A broad-band X-ray view of the precessing accretion disk and pre-eclipse dip in the pulsar Her X-1 with NuSTAR and XMM-Newton
McKinley C. Brumback, Ryan C. Hickox, Felix S. Fürst, Katja Pottschmidt, John A. Tomsick, Jörn Wilms, Rüdiger Staubert, Saeqa Vrtilek
DDraft version February 11, 2021
Typeset using L A TEX twocolumn style in AASTeX63
A broad-band X-ray view of the precessing accretion disk and pre-eclipse dip in the pulsar Her X-1with
NuSTAR and
XMM-Newton
McKinley C. Brumback,
1, 2
Ryan C. Hickox, Felix S. F¨urst, Katja Pottschmidt,
4, 5
John A. Tomsick, J¨orn Wilms, R¨udiger Staubert, and Saeqa Vrtilek Department of Physics & Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, NH 03755, USA Cahill Center for Astronomy and Astrophysics, California Institute of Technology, 1216 E California Blvd, Pasadena, CA 91125, USA European Space Astronomy Centre (ESA/ESAC), Operations Department, Villanueva de la Ca ˜ nada Madrid, Spain CRESST, Department of Physics and Center for Space Science and Technology, UMBC, Baltimore, MD 210250, USA NASA Goddard Space Flight Center, Code 661, Greenbelt, MD 20771, USA Space Sciences Laboratory, University of California, Berkeley, 7 Gauss Way, Berkeley, CA 94720, USA Dr. Karl Remeis-Sternwarte and Erlangen Centre for Astroparticle Physics, Sternwartstrasse 7, 96049 Bamberg, Germany Institut f¨ur Astronomie und Astrophysik, Universit¨at T¨ubingen, Sand 1, 72076 T¨ubingen, Germany Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA (Received 7 Aug 2020; Revised 15 Dec 2020, 26 Jan 2021; Accepted 27 Jan 2021)
Submitted to The Astrophysical JournalABSTRACTWe present a broad-band X-ray timing study of the variations in pulse behavior with superorbitalcycle in the low-mass X-ray binary Her X-1. This source shows a 35-day superorbital modulation inX-ray flux that is likely caused by occultation by a warped, precessing accretion disk. Our data setconsists of four joint
XMM-Newton and
NuSTAR observations of Her X-1 which sample a completesuperorbital cycle. We focus our analysis on the first and fourth observations, which occur duringthe bright “main-on” phase, because these observations have strongly detected pulsations. We addedan archival
XMM-Newton observation during the “short-on” phase of the superorbital cycle since ourobservations at that phase are lower in signal to noise. We find that the energy-resolved pulse profilesshow the same shape at similar superorbital phases and the profiles are consistent with expectationsfrom a precessing disk. We demonstrate that a simple precessing accretion disk model is sufficient toreproduce the observed pulse profiles. The results of this model suggest that the similarities in theobserved pulse profiles are due to reprocessing by a precessing disk that has returned to its originalprecession phase. We determine that the broad-band spectrum is well fit by an absorbed power lawwith a soft blackbody component, and show that the spectral continuum also exhibits dependenceon the superorbital cycle. We also present a brief analysis of the energy resolved light curves of apre-eclipse dip, which shows soft X-ray absorption and hard X-ray variability during the dip. INTRODUCTIONMagnetically dominated accretion occurs regularly inthe environments surrounding neutron stars that accretefrom a stellar companion via mass transfer mechanismssuch as stellar outflows and Roche lobe overflow (e.g.,Nagase 2001). Near the pulsar’s magnetosphere, mag-netic pressure from the strong magnetic field overwhelmsthe ram pressure from the accretion disk, which causesthe hot, ionized gas to accrete along the dipolar fieldlines. The structure of the accretion disk and magne-tized accretion flow are thought to be complex in na-ture (e.g., Ogilvie & Dubus 2001; Romanova et al. 2002,2003, 2004), however observational constraints on mag-netically dominated accretion structures are limited. The luminous X-ray pulsars LMC X-4, SMC X-1, andHer X-1 show superorbital periods, which are variationson time scales longer than the orbital period. These su-perorbital periods are attributed to warped disks, whereradiation pressure drives a tilt in the accretion disk (e.g.,Pringle 1996; Ogilvie & Dubus 2001). As the disk pre-cesses, the warped edge temporarily occults the pulsarand causes the changes in luminosity. The geometry ofthe accretion disk and the neutron star in these warpeddisk systems creates some of the best observational lab-oratories for studying magnetized accretion flow ontocompact objects because emission from the accretionand reprocessed emission from the accretion disk canboth be detected (Hickox et al. 2004). Brumback et al. a r X i v : . [ a s t r o - ph . H E ] F e b Brumback et al. (2020) (hereafter B20) used pulse phase-resolved spec-troscopy and tomography to model the warped inner ac-cretion disk structure around the bright X-ray pulsarsLMC X-4 and SMC X-1. This analysis assumed thatthe supeorbital period, which is present on timescalesof 30-60 days in these sources, is caused by the preces-sion of a warped inner accretion disk seen approximatelyedge-on (e.g., Gerend & Boynton 1976; Heemskerk &van Paradijs 1989; Wojdowski et al. 1998). In sourceswith this accretion disk geometry, the rotating, high en-ergy beam from the neutron star irradiates the inneraccretion disk. The disk reprocesses the beam’s radia-tion and releases softer X-rays which differ in pulsationshape and phase from the hard pulses (Shulman et al.1975; Neilsen et al. 2004; Zane et al. 2004; Hickox &Vrtilek 2005). B20 used the simple geometric warpeddisk model created by Hickox & Vrtilek (2005) to modelobserved changes in hard and soft pulse profile shape asa function of superorbital phase in LMC X-4 and SMCX-4 with broadband X-ray coverage.In this work, we will follow the method of B20 andprovide observational constraints on the geometry of thewarped inner accretion disk in Her X-1, a prototypeX-ray pulsar (Tananbaum et al. 1972), making use offull hard X-ray coverage from the
Nuclear SpectroscopicTelescope Array ( NuSTAR ). Her X-1 is a low mass X-ray binary consisting of a 1.5 M (cid:12) neutron star orbit-ing HZ Herculis, an approximately 2.2 M (cid:12)
