# The long stare at Hercules X-1 - I. Emission lines from the outer disk,
the magnetosphere boundary and the accretion curtain

P. Kosec  MIT Kavli Institute for Astrophysics and Space Research,
Massachusetts Institute of Technology, Cambridge, MA 02139  E. Kara  MIT Kavli
Institute for Astrophysics and Space Research, Massachusetts Institute of
Technology, Cambridge, MA 02139  A. C. Fabian  Institute of Astronomy,
Madingley Road, CB3 0HA Cambridge, UK  F. Fürst  Quasar Science Resources SL
for ESA, European Space Astronomy Centre (ESAC), Science Operations
Departement, 28692 Villanueva de la Canñada, Madrid, Spain  C. Pinto  INAF -
IASF Palermo, Via U. La Malfa 153, I-90146 Palermo, Italy  I. Psaradaki
University of Michigan, Dept. of Astronomy, 1085 S University Ave, Ann Arbor,
MI 48109, USA  C. S. Reynolds  Institute of Astronomy, Madingley Road, CB3 0HA
Cambridge, UK  D. Rogantini  MIT Kavli Institute for Astrophysics and Space
Research, Massachusetts Institute of Technology, Cambridge, MA 02139  D. J.
Walton  Centre for Astrophysics Research, University of Hertfordshire, College
Lane, Hatfield AL10 9AB, UK  R. Ballhausen  Department of Astronomy,
University of Maryland, College Park, MD 20742, USA  NASA-GSFC/CRESST,
Astrophysics Science Division, Greenbelt, MD 20771, USA  C. Canizares  MIT
Kavli Institute for Astrophysics and Space Research, Massachusetts Institute
of Technology, Cambridge, MA 02139  S. Dyda  Department of Astronomy,
University of Virginia, 530 McCormick Rd, Charlottesville, VA 22904, USA  R.
Staubert  Institut für Astronomie und Astrophysik, Universität Tübingen, Sand
1, 72076 Tübingen, Germany  J. Wilms  Dr. Karl Remeis-Observatory and Erlangen
Centre for Astroparticle Physics, Sternwartstr. 7, D-96049 Bamberg, Germany

###### Abstract

Hercules X-1 is a nearly edge-on accreting X-ray pulsar with a warped
accretion disk, precessing with a period of about 35 days. The disk precession
allows for unique and changing sightlines towards the X-ray source. To
investigate the accretion flow at a variety of sightlines, we obtained a large
observational campaign on Her X-1 with XMM-Newton (380 ks exposure) and
Chandra (50 ks exposure) for a significant fraction of a single disk
precession cycle, resulting in one of the best datasets taken to date on a
neutron star X-ray binary. Here we present the spectral analysis of the High
State high-resolution grating and CCD datasets, including the extensive
archival data available for this famous system. The observations reveal a
complex Fe K region structure, with three emission line components of
different velocity widths. Similarly, the high-resolution soft X-ray spectra
reveal a number of emission lines of various widths. We correct for the
uncertain gain of the EPIC-pn Timing mode spectra, and track the evolution of
these spectral components with Her X-1 precession phase and observed
luminosity. We find evidence for three groups of emission lines: one
originates in the outer accretion disk ($10^{5}$ RG from the neutron star).
The second line group plausibly originates at the boundary between the inner
disk and the pulsar magnetosphere ($10^{3}$ RG). The last group is too broad
to arise in the magnetically-truncated disk and instead must originate very
close to the neutron star surface, likely from X-ray reflection from the
accretion curtain ($\sim 10^{2}$ RG).

Accretion (14), Neutron stars (1108), X-ray binary stars (1811)

††facilities: XMM-Newton, Chandra, Swift, MAXI††software: SPEX (Kaastra et
al., 1996), XSPEC (Arnaud, 1996), Veusz

##  1 Introduction

Hercules X-1 (hereafter Her X-1) is a famous neutron star X-ray binary
(Giacconi et al., 1972; Tananbaum et al., 1972) widely known for the various
timescales of its variability. In addition to the 1.24 s rotation period of
the neutron star (Giacconi et al., 1973; Deeter et al., 1981; Staubert et al.,
2009) and the 1.7 d binary period (Davidsen et al., 1972; Bahcall & Bahcall,
1972; Middleditch & Nelson, 1976), the system exhibits a strong flux
variability with a period of about 35 days (Katz, 1973; Gerend & Boynton,
1976), the so-called super-orbital cycle. Each cycle begins with a Turn-on
during which the object switches into an X-ray bright High State with a
luminosity of $\sim 3\times 10^{37}$ erg/s for $7-10$ days. This is followed
by a Low State with an X-ray flux of about $5-10$% of the High State. Another,
weaker high flux state (with a flux of about 1/3 of the High State flux),
called the Short High (Fabian, 1973) then occurs for roughly a week, and
finally a second Low State follows until the end of each super-orbital cycle.
The cycle has been studied since 1970s and is not strictly periodic and varies
in length between 33 and 37 days (Leahy & Igna, 2010).

These variations have been studied in great detail and can be explained within
a scenario where the accretion disk of Her X-1 is seen almost edge on, is
warped and precesses each super-orbital period (Roberts, 1974; Petterson,
1975; Scott et al., 2000; Ogilvie & Dubus, 2001). In such a case, the compact
X-ray source is obscured from our view during the Low States by the outer
accretion disk, while directly observable during the High States.

Her X-1 exhibits a great variety of phenomena and its spectra are highly
complex. It has been studied thoroughly thanks to its proximity (6.1 kpc,
Leahy & Abdallah, 2014), combined with regularly appearing high X-ray flux and
thus provides us the opportunity to obtain very high quality X-ray spectra
with current observatories such as XMM-Newton and Chandra. Despite the
apparent changes in flux due to the obscuration by the precessing disk, Her
X-1 is stably accreting with a mass accretion rate of about 20% of the
Eddington limit for a canonical 1.4 M⊙ neutron star. The broadband spectrum is
composed of a pulsating Comptonization continuum from the accretion column of
the neutron star (Lamb et al., 1973; Ghosh & Lamb, 1979), as well as a soft
blackbody originating from the reprocessed primary component (Hickox et al.,
2004). A cyclotron resonance scattering feature modifies the spectrum around
40 keV (Truemper et al., 1978; Staubert et al., 2007), providing information
on the magnetic field of the neutron star ($\sim 3\times 10^{12}$ G).

The X-ray spectrum also contains many emission lines of varying widths (Pravdo
et al., 1977; Ramsay et al., 2002; Jimenez-Garate et al., 2002a, 2005), from
narrow lines ($\sim$100 km/s velocity widths) to strongly broadened features
($>$10000 km/s widths), plausibly originating through a number of different
phenomena from distinct regions of the accretion flow.

Despite the number of previous studies, Her X-1 still has not revealed all its
secrets. Recently, Kosec et al. (2020) detected a highly ionized and highly
variable accretion disk wind through narrow absorption lines seen in XMM-
Newton spectra. The existence of an outflow in Her X-1 has previously been
predicted by Schandl & Meyer (1994) and Leahy (2015). We proposed that the
observed strong wind parameter variation may be explained if the different
observations are sampling differing sightlines above the precessing warped
disk. Therefore the sightlines are sampling different parts (heights) of the
disk wind structure at different phases of the super-orbital precession cycle.
This discovery thus revealed a unique way to study the 3D structure of an
accretion disk wind in an X-ray binary.

To follow-up on these results, we were awarded a Large (380 ks) XMM-Newton
campaign on Her X-1 in AO-19 (PI: Kosec). The primary aim was to study the
evolution of the disk wind over the course of a single High State. At the same
time, the campaign produced a great wealth of serendipitous data on Her X-1.
In this paper, we focus on the properties of the numerous and diverse emission
lines found in its X-ray spectrum, identifying them with three distinct
regions of the accretion flow: the outer accretion disk, the boundary between
the disk and the neutron star magnetosphere and the accretion curtain (or
column) of the pulsar. Fig. 1 contains a schematic of the Her X-1 system and
shows our interpretation of the origin of these emission lines. The analysis
of the accretion disk wind properties will be presented in a separate
forthcoming publication (Paper II).

Figure 1: A schematic of the Her X-1 system, showing the different regions
producing emission lines of various velocity widths. The X-axis of the
schematic is in logarithmic scale. For simplicity, the scheme omits the
accretion disk wind (detected through its absorption lines), likely
originating from the inner parts of the accretion disk atmosphere.

The structure of this paper is as follows. In section 2, we describe the new
August 2020 campaign and show the XMM-Newton Reflection Grating Spectrometer
(RGS) lightcurve of Her X-1. Section 3 contains the details of our data
preparation and reduction, while in section 4 we describe the spectral model
used to fit the Her X-1 spectra from Chandra and XMM-Newton instruments. In
section 5 we present the results of this study and in section 6 we discuss
their implications. We summarize in section 7. Finally, appendices A and B
contain further technical details about spectral modelling.

Throughout the paper, we adopt a distance of Her X-1 of 6.1 kpc (Leahy &
Abdallah, 2014). All uncertainties are provided at 1$\sigma$ significance,
unless explicitly specified otherwise.

##  2 August 2020 XMM-Newton and Chandra Campaign on Her X-1

We were awarded a 380 ks XMM-Newton exposure to study the evolution of the
highly variable ionized disk wind in Her X-1. The campaign was composed of
three back-to-back full-orbit observations to track the wind variation during
a significant part of a single High State of Her X-1. The aim was to catch the
Turn-on moment of the High State, and observe for the next $\sim 400$ ks,
interrupted only by XMM-Newton’s orbit. Two additional Chandra observations
(35 ks + 15 ks) were obtained through a DDT request to provide coverage during
the first XMM-Newton observation gap, to resolve better the Fe K energy band
as well as to compare the results from the two observatories for consistency.

Figure 2: XMM-Newton/RGS (stacked) $0.35-1.8$ keV and Chandra HETG ($1-9$ keV)
lightcurves from the August 2020 campaign on Her X-1, with a resolution of 100
s. The campaign consisted of three full-orbit XMM-Newton observations as well
as two shorter Chandra observations. Aside from the High State and a brief low
flux period, we observed one full and two partial eclipses of Her X-1 by the
secondary and four absorption dipping periods. The $0.3-10$ keV EPIC pn
lightcurve has a very similar shape to the RGS lightcurve, but the absorption
dips are less pronounced due to the higher energy coverage of pn. Chandra
count rate during observation 23356 was scaled by the RGS/HETG count ratio
during observation 23360 with simultaneous coverage of both instruments. The
lightcurve of Chandra observation 23360 is not shown as the same time interval
is covered by XMM-Newton. The elapsed time of 0 corresponds to MJD
59071.69035.

Our observations were triggered and carried out between the 10th and the 16th
August 2020. The RGS lightcurve of the three XMM-Newton observations is shown
in Fig. 2. At the very beginning of the first observation, Her X-1 was already
in the High State, with an RGS count rate of $10-15$ ct/s ($30-50$ % of the
maximum during this High State). We inspected the concurrent Swift/BAT and
MAXI monitor lightcurves to determine the time of Turn-on (here defined as the
first moment when Her X-1 shows high flux after the second Low State of the
previous precession cycle). We found that the Turn-on could not have occurred
more than a few ks before the XMM-Newton campaign began, and estimated the
Turn-on moment to have occurred at MJD 59071.65. The initial brief high flux
state was followed by a low flux period including an eclipse of the X-ray
source by the secondary HZ Her. Then, around halfway through the first XMM-
Newton observation, the High State returned for the rest of the campaign.

The observed X-ray spike into high X-ray flux, followed by a low flux period
before the persistent High State continues is an interesting phenomenon, which
was not seen before in such clarity. It is most likely connected with the
outer edge of the accretion disk not being a sharp edge but a highly
structured entity of scattering and absorbing material. A similar highly
variable light curve was observed by XMM-Newton in August 2016. This complex
Turn-on behavior will be studied in a separate publication.

In addition to the high flux periods, the campaign covered one full and two
partial eclipses of Her X-1 by the secondary HZ Her, as well as three dipping
periods. The flux dips originate from cold matter absorption in the outer
accretion disk, and are possibly connected to the impact of the accretion
stream onto the disk (Choi et al., 1994; Schandl, 1996). The dips and eclipses
will be described and studied in detail in forthcoming publications.

