Observations of Her X-1 in low states during SRG/eROSITA all-sky survey
N. I. Shakura, D. A. Kolesnikov, P. S. Medvedev, R. A. Sunyaev, M. R. Gilfanov, K. A. Postnov, S. V. Molkov
AAstronomy & Astrophysics manuscript no. 40145corr © ESO 2021February 26, 2021
Observations of Her X-1 in low states during
SRG /eROSITA all-skysurvey
N. I. Shakura , (cid:63) , D. A. Kolesnikov , P. S. Medvedev , , R. A. Sunyaev , , M. R. Gilfanov , , K. A. Postnov , andS. V. Molkov Moscow State University, Sternberg Astronomical Institute, 119234 Moscow, Russia Kazan Federal University, 420008 Kazan, Russia Space Research Institute of the Russian Academy of Sciences, 117997 Moscow, Russia Max-Planck-Institut für Astrophysik (MPA), Karl-Schwarzschild-Str 1, D-85741 Garching, GermanyFebruary 26, 2021
ABSTRACT eROSITA (extended ROentgen Survey with an Imaging Telescope Array) instrument onboard the Russian-German ‘Spectrum-Roentgen-Gamma’ (SRG) mission observed the Her X-1 / HZ Her binary system in multiple scans over the source during the firstand second
SRG all-sky surveys. Both observations occurred during a low state of the X-ray source when the outer parts of the accre-tion disk blocked the neutron star from view. The orbital modulation of the X-ray flux was detected during the low states. We arguethat the detected X-ray radiation results from scattering of the emission of the central source by three distinct regions: (a) an opticallythin hot corona with temperature ∼ (2 − × K above the irradiated hemisphere of the optical star; (b) an optically thin hot haloabove the accretion disk; and (c) the optically thick cold atmosphere of the optical star. The latter region e ff ectively scatters photonswith energies above 5–6 keV. Key words.
X-rays: binaries – X-rays: individuals: Her X-1
1. Introduction
HZ Her / Her X-1 is an intermediate-mass X-ray binary consist-ing of an accreting neutron star with mass m x = . M (cid:12) and spinperiod P x ≈ .
24 s, and a donor star with mass m o = . M (cid:12) (Tananbaum et al. 1972). The light curve of HZ Her / Her X-1demonstrates clear eclipses because of the high inclination of thebinary system to the line of sight, about 90°. The optical star HZHer fills its Roche lobe (Crampton 1974) and shows a significantmodulation with an orbital period of P b = . ff ectof the donor star (Lyutyi et al. 1973), as was first found from theinspection of archival photo-plates (Cherepashchuk et al. 1972).The reflection e ff ect from the heated atmosphere of HZ Her wasalso observed in the extreme ultraviolet by the EUVE (ExtremeUltraviolet Explorer) satellite (Leahy & Marshall 1999; Leahy2000, 2003; Leahy & Dupuis 2010) and by the
Astron satellite(She ff er et al. 1992).Soon after the discovery of the X-ray source in 1971(Schreier et al. 1972; Tananbaum et al. 1972), a 35-day mod-ulation of the X-ray flux was discovered by the Uhuru satellite(Giacconi et al. 1973). For some time, only the Main-on state ofthe 35-day cycle was known. Using the data obtained by
Coper-nicus and
Ariel V satellites, Fabian et al. (1973) and Cooke &Page (1975), respectively, discovered a lower-amplitude Short-on state. Later on, Jones & Forman (1976) analyzed the archive
Uhuru observations and revealed the presence of the "Short-on"state in the data. Therefore, the 35-day X-ray cycle of Her X-1 comprises four states: (1) the Main-on lasting approximatelyseven orbits with the highest X-ray flux; (2) the first low state (cid:63) [email protected] lasting approximately four orbits; (3) the Short-on lasting ap-proximately four orbits with the X-ray flux about three times aslow as in the Main-on; and (4) the second low-state lasting ap-proximately four orbits (see, e.g., Shakura et al. (1998) for moredetails and Leahy & Wang (2020) for a recent update). The 35-day cycle is associated with a tilted, retrograde precessing accre-tion disk. In the middle of the Main-on and Short-on, the disk ismaximum open to the observer’s view, and the X-ray source isvisible. During the low states, the outer parts of the tilted diskblock the X-ray source from the observer’s view. The analysis ofa large amount of optical photometric data for HZ Her (Boyntonet al. 1973; Boynton 1978) supports the presence of such a disk.However, this interpretation is not unique. For example, in themodel elaborated by Leahy (2002), a geometrically thin twisteddisk with a thick inner ring and extended central X-ray source isused to explain the ASM / RXTE (All-Sky Monitor of the RossiX-ray Timing Explorer) light curve. This model was also appliedto explain orbital modulation of the extreme ultraviolet emissionat low states of Her X-1 observed by the
EUVE satellite (Leahy2003). Recent joint observations of Her X-1 by XMM-
Newton (X-ray Multi-Mirror Mission) and NuSTAR (Nuclear Spectro-scopic Telescope Array) telescopes confirmed the presence ofthe warped, retrograde precessing accretion disk Brumback et al.(2021).In 1985, using observations from
EXOSAT (The EuropeanX-ray Observatory SATellite), Parmar et al. (1985) for the firsttime detected X-ray flux during both the first and second lowstates. X-ray flux detected by the RXTE / ASM observations ofHer X-1 in the low state (Fig. 4, bottom panel, in Scott & Leahy(1999)) does not show significant orbital modulation outsideX-ray eclipses. More detailed RXTE / PCA (RXTE Proportional
Article number, page 1 of 10 a r X i v : . [ a s t r o - ph . H E ] F e b & A proofs: manuscript no. 40145corr
Fig. 1.