A/F typestar (Crampton & Hutchings 1974; Deeter et al. 1981;Reynolds et al. 1997). The binary orbit is 1.7 days and isnearly circular (Staubert et al. 2009). The orbital planeis highly inclined ( i = 85 − ◦ ), resulting in regulareclipses of the neutron star. The distance to the binaryis 6.6 kpc (Reynolds et al. 1997). Her X-1 is a cyclotronline source (Truemper et al. 1978), with a broad absorp-tion feature caused by cyclotron resonance scatteringbeing visible in the hard X-ray spectrum. The energyat which this feature occurs is caused by the strength ofthe pulsar’s magnetic field, and thus the feature allowsastronomers to directly measure the field strength. Thecentral energy of this cyclotron resonance scattering fea-ture (CRSF) has been found to correlate strongly withthe source flux (Staubert et al. 2007, 2016, 2017). Inaddition, the energy shows an interesting evolution withtime: after a fairly constant value around 37 keV forabout a decade after the discovery, a strong turn-up oc-curred to beyond 40 keV (Gruber et al. 2001), followedby a nearly 20 yr decline until ∼ . × G (Staubert et al. 2020). Tananbaum et al. (1972) dis- covered 1.24 s X-ray pulsations from the neutron starand a longer, approximately 35 day modulation in X-ray luminosity.This 34.85 day superorbital period in Her X-1 is likelycaused by a warped, precessing inner accretion disk (Gi-acconi et al. 1973; Ramsay et al. 2002; Zane et al. 2004).The superorbital period consists of a bright “main on”period lasting approximately 11 days and a shorter,fainter “short on” period lasting approximately 8 days,which are separated by 8 day off states (Tananbaumet al. 1972; Giacconi et al. 1973). During the brightmain on state, Her X-1 reaches characteristic X-ray lu-minosities of approximately 10 erg s − . During the35 day cycle, the neutron star eclipses every 1.7 daysand there are additional pre-eclipse dips seen every 1.62days (Jones & Forman 1976). These pre-eclipse dips arelikely caused by obscuration of the pulsar by materialat the interaction point between the accretion streamand the disk (e.g., Still et al. 2001). Another feature ofthe superorbital behavior in Her X-1 are the anomolouslow states (ALSs), which are defined by a significantdecrease in X-ray flux and pulsation strength withoutsignificant change in the optical and UV flux (e.g., Vr-tilek & Cheng 1996; Coburn et al. 2000; Staubert et al.2017). These states can last for several months and arelikely caused by a change in scale height of the accretiondisk, which obscurs the central accretor, or a change indisk inclination (e.g., Parmar et al. 1985).In this work we present joint XMM-Newton and
NuS-TAR observations of Her X-1 that sample a single su-perorbital cycle, allowing us to monitor and model theprecession of the accretion disk. Although the sourceis well-studied, previous Her X-1 observations lack thecombination of energy coverage, timing resolution, andsampling of different phases within a single superorbitalcycle needed to fully constrain the pulsar beam and diskgeometry over the precession cycle of the disk. Ramsayet al. (2002) and Zane et al. (2004) used
XMM-Newton to observe the precession of the inner accretion disk,but their analysis lacked
NuSTAR high energy cover-age. F¨urst et al. (2013) illustrated the importance ofhigh energy pulse profiles in Her X-1 by showing thedramatic changes in pulse shape and phase that occuracross the
NuSTAR energy band. However, the F¨urstet al. (2013) observations took place during one super-orbital phase so they could not demonstrate changes inpulse-profile at different superorbital phases. McCrayet al. (1982) and Vrtilek & Halpern (1985) had soft X-ray coverage of a complete 35 day cycle of Her X-1 with
Einstein ’s MPC. However,
Einstein ’s energy range of 1–20 keV does not fully constrain changes in the soft pul-sations, which Hickox et al. (2004) found peak below 1 odeling disk precession in Her X-1
NuSTAR and
XMM-Newton in order to conduct a broad-band study of the pulse pro-files and spectral shapes of Her X-1 during two consec-utive main-on states of the superorbital cycle, allowingus to test the periodic dependence of these features. Wealso supplement our observations with archival observa-tions that allow us to study the short-on state of thesuperorbital cycle.In Section 2 we describe the previously unpublishedjoint
XMM-Newton and
NuSTAR observations of HerX-1, as well as some archival data used in this anal-ysis. In Section 3 we describe the procedure used toextract pulse profiles and perform phase-averaged andphase-resolved spectroscopy and we present the resultsin Section 4. In Section 5 we model the observed pulseprofiles and simulate the inner disk geometry. We brieflyexamine the energy resolved light curves of a pre-eclipsedip in one of our observations in Section 6. In Section 7we discuss the implication of our results. OBSERVATIONSThe data used in this analysis are a set of four joint
NuSTAR (Harrison et al. 2013) and
XMM-Newton ob-servations of Her X-1 that took place between 09 Febru-ary and 14 March 2019. Following the convention usedin B20, we refer to these observations as ObservationH1, H2, H3, and H4. Table 1 shows the date of obser-vation, the observation ID number, superorbital phase,and exposure time for each observation. Figure 1 showsthe one day averaged MAXI light curve, folded on the35 day superorbital period, for Her X-1 with the obser-vations plotted as red vertical lines.We reduced these data using HEASoft version 6.26.1with
NuSTAR
CALDB v20191219 and XMMSAS ver-sion 18.0.0. For the
NuSTAR observations, we selecteda circular source region of radius 110 arcseconds withDS9 (Joye & Mandel 2003). We used a circular regionof the same size away from the source as the backgroundregion. The background counts make up approximately0.3% of the total counts. For the