The extreme Her X-1 count rate and the very long exposure result in one of the
best quality XMM-Newton datasets on a neutron star X-ray binary, captured in
high spectral resolution. As the goal of the campaign was to track the time
evolution of the accretion disk wind properties, we decided to split the full
campaign in a number of smaller segments. We split the campaign into 14 High
State segments in total, achieving a compromise between time sampling and data
quality. The segmenting is described in section 3.

##  3 Data Preparation and Reduction

In this work we analyze spectra from XMM-Newton and Chandra observations. We
use all sufficient quality archival and new observations of the High State of
Her X-1 with these instruments. The backbone of the work is the Large XMM-
Newton campaign which occurred in August 2020 (380 ks raw exposure), but the
XMM-Newton Her X-1 archive contains 11 further High State observations (190 ks
raw exposure in total). The August 2020 campaign was accompanied by two
Chandra DDT observations (PI: Kosec) with 50ks of exposure in total. We also
analyze an additional 20ks archival Chandra observation.

The new XMM-Newton observations are split into smaller segments in order to
perform time-resolved spectroscopy. We calculate the super-orbital
(precession) phase for each observation or observation segment analyzed. In
this work we consider the Turn-on moment (phase=0) to be the first moment when
the apparent luminosity of Her X-1 spikes to its High State value (roughly
1037 erg/s and higher, about $\sim$25 % of the maximum observed High State
luminosity). We use Swift/BAT (Krimm et al., 2013) and MAXI (Matsuoka et al.,
2009) lightcurves to determine the Turn-on moments for the current and the
following precession cycle, and determine the super-orbital phase, following
the approach in Kosec et al. (2020). We estimate the uncertainties on each
phase measurement. These are significantly smaller for the August 2020
observational campaign where the Turn-on moment can be very well constrained.
The super-orbital phases of observations 0134120101 and 0153950301 (determined
from RXTE data) were obtained from Leahy & Igna (2010).

We also determine the orbital phase of each observation/segment. We take the
midpoint of the clean exposure and calculate the orbital phase and its
uncertainty (taken to be half the segment duration) using the Her X-1 orbital
solution from Staubert et al. (2009).

###  3.1 XMM-Newton

XMM-Newton (Jansen et al., 2001) observed Her X-1 many times in the past.
However, many of the exposures occurred when the object was in its Low State
and are not analyzed here. There are 11 archival High State observations
(typically of 10-20 ks duration), most of them previously also analyzed by
Kosec et al. (2020). The new High State observations are split into 14
segments of varying exposure. The splits were chosen manually and were
motivated by the strength of the ionized wind absorption features, the
strength of which reduces with increasing super-orbital phase. The first
observation, 0865440101, is split into 7 segments. The second observation,
0865440401, is split into 5 segments, while the final observation, 0865440501,
into 2 segments. The details of the archival observations are shown in Table 1
and the details of the new observations (split into 14 segments) are in Table
2.

All XMM-Newton data were downloaded from the XSA archive and reduced using a
standard pipeline with sas v19, caldb as of 2021 June. We analyze data from
the Reflection Grating Spectrometers (RGS, den Herder et al., 2001) and from
the European Photon Imaging Camera (EPIC) pn instrument (Strüder et al.,
2001). We do not use Optical Monitor data due to confusion with the secondary
HZ Her, which is also bright in the optical and near-UV bands, and time
variable due to the illumination from the inner accretion flow.

Table 1: Details of archival XMM-Newton observations used in this work. All
exposures listed are clean. The pn count rates shown are after pile-up
correction. All Turn-on MJD dates have an uncertainty of 0.5 day.

Obs. ID | Start date | Start time | Turn-on | RGS1 | RGS2 | EPIC pn
---|---|---|---|---|---|---
|  |  |  | rate | exposure | rate | exposure | columns excluded | rate | exposure
|  | MJD | MJD | s-1 | s | s-1 | s |  | s-1 | s
0134120101 | 2001-01-26 | 51935.03629 | 51929.2 | 11.5 | 11300 | 2.481 | 112901 | 0 | 453 | 5660
0153950301 | 2002-03-17 | 52350.01778 | 52348.8 | 3.492 | 74202 | 19.2 | 7260 | 1 | 488 | 2770
0673510501 | 2011-07-31 | 55773.30710 | 55772.4 | 11.6 | 9530 | 12.6 | 9430 | 1 | 372 | 6800
0673510601 | 2011-09-07 | 55811.32099 | 55807.2 | 16.8 | 32240 | 18.0 | 32000 | 2 | 379 | 19390
0673510801 | 2012-02-28 | 55985.06984 | 55981.6 | 19.6 | 12800 | 21.1 | 12750 | 2 | 452 | 4940
0673510901 | 2012-04-01 | 56018.83835 | 56015.8 | 11.7 | 13120 | 12.8 | 12960 | 1 | 387 | 9430
0783770501 | 2016-08-17 | 57617.28046 | 57617.2 | 3.90 | 4950 | 4.20 | 4940 | 0 | 226 | 4930
0783770601 | 2016-08-17 | 57617.82213 | 57617.2 | 9.56 | 5290 | 10.4 | 5290 | 1 | 342 | 4490
0783770701 | 2016-08-18 | 57618.73301 | 57617.2 | 13.1 | 12330 | 14.3 | 12300 | 2 | 330 | 7040
0830530101 | 2019-02-09 | 58523.53161 | 58516.6 | 10.9 | 19890 | 12.2 | 19860 | 1 | 419 | 13650
0830530401 | 2019-03-14 | 58556.34063 | 58551.5 | 8.75 | 7330 | 9.70 | 7290 | 0 | 442 | 4020

Note. — 1values for RGS 1 2nd order spectra for observation 0134120101.
2values for RGS 2 2nd order spectra for observation 0153950301.

Table 2: Details of new XMM-Newton observations used in this work. The high flux periods of the 3 full-orbit observations were split into 14 segments for detailed analysis of wind time evolution. All exposures listed are clean. The pn count rates shown are after pile-up correction. The measured Turn-on time used for all the August 2020 segments is MJD 59071.65.  Obs. ID | Start date | Segment | Start time | RGS1 | RGS2 | EPIC pn
---|---|---|---|---|---|---
|  |  |  | rate | exposure | rate | exposure | columns excluded | rate | exposure
|  |  | MJD | s-1 | s | s-1 | s |  | s-1 | s
0865440101 | 2020-08-10 | 1 | 59071.69035 | 4.8 | 4650 | 5.28 | 4610 | 0 | 230 | 2620
|  | 2 | 59072.33948 | 10.1 | 11070 | 11.1 | 11080 | 2 | 230 | 9590
|  | 3 | 59072.46795 | 10.9 | 11070 | 12.1 | 11090 | 2 | 247 | 9050
|  | 4 | 59072.59642 | 11.3 | 11060 | 12.5 | 11100 | 2 | 253 | 8820
|  | 5 | 59072.72489 | 11.6 | 11060 | 12.9 | 11090 | 2 | 259 | 8630
|  | 6 | 59072.85337 | 11.6 | 10960 | 12.8 | 10990 | 2 | 256 | 8570
|  | 7 | 59072.98068 | 11.9 | 8160 | 13.3 | 8000 | 2 | 264 | 6190
0865440401 | 2020-08-12 | 8 | 59073.83832 | 13.3 | 20720 | 14.6 | 20520 | 2 | 284 | 20480
|  | 9 | 59074.07952 | 13.1 | 20850 | 14.4 | 20690 | 2 | 277 | 20600
|  | 10 | 59074.32073 | 13.2 | 20740 | 14.5 | 20780 | 2 | 281 | 20490
|  | 11 | 59074.56193 | 13.8 | 20840 | 15.3 | 20890 | 2 | 301 | 20590
|  | 12 | 59074.80313 | 13.9 | 20750 | 15.3 | 20590 | 2 | 307 | 20490
0865440501 | 2020-08-14 | 13 | 59075.69364 | 12.9 | 42040 | 14.3 | 42124 | 1 | 380 | 27640
|  | 14 | 59076.18207 | 12.6 | 42090 | 14.0 | 41830 | 1 | 376 | 41580

####  3.1.1 RGS

The RGS data were reduced using the rgsproc task. Any background flaring
periods exceeding the threshold count rate of 0.3 ct/s on CCD number 9 were
excluded. There were no such periods during the August 2020 campaign. Due to
the very high flux of Her X-1, the default RGS background regions were
strongly contaminated by source counts. Therefore, we used the blank field
background spectra for all High State RGS datasets. The source flux is very
high, up to 20 ct/s per detector, but there should not be significant pile-up
in RGS data. Appendix A of Kosec et al. (2020) contains a calculation of the
maximum Her X-1 count rate for each RGS CCD chip, which is found to be below
the recommended pile-up thresholds for all CCDs. We primarily use 1st order
grating spectra, and only analyze 2nd order spectra in a few cases where 1st
order spectra are missing. Since RGS 2 was not working during archival
observation 0134120101, we replaced its data by the 2nd order RGS 1 spectrum.
Conversely, RGS 1 was not operational during observation 0153950301, and we
replaced the spectrum with the 2nd order RGS 2 spectrum.

We use the 7 Å (1.8 keV) to 35 Å (0.35 keV) wavelength range. The data are
binned by a factor of 3 directly within the spectral fitting package spex
(Kaastra et al., 1996) to achieve an oversampling of the instrumental
resolution by roughly a factor of 3. Wherever used, the 2nd order RGS spectra
are binned by a factor of 6 to achieve similar sampling compared with 1st
order spectra.

####  3.1.2 EPIC pn

The EPIC pn instrument was in Timing mode during all of the High State
observations. Nevertheless, many Her X-1 observations are still piled-up due
to the extreme count rate, reaching as high as 800 ct/s in some observations.
The data were reduced using regular routines with epproc. Only events of
PATTERN$\leq$4 (single/double) were accepted for pn data. Due to the high
source flux, regular background flaring period identification methods in EPIC
pn are not valid. We identified any flaring periods by eye on a case-by-case
basis, but periods where background flaring was important in comparison with
source flux were very rare.

We mitigate pile-up by excluding 1 or 2 central pixel columns wherever
necessary. The amount of excluded pixels is chosen so that the pile-up in the
most affected spectral bins is at most 5%. This strategy results in a spread
of final pn count rates in different observations depending on the exact
pointing of the satellite. In some cases the central two columns showed
similar count statistics and both had to be removed (resulting in lower final
count rates), in other cases one central column was exposed much more than the
neighbouring ones and was the only one we had to remove (resulting in higher
final count rates). The background regions were a few columns as far from the
source on the chip as possible. Background was not important in any of the
observations analyzed.

The reduced spectra were binned to oversample the instrumental resolution by
at most a factor of 3, and to at least 25 counts per bin using the specgroup
routine. They were used in the energy range between 1.8 keV (7 Å) and 10 keV.
We found an issue with EPIC pn gain calibration, resulting in energy shifts of
the order of 100 eV at $6-7$ keV. The issue, as well as our mitigation
strategy is described in detail in Appendix A.

###  3.2 Chandra

Chandra (Weisskopf et al., 2002) observed Her X-1 13 times in the past,
similarly to XMM-Newton. However, only three observations occurred during the
High State and were of sufficient quality for this study. All these
observations used the High Energy Transmission Gratings (HETG, Canizares et
al., 2005). One exposure happened in 2002, while the remaining two were part
of the Her X-1 campaign of August 2020. The details of all Chandra
observations are listed in Table 3. All observations were carried out in the
Continuous Clocking mode to avoid pile-up.