Swift / BAT X-ray flux of Her X-1 as a function of time (Krimmet al. 2013). Vertical lines indicate the
SRG / eROSITA observations ofHer X-1. Counter Array) observations of Her X-1 in the low state startingat MJD 52261.52 measured orbital modulation of the flux (˙Inam& Baykal 2005; Leahy & Igna 2011; Abdallah & Leahy 2015).In 2002,
Chandra detected Her X-1 during its low-state (Ji et al.2009). In 2017, a low-state preceding a turn-on of Her X-1 wasobserved with the
AstroSat satellite (Leahy & Chen 2019).Mavromatakis (1993) analyzed a Short-on of Her X-1 usingthe data obtained by the
ROSAT (ROentgen SATellite) all-sky X-ray survey. Since 2019, a new, deeper all-sky X-ray survey hasbeen carrying out by
SRG / eROSITA mission from the vicinityof the Earth-Moon L point (see Predehl et al. (2020) for a de-scription of the SRG / eROSITA telescope).Her X-1 was observed several times at the beginning ofMarch and September 2020. The period of rotation of the SRG / eROSITA satellite is about four hours. The spin axis of the satel-lite precesses around the direction to the ecliptic poles with a rateof about 1° d − . In the sky scans, Her X-1 was seen in the fieldof view of the SRG / eROSITA telescope during 14–16 four-hourintervals, which amounts to 1.5 orbital periods of Her X-1. Allthe observations of Her X-1 happened during the low state of theX-ray source; see Fig.1.The SRG / eROSITA telescope has detected a clear signalfrom the source modulated with the orbital period of the Her X-1 / HZ Her binary. Near the orbital phase zero (the eclipse center),the X-ray flux was minimal. Outside the minimum, the X-rayflux was observed to vary with the orbital phase.In the present paper, we analyze and model the X-ray fluxvariation from Her X-1 detected by the
SRG / eROSITA in thelow state of the source. The structure of the paper is as follows. InSection 2, SRG / eROSITA observations and their spectral mod-eling are presented. In Section 3, scattering of X-rays in a hotcorona above the irradiated atmosphere of HZ Her is describedand calculated. Orbital modulation in the low states of Her X-1observed by SRG / eROSITA are computed in Section 4. In Sec-tion 5 we discuss X-ray reflection in the cold photosphere of HZHer and in Section 6 we formulate our main results. In Appen-dices A and B, we provide details of the calculation of X-rayscattering in a hot optically thin corona above the illuminatedpart and photosphere of the optical star, respectively.
2. X-ray data
In the first all-sky survey, the position of Her X-1 was scanned bythe
SRG observatory 14 times with a four-hour cadence duringMarch 5–7, 2020. In these observations, we used data from sixeROSITA cameras, excluding the fifth telescope module (TM).The net count rate for the source was 3 . ± .
08 cts / s in the0.3–10 keV energy band with a total exposure time of 570 sec.During the second all-sky survey, the source was observed with SRG / eROSITA on Sep. 4–6, 2020 in a similar manner. All sevenTMs were watching the source simultaneously, and the total ex-posure time was 588 sec. The net count rate for the source wasobtained at the level of 5 . ± . / s in the 0.3–10 keV energyband.The eROSITA raw data were processed by the calibrationpipeline based on the eROSITA Science Analysis Software Sys-tem (eSASS) and using pre-flight calibration data. We extractedthe source spectra and light curves using a circular region witha radius of 80 arcsec (corresponding to 99% encircled energy)centered on the source position. An annulus region with innerand outer radii of 100 arcsec and 200 arcsec around Her X-1 waschosen for the background extraction. We also exclude a circularpart with a 15 arcsec radius masking a faint source in the back-ground extraction area.Although the source is quite bright, it is not bright enoughfor the photon pile-up to become important. Indeed, the sourcecount rate did not exceed the nominal ∼ ≈ . / s wasachieved in TM5 during the second sky survey, which is com-patible with the above threshold. We further checked the sourceimage and spectrum for the pile-up signatures and did not findany. We thus conclude that the source is not subject to significantpile-up e ff ects.The spectra were extracted for the total exposure in each sur-vey and for each source passage by SRG / eROSITA (14 spectraper survey). We fitted spectra in the 0.3–8 keV energy range. Forthe final spectral analysis (Table 1, Fig. 2–4) we used combineddata of all operational telescope modules. The spectra were nextrebinned so as to ensure a minimum of five counts per energybin by means of the standard tool GRPPHA . We then used theC-statistic (Cash 1979) with correction for the background sub-traction (“W-statistic”) in the
XSPEC package (version 12.11.0,Arnaud 1996) to analyze the data.
We start with analyzing the spectra averaged over all passagesin each survey. The X-ray spectra obtained from the first andsecond all-sky surveys have similar shapes (see Fig. 2), with nor-malization being higher during the scans in September 2020. Thespectra can be characterized by a complex shape at low energies,an almost flat continuum above 2 keV, and a hint of the presenceof emission lines.Extensive studies of Her X-1 at di ff erent phases of the 35-day cycle by di ff erent X-ray satellite have established the broad-band continuum emission model involving, in particular, a ther-mal blackbody component with a temperature of ≈ . ff at higher energies (up to ∼
200 keV,see McCray et al. 1982a; Leahy et al. 1994; Leahy 1995; Leahy& Yoshida 1995; Oosterbroek et al. 1997; Leahy 1997; dal Fi-ume et al. 1998; Leahy 2001; Kuster et al. 2005; Klochkov et al.