XMM-Newton ob-servations we used the EPIC-pn instrument in TimingMode exclusively to obtain the maximum possible tim-ing resolution and to minimize the effects of pileup, andselected only single and double events from the EPIC-pndata. We used the XMMSAS tool epatplot to evalu-ate the observations for pileup by comparing the modelof expected single and double events to data. In the observations that took place during Her X-1’s brightmain on phase (obsIDs 0830530101 and 0830530401),we found differences in the models indicative of pileup.We excised the brightest central pixels and examinedthe models again until we found good agreement. Ulti-mately, we found it was only necessary to exclude thecentral pixel to reduce pileup.We performed a barycentic correction to ObservationsH1–H4 using the NuSTARDAS tool barycorr and theXMMSAS tool barycen . We accounted for the effect ofthe neutron star’s orbit by correcting the photon arrivaltimes using the Her X-1 orbital ephemeris described inStaubert et al. (2009).We show the
NuSTAR
XMM-Newton
XMM-Newton count rates have been ar-bitrarily offset from the
NuSTAR count rates in Obser-vations H2, H3, and H4 for clarity. Observation H4 cap-tured a pre-eclipse dip with both telescopes. We alsoshow the pulsed fractions for the
NuSTAR
XMM-Newton
XMM-Newton or NuS-TAR ), Observation H3 (where
XMM-Newton pulsationswere not detected), or data after the onset of the dip inH4 (where the soft pulses dramatically weaken).Because we were unable to extract both hard and softpulse profiles from Observations H2 and H3, we turnedto archival data of Her X-1 to increase our coverage ofthe 35 day superorbital cycle. As mentioned in the intro-duction, many previous works have presented changesin pulse profile shape across the superorbital cycle. Wefocused on the
XMM-Newton data archive because the0.2–12 keV energy range would allow us to directly com-pare the soft data to our observations while offeringsome overlap with our
NuSTAR data. For the sakeof brevity, we selected a single archival
XMM-Newton observation of Her X-1. ObsID 0111061201 took placeon 16 March 2001 as part of a series of
XMM-Newton observations of Her X-1 and was first presented in Ram-say et al. (2002). Because this observation is the thirdin its original series, we refer to it as Observation R3in this work. Observation R3 took place at superor-bital phase 0.60. We reduced these data following theanalysis steps described in Ramsay et al. (2002), whichare broadly consistent with the reduction process de-scribed in this work. However, we added the correctiondescribed in Ramsay et al. (2002) to
FTCOARSE , which
Brumback et al.
H1 H2 H3 H4R3 “main on” “short on”
Figure 1.
The one day averaged 2–20 keV MAXI (Matsuoka et al. 2009) light curve of Her X-1, which we folded on the 35 daysuperorbital cycle and plotted twice for clarity. We show the times of the joint
XMM-Newton and
NuSTAR observations usedin this analysis as red vertical, dashed lines. We label the observations H1 through H4 to show their place in this series. Theteal vertical dotted line shows the superorbital phase of the archival
XMM-Newton observation 0111061201; this is the thirdobservation in a series of observations first analyzed by Ramsay et al. (2002), which we refer to as Observation R3. The mainon and short on time periods of the superorbital cycle are marked with brackets.
Table 1.
Description of Her X-1 Observations a Name Date Mid-exposure Time (MJD) φ SO Observation ID Observatory Telescope Mode Exposure (ks)H1 09 Feb. 2019 58523.619 0.20 30402034002
NuSTAR · · ·
XMM-Newton
Fast Timing Mode 21.9H2 13 Feb. 2019 58528.147 0.33 30402034004
NuSTAR · · ·
XMM-Newton
Fast Timing Mode 27.2R3 b
16 Mar. 2001 51984.992 0.60 0111061201
XMM-Newton
Fast Timing Mode 11H3 28 Feb. 2019 58542.515 0.74 30402034006
NuSTAR · · ·
XMM-Newton
Fast Timing Mode 32.6H4 14 Mar. 2019 58556.515 1.14 30402034008
NuSTAR · · ·
XMM-Newton
Fast Timing Mode 29.1 a These observations span two consecutive superorbital cycles. The turn on for the first cycle was 58516.6 MJD and the turn on forthe second cycle was 58551.5 MJD. b This is the third observation in an archival data set of Her X-1 first presented in Ramsay et al. (2002) and later used in Zane et al.(2004) and Jimenez-Garate et al. (2002). In this work, we use Observation R3 as an alternative to the weak pulsations in ObservationH3. odeling disk precession in Her X-1 barycen to apply a barycentric cor-rection to this data set. However we did not use theStill et al. (2001) orbital ephemeris for Her X-1, whichwas used by Ramsay et al. (2002), and instead chose tocorrect the photon arrival times with the more recentlyupdated Staubert et al. (2009) ephemeris. DATA ANALYSIS3.1.
Timing Analysis
We used HENDRICS’s Z statistics search, which isfunctionally similar to epoch folding, to determine thespin period and spin period derivative of each observa-tion (Buccheri et al. 1983; Bachetti 2015). For all obser-vations used in this work, we found that the spin periodderivative was consistent with zero. We estimated theuncertainty in the spin period by creating pulse profilesfrom the beginning and end of each observation and cal-culating δ frequency = δ phase /δ time . While we were ableto precisely measure the spin period in Observations H1and H4 due to their length and good signal to noise ratio,the fainter observations (which do not show pulsationsacross the entire observations) had higher uncertainties,as can be seen in Table 2. We do not list any periodfor Observation H2 because we were unable to detectpulsations during this observation. All errors are 90%confidence unless otherwise specified.For the archival data set, Observation R3, our use of adifferent orbital ephemeris necessitated redoing the pul-sation search, which we did using the method describedabove. We detected pulsations with a spin period of1.2379 ± NuSTAR data and the 0.3–0.7 keV energy rangefrom the
XMM-Newton data. We selected these energyranges specifically for two reasons. The first is to sepa-rate soft, reprocessed emission (less than 1 keV) from theaccretion disk and hard emission from the pulsar beam.The second was that an analysis of the energy-resolvedpulse profiles indicated changes in the soft pulse profilebeginning at approximately 0.8 keV. We show the en-
Table 2.