Table 3: Details of Chandra observations used in this work. The fourth and the fifth columns contain the MEG and HEG count rates obtained by stacking the positive and negative 1st orders of each instrument. Obs. ID | Start date | Start time | Turn-on | MEG rate | HEG rate | Clean exposure
---|---|---|---|---|---|---
|  | MJD | MJD | s-1 | s-1 | s
2704 | 2002-07-05 | 52460.73963 | 52454.3 | 18.4 | 9.87 | 18650
23356 | 2020-08-12 | 59073.22907 | 59071.65 | 11.6 | 7.97 | 17010
23360 | 2020-08-14 | 59075.91068 | 59071.65 | 11.1 | 7.63 | 14830

Observations 2704 and 23360 were downloaded from the TGCAT archive (fully
reduced, Huenemoerder et al., 2011). Her X-1 went into eclipse towards the end
of observation 23356. Only the high flux part of the observation was extracted
from 23356 by identifying the correct good time interval (GTI) times and
applying the chandra_repro routine (Fruscione et al., 2006). All observations
were reduced using standard masks. We use data from both Medium Energy Grating
(MEG) and High Energy Gratings (HEG), stacking the positive and negative first
order spectra for each instrument using the combine_grating_spectra routine.

The data are analyzed in full spectral resolution without any binning. In the
archival observation from 2002 (before the recent decline of Chandra’s soft
X-ray effective area), we use the MEG spectra between 0.6 keV (20 Å) and 5
keV. During the new observations, we use MEG data in the 0.8 to 5.0 keV range.
The HEG data are always used in the 1 to 9 keV range.

##  4 Spectral Modelling

All reduced spectra were converted from ogip format into spex format using the
trafo routine. The fitting was done in the spex fitting package (Kaastra et
al., 1996) using Cash statistics (Cash, 1979). The spex usage was motivated by
the pion model (Miller et al., 2015; Mehdipour et al., 2016), which we used to
describe the ionized absorption from the Her X-1 accretion disk wind. pion is
a photoionization spectral model which can describe both photoionized emission
and absorption. The ionization balance is calculated on the go within spex
using the currently loaded continuum model as the spectral energy
distribution.

We use cross-calibration constants to account for any minor calibration
differences between the XMM-Newton RGS1, RGS 2 and EPIC pn instruments. RGS 1
and RGS 2 spectra were not stacked, and are fitted simultaneously with the
EPIC pn spectra. We find that RGS 1 and 2 agree within 2%, and EPIC pn and RGS
agree within 7.5% in most cases. Similarly, we use cross-calibration constants
when simultaneously fitting Chandra MEG and HEG spectra (6% maximum
difference).

In the subsections below we describe the various spectral components and their
properties before proceeding to the results. Thanks to the very high flux of
Her X-1 and the long exposures, the data quality is extremely high with
millions of counts in each observation or observation segment. However, the
spectrum of Her X-1 is also very complex and requires many spectral
components. As our main goal for the program is to study the absorption lines
from the disk wind, the broadband continuum must be modelled accurately to
prevent the absorber models from fitting residuals due to incorrect continuum
modelling instead of real disk wind features.

We adopt phenomenological models for the various emission components, and
apply a physical model for the ionized absorption from the accretion disk wind
(pion). A simple continuum modelling is required to reduce the computational
cost of the fitting analysis, particularly due to the usage of the pion model.

As noted previously, we found an issue with the gain calibration of the EPIC
pn spectra. The effect is that pn photon energies appear to be too high, by as
much as a factor of 1.015-1.02. The issue is described in greater detail in
Appendix A. Our solution is to systematically blueshift all spectral models
fitting the EPIC pn spectra with a reds component within spex. The RGS spectra
have the same reds component applied but its blueshift is set to 0. The actual
EPIC pn gain shift value is unknown but we use several fixed parameters to
anchor our spectral model between the RGS and the EPIC pn data. These
parameter include some Fe K region emission lines (described in more detail
below) as well as the wavelengths of the ionized wind absorption lines. The
absorption lines are modelled with a single pion photoionization grid using
only one blueshift parameter, thus coupling their line positions between the
RGS and EPIC pn energy bands.

Secondly, we found a broad residual around 23Å in the RGS band which affected
our broadband continuum fit. The residual could be due to instrumental
calibration or imperfect modelling of interstellar hot gas and dust. It is
described in more detail in Appendix B. To simplify the spectral modelling, in
this paper we thus ignore the affected wavelength range between 22.25 and 24 Å
($0.52-0.56$ keV).

###  4.1 Broadband spectrum of Hercules X-1

The hard X-ray ($>2$ keV) spectrum of Her X-1 is dominated by the pulsating
emission from the accretion column. The emission can be described as a
powerlaw with a cutoff of $\sim 20$ keV (beyond the reach of XMM-Newton and
Chandra bandpass). Here we model the accretion column emission with a comt
comptonization model in spex (Titarchuk, 1994).

The soft X-ray ($<1$ keV) spectra of the High State are instead dominated by
soft excess resembling a black body with a temperature of 0.1 keV (Hickox et
al., 2004). This component pulsates at the neutron star rotation period as
well (Ramsay et al., 2002) and thus does not correspond to accretion disk
thermal emission. The blackbody is likely accretion column beam radiation
reprocessed off the warped disk (Brumback et al., 2021). We attempted to model
the soft X-rays of the high quality new XMM-Newton observations with a single
blackbody of $\sim 0.1$ keV temperature but could not recover a reasonable
broadband continuum fit. This is due to the overall spectral shape being
broader than a single blackbody (previously also found by Kosec et al., 2020).
We note that our soft X-ray coverage is resolved in high spectral resolution
with the RGS detectors and thus the broad continuum shape is not due to
resolution issues. To achieve a better fit with our phenomenological model, we
introduce a broader blackbody shape, the mbb model (blackbody modified by
coherent Compton scattering, Kaastra & Barr, 1989), as well as a second,
regular blackbody. This results in significant fit quality improvements
($\Delta$C-stat$>100$).

Physically, the second blackbody could correspond to accretion disk thermal
emission while the hotter blackbody is reprocessed emission of the primary
accretion column beam radiation. Alternatively, it may be that the reprocessed
column radiation can not actually be perfectly described with a single
blackbody spectrum. The temperature of the second blackbody is lower than that
of the first, around 0.05 keV or even less. It is thus difficult to constrain
it with our RGS data which end at 35Å (0.35 keV). For this reason, we fix the
second blackbody to 0.05 keV (the best-fitting temperature wherever it can be
constrained) to avoid it running away to too low temperatures with
unphysically large emitting areas and luminosities (below our energy
coverage).

The soft X-ray spectra of Her X-1 around 1 keV also show another spectral
component named the ‘broad 1 keV feature’ (Fürst et al., 2013). The component
is further shown at high spectral resolution in Fig. 2 of Kosec et al. (2020),
as well as in our new high quality spectra (Fig. 5). Even at RGS resolution,
the feature is reasonably well fitted with a single broad Gaussian with a
width of $0.35-0.4$ keV and it does not appear to be composed of a smaller
number of narrow features. The component is plausibly a blend of a forest of
Fe L and Ne IX-X lines (possibly similar to the broad Fe L emission lines seen
in some AGN, Fabian et al., 2009) but physical models need to be applied to
understand its nature properly. Here, as a preliminary study, we track its
evolution phenomenologically with a simple Gaussian component.

###  4.2 The complex Fe K band

The Low State Her X-1 spectrum contains a strong and narrow ($<0.1$ keV)
emission line very close to the neutral Fe energy of 6.4 keV (Jimenez-Garate
et al., 2005), possibly originating on the irradiated face of the secondary HZ
Her (Zane et al., 2004). In the High State instead the Fe emission is much
broader ($0.3-0.5$ keV) and located at higher energies, closer to the Fe XXV
transition at 6.67 keV (Ramsay et al., 2002; Zane et al., 2004). In our
previous study (Kosec et al., 2020), we modelled this region with a single
Gaussian line, finding rest-frame energies of 6.5-6.6 keV and widths as large
as 1 keV (full width half maximum, FWHM). Other studies suggest that the Fe K
band is more complex, finding evidence for two or even three Gaussian
components of various widths including a very broad component (FWHM$\sim 2$
keV) (Fürst et al., 2013; Asami et al., 2014). On top of the emission features
are imprinted the narrow absorption lines from the disk wind (Kosec et al.,
2020), leading to a complex spectral region.

We initially fitted the high quality XMM-Newton spectra from the new 2020
campaign with a single Gaussian for the Fe feature, but discovered strong
residuals in the Fe K band indicating that the single Gaussian is indeed
insufficient. This is shown in Fig. 3. Instead of a single Gaussian with an
energy of 6.6 keV and a FWHM of 0.8 keV, a much better fit (by
$\Delta$C-stat$\sim 700$ for unsegmented observation 0865440501) is obtained
by adding two Gaussians, a medium-width one at 6.6 keV with a FWHM of 0.4-0.5
keV and a second, broad one at 6.7 keV with a FWHM width of 1.9 keV (best-
fitting energies are given without any gain correction here). The broad
Gaussian indicates extreme plasma velocities of 0.1-0.15c. However, the line
properties are similar to what Fürst et al. (2013) and Asami et al. (2014)
found using NuSTAR and Suzaku data, respectively (thus arguing against the
EPIC pn residual being of instrumental origin).

Figure 3: EPIC pn spectrum of the High State from observation 0865440501 (80
ks clean exposure), focusing on the Fe K region. The data are shown in the top
plot in black (errorbars are so small they are difficult to see in the
spectrum). The blue curve shows the best-fitting model containing one broad
Gaussian, while the red curve corresponds to the model containing two broad
Gaussian lines. The red dashed lines in the top subplot are the individual
spectral components in the more complex, two Gaussian model. The Gaussian
components are shifted by a constant amount for better visual clarity. The
bottom subplot shows the residuals to the blue model in black, as well as how
the model with two Gaussians fits the data (in red).

Fig. 3 hints that the Fe K band is likely even more complex. A sharp residual
at around $6.4-6.5$ keV is seen in the more complex 2-Gaussian spectral model,
indicating the presence of a narrow (less than $0.1-0.2$ keV width) emission
line close in energy to neutral Fe transition. However, it is difficult to
constrain this narrowest emission line with the limited energy resolution of
the EPIC instrument. We therefore turn to the HETG observations of Her X-1
High State. HETG spectra have poorer statistics due to a lower effective area
than EPIC pn but offer significantly better spectral resolution. The spectra
of the three Chandra observations, focusing on the Fe K band, are shown in
Fig. 4.

Figure 4: Spectra from the three Chandra observations of Her X-1 High State,
focusing on the Fe K band. The data are fitted with a simple spectral model
consisting of a powerlaw plus two Gaussians, shown in blue. The red dashed
lines show the positions of Fe I (6.4 keV) and Fe XXV (6.67 keV) transitions.
The super-orbital phase $\phi$ of each Chandra observation is given below its
ID.

The HETG resolution is sufficient to resolve the emission lines. A narrow line
near 6.4 keV is clearly resolved, which does not appear to vary significantly
in position or width. Its FWHM width is around 50 eV. This is consistent with
the Fe I transition energy and thus we denote this feature ‘Fe I’ in the text
below. However, we note that this component could also contain line emission
from other low ionization Fe ions (up to at least Fe XIII), the transition
energies of which are difficult to distinguish from 6.4 keV using our data. A
second, medium-width Gaussian is also present, and is consistent with the Fe
XXV transition at 6.67 keV. The width of this feature appears to be highly
variable. Any broad emission component with FWHM$\sim 1.5-2$ keV is not
statistically significant in any of the Chandra observations (regardless of
spectral binning) due to lower count statistics in the HETG spectra.

Based on the findings above, we build our spectral model for the Fe K band of
Her X-1, which contains three emission lines. A narrow line at 6.4 keV, with a
FWHM width of about 50 eV, a medium-width line at around 6.67 keV, with a FWHM
width of $\sim$0.5 keV (but highly variable between the observations), and a
very broad line around 6.5 keV with a FWHM width of 1.5-2.0 keV. In the
Chandra analysis, the last line is not present in the model and all the line
positions and widths are left free to vary. In the XMM-Newton analysis, we fix
the width of the narrowest Gaussian to 50 eV ($\sim 1000$ km/s velocity width)
as it is too narrow for the EPIC pn spectral resolution. Unfortunately, we
cannot fit for the two narrower line energies using XMM-Newton observations
due to issues with EPIC pn gain (Appendix A). Instead, we fix the energies to
6.4 and 6.67 keV and use the features as one of the anchors for the EPIC pn
spectrum. Finally, the broadest feature, which does not have an obvious
identification, has both the energy and width left free to vary, although we
require the energy to be at least 6.4 keV.

