with XMM). One of these full-band spectral fits (Orbit 1 with XMM) is shown in Fig. 8.

All of the other spectral fit parameters are left free to vary (and are decoupled between the 5 data groups) except the elemental abundances in the pion component, which are all coupled among the 5 data groups. We note that all relevant elemental abundances across the XMM-Newtonand XRISMenergy band are fitted (except the reference elements O or Fe) regardless of signal-to-noise, as leaving them fixed to 1 may bias the spectral fit. This very complex spectral model is then fitted in spex and we extract its statistical uncertainties. The best-fitting elemental abundances are given in Table 3 for both the O and Fe reference spectral fits. We note that the spectral fit quality of both approaches is nearly the same, and they differ by \(\Delta\)C-statof \(\sim0.1\) for 44767 degrees of freedom. However, as expected, the best-fitting wind column densities N\(_{\rm H}\)are different - setting Fe as the reference element results in 30% lower N\(_{\rm H}\)column densities in each data group, caused by increasing the strength of the lines of Fe (and other elements) by the same factor.

The abundances of N and Ne are super-Solar compared with O, in agreement with previous measurements [21]. The abundance of C was not previously measured in the disk wind but was found to be sub-Solar (C/O of \(0.3-0.6\)) in Her X-1 using Low state observations [45]. Here we only obtained a very stringent upper limit of 0.08 on its value. The discrepancy with the study of [45] could be introduced if there is a strong emission line component of C VI below the wind absorption, that may not necessarily be related to the disk wind. Due to low Doppler shifts of the wind, if there exists such a component, this would be very hard to separate, especially in RGS data. This same caveat in principle applies to all elemental measurements.

The abundances of Mg, Si, S and Ar are mildly sub-Solar, but have relatively large uncertainties. They are all consistent with the abundance of Fe at \(1\sigma\) uncertainties. Our previous study using ChandraHETG [23] indicated a super-Solar abundance of Mg, Si, and S, however our current results cannot be directly compared to that study, because in [23] we fixed the abundances of both O and Fe to the best-fitting values from [21]. On the other hand, the abundances of Ca and Ni are super-Solar, but again with significant uncertainties (abundances are consistent with Fe at \(2\sigma\) level).

The biggest surprise is the abundance of Fe, which is tightly constrained to \(0.70_{-0.10}^{+0.08}\). This result is in significant tension with previous XMM-Newtonresults which indicated an abundance of \(2.1 \pm 0.3\). We investigated this difference using the simultaneous XMM-NewtonEPIC-pn and XRISMdata. To simplify the comparison as much as possible, we used the phenomenological slab model to fit the strength of the Fe XXV and XXVI lines. We found that EPIC-pn consistently overestimated the strength of these lines. If the Fe XXV/XXVI lines are overestimated in spectral modeling, the physical pion component will require a high N\(_{\rm H}\)column density, or a high Fe abundance. This overestimation is likely due to the limited spectral resolution of EPIC-pn in the Fe K energy band, and a degeneracy between the optical depth of the wind absorption lines (at 6.7 and 7.0 keV) and the strength of the broadened Fe XXV emission line at the same location at 6.7 keV. Fixing the Fe abundance in the EPIC-pn data in a wind model using pion to the value from the current combined analysis (Fe \(=0.7\)) instead resulted in much higher column densities, underlying this disk wind-emission line degeneracy.

The spectral resolution of XRISMallowed us to finally resolve the individual features of the complex Fe K band of Her X-1, resulting in a much more confident measurement of the Fe line optical depths, and so a more confident measurement of the Fe/O elemental abundance ratio. It could be possible to further improve the quality of this elemental abundance study to include all of the previous high-quality XMM-Newton(primarily RGS) data from the 2020 campaign as well as the ChandraHETG data. This would primarily reduce the uncertainties on the lighter elements within the RGS energy band (considering the wealth of available XMM-Newtondata) such as C, N, O, Ne and Mg. This is beyond the scope of the current paper as it would require more significant computational resources and is left for a future study.

References↩︎