Best Fit Spin Periods forHer X-1 ObservationsObservation Spin Period (s) a H1 1.237721(6)H2 N/AH3 1.2377(4)R3 1.2379(2)H4 1.237721(8) a For Observations H1–H4, we used
NuSTAR
XMM-Newton
EPIC-pn 0.2–12 keVdata. ergy resolved pulse profiles and discuss those results inmore detail in Appendix A.We then used the epoch folding tool fold events from the Stingray (Huppenkothen et al. 2019) softwareto create energy resolved pulse profiles (see Figure 3).The pulse profiles in Figure 3 contain 20 bins per pulsephase. We selected this binning based on the resolutionof our simulated pulse profiles, which are not capable ofreproducing fine structure within the pulse profile (seeFigure 4 and discussion in Sections 4 and 5). Whenmaking the pulse profiles, we used the start time of eachobservation as phase zero for that pulse profile becausewe are interest in the relative change in phase betweenhard and soft profiles rather than phase difference be-tween observations. However, to highlight these relativephase shifts, we shifted the pulse profiles of R3 and H4so that the hard peaks were aligned with those of Ob-servation H1.Using the above method, we were also able to createa pulse profile from the
NuSTAR data of ObservationH3. While we could not use this observation in ourmodeling analysis due to the lack of detected
XMM-Newton pulsations, we show the
NuSTAR pulse profilein Appendix A for completeness.For data where pulsations were detected, we calcu-lated the pulsed fractions by first dividing the
XMM-Newton and
NuSTAR data into 5 ks time intervals. Foreach of these time intervals, we calculated the pulsedfractions that we showed in Figure 2 as
P F = ( P max − P min ) / ( P max + P min ), where P max is the maximum ofthe pulse profile and P min is the minimum of the pro-file. The errors were calculated from a distribution of100 pulse profiles made with randomly selected periods Brumback et al.
Observation H1 ( φ SO =0.20)Observation H3 ( φ SO =0.74) Observation H4 ( φ SO =0.14)Observation H2 ( φ SO =0.33) NuSTAR light curve
XMM light curve
NuSTAR
NuSTAR light curve
XMM light curve
NuSTAR
XMM
NuSTAR light curve
XMM light curveNo
XMM or NuSTAR pulsations detectedNo
XMM pulsations detected
NuSTAR light curve
XMM light curve
NuSTAR
XMM
Figure 2.
NuSTAR
XMM-Newton
NuSTAR data (grey stars) and 0.3–0.7 keV
XMM-Newton data (pink triangles) where pulsations are detected. We offset the
XMM-Newton light curves by a value of 20 in ObservationsH2 and H3 and 30 in Observation H4 for clarity. A pre-eclipse dip is visible in both the
NuSTAR and
XMM-Newton light curvesof Observation H4. For this analysis, we only used data where pulsations were strongly detected in both
XMM-Newton and
NuSTAR . For clarity, we have filtered the light curves of the bright observations H1 and H4 in order to remove bins with lowexposure fraction caused by
XMM-Newton ’s Counting Mode. between 0.5–1 seconds and 1.25–2 seconds (that is, closeto but not precisely the actual pulse period).3.2.
Phase-averaged Spectroscopy
To create joint spectra we extracted
NuSTAR and
XMM-Newton source and background spectra from theregions described in Section 2 using NuSTARDAS andXMMSAS, respectively. However, we did not extractbackground spectra from the
XMM-Newton data be-cause the high source flux dominated the EPIC-pn CCDin Timing Mode, leaving no source-free region for back-ground calculation (e.g., Ng et al. 2010). We groupedthe
NuSTAR spectra into bins with a signal to noise ra-tio of 10 and the
XMM-Newton spectra with 100 countsper bin. In order to fit the spectra over our desiredenergy range of 0.3–60 keV, for consistency with ourtiming analysis, we were required to use
XMM-Newton data outside of the nominal calibration range of 0.7–12keV for EPIC-pn in Timing Mode. We do not believethis affected the quality of our spectral fits since the fea-tures at low energies (the blackbody component and 1keV bump feature, see below) are strongly preferred bythe data and have been seen before in this source (e.g.,Jimenez-Garate et al. 2002; Hickox et al. 2004). We fitted the phase-averaged spectrum over the 0.3–60keV energy range using Xspec version 12.10.1 (Arnaud1996). We found that the double power law parame-ters were degenerate with the absorption models usedto describe the cyclotron resonance scattering feature(CRSF) when using the Negative and Positive EXpo-nential (NPEX, e.g., Mihara et al. 1998) to describe thecontinuum (as was done B20). Therefore, we used acontinuum model of a power law with a high energycut-off ( powerlaw*highecut ) that did not show de-generacy. This continuum model creates a discontinuityat the cut-off energy that we corrected for by adding aGaussian absorption feature with its energy tied to thecut-off energy and a free width and depth (e.g., Coburnet al. 2002 and references therein).Following the spectral model of B20, we also in-cluded an absorbing column (tbnew), a blackbody with kT ∼ . α (6.4 keV) and a ≈ XMM-Newton ’s RGS instrument(Jimenez-Garate et al. 2002) and with
Suzaku (F¨urstet al. 2013). Both Jimenez-Garate et al. (2002) andF¨urst et al. (2013) suggest that this feature is an un-resolved complex of lines from Ne and Fe. The
XMM- odeling disk precession in Her X-1 Observation H4 ( φ SO =0.14)Observation H1 ( φ SO =0.20) Observation H1 ( φ SO =0.20)Observation R3 ( φ SO =0.60) Observation H4 ( φ SO =0.14) Observation H1 ( φ SO =0.20)Observation R3 ( φ SO =0.60) Observation H4 ( φ SO =0.14) Figure 3.