###  4.3 The soft X-ray lines

The soft X-ray ($<$1 keV) High State spectrum contains several strong emission
line features. An example high quality RGS spectrum (from observation
0865440401) is shown in Fig. 5. These spectral features have also been
previously discussed in our first paper (Kosec et al., 2020).

Figure 5: RGS spectrum (RGS 1 and 2 stacked for visual purposes) from the full
100ks long observation 0865440401 (top panel), fitted with the full spectral
model. Notable spectral components and features are described with labels. The
red shaded region was ignored in this analysis (Appendix B). The bottom
subpanel shows the ratio residuals to the best-fitting model.

Medium-width ($5000-10000$ km/s) O VIII and N VII emission lines are apparent
in the RGS spectra. These were previously modelled with a collisional
ionization equilibrium model (cie). However, with the new high quality data
from 2020 we noticed that the model consistently over-estimated the line
widths (reaching as high as $15000-20000$ km/s velocity widths). Here we
simplify the model for these features to two Gaussians, with the velocity
width tied between the two components. The velocity widths appear to range
between 5000 and 10000 km/s using this new model. We also do not fix the
wavelengths of the two features to the rest-frame transitions of O VIII and N
VII as we notice clear deviations from those positions in some XMM-Newton
observations.

It is crucial to describe these medium-width emission features correctly as
the narrow O VIII and N VII absorption lines from the disk wind are located on
top of these broadened features. Over-predicting the line widths would then
reduce the recovered narrow absorption line depths.

The soft energy band also contains narrower emission lines with widths of
$\sim$1000 km/s. They most likely originate in the so-called accretion disk
corona (ADC) 111We note that the ADC is a different type of region than a
typical accreting black hole corona, which is located very close to the
compact object. above the disk (see Fig. 9 of Jimenez-Garate et al., 2002a;
Kuster et al., 2005). The most prominent are the intercombination lines of O
VII and N VI, which we model with Gaussian lines. There is also evidence for
the intercombination line of Ne IX at 13.55 Å, but the line is not very
prominent in the individual observational segments. Therefore we do not model
it here in order to decrease the computational cost of the fitting procedure.
We free all the O VII and N VI Gaussian parameters, but require their widths
to be at most $FWHM=0.5$ Å (velocity widths at most of roughly 3000 km/s).
This is to prevent the widths running away to too large values and the
Gaussians acting as broadband continuum components instead.

From the residual plot in Fig. 5, it can be seen that many more, weaker
features are still present in the spectrum. These features are currently not
modelled as the present initial study focuses only on the strongest components
of the soft X-ray spectrum. The weaker residuals will be described and studied
in depth in a future publication.

###  4.4 The final spectral model

To summarize the subsections above, the final spectral continuum model used
for Her X-1 High State analysis is as follows. The broadband components are
described with a comt Comptonization component (primary accretion column
radiation), mbb and bb blackbody components (accretion column reprocessed
radiation) and a broad Gaussian residual near 1 keV (possibly broad Fe L and
Ne IX/X emission). The Fe K band is modelled using three Gaussian components
of various widths (Fe I, Fe XXV and very broad Fe K). The soft X-ray band
contains two further medium-width Gaussians (O VIII and N VII) and two narrow
Gaussians (O VII and N VI intercombination lines). For each of the spectral
components as well as for the full model, we calculate the $0.01-80$ keV
observed luminosity using spex, assuming a 6.1 kpc distance of Her X-1 (Leahy
& Abdallah, 2014).

On top of this continuum we apply the photoionized absorber model pion which
describes the accretion disk wind features. pion calculates the ionization
balance from the SED of the spectral components and self-consistently
determines the optical depths of the absorption lines. We fit for the column
density, ionization parameter, velocity width as well as the blueshift of
these absorption lines, while fitting for the non-Solar abundances of the Her
X-1 system. More details of the pion modelling as well as the results are
given in Paper II.

All of these components are obscured by Galactic neutral absorption, modelled
using a hot component. The neutral column density towards Her X-1 is very low,
around $1.5\times 10^{20}$ cm-2 (HI4PI Collaboration et al., 2016), however
many of our fits prefer even lower column values. This is understandable since
Her X-1 is located within our Galaxy and the given neutral column density is
the integral of all neutral gas along the line of sight towards (and beyond)
the Her X-1 position. We set a lower limit on the column density of $1.0\times
10^{20}$ cm-2.

We correct the EPIC pn gain issue by applying a reds component which
blueshifts the EPIC pn spectral model by a multiplication factor. Further
details of this gain correction are shown in Appendix A.

The final spectral model for XMM-Newton data is therefore, in symbolic form:
reds$\times$hot$\times$pion$\times$[comt \+ mbb + bb \+ gaus(Fe L) +
3$\times$gaus(Fe K) + 4$\times$gaus(O VIII, N VII, O VII and NVI)]. All
components and parameters of this spectral fit are summarized in Table 4
(Appendix C). The model for Chandra data with its more limited statistics and
no gain issues is significantly simpler, especially in the soft X-ray band:
hot$\times$pion$\times$[comt \+ mbb \+ gaus(Fe L) + 2$\times$gaus(Fe K) +
gaus(O VIII)].

##  5 Results

This section contains the results of time-resolved analysis of all the new and
archival XMM-Newton and Chandra Her X-1 High State observations. Many archival
XMM-Newton observations occurred years before the August 2020 observational
campaign (which captured a part of a single disk precession cycle). Possible
long-term variations in the accretion flow of Her X-1 could introduce
systematic differences between the archival and the 2020 results. For this
reason, we show the archival and the new 2020 XMM-Newton observation
measurements apart in all relevant figures below (by using different colours
for these measurements). In general, we find that the archival results are
consistent with the 2020 results, indicating a very stable accretion flow in
Her X-1, with limited long-term systematic parameter variations or trends over
the past 20 years. This is in agreement with the observed stable super-orbital
35 day cycle in the past 20-year period, with the exception for the anomalous
low state that occurred in 2003 (Leahy & Wang, 2020).

We focus on the properties and variability of the various emission line
components, modelled as described in the previous section. Our primary goal is
to show how these plethora of lines are related to each other, and determine
their likely origin and location within the accreting system. We want to test
if the different line properties correlate more with the observed Her X-1
luminosity (i.e. they are varying in line with the X-ray continuum flux, which
originates in the inner accretion flow), the super-orbital phase (i.e. their
changes are largely driven by geometric effects due to warped disk precession)
or the orbital phase (i.e. they are somehow related to the secondary HZ Her).

We make an important note about the measured X-ray luminosities. The X-ray
continuum or line flux variations in Her X-1 do not correspond to intrinsic
accretion luminosity variations (e.g. due to time variable mass accretion rate
onto the neutron star). Even during the High State, most of the flux
variability is likely due to obscuration (column density or covering fraction)
changes, either by the warped accretion disc, or by the ionized accretion disk
atmosphere (Scott et al., 2000). Therefore, all the measured X-ray
luminosities (of the continuum or the emission lines) are strictly the
observed, apparent luminosities obtained by converting the flux values using
the distance of Her X-1 of 6.1 kpc, and should not be taken at face value as
intrinsic luminosities. We list these apparent luminosity values in the units
of erg/s rather than using the raw X-ray fluxes to allow a more
straightforward comparison to other X-ray binaries.

###  5.1 The narrow emission lines

We focus on the three strongest narrow lines: Fe I, O VII and N VI with
similar, low line widths.

Figure 6: The observed luminosity of the narrow Fe I line versus the super-
orbital phase. The observations with XMM-Newton during the 2020 campaign, or
previously, as well as Chandra observations are shown in distinct colours.

The luminosity of the Fe I line varies in the range $(1-4)\times 10^{34}$
erg/s (about 1/1000 of the observed Her X-1 luminosity). We find that it
significantly correlates with the super-orbital phase of Her X-1 (Fig. 6,
Pearson correlation coefficient 0.70, p-value $3.5\times 10^{-5}$), much more
than with the observed Her X-1 luminosity (Pearson coefficient 0.17). We do
not observe any significant correlations with the orbital phase during the
High State (Pearson coefficient -0.32). The correlation with super-orbital
phase appears especially strong in the new August 2020 observations (Pearson
coefficient 0.76), taken over the course of a single precession cycle (thus
avoiding confusion with any possible long-term variations in the Her X-1
system).

The soft X-ray spectra of Her X-1 High State contain strong intercombination
lines of the O VII and N VI He-like triplets. We do not find clear
correlations between the observed O VII(i) and N VI(i) line luminosities and
Her X-1 orbital or super-orbital phase. There is a positive trend of O VII(i)
and N VI(i) luminosity with the observed Her X-1 luminosity but with many
outliers (Pearson correlation coefficients 0.56 and 0.55, respectively).

While these features are very narrow during the Low State ($<$300 km/s,
Jimenez-Garate et al., 2005), we find that they are significantly broader
during the High State, as well as about $3-5$ times brighter. The measured
line widths are found to be highly correlated with the observed line
luminosities, and are shown in Fig. 7. The Pearson correlation is 0.76
(p-value $2.8\times 10^{-5}$) for O VII(i) and 0.74 (p-value $2.4\times
10^{-5}$) for N VI(i). The N VI(i) width is less than 0.1 Å ($<400$ km/s
velocity width) at the lowest luminosities, reaching up to 0.3 Å (1300 km/s)
at maximum. The O VII(i) feature is broader, with a width of at least 0.1 Å
(600 km/s) at minimum fluxes, and reaching widths of 0.5 Å (3000 km/s) at
maximum fluxes.

Figure 7: Left panel: The best-fitting FWHM line width of the O VII(i) line
versus its observed luminosity. Right panel: FWHM line width of the N VI(i)
line versus its observed luminosity. The left Y-axes on each panel show the
line widths in Å, while the right Y-axes show the velocity widths in km/s.

We find that the O VII(i) best-fitting wavelength is weakly anticorrelated
with its observed luminosity (Pearson correlation -0.50, p-value $1.5\times
10^{-2}$), beginning at its rest-frame wavelength of 21.8 Å for low O VII(i)
luminosities but reaching as low as 21.7 Å. This likely indicates some
contamination with the O VII resonance line at 21.6 Å (0.2 Å away from the O
VII(i) line). The O VII(r) line, clearly weak at low O VII(i) luminosities,
could increase in importance, pulling down the wavelength of our single
Gaussian - this is not a spectral resolution issue but a modelling problem.
Therefore, the O VII(i) width could be over-estimated at the largest line
luminosities, where it appears the broadest (FWHM$>0.3$ Å). Nevertheless, in
observations with lower O VII(i) widths where no contamination occurs (best-
fitting line position at 21.8 Å with FWHM widths of $0.1-0.2$ Å), the line
broadening of $600-1200$ km/s is still much larger than observed in the Low
and Short High states by Jimenez-Garate et al. (2002a).

The N VI(i) line does not suffer from the same issue as O VII(i), thanks to
both its smaller broadening as well as due to the higher wavelength separation
from the N VI(r) line ($\sim$0.3 Å). The Pearson correlation coefficient of N
VI(i) observed luminosity and wavelength is -0.26 (p-value 0.21), indicating
low correlation between the two parameters. We still observe a similar
positive trend of the line broadening with the line luminosity, as well as
some variations around the best-fitting line position. The wavelength
variations are at most 0.05 Å, smaller than the changes in the contaminated O
VII(i) line wavelength. We note that the expected variations due to the
neutron star orbital motions should be significantly lower at about 0.02 Å
around the line rest-frame.

###  5.2 The medium-width emission lines

We resolve the Fe K band of Her X-1 into multiple line components using
Chandra HETG and XMM-Newton EPIC spectra, and constrain their widths. Chandra
observations hint at strong variability particularly in the broadening of the
medium-width Fe XXV feature. The FWHM width of the line is indeed strongly
variable, between $\sim$0.2 keV (4000 km/s) and as high as 0.8 keV (15000
km/s). There is a negative trend of the width with the super-orbital phase,
shown in Fig. 8 (top subplot), but with many outliers (Pearson coefficient
-0.38, p-value $4.7\times 10^{-2}$). We find a possible weak correlation
between the Fe XXV luminosity and the observed Her X-1 luminosity (Pearson
coefficient 0.43, p-value $2.3\times 10^{-2}$).