Article number, page 2 of 10. I. Shakura et al.: Her X-1 during
SRG / eROSITA survey ≈
200 sec observations, we usea simplified model to describe the continuum emission by com-bining a blackbody component and a power law. We also applythe
TBabs model (Wilms et al. 2000) with the neutral hydro-gen column density fixed at the Galactic value in the direction toHer X-1, N H = . × cm − , obtained from the HI4PI map(HI4PI Collaboration et al. 2016).In addition to the complex continuum, the spectrum ofHer X-1 shows a wealth of X-ray lines. The first spectral fea-tures were discovered in observations by BeppoSAX (Satelliteper Astronomia X), which revealed a broad Fe L line complexat 0.9–1 keV, the Fe K line complex at 6.4 keV (Oosterbroeket al. 1997; McCray et al. 1982a; Oosterbroek et al. 2001), andalso a cyclotron absorption feature at ∼
40 keV (see Truemperet al. (1978), Staubert et al. (2016), Staubert et al. (2017), andStaubert et al. (2020) for a recent discussion). The low-energyX-ray lines were then studied in depth by Jimenez-Garate et al.(2005) and Ji et al. (2009) using high-resolution gratings spec-tra from
Chandra , which resolved a dozen recombination linesoriginating from photoionized gas emission.
In this paper, we put forward a model that attributes the pho-toionized component to the emission from a hot optically thincorona above the donor star (see Section 3 and Fig. 3). To investi-gate the contribution of this component to the Her X-1 spectrumin the low state, we use
XSTAR ’s photemis (v. 2.54, Kallman &Bautista 2001) semi-analytic model in XSPEC . Using
XSTAR , wecalculate the ion fractions and atomic level populations file to re-produce relevant physical conditions. In
XSTAR run, we assumea spherical geometry of the wind, set the gas density to 10 cm − , and fix elemental abundances to the solar values whichare defined in XSTAR relative to Grevesse et al. (1996). For theilluminating source, we set the luminosity 2 × erg / s and apower-law spectrum with photon index Γ =
1, which roughlycorresponds to the central source in Her X-1. We set the initialgas temperature at T init = K and allow
XSTAR to calculateit assuming the thermal equilibrium of gas. Due to insu ffi cientcounts, we do not try to fit the ionization parameter value and fixit at ξ = L i / nR = L i is the ionizingluminosity, R is distance from the ionizing source, and n is thegas number density. This photoionization parameter value fol-lows from theoretical calculations of induced stellar wind fromX-ray illuminated atmosphere of HZ Her (Basko & Sunyaev1973; Basko et al. 1974). Then the equilibrium gas temperatureis T eq ≈ × K.We thus fit the broadband (0.3–8 keV) spectra using the com-bined model which reads in
XSPEC as TB abs ( bbodyrad + pow - erlaw + photemis ). Figure 2 shows the best-fit model and thecontribution of various components to the eROSITA spectra.The best-fit parameters and the 90% confidence ranges are listedin Table 1. We found no evidence for the photoionization compo-nent in the spectrum from the first survey with a 90% upper limiton its emission measure at 8 × cm − . For the second survey,we found a marginal improvement of the fit ( δ C-statistic = − δ d.o.f. = + ≈ . σ . We found no significant variation in the blackbody tem-perature and normalization between the averaged spectra fromthe first and the second surveys. The found best-fit values are in Table 1.
Best-fit parameters obtained from fitting to the survey-averaged energy spectrum of Her X-1 from the first and the second
SRG all-sky surveys. Errors are quoted at the 90% confidence level.
Parameters First survey Second survey N H , cm − . × ∗ . × ∗ kT bb , eV 103 + − ± R bb a , km 41 . + . − . . + . − . Γ pow . + . − . . + . − . K pow b , 2 . ± . × − . + . − . × − ph keV − cm − s − EM photemis c , cm − < × . + . − . × ξ ∗ ∗ C-stat / d.o.f. 277 /
237 290 / Notes.
We use typical interstellar abundances by Wilms et al. (2000)for the tbabs component, while for the photemis component elemen-tal abundances are fixed to the solar values relative to Grevesse et al.(1996). The parameters R bb and EM photemis are calculated assuming thedistance of 6.6 kpc to Her X-1(Reynolds et al. 1997). ( a ) The size of the thermal region derived from the thermal black-body component normalization: R km = √ norm bb × D . ( b ) Normaliza-tion of the power-law component at 1 keV. ( c ) The emission measureof the gas obtained from the photemis best-fit normalization: EM = π D × norm photemis ( * ) Parameter is fixed during the fit. good agreement with the
Chandra results for observations in thelow state of Her X-1 (Ji et al. 2009).