Joint pulse profiles for the Her X-1 observations H1, R3, and H4. The same relative phase shift between the
NuSTAR
XMM-Newton
NuSTAR pulse profile.
Newton
EPIC-pn camera does not have the spectral res-olution to resolve the complex structure of these fea-tures and, therefore, we allowed for a single Gaussianemission line at 0.9 keV that encompassed the “bump”and described the shape of the spectrum phenomeno-logically. We allowed the Fe K α line to contain both abroad ( σ = 0 . σ = 0 . × cm − , which we calculated using the HI4PI Map (HI4PICollaboration et al. 2016) and the HEASARC N H cal-culator. We set the abundances to those described inWilms et al. (2000) and the cross sections to those fromVerner et al. (1996).Unlike LMC X-4 and SMC X-1 which were modeledin B20, Her X-1 is a cyclotron line source. To model the cyclotron resonance scattering feature (CRSF) wetested two possible models: the Gaussian absorptionmodel gabs and the cyclotron absorption model cy-clabs (e.g., Mihara et al. 1990). While we found thatboth models were capable of fitting the CRSF with asimilar reduced χ , the cyclabs model proved degen-erate with the continuum model, resulting in unreason-able values for the CRSF energy and the power law fold-ing energy. Additionally, the gabs model is used byStaubert et al. (2020) in their long term monitoring ofHer X-1’s CRSF, and using gabs in our spectral modelsprovides results that are consistent with their analysis.For these reasons, We used the gabs model in both ob-servations.We show the phase-averaged spectra and the residu-als to our model fit for Observations H1, H2, H3, andH4 in Figure 5. In Figure 5 we show the joint XMM-Newton and
NuSTAR spectrum in the first panel, theratio of data to model for our best fit spectral model
Brumback et al. N o r m a li z e d C o un t R a t e Obs. H1 NuSTAR 8-60 keVObs. H4 NuSTAR 8-60 keVSimulated profile - antipodal beamsSimulated profile - best fit pencil beams
Figure 4.
Pulse profiles in the hard
NuSTAR band for Observation H1 (blue circles) and Observation H4 (purple triangles)binned with 128 bins per phase. Fine structure in the hard pulse profiles are visible including two bumps within the interpulse ofObservation H4 and a notch in the main pulse of both observations. The differences in fine structure between Observations H1and H4 originate from the small difference in superorbital phase between these observations, which emphasizes that the pulseprofiles are excellent trackers of superorbital phase (e.g., F¨urst et al. 2013; Staubert et al. 2013). We also show the simulatedpulse profiles from an antipodal pencil beam configuration (black dashed line) and our best fit non-antipodal pencil beam (greyline) from our warped disk model (see Section 5). Both of these simulated pulse profiles were binned with 128 bins per phaseand smoothed with a Savitzky-Golay filter. Our warped disk model is not capable of reproducing fine structure in the pulseprofiles, and we therefore fit the coarser structure. We can also see that an antipodal beam geometry is insufficient to describethe hard pulse shape in Her X-1 with our model. in the middle panel, and the ratio of data to model forour best fit model without the absorption feature rep-resenting the CRSF in the bottom panel. The bottompanels of Figure 5 demonstrate that the presence of aCRSF in the model is strongly preferred by the data foreach observation. We note that Observations H2 andH3, which were fainter than the other two observations,have reduced signal at high energies which made theCRSF absorption model less well constrained comparedto Observations H1 and H4. In order to fit our spectralmodel while including the CRSF, we fixed the valuesfor line energy, width, and strength in Observations H2and H3 to the average of the CRSF model parameters inObservations H1 and H4. Table 3 contains the spectralparameters.We also calculated the flux of the entire modeled spec-trum (0.3–60 keV) and the high energy band (8–60 keV)using the Xspec flux tool. We calculated the flux of the blackbody model component using Xspec model compo-nent cflux .As in B20, we attempt to minimize differences in the
NuSTAR and
XMM-Newton response functions by notmodeling the spectra from these telescopes in their over-lapping energy ranges. As we discussed in B20, this in-troduces somewhat artificial inflation to the calibrationconstants between the spectra. The differences in crosscalibration are a known issue, albiet a poorly understoodone, with the absolute calibration of
XMM-Newton inTiming Mode (e.g., B20). These values should not betaken as a reflection of the relative fluxes seen by
NuS-TAR and
XMM-Newton .We do not present a spectral analysis of ObservationR3 in this work, since it is presented with a comparablespectral model in Ramsay et al. (2002). RESULTS4.1.
Pulse Profiles odeling disk precession in Her X-1 H1 0.3-60 − − no r m a li z ed c oun t s s − k e V − r a t i o Energy (keV) − − no r m a li z ed c oun t s s − k e V − r a t i o Energy (keV) − − no r m a li z ed c oun t s s − k e V − r a t i o Energy (keV)
H2 0.3-60 - rescaled bottom − − no r m a li z ed c oun t s s − k e V − r a t i o Energy (keV) − − no r m a li z ed c oun t s s − k e V − r a t i o Energy (keV) − − no r m a li z ed c oun t s s − k e V − r a t i o Energy (keV)
H3 0.3-60
H4 0.3-60 − − no r m a li z ed c oun t s s − k e V − r a t i o Energy (keV) − − no r m a li z ed c oun t s s − k e V − r a t i o Energy (keV)
Figure 5.
Joint
XMM-Newton (red) and
NuSTAR (FPMA - blue, FPMB - black) spectra for the Her X-1 observations H1( φ SO = 0 .
22, top left panel), H2 ( φ SO = 0 .
33, top right panel), H3 ( φ SO = 0 .
74, bottom left panel), and H4 ( φ SO = 0 .