Figure 8: The 1D velocity (left Y-axes) and FWHM widths (right Y-axes) of the
Fe XXV (top panel) and O VIII/N VII (bottom panel) lines versus the super-
orbital phase. The right Y-axis on the bottom panel only contains the FWHM
width of the O VIII line. The observations with XMM-Newton during the 2020
campaign are shown in black, archival XMM-Newton observations are in blue, and
Chandra observations are in red colour.

The medium-width O VIII and N VII lines were detected and briefly described by
Kosec et al. (2020) but that study focused on the disk wind absorption. We
note that the velocity widths of the two features are tied in the spectral
fit, but their wavelengths, and their normalizations are decoupled.

We find that the observed luminosities of the two lines are highly correlated
(Pearson coefficient 0.78, p-value $4.9\times 10^{-6}$), indicating that they
very likely have a common origin. There are no tight correlations between the
line luminosities and Her X-1 super-orbital phase or orbital phase. On the
other hand, we do find positive trends with the observed Her X-1 luminosity
for both O VIII (Pearson coefficient 0.76, p-value $1.0\times 10^{-5}$) and N
VII (Pearson coefficient 0.73, p-value $4.0\times 10^{-5}$). There is also a
negative trend of the width of the lines with the super-orbital phase (Fig. 8,
bottom subplot). At the beginning of the precession cycle, the widths (of O
VIII) are as large as 1.4 Å (velocity width of 10000 km/s), while towards the
end of the High State they are much lower, at around 0.5 Å (velocity widths of
3500 km/s). We therefore observe similar trends in line width evolution as
with the Fe XXV line.

Finally, we also detect a curious evolution of the best-fitting wavelengths of
the two lines with the super-orbital phase. This cannot be explained by a gain
shift issue since these lines are in the RGS energy band, and RGS does not
suffer from the same gain problem as pn. The O VIII line is initially
redshifted from the rest-frame transition by about 0.2 Å ($\sim$3000 km/s),
then later systematically blueshifted (by up to 1500 km/s), followed by a
return back to the rest-frame wavelength, and tending towards redshift at the
end of the High State again. The N VII line (which is more poorly constrained
than O VIII) is systematically redshifted throughout the High State by as much
as 0.5 Å (6000 km/s), but appears to be trending towards the rest-frame
wavelength around the end of the High State. We note that the shifts are
always lower than the line FWHM widths, and their identification is secure as
they are by far the strongest features of these widths in the Her X-1 RGS
spectra.

Figure 9: The best-fitting wavelength of the O VIII line (top subplot) and the
N VII line (bottom subplot) versus the super-orbital phase. The observations
with XMM-Newton during the 2020 campaign, and previously are shown in distinct
colours. The red dashed horizontal lines indicate the rest-frame wavelengths
of the two transitions.

###  5.3 The broad Fe L and Fe K lines

Figure 10: The observed luminosity of the Broad Fe K line with respect to the
super-orbital phase (left subplot) and the observed Her X-1 luminosity (right
subplot). The observations with XMM-Newton during the 2020 campaign, or
previously are shown in distinct colours. The line could not be constrained in
any Chandra observation.

We track the evolution of the broadest Fe K line component (FWHM$\sim 2$ keV)
over 25 XMM-Newton observations and observation segments. We find that the
observed luminosity of the line strongly correlates with the observed Her X-1
luminosity (Fig. 10, right subplot, Pearson coefficient 0.9 and p-value
$9.3\times 10^{-10}$). A similar correlation with the observed Her X-1
luminosity was previously observed for the full Fe K complex (unresolved into
separate line components) in RXTE data (Vasco, 2012). The observed strong
correlation is consistent with the origin of the broad line as due to
reprocessing of the primary continuum in the inner accretion flow of Her X-1.
Alternatively, the line luminosity variation (particularly during the August
2020 campaign) may be explained as being correlated with the super-orbital
phase early on in the cycle (phase$<0.1$), after which the luminosity becomes
roughly constant (around phase$\sim 0.1$ and beyond). This can be seen in Fig.
10, left subplot).

The width of the line is extreme and requires large 1D velocities. In our
observations the FWHM width (shown in Fig. 11) is inconsistent with a constant
and varies from 1.5 keV to 3 keV (velocity widths from 30000 to 60000 km/s).
The line is narrower when the observed Her X-1 luminosity or super-orbital
phase is low. The best-fitting energy of the Fe K line is inconsistent with a
constant, and varies from 6.4 keV (pegged to the lowest allowed energy during
spectral fitting) up to 6.6 keV. However, no clear correlation in the
evolution of the energy with the observed Her X-1 luminosity or super-orbital
phase is observed.

Figure 11: The Broad Fe K line width versus the observed Her X-1 luminosity.
The observations with XMM-Newton during the 2020 campaign, or previously are
shown in distinct colours. The line could not be constrained in any Chandra
observation.

The broad Gaussian around 1 keV, possibly originating from a forest of Fe L
emission lines (with likely contribution from Ne IX and Ne X), appears
similarly extreme as the Fe K feature. With an energy of $0.95-0.96$ keV, it
shows FWHM widths ranging from 0.32 to 0.45 keV (velocity widths from 40000 to
60000 km/s). There is no strict trend of the widths with the observed Her X-1
luminosity or super-orbital phase, but lower phases tend to show higher 1 keV
line widths. The observed luminosity of this component is highly correlated
with Her X-1 luminosity (Pearson coefficient 0.68, p-value $6.3\times
10^{-5}$), similarly to the Fe K broad component (Fig. 12, right subplot).
There is one clear outlier, which is the archival Chandra observations.
However, the remaining Chandra observations (from August 2020) seem to agree
well with the XMM-Newton measurements. Similarly as with the Fe K broad
component, the observed luminosity evolution could instead be interpreted to
evolve with the super-orbital phase as a fast rise after Turn-on (phases
$<0.05$), followed by roughly constant luminosity for the remainder of the
sampled High State (Fig. 12, left subplot).

Figure 12: The Broad Fe L line (1 keV residual) width versus the super-orbital
phase (left subplot) and the observed Her X-1 luminosity (right subplot). The
observations with XMM-Newton during the 2020 campaign, previously, and with
Chandra are shown in distinct colours.

##  6 Discussion

The excellent Her X-1 XMM-Newton and Chandra dataset, including the recent
August 2020 large campaign, allows us to study the time variation of various
spectral lines and components in the luminous and nearby neutron star X-ray
binary Her X-1. We were able to split the available data into 28 intervals for
an extensive time-resolved, high-spectral resolution study. In this paper, we
focus on the evolution of the emission lines observed in the High State of Her
X-1.

The lines we studied can be separated into three groups by velocity width:
narrow lines with widths of about 1000 km/s (Fe I, O VII(i), N VI(i)), medium-
width lines with widths of $5000-10000$ km/s (Fe XXV, O VIII, N VII) and
extremely broad lines with velocity widths of $30000-60000$ km/s (Fe K, Fe L).
Below we discuss the plausible nature of the three emission line groups, and
the location of the plasma which emits them.

###  6.1 Origin of the narrow lines

The soft X-ray High State spectra contain strong narrow intercombination lines
of O VII and N VI. The presence of these transitions (and the lack of strong
forbidden lines) indicates either collisional excitation due to a high density
environment (at least $10^{10}$ cm-3, Porquet & Dubau, 2000), or alternatively
photoexcitation of the forbidden lines of the He-like triplets by intense UV
radiation (Mewe & Schrijver, 1978). The same transitions also dominate the Low
State spectra, and were previously discussed in detail by Jimenez-Garate et
al. (2002a) and Jimenez-Garate et al. (2005).

We find that the measured widths ($500-2000$ km/s) of these lines are
significantly larger than the broadening found in the same transitions in
previous Her X-1 studies of the Low and the Short High states ($<$300 km/s,
Jimenez-Garate et al., 2002a, 2005; Ji et al., 2009). The soft X-ray lines are
thought to originate in the ionized atmosphere and in the accretion disk
corona above the disk (Jimenez-Garate et al., 2002b). From the very low widths
seen in the lower flux states, it is likely that only the very outermost part
of the atmosphere/corona is observable, and the inner parts are hidden from
our sight by the warped disk. Our findings in this work indicate that during
the Main High state, we are able to view the corona/atmosphere at radii closer
to the central compact object, where the Doppler motions due to orbital
motions are larger. Velocity widths of about 1000 km/s correspond to disk
radii of $\sim 2\times 10^{10}$ cm, compared with the radii of $(8-10)\times
10^{10}$ cm estimated by Jimenez-Garate et al. (2005) from the Low State
spectra. For reference, the outer radius of the accretion disk is thought to
be about $2\times 10^{11}$ cm (Cheng et al., 1995).

In fact, the line broadening of the narrow lines is similar to the outflow
velocity of the highly ionized disk wind ($300-1000$ km/s, Kosec et al.,
2020). However, we note that the ionization parameter of the wind
($\log(\xi$/erg cm s-1) of $3-4$, Kosec et al., 2020, Paper II) is about two
orders of magnitude higher than the ionization parameter required for the
production of O VII(i) and N VI(i) ($\log(\xi$/erg cm s-1) of $1-2$, Ji et
al., 2009). Therefore they cannot originate from the same plasma, but they
could be located at similar distances from the X-ray source. For instance, the
intercombination lines could originate in high density clumps (or an accretion
disk atmosphere) near the base of the disk wind.

We also detect a significant variation of Fe I line flux with super-orbital
phase, indicating that most of its flux during the High State cannot originate
from the heated surface of the secondary HZ Her. A strong evolution with
orbital phase was observed in the Low State (Zane et al., 2004), but this is
not the case in the High State. Instead, most of the flux of the Fe I line
likely originates from dense, neutral or very low ionization clumps in the
accretion disk or the ADC at distances of several $10^{10}$ cm from the
neutron star - at similar locations where O VII(i) and N VI(i) are produced.
The line cannot originate very close to the neutron star given its low width
($\sim$1000 km/s at most), but most of its luminosity also cannot arise beyond
the outer disk given the clear evolution with the super-orbital phase.

The Fe I luminosity could then naturally vary with super-orbital phase as the
area of the warped disk (and the ADC) observed from our point of view
increases over time during the High State phase of disk precession (similar to
the proposed cause of variation in the reprocessed blackbody emission,
Brumback et al., 2021). These regions are obscured by the warped disk in the
Low State. The Fe I material is plausibly even denser than the plasma
producing the soft X-ray lines. These findings underline the strongly
multiphase nature of the disk atmosphere/corona. Multiphase ADC structure in
Her X-1 was previously discussed by Jimenez-Garate et al. (2005) and was also
found in other ADC X-ray binaries (Psaradaki et al., 2018).

###  6.2 Origin of the medium-width lines

The velocity widths of the three medium-width lines, Fe XXV, O VIII and N VII
are close to each other and vary from $10000-15000$ km/s at the beginning of
the High State down to about $3500-4000$ km/s towards the end of the High
State (Fig. 8). The similar trend of the velocity widths with super-orbital
phase could indicate a common origin. Their widths correspond to circular
velocities in the range between 400 and 7000 RG. This region is close to the
inner accretion disk boundary and the neutron star magnetosphere, thought to
be around $2\times 10^{8}$ cm from the neutron star ($\sim$1000 RG), given the
Her X-1 field of $10^{12}$ G (Truemper et al., 1978). We therefore argue that
all three spectral features have a common origin in accretion flows in the
vicinity of this region. The magnetosphere boundary could create a shock, or
the boundary region could be strongly illuminated by the accretion column
radiation, and so the plasma may be strongly ionized, reprocessing the primary
radiation and producing the observed emission lines.