Due to a minor contribution from the photoionized emission (seeFig. 2), to construct the X-ray orbital light curve during the firstand the second survey, we simplify the spectral model by elim-inating the photoionization component. We also fix the black-body component temperature at 0.1 keV (see Table 1). Thus, thebroadband spectral model in the low state of Her X-1 can befitted by three parameters: the power-law and blackbody com-ponent normalizations and the power-law photon index. The ob-tained model makes it possible to investigate the evolution ofthe continuum components during individual scans, for whichthe total number of counts is low, namely about 100. We notethat the X-ray spectrum of Her X-1 was described by the black-body and power-law components for the first time by McCrayet al. (1982a) using the
Einstein observations. The blackbodyradiation is emitted by the inner parts of the accretion disk. Thepower-law tail is produced near the surface of the accreting mag-netized neutron star. During the low state, the accretion disk andthe inner parts of the neutron star are obscured from the view ofthe observer by the outer parts of the warped disk. Both spectralcomponents are observed directly at the Main-on and Short-onstates of the 35-day cycle.The obtained X-ray flux of the power-law component, domi-nating in the energy range 0.2–8 keV, as a function of time duringthe first and the second
SRG all-sky surveys is shown in Fig. 4by dots with error bars. The power-law component dominatesover the blackbody one above ∼ . Article number, page 3 of 10 & A proofs: manuscript no. 40145corr −2 −1 N o r m a li z ed c oun t s , s − , k e v − Energy, keV R a t i o −2 −1 Energy, keV Fig. 2. eROSITA spectra of Her X-1 obtained during the first and the second sky surveys (left and right panels, respectively). The solid black lineshows the best-fit model (see Table 1), and the green dashed line shows the contribution from the proper emission of hot photoionized plasma (notdetected in the first survey). Thin red and blue lines show the blackbody and power-law components, respectively. The bottom panels show theratio of the data to the folded model. The visible excess in the residuals at higher energies is due to the Fe K complex and possible reflection fromthe cold photosphere of the optical star, which are unaccounted for in the spectral modeling (see Section 5).
3. Scattering in a hot optically thin corona abovethe donor star
Basko & Sunyaev (1973) andBasko et al. (1974) were the first toshow that, in an X-ray binary with an optical donor star, abovethe irradiated side of the donor, a hot ( T ∼ (2 − × K)corona is formed that is optically thin to scattering free elec-trons ( τ s (cid:46) . − . n ∼ cm − . The absorption optical depth in the corona isnegligible ( τ a (cid:28) Ξ is defined as Ξ =
Fnck B T = L x π r nck B T = ξ π ck B T ≈ ξ T . (1)The value of Ξ in the corona is about 5–10. Along with thermallystable states, there are thermally nonstable states of the corona(see, e.g., Mehdipour et al. 2016). Therefore, we expect thermalstratification of the coronal plasma and hence time variations ofthe scattered X-ray flux, which is indeed observed (see Fig. 4).Further away from the stellar surface, the corona is transformedinto a hot stellar wind with a temperature of about 10 K.In Appendix A, the scattered X-ray flux from such a coronailluminated by a point-like central X-ray source is computed an-alytically using the single scattering approximation. The calcu-lations presented in Appendix A suggest that the scattered X-rayluminosity of the corona is about 2 × erg s − . The proper X-ray luminosity of the hot photoionized coronal plasma is muchsmaller, of the order of 3 × erg s − . The characteristic timeof emission is approximately some tens of seconds.In the case of Her X-1, accurate computation of scatteringfrom the hot corona above the X-ray-illuminated atmosphere ofHZ Her requires taking into account the shadow from the tilted,twisted accretion disk around the neutron star and the compli-cated geometry of the corona. In our calculations, we use severalsimplifying approximations.1. The corona is assumed to have a constant density and tem-perature; its size is equal to that of exponential atmosphere, H = k B T R / m p GM . Depending on the temperature, H ∼ . . R . The corona is virtually absent inside the X-rayshadow produced by a warped accretion disk around the cen-tral source; see Fig. 4.2. The observed X-ray flux is assumed to be proportional to thevisible volume of the hot irradiated plasma. The corona canbe partially screened from the observer by the star itself andby the accretion disk.3. Each volume element dV of the corona is assumed to scat-ter photons independently from others. The flux scattered bya volume element is proportional only to the incident X-rayflux F = L x / π r , where r is the distance between the vol-ume element dV and the central X-ray source with luminos-ity L x .In a homogeneous corona, the specific luminosity of single-scattered X-ray radiation from the corona reads: dLd Ω = (cid:90) n σ T L x π r dV , (2)where the integral is taken over the volume visible from a givendirection, x ( γ ) is the scattering diagram, γ is the angle betweenthe given direction and the line connecting the volume element dV and X-ray source, σ T is the Thomson cross-section, and n isthe number density of electrons in the volume element dV .The integral in Eq. (2) is calculated numerically using thefollowing procedure. The corona is approximated by N fixedrandomly distributed points filling the layer with height H abovethe donor star’s irradiated surface; see Fig. 4. Each point ischecked for whether it is blocked from the view of the observerby the donor star or the accretion disk or falls within the disk’sX-ray shadow region. For points which are not blocked and arenot inside the shadow, the distance r to the X-ray source is cal-culated. Then, the integral (2) can be approximated as: dLd Ω = VN N (cid:88) i = δ i n σ T L x π r i , (3) Article number, page 4 of 10. I. Shakura et al.: Her X-1 during
SRG / eROSITA survey Fig. 3.