16, bottomright panel). The
XMM-Newton spectrum is modeled from 0.3–5 keV while the
NuSTAR spectra are modeled from 5–60 keV.For each spectrum, the top panel shows the spectrum and model components, the middle pannel shows the ratio of data tomodel for the best fit model, and the bottom panel shows the ratio of data to model with the CRSF feature removed.Table 3 contains the spectral parameters.
Her X-1’s pulse profiles from Observations H1 and H4(Figure 3) are somewhat similar in shape and relativephase. The hard
NuSTAR profile has a strong, narrowmain peak and a weaker, broader second peak. Thesoft
XMM-Newton pulses have a broad, single-peakedstructure. The main peaks of the hard and soft profilesare almost 180 ◦ out of phase in both Observation H1and Observation H4.The hard pulse profile from Observation R3 has a sim-ilar shape to the hard pulses in observations H1 and H4.However, the shape of the soft pulse changes, with thepulse steadily building strength up to the pulse maxi-mum and then dropping off rapidly, as opposed to the rapid rise and slow decline of the pulses in ObservationsH1 and H4. There is also a change in the relative phasebetween the maxima of the hard and soft pulsations.The peaks of the hard and soft pulse profiles are sep-arated by approximately 0.5 phase in Observations H1and H4 and by approximately 0.2 phase in ObservationR3.The differences between these three pulse profilesdemonstrate that the shape and relative phase of thesoft pulses changes with superortibal cycle. The sim-ilarity in the relative phase of the pulse profiles fromObservations H1 and H4, which both take place around φ SO ≈ .
2, shows that the pulses return to their original0
Brumback et al.
Table 3.
Her X-1 phase-averaged spectral parameters a Parameter Observation H1 Observation H2 Observation H3 Observation H4Flux total (erg cm − s − ; 0.3–60 keV) (6.418 ± × − (2.70 ± × − (9.72 ± × − (5.72 ± × − Flux power law (erg cm − s − ; 8–60 keV) (4.559 ± × − (2.05 ± × − (7.67 ± × − (4.405 ± × − Flux blackbody (erg cm − s − ; 0.3–5 keV) (1.189 ± × − (2.54 ± × − (7.45 ± × − (9.18 ± × − Photon Index 0.933 ± ± ± ± A powerlaw (3.90 ± × − (1.30 ± × − (2.48 ± × − (3.34 ± × − Cut-off Energy (keV) 19.8 ± ± ± ± ± ± ± ± CRSF (keV) 36.5 ± ± σ CRSF (keV) 5.1 ± ± ± ± kT BB (keV) 0.0919 ± ± ± ± A BB (keV) (2.58 ± × − (5.7 ± × − (1.59 ± × − (2.09 ± × − E Fe K α , broad (keV, fixed) 6.4 6.4 6.4 6.4 σ Fe K α , broad (keV, fixed) 0.5 0.5 0.5 0.5 A Fe K α , broad (photons cm − s − ) (1.00 ± × − (1.4 ± × − (1.03 ± × − (1.27 ± × − E Fe K α , narrow (keV, fixed) 6.4 6.4 6.4 6.4 σ Fe K α , narrow (keV, fixed) 0.1 0.1 0.1 0.1 A Fe K α , narrow (photons cm − s − ) (4.40 ± × − (5 ± × − (2.67 ± × − (2.3 ± × − E bump (keV, fixed) 0.9 0.9 0.9 0.9 σ bump (keV, fixed) 0.191 ± ± ± ± A bump (photons cm − s − ) (2.46 ± × − (5.6 ± × − (1.44 ± × − (1.58 ± × − c FPMA ± ± ± ± c FPMB ± ± ± ± c EPIC-pn (fixed) 1 1 1 1 χ a For the continuum model constant * tbnew * (powerlaw * highecut * gabs * gabs + bbody + gauss + gauss +gauss) . The errors on the flux are 1 σ and the errors on the parameters are 90% confidence intervals. b We select 8–60 keV for the power law flux because this energy range is consistent with the hard band used in our timing analysis. configuration after a complete precession cycle. How-ever, if we create pulse profiles with finer binning wecan also see differences in the fine structure of the hardpulse profiles that arise from the difference in superor-bital cycle between Observation H1 and H4 (e.g., F¨urstet al. 2013; Staubert et al. 2013). In Figure 4 we showthe hard band pulse profile from Observations H1 andH4 made with 128 bins per phase. Both pulse profilesshow a notch in the bright main pulse as well as struc-ture within the interpulse. There are small differencesin the fine structure of these profiles, which become evenmore noticeable in the energy-resolved pulse profiles inAppendix A, but these differences are consistent with ex-pectations from the slightly different superorbital phaseof these observations, based on the Staubert et al. (2013)template. Notably, Observation H4’s interpulse contains two distinct bump like features, where typically only oneis observed, however such fluctuations have been occa-sionally seen in Her X-1’s pulse profiles with no obviouscorrelation to superorbital phase (Staubert et al. 2013). By showing simulated pulse profiles (see Section 5) inFigure 4 with similar phase binning we demonstrate thatthe warped disk model is not capable of reproducing thefine structure in the pulse profiles. For this reason, weuse coarse binned pulse profiles throughout our warpeddisk modeling procedure.4.2.