However, we do not find evidence for double-peaked broad emission lines, as
seen in 4U 1626-67 (Schulz et al., 2001; Hemphill et al., 2021). Such a shape
might be difficult to identify for the Fe XXV line (located in the complex Fe
K region), but can be clearly rejected for the O VIII and N VII lines,
observed at higher spectral resolution. The accretion flow in Her X-1 is
oriented almost edge-on towards the observer, and therefore the red and blue
components should be easily separable using the RGS spectra (given the
expected velocities of 1000s km/s), if the inner disk edge is fully visible at
each super-orbital phase. If only a segment of the inner edge is visible (due
to obscuration), the medium-width lines might not have a standard double-
peaked diskline shape, and could still originate from X-ray reflection of the
primary continuum. Over the super-orbital cycle, the visible disk segment may
change, potentially explaining the observed systematic shifts in the line
centroids (Fig. 9). Alternatively, the emission lines could originate in a
shock around the magnetospheric boundary. In this case the expected line shape
is difficult to predict. Further work is required to determine the exact
emission process.

We note that similar medium-width emission lines ($2000-10000$ km/s widths,
particularly O VIII and N VII) have been detected in some ultraluminous X-ray
sources (e.g. Pinto et al., 2020, 2021). At least a fraction, but possibly a
majority of ULXs are powered by magnetized neutron stars, accreting highly
above their Eddington limit (e.g. Bachetti et al., 2014; Fürst et al., 2016;
Israel et al., 2017; Koliopanos et al., 2017; Walton et al., 2018).
Furthermore, broadened emission lines of O and N were recently also detected
in the highly magnetized neutron stars SMC X-3 and RX J0209.6-7427, accreting
mildly in excess of their Eddington limits (Koliopanos & Vasilopoulos, 2018;
Kosec et al., 2021). All these features, detected in a range of objects could
originate in equivalent physical regions in the vicinity of the magnetospheric
boundary. If this is indeed the case, the width of the detected features could
be used to estimate the magnetosphere size (and the surface magnetic field
strength) for each system. Further work is necessary to establish or reject
this apparent similarity between the different accreting systems.

Figure 13: The observed luminosity of the broad Fe L line versus the observed
luminosity of the broad Fe K line. The observations with XMM-Newton during the
2020 campaign, and previous observations are shown in distinct colours.

###  6.3 Origin of the broad lines

Asami et al. (2014) previously discussed the possible nature of the broad Fe K
feature. They rejected the origin as a high column density partial covering
(neutral or ionized) absorber, or line broadening due to Comptonization from
the accretion disk corona. They found no plausible line origins, given the
likely disk truncation radius of $\sim 1000$ RG (with maximum orbital
velocities of 10000 km/s).

We find that the velocity widths of the broad Fe L and Fe K components are
largely similar (30000 to 60000 km/s, 0.1 to 0.2c). Furthermore, both
components are highly correlated with the observed Her X-1 luminosity and the
correlations are even tighter with the observed primary Comptonization
luminosity (Pearson coefficients 0.92 and 0.69 for Fe K and L, respectively).
As a result the apparent luminosity of both lines is clearly correlated
(Pearson coefficient 0.75, p-value $1.9\times 10^{-5}$), which is shown in
Fig. 13. These findings likely indicate a common origin of the two broadest
features in reprocessing (X-ray reflection, George & Fabian, 1991; Ross &
Fabian, 2005) of the primary continuum.

However, considering that the disk is most likely truncated by the
magnetosphere at $\sim 1000$ RG, it is impossible that such a broad X-ray
reflection component could originate in reprocessing of primary continuum by
the inner accretion disk. The disk would have to extend in as close as 25 RG
to the neutron star to reach orbital velocities as large as the observed line
velocity widths. If these broad lines arise in a standard relativistic X-ray
reflection off of the inner accretion disk as seen in other NS XRBs (Ludlam et
al., 2017), and black hole XRBs (Remillard & McClintock, 2006), then an
accretion disk would have to exist within the neutron star magnetosphere, or
the magnetosphere would have to be much smaller (e.g. if the magnetic field is
multi-polar). The broad lines also cannot originate from the neutron star
surface considering the line shapes are at least roughly symmetric - it is not
clear how the blueshifted line wing could arise from the (almost stationary)
highly gravitationally redshifted surface.

The only other possibility is the reprocessing of the primary accretion column
radiation by the column/accretion curtain itself. The matter infalling along
the neutron star field lines has a low toroidal velocity given the slow
rotation frequency of Her X-1, but it can easily reach velocities above 0.1c
in the direction of the field lines before reaching the star surface. At
different neutron star rotation phases, the projected velocity vector of the
matter following the field lines can therefore produce both significant
blueshifts and redshifts.

The accretion column and curtain are therefore the best candidates for the
origin of these very broad emission features. The accretion curtain, or part
of it could be optically thick (Mushtukov et al., 2018) and thus plausibly
produce an X-ray reflection spectrum. If this interpretation is correct, it
represents the first detection of an X-ray reflection signature from the
magnetically channeled flow of a neutron star.

A broad Fe K line (up to 2 keV FWHM) was detected in the transient super-
Eddington neutron star X-ray binary Swift J0243.6+6124 (Jaisawal et al.,
2019). A cyclotron scattering feature was not found in its X-ray spectrum and
so its magnetic field (and magnetosphere size) cannot be directly measured as
in the case of Her X-1. Jaisawal et al. (2019) concluded that the broad line
could thus be either due to X-ray reprocessing from the inner disk (requiring
a very low magnetic field of $10^{11}$ G), from the accretion curtain, or from
a photoionized ultrafast outflow.

In our further work, we will apply X-ray reflection models to describe the Her
X-1 broad line emission physically and study the properties of the accretion
curtain - its geometry, and possibly the density of the reprocessing layer.

We further note that reprocessing of the primary continuum by an accretion
curtain will not produce a standard relativistic X-ray reflection spectral
shape with a sharp blue wing and a broad red wing (Fabian et al., 1989; George
& Fabian, 1991). First, the accretion curtain geometry is significantly
different from that of a standard thin disk. Secondly, and more importantly,
the whole curtain structure rotates with the rotation period of the neutron
star. The periodic rotation could qualitatively explain the roughly Gaussian
shape of the emission lines, observed instead of a strongly double-peaked,
disk line shape.

Importantly, if the broad Fe features originate in the accretion curtain, they
will show periodic variations over the neutron star pulse period. Tentative
variability in the pulse-resolved broad Fe K line energy was previously
detected by Fürst et al. (2013) using NuSTAR data (Fig. 9 of their paper). The
Fe K line normalization is also variable over the pulse phase (Vasco et al.,
2013). We will test this hypothesis with a pulse-resolved spectral analysis of
the August 2020 XMM-Newton dataset, in which such variation could be detected
in more detail at a much higher statistical significance (thanks to the
superior spectral resolution of EPIC pn). This will be addressed in a future
publication.

##  7 Conclusions

To sum up, our analysis of the extensive XMM-Newton and Chandra observations
suggests that various emission lines detected in the High State Her X-1 X-ray
spectrum originate in physically very distinct regions of the accretion flow.
Our interpretation of their origin is summarized in a schematic in Fig. 1. Our
conclusions are as follows:

  * •

The narrow emission lines of Fe I, O VII(i) and N VI(i), with velocity widths
of $500-2000$ km/s likely originate in the atmosphere (ADC) above the outer
parts of the warped accretion disk, roughly $10^{5}$ RG away from the neutron
star. These lines show significantly larger widths than the same transitions
observed during the Low State, indicating that during the High State we are
able to observe the inner parts of the atmosphere closer to the neutron star,
while only its outskirts (at $10^{6}$ RG) are observable in the Low State.
Such findings agree with the precessing warped disk interpretation of the
long-term Her X-1 flux variability.

  * •

The medium-width emission lines of Fe XXV, O VIII and N VII, with velocity
widths of $3000-10000$ km/s likely also share a common origin. They may
originate at the boundary between the inner accretion disk and the
magnetosphere of the neutron star, about $10^{3}$ RG away from the compact
object.

  * •

The broad emission lines, denoted Fe K and Fe L, show widths of $0.1-0.2$c,
and must originate closer to the neutron star than the inner accretion disk
edge. Their luminosities strongly correlate with the observed luminosity of
Her X-1, and hence they are most likely produced by reprocessing of the
primary continuum by the accretion curtain of the neutron star, at distances
of $\sim 10^{2}$ RG from the star. The relativistic motion of the accretion
curtain material, infalling along the rotating magnetic field lines naturally
imprints the observed extreme line widths.

Support for this work was provided by the National Aeronautics and Space
Administration through the Smithsonian Astrophysical Observatory (SAO)
contract SV3-73016 to MIT for Support of the Chandra X-Ray Center and Science
Instruments. PK and EK acknowledge support from NASA grants 80NSSC21K0872 and
DD0-21125X. RB acknowledges support by NASA under Award Number 80GSFC21M0002.
CRC acknowledges support by NASA through the Smithsonian Astrophysical
Observatory (SAO) Grant GO8-19011C to MIT, and by contract SV3-73016 to MIT
for Support of the Chandra X-Ray Center (CXC) and Science Instruments. This
work is based on observations obtained with XMM-Newton, an ESA science mission
funded by ESA Member States and USA (NASA).

##  Appendix A The gain shift of the EPIC-pn Timing mode spectra

During the combined XMM-Newton RGS and EPIC pn spectral analysis, we found a
problem with the energy gain of the EPIC pn (Timing mode) spectra. In general,
we find that the apparent photon energies in EPIC are too large, by as much as
100 eV at $6-7$ keV. The issue was initially discovered when fitting the
ionized wind absorption lines. While the absorption lines within the RGS band
aligned themselves perfectly, the Fe XXV/XXVI lines in the EPIC energy band
always appeared offset. This is shown in Fig. 14, where the photoionization
model is centred on the N VII, O VIII and Ne X lines in the RGS band but is
clearly offset for the Fe XXV/XXVI absorption.

Additionally, we found that while fitting the spectra of the absorption dips
of Her X-1, the Fe K edge at 7.1 keV was always systematically offset,
apparently blueshifted by $\sim$0.01c. Furthermore, the best-fitting energy of
the prominent (in dip spectra) narrow Fe I line was often around $6.45-6.48$
keV in the EPIC pn fits. Suspiciously, the Fe I line was always very close to
6.40 keV in all Chandra HETG spectra of Her X-1.

Figure 14: XMM-Newton RGS 1, RGS 2 and EPIC pn spectra from the High State
part of observation 0865440101. Only narrow energy bands around the strongest
disk wind absorption lines N VII, O VIII, Ne X and Fe XXVI are shown. The
first three subplots contain RGS 1 and RGS 2 data only, the fourth subplot
only contains EPIC pn data. The fourth subplot shows the effect of applying or
removing the EPIC pn gainshift correction, described in Appendix A. The Fe
XXVI residual can be correctly aligned with the residuals in RGS spectra by
applying a blueshift to the EPIC spectral model of about -0.016c (a linear
shift of 110 eV at 7 keV).

The findings above suggest a gain inaccuracy in the EPIC pn Timing mode. A
similar gain issue, but in other EPIC pn observing modes was previously
discussed by multiple authors, including Ponti et al. (2013), Cappi et al.
(2016), Zoghbi et al. (2019), Grafton-Waters et al. (2021) and Costanzo et al.
(2021) but with a significantly lower value of about 50 eV (in the same
‘blueshift’ direction as found here). The shift could be caused by uncorrected
charge transfer inefficiency (CTI) evolution in EPIC pn or alternatively by
optical loading, and appears to be significantly worse in Timing mode spectra.

A gain shift of the order of 100 eV at $6-7$ keV is detrimental to our ionized
absorption analysis as well as to our study of the Fe K emission lines. This
is due to the excellent counting statistics of our EPIC spectra which can
easily drive the spectral fits into completely wrong parameter spaces if the
data are not calibrated precisely. The shift therefore had to be corrected,
but it was not clear what the shift value is or whether it is constant at all,
even within the August 2020 XMM-Newton campaign. We found that the gain shift
during the absorption dipping states (where overall count rates are lower)
appeared lower than during the full High State observations with extreme count
rates.

If the gain is shifted, the incorrectly assigned energies of photons around
the instrumental edges such as Si K-edge (1.8 keV), Au L-edge (2.2 keV) and Au
M-edge (11.9 keV) should create residuals in the source spectra. We indeed
observe very strong residuals exactly at the Au M-edge, shown in Fig. 15, in
all three August 2020 XMM-Newton observations. The residuals can be removed
from the spectra by shifting the photon energies by $100-200$ eV (exact value
depends on the observation).