Schematic geometrical model of Her X-1 / HZ Her used to cal-culate the X-ray orbital light curve. The model includes the Roche-lobefilling star (to the left), a hot corona above its X-ray-illuminated part (inorange), the accretion disk around the neutron star (to the right), and ahot halo above the accretion disk (disk corona, in yellow). Also shownis the accretion disk shadow on the illuminated part of HZ Her. where V is the full volume of the corona including the X-rayshadow and blocked regions. The volume V is computed numer-ically. δ i = i is blocked from the view of the observerby the star or the accretion disk, or is inside the disk’s X-rayshadow region, and δ i = i is not blocked, nor fallsinside the shadow region.
4. Orbital X-ray light curve in the low state of HerX-1
As shown in the previous section, X-ray emission in the low-state of Her X-1 is dominated by the scattered radiation in the hotcorona above the illuminated atmosphere of HZ Her. To calcu-late the orbital X-ray light curve, we use the geometrical modelof a binary system with a Roche-lobe-filling star and a tilted,warped accretion disk around the compact star, as implementedin the numerical code developed in Kolesnikov et al. (2020) andsupplemented here with a scattering X-ray corona above the il-luminated atmosphere of the optical star (see Fig. 3).A hot halo above the accretion disk itself (the disk corona)also scatters X-rays from the central source (see, e.g., Bochkarev(1989); Bochkarev & Karitskaya (1992)).
Ginga / LAC observa-tions of Her X-1 during a short-on state suggested the presenceof an extended X-ray source (Leahy 2000; Leahy & Chen 2019).Later on, evidence for a hot disk corona in Her X-1 was foundfrom RXTE observations (Leahy 2015). In our modeling, we as-sume that the hot accretion disk corona constantly adds to thetotal flux at all orbital phases except for eclipses of the centralX-ray source and the accretion disk (0.0–0.13 and 0.87–1.0). Tocalculate the X-ray light curve at the eclipse phases, one shouldspecify the accretion disk corona structure. This can be quitecomplicated (see, e.g., the modeling of orbital X-ray light curvewith a nonconstant density disk corona in Leahy (2015)). In analmost edge-on binary like Her X-1, some orbital modulationfrom the structured accretion disk corona can be due to eclipsesof the corona’s inner parts by the outer boundary of the twistedtilted accretion disk. However, the quality of X-ray data underanalysis does not allow us to test such additional e ff ects to scat-tering on the coronal plasma above the illuminated atmosphereof HZ Her. A continuous set of dedicated observations during theX-ray eclipse is needed to probe the central X-ray source’s hotcorona. This is a di ff erent problem, and in this paper we excludethe eclipse phases (0.0–0.13 and 0.87–1.0) from our analysis. AB Fig. 4.
X-ray flux of the power-law component in the energy range 0.2 –8 keV from Her X-1 as a function of time during the first (A) and second(B) survey. The solid line is the theoretical flux calculated as describedin Section 4. Figures inside plots show the brightness of scattered X-rays in the corona at the orbital phase 0.5. The white region is the X-ray shadow. The solid vertical lines indicate the orbital phase zero. Thedotted vertical lines a, b, and c before and after the orbital phase zeroindicate di ff erent accretion disk ingress and egress moments. Here, c–aand a–c intervals before and after phase zero, respectively, indicate theorbital phases where the donor star partially covers the accretion disk.Line b indicates expected moments of ingress and egress of the X-raysource. The a–a interval covers the total eclipse of the disk by the donorstar. The model X-ray light curve of Her X-1 in the low statesobserved during the first and second eROSITA surveys is pre-sented in Fig. 4 (A and B, respectively). The solid curves indi-cate the calculated X-ray flux scattered in the hot corona aboveHZ Her and accretion disk while taking into account shadowsfrom the precessing, tilted, warped accretion disk. On the leftpanels of the plots, the X-ray brightness of the corona abovethe illuminated atmosphere of HZ Her (in color) and the diskshadows (in white) are shown for the orbital phase 0.5. The or-bital ephemeris of Her X-1 is taken from Staubert et al. (2009).The disk corona’s contribution is presented in Table 2 in unitsof scattered flux from the donor star’s corona. Dots with verticalbars show the observed eROSITA flux. We assume that the X-rayluminosity of the central source remained constant during botheROSITA observations.Observations A and B occurred at di ff erent phases of the 35-day cycle of Her X-1. The first (A) and second (B) survey ob- Article number, page 5 of 10 & A proofs: manuscript no. 40145corr
Table 2.
Model parameters during first and second survey
Parameters First survey Second surveyMass ratio q = m x / m o . a . i
87° 87°Relative outer edge semi-width h out / R o .
15 0 . θ out
15° 18°Disk inner edge tilt θ in
10° 3°Disk phase angle Φ − − Z = ϕ out − ϕ in − . . H / R opt .
15 0 . Notes. ( a ) Leahy & Abdallah (2014) servations happened in the low states preceding and followingthe Short-on. According to the
Swift / BAT (Swift Burst AlertTelescope) X-ray data (see Fig. 1), the 35-day phase of the mid-dle of eROSITA observations is Φ ≈ . Φ ≈ . ff erence is clearlyseen in the observed and calculated light curves that are mostlyshaped by the form of the precessing disk shadow shielding thecorona from the central X-ray source.Figure 4 suggests that the modulation of the X-ray emissionobserved during both the first and second observations of HerX-1 can be explained by scattering in the hot corona above theilluminated atmosphere of HZ Her with an account of shadowsproduced by the precessing, tilted, warped accretion disk aroundthe central neutron star (Kolesnikov et al. 2020).