Spectroscopy
Our spectroscopic analysis indicates that an absorbedpower law and soft blackbody component is a good de-scription of the broadband X-ray continuum of Her X-1. Because Observations H1 and H4 capture a similar odeling disk precession in Her X-1 MODELING THE WARPED INNER DISKTo constrain the geometry of the inner accretion diskduring its precession we used the same model as B20,which was first presented in Hickox & Vrtilek (2005).A full description of the model, its underlying assump-tions, and a schematic diagram can be found in B20.We briefly describe an important assumption here forclarity.A fundamental assumption of the B20 warped diskmodel is that the emission below 1 keV follows the black-body emission of the accretion disk and that hard X-rayemission follows the power law. We demonstrate thisrelationship by performing a simplistic phase resolvedspectral analysis. For Observations H1 and H4, wherestrong pulsations were detected, we used the HEN-DRICS tool
HENphasetag to assign pulse phase valuesto each photon in the
NuSTAR and
XMM-Newton eventfiles. We then filtered the data into 8 equal phase bins using xselect for
NuSTAR data and evselect for
XMM-Newton data. We extracted spectra and groupedthem with a minimum of 100 counts per bin. We mod-eled the joint phase-resolved spectra between 0.3–47 keVdue to the poorer statistics in these spectra.We attempted to use the phase-averaged spectralmodel to also describe the phase-resolved spectra, butthe reduced signal to noise in the phase-resolved spectrarequired that we reduce degeneracy between some modelparameters. We fixed the blackbody temperature, thewidth of the CRSF, and the width of the 0.9 keV bumpfeature to their phase averaged values. We also removedthe broad iron line model component and only used thenarrow emission line at 6.4 keV. This simplified spectralmodel allowed us to evaluate the changes in the black-body and power law normalizations.In Figure 6 we show the power law flux and the
NuS-TAR
XMM-Newton
XMM-Newton and
NuSTAR pulseprofiles and assume that the profiles follow any changesin the respective strength of the blackbody and powerlaw.With this relationship verified, we will now describethe warped disk model itself. This model uses a simplewarped disk geometry, represented by a series of con-centric circles that are tilted and twisted relative to oneanother, to describe the inner accretion disk. The disk isdefined by the radius and tilt angle of the inner ( r in , θ in )and outer ( r out , θ out ) rings and their relative twist anglewith respect to one another ( θ tw ). The height of theobserver is set by the observer angle ( θ obs ).The pulsar emission geometry can be represented ei-ther as a narrow pencil beam or by a wider fan beam.The beam geometry consists of two beams, whose loca-tion on the neutron star surface are defined by θ b and φ b , which are the angle out of the rotational plane andthe azimuthal angle, respectively. The pencil beam pro-file is a two-dimensional Gaussian with width σ b . Thefan beam is also a two dimensional Gaussian with anadditional opening angle ( θ fan ).Once the disk and emission geometry are specified,the model calculates the simulated pulse profile at 30pulse phases and 8 disk precession angles. As the pulsarrotates, the beam profile irradiates the inner accretion2 Brumback et al.
H1 referee edits: 0.3-0.7 pp, modeling to 0.3-60 keV
Obs. H1 Obs. H1 P o w e r L a w F l u x ( - e r g / s / c m Obs. H1 Obs. H1
H4 referee edits: 0.3-0.7 pp, modeling to 0.3-60 keV
Obs. H4Obs. H4 P o w e r L a w F l u x ( - e r g / s / c m Figure 6.
Left: Power law flux (8–60 keV, blue points) compared to the
NuSTAR φ SO = 0 .
20) and Observation H4 (bottom row, φ SO = 0 . XMM-Newton disk. The hard pulse profile is made by calculating theluminosity of the beam visible to the observer as a func-tion of pulse phase and disk precession angle. We gener-ate the soft pulse profile by calculating the luminosity ofthe irradiated disk visible to the observer. We then com-pare the simulated pulse profiles to the observed profiles.This model does not include the effects of general rela-tivity or light bending.When modeling Her X-1’s inner disk, we are able touse previous models of Her X-1’s warped disk to guideour choice of parameters. Scott et al. (2000) created amodel disk that would reproduce observed changes inHer X-1’s observed pulse profiles between the main onand short on of the superorbital cycle. They used a lowobserver elevation consistent with the high inclinationof the source ( θ obs = − ◦ ) and defined the disk as hav-ing an inner tilt angle ( θ in ) of 11 ◦ and an outer tilt angle( θ out ) of 20 ◦ . Furthermore, they used a twist angle of139 ◦ between the inner and outer rings of the disk. Sim-ilar parameters were used by Leahy (2002), who createda warped disk to reproduce the observed 35 day supeor-bital modulation as seen by RXTE . Leahy (2002) foundan the observer angle of 5 ◦ and an outer tilt angle to30 ◦ best reproduced the shape of the superorbital cycle.For this work, we adopted the disk parameters foundby Scott et al. (2000) and used an observer elevation of-5 ◦ . We also tried using the Scott et al. (2000) outer disk tilt angle of 20 ◦ but ultimately found a better fit toour observed pulse profiles with the Leahy (2002) valueof 30 ◦ . Our full set of model parameters are shown inTable 4.We kept the disk geometry set to the values describedabove for all three observations. We allowed the loca-tion of the two beams and their widths to vary untilwe matched the observed shape of the hard pulse pro-files (Table 4). We allowed the model disk to precesssaround the pulsar, which changed the shape and phaseof the soft pulse profile component. We calculated thesimulated hard and soft pulse profiles at eight equallyspaced disk precession angles. We then fit the simu-lated pulse profile to the observed pulse profile, allow-ing the overall amplitude of the simulated pulsationsto scale, and estimated the goodness of fit by calculat-ing r = (cid:80) ( P obs ( φ spin ) − P sim ( φ spin )) /P obs , where P obs is the observed pulse profile and P sim is the simulatedpulse profile. The disk precession phase with the lowest r value represents the orientation of the disk that repro-duces the observed pulsations best, and these phases arehighlighted in green in Figures 7 and 8. We performedthe fits for the pencil and fan beam configurations inde-pendently.Because the energy-resolved pulse profiles for Obser-vation H1 and Observation H4 are extremely similar, thebest fit beam geometry and disk precession angle is the odeling disk precession in Her X-1 φ SO ≈ . THE PRE-ECLIPSE DIPObservation H4 captured a pre-eclipse dip with both