We first attempted to correct the issue by using the gain function in xspec,
which allows to shift the energy scale of a spectrum with a multiplicative and
a linear parameter. We used the residuals around the positions of the
instrumental edges and fitted for the gain shift using both multiplicative and
linear parameters, following the approach described in XMM-CAL-
SRN-0369222xmmweb.esac.esa.int/docs/documents/CAL-SRN-0369-0-0.pdf.
Unfortunately, this did not produce satisfactory results with a significant
gain shift variation and the shift values were changing depending on the
spectral model chosen (both a multiplicative and additive shift was required).
The results of the gain fitting using this method could be affected by
residual pile-up above 10 keV (which we did not correct for) as well as
residual pile-up around 2 keV. The residual pile-up effects around 2 keV
should not be significant but the count rate at these energies is very high,
leading to extremely small errorbars. Finally, there are possibly real,
physical emission features from Si and S in this energy band. As a result, any
inaccuracies made in the 2 keV band (further compounded by the limited EPIC
spectral resolution at these energies) can have detrimental effects on our
ability to correct the gain shift in the Fe K band at $6-7$ keV.

Figure 15: EPIC pn $9-13$ keV spectra of the Her X-1 High flux states from the
three August 2020 XMM-Newton observations. The spectra are fitted with simple
powerlaw models, and all show strong residuals around the instrumental Au
M-edge (11.9 keV, blue dotted line), indicating a significant gain shift at
these energies.

Therefore, due to the issues described above, as well as due to issues with
exporting our photoionization model pion into xspec, we decided to simplify
our gain correction approach and perform it completely within spex. Our method
is similar to the gain shift correction of the EPIC pn Timing mode
observations of Cyg X-1 by Duro et al. (2016). We added a simple Doppler shift
component (reds in spex) to the full spectral model, . The value of the shift
(in the units of speed of light, $c$) for RGS 1 and RGS 2 spectra was fixed to
0, but was a free parameter for EPIC pn spectra (in the simultaneous RGS/EPIC
fit) and the parameter was explicitly fitted for. This way we did not fit for
the position of the instrumental edges as we did using the gain function in
xspec, since our gainshift correction was part of the final spectral model.
Therefore the EPIC spectrum had to be anchored by certain spectral model
parameters. We chose to freeze the energies of the Fe I and Fe XXV lines to
6.4 and 6.67 keV, respectively, as they appeared stable in all Chandra HETG
observations of Her X-1. Furthermore, the blueshift of the photoionization
pion grids was always anchored by the strong narrow absorption lines in the
RGS spectra (N VII, O VIII and Ne X), thus fixing the positions of the Fe XXV
and XXVI absorption lines, and anchoring the EPIC spectrum with respect to the
RGS spectra. We accounted for the gain shift using only one multiplicative
parameter (ignoring any additive gain shifts), but the best-fitting solution
was centred on the crucial Fe K band where many of our spectral components
have discrete line features. Any inaccuracies outside of the Fe K band should
not be critical to our modelling (our EPIC pn model outside the Fe K band is
just a broad Comptonization shape).

We track the best-fitting gainshift parameter for all the High State
observations or observational segments, but we do not find an obvious
correlation between the parameter and other observational properties such as
EPIC pn count rate (pile-up corrected or uncorrected), the observed Her X-1
luminosity or super-orbital phase. In Fig. 16, we show the gainshift value
versus the raw pn count rate (uncorrected for pile-up). In general, the shift
appears to vary between -0.01c and -0.02c for most observations but with a
couple of outliers. The lower luminosity observations (0783770501 and the
first segment of 0865440101) appear to need smaller shifts. We also note that
the two oldest observations, 0134120101 and 0153950301, from 2001 and 2002 do
not require large shifts despite high EPIC pn count rates. The remaining
observations or segments do not show any strong trends. Therefore, it is
unclear what is the main driver for the gain variation.

Figure 16: Gainshift value (as a fraction of the speed of light) for each
observation or observation segment versus raw EPIC pn count rate (no pile-up
corrections applied). The August 2020 XMM-Newton observations are shown in
black, older archival observations are in blue. We highlight the two oldest
observations carried out in 2001 and 2002.

##  Appendix B Instrumental residuals in RGS or interstellar gas/dust?

Figure 17: RGS spectra (stacked for visual purposes) from observation
0865440501 around the excluded 22.25-24 Å region. Two spectral models are
shown and the most important model features are denoted with labels. The green
model includes the problematic region while the blue model ignores it. The
green model clearly over-predicts the broadening of the medium-width O VIII
and N VII features. The position of the possible instrumental feature is
indicated by the arrow.

We further found strong residuals in the $22.5-23.5$ Å range in the RGS
spectra. Thanks to the excellent data quality, they are highly statistically
significant. The residuals are located near the O K edge, where the absorption
lines of various ionization levels of O as well as ISM dust are commonly
found. We attempted to fit the features with a warm ISM plasma model as well
as with the amol ISM dust model (Pinto et al., 2010). However, we were not
able to reach good fits. A very high quality spectrum of this region (from the
fully stacked observation 0865440501, with roughly 80 ks of clean exposure) is
shown in Fig. 17. As is seen from the plot, the residuals do not appear as a
set of narrow absorption features that could be fitted with a range of O lines
of different ionizations. Furthermore, we note that the neutral absorption
column towards Her X-1 is very low, around $1\times 10^{20}$ cm-2 hence no
very strong warm ISM O lines are expected. Instead, what we observe is a broad
absorption feature around $\sim 22.75$ Å, with a possible emission residual
above 23.5 Å. These residuals broaden our phenomenological models of the O
VIII and N VII lines. Particularly the N VII feature often attempts to
describe the residuals just below 24 Å, resulting in a mis-fit of both O VIII
and N VII features (considering their widths are coupled). This has
detrimental effect on our ionized absorption fits in the later parts of the
super-orbital cycle, when the narrow disk wind lines are very weak.

Residuals in this energy range were present in multiple previous RGS studies
of the O K edge (e.g., Costantini et al., 2012; Pinto et al., 2013). They were
later discussed in particular by Psaradaki et al. (2020, Fig. 6), who
interpret them as instrumental features in RGS. Regardless of the origin of
the features, we decided to ignore the $22.25-24$ Å band from this study. The
band is unimportant for disk wind modelling considering there are no strong
highly ionized transitions between 22.5 and 24 Å. It is also unlikely to have
a strong impact on the modelling of the remaining included (phenomenological)
emission components.

##  Appendix C Summary of spectral fit components and parameters

Table 4: Summary of the XMM-Newton spectral fit components and parameters. All line widths are defined as FWHM. Component |  spex name | Parameter | Notes
---|---|---|---
Multiplicative components
EPIC pn gain correction | reds | z | Gain shift parameter |
Interstellar absorption | hot | nh | Column density |
Disk wind absorption | pion | nh | Column density |
|  | $\log\xi$ | Ionization parameter |
|  | v | Velocity width |
|  | z | Outflow velocity |
Continuum components
Primary Comptonization | comt | norm | Normalization |
|  | $T_{0}$ | Seed temperature |
|  | $T_{1}$ | Electron temperature |
|  | $\tau$ | Optical depth |
Hotter blackbody | mbb | norm | Normalization |
|  | T | Temperature |
Cooler blackbody | bb | norm | Normalization |
|  | T | Temperature | fixed to 0.05 keV
Broad emission lines
Fe K | gaus | norm | Normalization |
|  | e | Energy | lower limit of 6.4 keV
|  | fwhm | Line width |
Fe L | gaus | norm | Normalization |
|  | e | Energy |
|  | fwhm | Line width |
Medium-width emission lines
Fe XXV | gaus | norm | Normalization |
|  | e | Energy | fixed to 6.67 keV
|  | fwhm | Line width |
O VIII | gaus | norm | Normalization |
|  | w | Wavelength |
|  | awid | Line width |
N VII | gaus | norm | Normalization |
|  | w | Wavelength |
|  | awid | Line width | velocity width coupled to O VIII
Narrow emission lines
Fe I | gaus | norm | Normalization |
|  | e | Energy | fixed to 6.4 keV
|  | fwhm | Line width | fixed to 0.05 keV
O VII(i) | gaus | norm | Normalization |
|  | w | Wavelength |
|  | awid | Line width | upper limit of 0.5 Å
N VI(i) | gaus | norm | Normalization |
|  | w | Wavelength |
|  | awid | Line width | upper limit of 0.5 Å