5. X-ray absorption and scattering in the coldoptically thick donor’s photosphere
Above, we calculate the X-ray light curve from Her X-1 in thelow state in the energy range where the scattered radiation fromthe hot corona above HZ Her dominates. At high photon ener-gies, the X-ray reflection from the cold photosphere of HZ Hershould also be taken into account (Basko et al. 1974). Evidencefor hard X-ray reflection from HZ Her during the low state ofHer X-1 was found from RXTE / PCA observations by Abdallah& Leahy (2015).Indeed, as shown in Appendix B, in the hot corona above theoptical star, the photon scattering optical depth τ s (cid:46) .
1, whichmeans that only (cid:46)
10% of incident photons can be scattered.The rest of the photons are absorbed and partially reflected bythe photosphere of the cold donor. The absorption cross-sectionin the cold plasma strongly depends on the photon energy, σ a ∼ E − . The single scattering albedo is approximately λ ≈ / I ( τ = , µ, φ ) of scattered photons in the coldphotosphere is calculated in Appendix B.As seen from Fig. B.1 in Appendix B, above 8 keV, the X-ray reflection from the cold photosphere of HZ Her could add ∼
30% to the total flux. The increase in the spectral residualsat high energies visible in the lower panels of Fig. 2 could beattributed to this reflection.
6. Discussion and Conclusion
In this paper, we present the
SRG / eROSITA X-ray observationsof Her X-1 during two low-states of the 35-day cycle. Obser-vations were performed during the first and second surveys in March and September 2020, and each covered about 1.5 binaryorbital periods. Orbital modulation of X-ray flux during the low-states was clearly detected (see Fig. 4).In both observations, the X-ray spectrum of the source canbe fitted by a blackbody and power-law component, with onlya minor contribution of proper emission from the hot photoion-ized plasma (see Fig. 2 and Table 1). The power-law compo-nent dominates above ∼ . / PCA observations (˙Inam & Baykal 2005; Abdallah &Leahy 2015). In Abdallah & Leahy (2015), the X-ray spectraare modeled by three components: (1) a power-law componentwith photon index Γ ≈ N H ≈ − cm − , (2) anunabsorbed power-law component with the same Γ due to scat-tering in a hot corona above the accretion disk, and (3) the Fe K α line. In the model of these latter authors, the orbital modula-tion is due to variable absorption of the hard reflected componentfrom the cold photosphere, while the scattered component fromthe disk corona remains constant.The picture is di ff erent in the case of eROSITA observations.The eROSITA 0.3–7 keV spectra (see Table 1 and Fig. 2) arebest fitted by one power-law component with Γ ≈ N H ≈ cm − due to scattering in a hot plasma above the irra-diated photosphere of HZ Her, a black-body component with kT ≈ . Article number, page 6 of 10. I. Shakura et al.: Her X-1 during
SRG / eROSITA survey The spectra obtained during short eROSITA scans with limitedcount statistics also do not require a partial-covering cold ab-sorber with N H ∼ cm − (Leahy & Chen 2019). We suggestthat the observed orbital modulation of the X-ray emission in thelow state is due to the changing view of the scattering hot plasmaabove the irradiated photosphere of HZ Her partially shadowedby the tilted, twisted accretion disk.Our analysis excluded the orbital phases around the X-rayeclipse (0.0–0.13 and 0.87–1.0). However, these phases are veryinteresting because they can be used to probe the structure ofthe hot corona above the accretion disk (see the analysis ofRXTE / PCA eclipses in Leahy (2015)).We conclude that one of the best-studied X-ray binaries,Her X-1 / HZ Her, continues to reveal intriguing physical prop-erties that can help us to understand the complicated structureof accretion flows around magnetized neutron stars. The firsteROSITA observations have already significantly contributed toour improved understanding of this problem.
Acknowledgements.
The authors thank the anonymous referee for useful notesthat helped us improve the presentation of the results. The research is supportedby the RFBR grant no. 18-502-12025 and the Interdisciplinary Scientific andEducational School of Moscow University’ Fundamental and Applied SpaceResearch’. PM acknowledges the hospitality of the Max-Planck Institute forAstrophysics, where part of this work was done. This work is based on obser-vations with eROSITA telescope onboard
SRG observatory. The
SRG observa-tory was built by Roskosmos in the interests of the Russian Academy of Sci-ences represented by its Space Research Institute (IKI) in the framework of theRussian Federal Space Program, with the participation of the Deutsches Zen-trum für Luft- und Raumfahrt (DLR). The
SRG / eROSITA X-ray telescope wasbuilt by a consortium of German Institutes led by MPE, and supported by DLR.The SRG spacecraft was designed, built, launched, and is operated by the Lav-ochkin Association and its subcontractors. The science data are downlinked viathe Deep Space Network Antennae in Bear Lakes, Ussurijsk, and Baykonur,funded by Roskosmos. The eROSITA data used in this work were processed us-ing the eSASS software system developed by the German eROSITA Consortiumand proprietary data reduction and analysis software developed by the RussianeROSITA Consortium.