## References

  * Arnaud (1996) Arnaud, K. A. 1996, in Astronomical Society of the Pacific Conference Series, Vol. 101, Astronomical Data Analysis Software and Systems V, ed. G. H. Jacoby & J. Barnes, 17
  * Asami et al. (2014) Asami, F., Enoto, T., Iwakiri, W., et al. 2014, PASJ, 66, 44, doi: 10.1093/pasj/psu005
  * Bachetti et al. (2014) Bachetti, M., Harrison, F. A., Walton, D. J., et al. 2014, Nature, 514, 202, doi: 10.1038/nature13791
  * Bahcall & Bahcall (1972) Bahcall, J. N., & Bahcall, N. A. 1972, ApJ, 178, L1, doi: 10.1086/181070
  * Brumback et al. (2021) Brumback, M. C., Hickox, R. C., Fürst, F. S., et al. 2021, ApJ, 909, 186, doi: 10.3847/1538-4357/abe122
  * Canizares et al. (2005) Canizares, C. R., Davis, J. E., Dewey, D., et al. 2005, PASP, 117, 1144, doi: 10.1086/432898
  * Cappi et al. (2016) Cappi, M., De Marco, B., Ponti, G., et al. 2016, A&A, 592, A27, doi: 10.1051/0004-6361/201628464
  * Cash (1979) Cash, W. 1979, ApJ, 228, 939, doi: 10.1086/156922
  * Cheng et al. (1995) Cheng, F. H., Vrtilek, S. D., & Raymond, J. C. 1995, ApJ, 452, 825, doi: 10.1086/176351
  * Choi et al. (1994) Choi, C. S., Nagase, F., Makino, F., Dotani, T., & Min, K. W. 1994, ApJ, 422, 799, doi: 10.1086/173772
  * Costantini et al. (2012) Costantini, E., Pinto, C., Kaastra, J. S., et al. 2012, A&A, 539, A32, doi: 10.1051/0004-6361/201117818
  * Costanzo et al. (2021) Costanzo, D., Dadina, M., Vignali, C., et al. 2021, arXiv e-prints, arXiv:2112.09096.  https://arxiv.org/abs/2112.09096
  * Davidsen et al. (1972) Davidsen, A., Henry, J. P., Middleditch, J., & Smith, H. E. 1972, ApJ, 177, L97, doi: 10.1086/181060
  * Deeter et al. (1981) Deeter, J. E., Boynton, P. E., & Pravdo, S. H. 1981, ApJ, 247, 1003, doi: 10.1086/159110
  * den Herder et al. (2001) den Herder, J. W., Brinkman, A. C., Kahn, S. M., et al. 2001, A&A, 365, L7, doi: 10.1051/0004-6361:20000058
  * Duro et al. (2016) Duro, R., Dauser, T., Grinberg, V., et al. 2016, A&A, 589, A14, doi: 10.1051/0004-6361/201424740
  * Fabian (1973) Fabian, A. C. 1973, Nature, 244, 212, doi: 10.1038/244212a0
  * Fabian et al. (1989) Fabian, A. C., Rees, M. J., Stella, L., & White, N. E. 1989, MNRAS, 238, 729, doi: 10.1093/mnras/238.3.729
  * Fabian et al. (2009) Fabian, A. C., Zoghbi, A., Ross, R. R., et al. 2009, Nature, 459, 540, doi: 10.1038/nature08007
  * Fruscione et al. (2006) Fruscione, A., McDowell, J. C., Allen, G. E., et al. 2006, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 6270, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, ed. D. R. Silva & R. E. Doxsey, 62701V, doi: 10.1117/12.671760
  * Fürst et al. (2013) Fürst, F., Grefenstette, B. W., Staubert, R., et al. 2013, ApJ, 779, 69, doi: 10.1088/0004-637X/779/1/69
  * Fürst et al. (2016) Fürst, F., Walton, D. J., Harrison, F. A., et al. 2016, ApJ, 831, L14, doi: 10.3847/2041-8205/831/2/L14
  * George & Fabian (1991) George, I. M., & Fabian, A. C. 1991, MNRAS, 249, 352, doi: 10.1093/mnras/249.2.352
  * Gerend & Boynton (1976) Gerend, D., & Boynton, P. E. 1976, ApJ, 209, 562, doi: 10.1086/154751
  * Ghosh & Lamb (1979) Ghosh, P., & Lamb, F. K. 1979, ApJ, 232, 259, doi: 10.1086/157285
  * Giacconi et al. (1973) Giacconi, R., Gursky, H., Kellogg, E., et al. 1973, ApJ, 184, 227, doi: 10.1086/152321
  * Giacconi et al. (1972) Giacconi, R., Murray, S., Gursky, H., et al. 1972, ApJ, 178, 281, doi: 10.1086/151790
  * Grafton-Waters et al. (2021) Grafton-Waters, S., Branduardi-Raymont, G., Mehdipour, M., et al. 2021, A&A, 649, A162, doi: 10.1051/0004-6361/202039022
  * Hemphill et al. (2021) Hemphill, P. B., Schulz, N. S., Marshall, H. L., & Chakrabarty, D. 2021, ApJ, 920, 142, doi: 10.3847/1538-4357/ac0ade
  * HI4PI Collaboration et al. (2016) HI4PI Collaboration, Ben Bekhti, N., Flöer, L., et al. 2016, A&A, 594, A116, doi: 10.1051/0004-6361/201629178
  * Hickox et al. (2004) Hickox, R. C., Narayan, R., & Kallman, T. R. 2004, ApJ, 614, 881, doi: 10.1086/423928
  * Huenemoerder et al. (2011) Huenemoerder, D. P., Mitschang, A., Dewey, D., et al. 2011, AJ, 141, 129, doi: 10.1088/0004-6256/141/4/129
  * Israel et al. (2017) Israel, G. L., Belfiore, A., Stella, L., et al. 2017, Science, 355, 817, doi: 10.1126/science.aai8635
  * Jaisawal et al. (2019) Jaisawal, G. K., Wilson-Hodge, C. A., Fabian, A. C., et al. 2019, ApJ, 885, 18, doi: 10.3847/1538-4357/ab4595
  * Jansen et al. (2001) Jansen, F., Lumb, D., Altieri, B., et al. 2001, A&A, 365, L1, doi: 10.1051/0004-6361:20000036
  * Ji et al. (2009) Ji, L., Schulz, N., Nowak, M., Marshall, H. L., & Kallman, T. 2009, ApJ, 700, 977, doi: 10.1088/0004-637X/700/2/977
  * Jimenez-Garate et al. (2002a) Jimenez-Garate, M. A., Hailey, C. J., den Herder, J. W., Zane, S., & Ramsay, G. 2002a, ApJ, 578, 391, doi: 10.1086/342348
  * Jimenez-Garate et al. (2002b) Jimenez-Garate, M. A., Raymond, J. C., & Liedahl, D. A. 2002b, ApJ, 581, 1297, doi: 10.1086/344364
  * Jimenez-Garate et al. (2005) Jimenez-Garate, M. A., Raymond, J. C., Liedahl, D. A., & Hailey, C. J. 2005, ApJ, 625, 931, doi: 10.1086/426702
  * Kaastra & Barr (1989) Kaastra, J. S., & Barr, P. 1989, A&A, 226, 59
  * Kaastra et al. (1996) Kaastra, J. S., Mewe, R., & Nieuwenhuijzen, H. 1996, in UV and X-ray Spectroscopy of Astrophysical and Laboratory Plasmas, 411–414
  * Katz (1973) Katz, J. I. 1973, Nature Physical Science, 246, 87, doi: 10.1038/physci246087a0
  * Koliopanos & Vasilopoulos (2018) Koliopanos, F., & Vasilopoulos, G. 2018, A&A, 614, A23, doi: 10.1051/0004-6361/201731623
  * Koliopanos et al. (2017) Koliopanos, F., Vasilopoulos, G., Godet, O., et al. 2017, A&A, 608, A47, doi: 10.1051/0004-6361/201730922
  * Kosec et al. (2020) Kosec, P., Fabian, A. C., Pinto, C., et al. 2020, MNRAS, 491, 3730, doi: 10.1093/mnras/stz3200
  * Kosec et al. (2021) Kosec, P., Pinto, C., Reynolds, C. S., et al. 2021, MNRAS, 508, 3569, doi: 10.1093/mnras/stab2856
  * Krimm et al. (2013) Krimm, H. A., Holland, S. T., Corbet, R. H. D., et al. 2013, ApJS, 209, 14, doi: 10.1088/0067-0049/209/1/14
  * Kuster et al. (2005) Kuster, M., Wilms, J., Staubert, R., et al. 2005, A&A, 443, 753, doi: 10.1051/0004-6361:20042355
  * Lamb et al. (1973) Lamb, F. K., Pethick, C. J., & Pines, D. 1973, ApJ, 184, 271, doi: 10.1086/152325
  * Leahy & Wang (2020) Leahy, D., & Wang, Y. 2020, ApJ, 902, 146, doi: 10.3847/1538-4357/abb611
  * Leahy (2015) Leahy, D. A. 2015, ApJ, 800, 32, doi: 10.1088/0004-637X/800/1/32
  * Leahy & Abdallah (2014) Leahy, D. A., & Abdallah, M. H. 2014, ApJ, 793, 79, doi: 10.1088/0004-637X/793/2/79
  * Leahy & Igna (2010) Leahy, D. A., & Igna, C. D. 2010, ApJ, 713, 318, doi: 10.1088/0004-637X/713/1/318
  * Ludlam et al. (2017) Ludlam, R. M., Miller, J. M., Bachetti, M., et al. 2017, ApJ, 836, 140, doi: 10.3847/1538-4357/836/1/140
  * Matsuoka et al. (2009) Matsuoka, M., Kawasaki, K., Ueno, S., et al. 2009, PASJ, 61, 999, doi: 10.1093/pasj/61.5.999
  * Mehdipour et al. (2016) Mehdipour, M., Kaastra, J. S., & Kallman, T. 2016, A&A, 596, A65, doi: 10.1051/0004-6361/201628721
  * Mewe & Schrijver (1978) Mewe, R., & Schrijver, J. 1978, A&A, 65, 99
  * Middleditch & Nelson (1976) Middleditch, J., & Nelson, J. 1976, ApJ, 208, 567, doi: 10.1086/154638
  * Miller et al. (2015) Miller, J. M., Kaastra, J. S., Miller, M. C., et al. 2015, Nature, 526, 542, doi: 10.1038/nature15708
  * Mushtukov et al. (2018) Mushtukov, A. A., Verhagen, P. A., Tsygankov, S. S., et al. 2018, MNRAS, 474, 5425, doi: 10.1093/mnras/stx2905
  * Ogilvie & Dubus (2001) Ogilvie, G. I., & Dubus, G. 2001, MNRAS, 320, 485, doi: 10.1046/j.1365-8711.2001.04011.x
  * Petterson (1975) Petterson, J. A. 1975, ApJ, 201, L61, doi: 10.1086/181942
  * Pinto et al. (2013) Pinto, C., Kaastra, J. S., Costantini, E., & de Vries, C. 2013, A&A, 551, A25, doi: 10.1051/0004-6361/201220481
  * Pinto et al. (2010) Pinto, C., Kaastra, J. S., Costantini, E., & Verbunt, F. 2010, A&A, 521, A79, doi: 10.1051/0004-6361/201014836
  * Pinto et al. (2020) Pinto, C., Walton, D. J., Kara, E., et al. 2020, MNRAS, 492, 4646, doi: 10.1093/mnras/staa118
  * Pinto et al. (2021) Pinto, C., Soria, R., Walton, D. J., et al. 2021, MNRAS, 505, 5058, doi: 10.1093/mnras/stab1648
  * Ponti et al. (2013) Ponti, G., Cappi, M., Costantini, E., et al. 2013, A&A, 549, A72, doi: 10.1051/0004-6361/201219450
  * Porquet & Dubau (2000) Porquet, D., & Dubau, J. 2000, A&AS, 143, 495, doi: 10.1051/aas:2000192
  * Pravdo et al. (1977) Pravdo, S. H., Becker, R. H., Boldt, E. A., et al. 1977, ApJ, 215, L61, doi: 10.1086/182478
  * Psaradaki et al. (2018) Psaradaki, I., Costantini, E., Mehdipour, M., & Díaz Trigo, M. 2018, A&A, 620, A129, doi: 10.1051/0004-6361/201834000
  * Psaradaki et al. (2020) Psaradaki, I., Costantini, E., Mehdipour, M., et al. 2020, A&A, 642, A208, doi: 10.1051/0004-6361/202038749
  * Ramsay et al. (2002) Ramsay, G., Zane, S., Jimenez-Garate, M. A., den Herder, J.-W., & Hailey, C. J. 2002, MNRAS, 337, 1185, doi: 10.1046/j.1365-8711.2002.06002.x
  * Remillard & McClintock (2006) Remillard, R. A., & McClintock, J. E. 2006, ARA&A, 44, 49, doi: 10.1146/annurev.astro.44.051905.092532
  * Roberts (1974) Roberts, W. J. 1974, ApJ, 187, 575, doi: 10.1086/152667
  * Ross & Fabian (2005) Ross, R. R., & Fabian, A. C. 2005, MNRAS, 358, 211, doi: 10.1111/j.1365-2966.2005.08797.x
  * Schandl (1996) Schandl, S. 1996, A&A, 307, 95
  * Schandl & Meyer (1994) Schandl, S., & Meyer, F. 1994, A&A, 289, 149
  * Schulz et al. (2001) Schulz, N. S., Chakrabarty, D., Marshall, H. L., et al. 2001, ApJ, 563, 941, doi: 10.1086/323988
  * Scott et al. (2000) Scott, D. M., Leahy, D. A., & Wilson, R. B. 2000, ApJ, 539, 392, doi: 10.1086/309203
  * Staubert et al. (2009) Staubert, R., Klochkov, D., & Wilms, J. 2009, A&A, 500, 883, doi: 10.1051/0004-6361/200911690
  * Staubert et al. (2007) Staubert, R., Shakura, N. I., Postnov, K., et al. 2007, A&A, 465, L25, doi: 10.1051/0004-6361:20077098
  * Strüder et al. (2001) Strüder, L., Briel, U., Dennerl, K., et al. 2001, A&A, 365, L18, doi: 10.1051/0004-6361:20000066
  * Tananbaum et al. (1972) Tananbaum, H., Gursky, H., Kellogg, E. M., et al. 1972, ApJ, 174, L143, doi: 10.1086/180968
  * Titarchuk (1994) Titarchuk, L. 1994, ApJ, 434, 570, doi: 10.1086/174760
  * Truemper et al. (1978) Truemper, J., Pietsch, W., Reppin, C., et al. 1978, ApJ, 219, L105, doi: 10.1086/182617
  * Vasco (2012) Vasco, D. 2012, PhD thesis, Eberhard Karls University of Tubingen, Germany.  http://nbn-resolving.de/urn:nbn:de:bsz:21-opus-63466
  * Vasco et al. (2013) Vasco, D., Staubert, R., Klochkov, D., et al. 2013, A&A, 550, A111, doi: 10.1051/0004-6361/201220181
  * Walton et al. (2018) Walton, D. J., Fürst, F., Heida, M., et al. 2018, ApJ, 856, 128, doi: 10.3847/1538-4357/aab610
  * Weisskopf et al. (2002) Weisskopf, M. C., Brinkman, B., Canizares, C., et al. 2002, PASP, 114, 1, doi: 10.1086/338108
  * Zane et al. (2004) Zane, S., Ramsay, G., Jimenez-Garate, M. A., Willem den Herder, J., & Hailey, C. J. 2004, MNRAS, 350, 506, doi: 10.1111/j.1365-2966.2004.07660.x
  * Zoghbi et al. (2019) Zoghbi, A., Miller, J. M., & Cackett, E. 2019, ApJ, 884, 26, doi: 10.3847/1538-4357/ab3e31