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Appendix A: X-ray scattering in an optically thincorona above the donor star
The radiation intensity I ( τ, µ, φ ) in a plane-parallel atmospherewith absorption and scattering obeys the radiative transfer equa-tion, see Fig. A.1: µ dI ( τ, µ, φ ) d τ = I ( τ, µ, φ ) − S ( τ, µ, φ ) , (A.1)where µ = cos θ , τ is the optical depth, d τ = − ( κ + σ ) dz , κ is theabsorption coe ffi cient, and σ is scattering coe ffi cient.The source function S ( τ, µ, φ ) is defined as follows S ( τ, µ, φ ) = S inc ( τ, µ, φ ) + λ π (cid:90) I ( τ, µ (cid:48) , φ (cid:48) ) x ( µ, φ, µ (cid:48) , φ (cid:48) ) d µ (cid:48) d φ (cid:48) , (A.2)where the integration is taken over all directions, λ = σ/ ( κ + σ )is the single-scattering albedo, and x ( µ, φ, µ (cid:48) , φ (cid:48) ) is the scatteringdiagram. In the case of random scatterings, the scattering dia-gram depends only on the angle between the incident and scat-tering direction, x (cos γ ),cos γ = µµ (cid:48) + (cid:113) − µ (cid:113) − µ (cid:48) cos ( φ − φ (cid:48) ) . (A.3)The first part in Eq. A.2 allows for single-scattering of the inci-dent radiation: S inc ( τ, µ, φ ) = λ π (cid:90) I inc ( τ, µ (cid:48) , φ (cid:48) ) x ( µ, φ, µ (cid:48) , φ (cid:48) ) d µ (cid:48) d φ (cid:48) , (A.4)where integration is taken over all directions, I inc is the intensityof the direct radiation: I inc ( τ, µ, φ ) = Fe − τ/µ δ ( µ − µ ) δ ( φ ) , (A.5) F is the illumination flux perpendicular to the unit surface area, µ = cos θ , θ is the angle between the normal to the surface andincident ray, and δ ( ... ) is the Dirac delta function. By substitutingA.5 into A.4, the integral A.4 can be calculated to give: S inc ( τ, µ, φ ) = λ F π x (cos γ ) e − τ/µ , (A.6)wherecos γ = µµ + (cid:113) − µ (cid:113) − µ cos φ. (A.7)With known source function S ( τ, µ, φ ), the intensity of theescaped radiation reads (Sobolev 1975; Nagirner 2001) I ( τ = , µ, φ ) = I = (cid:90) τ S ( τ, µ, φ ) e − τ/µ d τµµ . (A.8)If τ (cid:28)
1, only single scattered photons can be taken intoaccount. Substituting Eq. A.6 into Eq. A.8 yields: I = λ F π x (cos γ ) (cid:90) τ e − τ (cid:18) µ + µ (cid:19) d τµµ . (A.9)The integral in Eq. A.9 can be calculated to give: (cid:90) τ e − τ (cid:18) µ + µ (cid:19) d τµµ = µ µ + µ (cid:32) − e − τ (cid:18) µ + µ (cid:19) (cid:33) . (A.10) Fig. A.1.
Scheme of scattering of radiation by the semi-infinite plane-parallel atmosphere. n is the normal vector to the surface, θ is the anglebetween the direction of the incident ray and normal vector n , θ is theangle between scattered ray and normal vector n , φ is the azimuth angleof scattered ray, and γ is the angle between the incident ray and scatteredray. Fig. A.2.
Spherical star illuminated by an isotropic point-like X-raysource. R is the radius of the star, a is the distance between star cen-ter and X-ray source, and r is the distance between X-ray source andsurface of the star. The observer is located to the right-hand side of thefigure. After expanding the exponent on the right-hand side of Eq. A.10in series, and substituting it to the Eq. A.9 we obtain I = λ π F τ µ x (cos γ ) . (A.11)A useful quantity is the specific luminosity due to scattering: dLd Ω (cid:20) ergs sr (cid:21) = (cid:90) I µ ds , (A.12)where the integral is calculated over the visible surface of thestar. Usually, this integral is computed numerically.As an example, consider the simple case of a spherical starwith radius R illuminated by an isotropic point-like X-ray sourcelocated at the distance a from the star center (see Fig. A.2): F = L x π r . (A.13)Here the distance r is defined by the cosine theorem: r = a + R − aR cos θ. (A.14) Article number, page 8 of 10. I. Shakura et al.: Her X-1 during
SRG / eROSITA survey The surface element on the star is: dS = R d Ω = R sin θ d θ d φ. (A.15)Then Eq. (A.12) turns into: dLd Ω (cid:20) ergs sr (cid:21) = L x π R a λτ (cid:90) θ ∗ x (cos γ ) sin θ d θ − cos θ . (A.16)For instance, in the case of spherically symmetric source x (cos γ ) =
1, the integral in (A.16) is simplified: (cid:90) θ ∗ sin θ d θ − cos θ . (A.17)For θ ∗ =
30° and R / a = /
2, the integral (A.17) is = ln 3 ≈ . x (cos γ ) =
34 (1 + cos γ ) . (A.18)We can use the sine theorem R sin β = a sin ( β + θ ) (A.19)to find the relation between the scattering angle γ and θ, sin γ = (cid:16) + R sin θ a − R cos θ (cid:17) . (A.20)The integral in equation A.16 becomes (cid:90) θ ∗ − (cid:16) + R sin θ a − R cos θ (cid:17) sin θ d θ (cid:16) − cos θ (cid:17) . (A.21)For θ ∗ =
30° and R / a = /
2, the integral A.21 is ≈ .
24. Thedi ff erence between A14 and A17 is approximately 20%.X-ray flux scattered by the corona at the distance d to thesystem at a given orbital phase is q (cid:48) (cid:20) ergs cm (cid:21) = d dLd Ω . (A.22)The observable X-ray flux from the neutron star at the Main-onphases of 35-day cycle is q x = L x π d . (A.23)Therefore, the fraction of the X-ray flux scattered by the coronais q (cid:48) / q x = π ( dL / d Ω ) / L x .The scattered flux q (cid:48) is approximately equal to the flux ob-servable by eROSITA in the low state of Her X-1 (the power-law component at ∼ q x is approximately equal to the flux observable duringthe Main-on; see, e.g., Oosterbroek et al. (1997); dal Fiume et al.(1998) (the power-law component at ∼ q (cid:48) / q x ≈ κ = λ = τ = τ σ ) and tak-ing q (cid:48) / q x = .
01, from Eq. (A.16) we find the scattering opticaldepth: τ σ = q (cid:48) q x a R . ≈ . (A.24) Appendix B: Scattering and absorption of X-rayphotons in a semi-infinite atmosphere
Theory of radiation transfer with electron scattering was de-veloped in the classical works of Ambartsumian (1960), Chan-drasekhar (1989) and Sobolev (1985). Zel’dovich & Shakura(1969), Shakura (1972) and Shakura & Sunyaev (1973) studiedthe e ff ect of electron scattering on the spectrum emitted by anisothermal semi-infinite atmosphere. Such a spectrum is referredto as the “modified blackbody” (see, e.g., Shapiro & Teukol-sky (1983), Rybicki & Lightman (1986), Frank et al. (2002) andKato et al. (2008)). The integral radiation flux from photosphereswith electron scattering was calculated by Syunyaev & Shakura(1974). Following the classical papers, the solution of the radia-tion transfer equation (A.1) with the source function A.2 reads: I ( τ = , µ, µ ) = F ρ ( µ, µ ) µ , (B.1)where ρ ( µ, µ ) is the atmosphere brightness coe ffi cient: ρ ( µ, µ ) = λ (cid:32) x φ ( µ ) φ ( µ ) µ + µ + x φ ( µ ) φ ( µ ) µ + µ (cid:33) . (B.2)Following Busbridge (1960) φ i ( µ ) is defined as: φ ( µ ) = H ( µ ) q ( µ ) ,φ ( µ ) = H ( µ ) q ( µ ) , (B.3)where q ( µ ) and q ( µ ) are the following polynomials (Sobolev1968): q ( µ ) = + N M − M N ∆ µ + M N − N M ∆ µ q ( µ ) = − q ( µ ) − − λ )2 ∆ ( M µ − M µ ) . (B.4)Here M , M , M , N , N , ∆ coe ffi cients are defined as: M = − λ − λ ) (cid:90) H ( µ ) (cid:20) x P ( µ ) (cid:21) µ d µ, M = − λ (cid:90) H ( µ ) (cid:20) − x P ( µ ) (cid:21) d µ, M = − λ (cid:90) H ( µ ) (cid:20) − x P ( µ ) (cid:21) µ d µ, N = − λ x − λ ) (cid:90) H ( µ ) P ( µ ) d µ, N = λ x − λ ) (cid:90) H ( µ ) P ( µ ) µ d µ, N = − λ (cid:90) H ( µ ) (cid:20) − x P ( µ ) (cid:21) d µ, ∆ = M N − M N , (B.5)where P ( µ ) is the 2d-order Legendre polynomial. For theRayleigh scattering diagram A.18, N = M .The function H ( µ ) is defined as (Chandrasekhar 1950): H ( µ ) = + µ H ( µ ) (cid:90) ψ ( µ ) H ( µ (cid:48) ) µ + µ (cid:48) d µ (cid:48) , (B.6) Article number, page 9 of 10 & A proofs: manuscript no. 40145corr
Fig. B.1.
Ratio of the continuum X-ray fluxes at low state to Main-onstate as a function of photon energy. A fluorescent iron line is not in-cluded. The dashed and solid lines show the calculated fraction of scat-tered X-ray radiation from the photosphere q phot / q x without and withtaking into account the shadow from the disk, respectively. The grayarea shows the observable ( q (cid:48) + q phot ) / q x fraction with an addition ofX-rays scattered in the corona ( ∼ where ψ ( µ ) is the characteristic function: ψ ( µ ) = λ (cid:20) + x − λ ) µ − P ( µ ) (cid:21) . (B.7)Here x = x = / (cid:90) ψ ( µ ) d µ ≤ . (B.8)X-ray flux scattered by the photosphere at the distance d tothe system at a given orbital phase is q phot = L x π d (cid:90) ρ ( µ, µ ) µµ r ds , (B.9)where the integral is taken over the visible part of the irradiatedsurface of the donor star.In Fig. B.1, we plot the scattered flux ratio q phot / q x from thecold photosphere of HZ Her as a function of the photon energy(the dashed and solid curves for calculation without and withtaking into account the disk shadow, respectively). Besides, thegray strip shows the total ratio of scattered flux from the hotcorona q (cid:48) and the reflected flux from the cold photosphere q phot to the flux from the central X-ray source q x . The low and up-per contributions from the scattering corona q (cid:48) min / q x = .
01 and q (cid:48) max / q x = .
02 are used (see Appendix A).We note that the theory described above was applied for thefirst time by Mescheryakov et al. (2011) to calculate the verticalstructure of accretion disks.02 are used (see Appendix A).We note that the theory described above was applied for thefirst time by Mescheryakov et al. (2011) to calculate the verticalstructure of accretion disks.