NuSTAR and
XMM-Newton , as seen in the light curvein Figure 2. This observation began at 58556.278576MJD and ended at 58556.750799 MJD, with the nexteclipse occurring at 58556.874225 MJD. Giacconi et al.(1973) noted the presence of pre-eclipse dips in longterm UHURU light curves or Her X-1. During thesedips the flux of Her X-1 drops significantly as most ofthe pulsating emission becomes heavily absorbed (Giac-coni et al. 1973; Stelzer et al. 1999). The unabsorbedemission spectrum is well described by a power law, sug-gesting that this persistent emission results from X-rayscattering in the obscuring matterial (Vrtilek & Halpern1985; Choi et al. 1994; Leahy et al. 1994; Reynolds &Parmar 1995). Modeling of long term X-ray light curvessuggest that these dips are caused by obscuration of ma-terial at the impact region of the accretion stream andaccretion disk (e.g., Igna & Leahy 2012).This dip presented an opportunity to examine the on-set of the dip as a function of energy across a wide rangeof X-ray energies. In Figure 10 we show energy-resolvedlight curves of the onset of the dip, binned by 30 seconds.In the soft (0.5-1 keV) X-rays, the transition from brightto faint emission is almost immediate, taking place in asingle 30 s time bin. In the middle (7-12 keV) and hard(15-60 keV) X-rays the transition occurs more slowly,over hundreds of seconds. The varying response of theenergy resolved light curves is consistent with the gener-ally held picture of an increase in absorber column den-sity and scattering of the hard X-ray continuum (e.g.,Vrtilek & Halpern 1985; Leahy et al. 1994).The black arrow in Figure 10 marks a short re-brightening event seen during the onset of the pre-eclipsedip in the higher energy X-ray bands. This event couldbe related to the “spike” phenomenon first seen by Vr-tilek & Halpern (1985), where short increases in X-rayluminosity were seen during Her X-1’s pre-eclipse dips.Vrtilek & Halpern (1985) reported that these spikes reached as much as 80% of the pre-dip flux, lasted about5–8 minutes, and repeated with a period of 108 minutes.While the soft (0.5–1 keV) energy band is mostly ob-scured during the pre-eclipse dip, we do see variationsin brightness within the dip in the middle (7-12 keV)and hard (15-60 keV) energy bands, which we show inFigure 11. We performed an epoch folding search of thedip light curve to check for periodic behavior and foundno significant periods within the pre-eclipse dip.To further check for the 108 minute period found byVrtilek & Halpern (1985), we included vertical dashedlines in Figure 11 at 108 minute intervals starting withthe re-brightening event marked with the black arrow inFigure 10. While the first, second, and third interval doalign with some variations in the light curve, there is sig-nificantly more variation present than can be describedwith a 108 minute period. Additionally, the variationswe see in this dip appear less pronounced than thoseseen by Vrtilek & Halpern (1985).While we do not see the clear spiking phenomenon ob-served by Vrtilek & Halpern (1985), we do see significantvariability in the hard X-ray flux during the pre-eclipsedip. This variability seems consistent with that observedby Leahy et al. (1994) and could possibly be caused byirregularities in the structure of the obscuring material.We leave a more detailed analysis of the variations seenin Observation H4 and their spectral similarity to thespikes of Vrtilek & Halpern (1985) to a later analysis. DISCUSSIONSeveral previous works including McCray et al. (1982),Scott et al. (2000), Leahy (2002), Ramsay et al. (2002),Zane et al. (2004), Hickox et al. (2004), Kuster et al.(2005), and Staubert et al. (2013) suggested that thechanges in pulse profile shape with superorbital phase inHer X-1 were caused by reprocessing in the inner accre-tion disk during its precession around the neutron star.In this work we use three observations of Her X-1 atdifferent superorbital phases to show that the observedchanges in pulse profile shape and relative phase can bemodeled by a simple precessing accretion disk.If disk precession is the cause of the changes in shapeand phase of the pulse profiles, then we expect that ob-servations from the same superorbital phase should havesimilar pulse profile shapes. We confirm this expectationwith the Observation H1 and H4 pulse profiles, whichhave similar pulse shapes and the same relative phaseoffset between the hard and soft pulsations. These re-sults are strengthened by good agreement with archivaldata of Her X-1, particularly the
NuSTAR pulse profilespresented in F¨urst et al. (2013) from superorbital phases4
Brumback et al. obs_elev = -5 obs_elev = -5
Figure 7.
Observed hard (blue) and soft (red) pulse profiles compared with simulated (black) pulse profiles from the warpeddisk model with a pencil beam for the three Her X-1 observations. The disk precession angles ( φ ) correspond to the 35 daysuperorbital phase. For each disk precession angle, we calculate the goodness of fit with the parameter r ( r = (cid:80) ( P obs ( φ spin ) − P sim ( φ spin )) /P obs , where P obs is the observed pulse profile and P sim is the simulated pulse profile). For the soft pulses, a disk precession of φ SO = 0 .
25 (highlighted in green) best describes the observed pulse profiles ofObservations H1 and H4, while a disk precession of φ SO = 0 .
75 best describes Observation R3. odeling disk precession in Her X-1 Table 4.
Disk Model ParametersObservation H1 Observation R3 Observation H4Parameter Pencil Beam Fan Beam Pencil Beam Fan Beam Pencil Beam Fan Beam r in (10 cm) 0.8 0.8 0.8 0.8 0.8 0.8 r out (10 cm) 1 1 1 1 1 1Inner tilt θ in ( ◦ ) 10 10 10 10 10 10Outer tilt θ out ( ◦ ) 30 30 30 30 30 30Twist angle φ tw ( ◦ ) 139 139 139 139 139 139Beam angle from rotational plane θ b1 ( ◦ ) 0 40 0 40 0 40Beam angle from rotational plane θ b2 ( ◦ ) 60 60 60 60 60 60Beam azimuth φ b1 ( ◦ ) 0 0 0 0 0 0Beam azimuth φ b2 ( ◦ ) 210 140 220 130 210 140Beam half-width σ b ( ◦ ) 45 60 45, 60 a
60 45 60Fan beam opening angle θ fan ( ◦ ) 0 60 0 60 0 60Observer elevation θ obs ( ◦ ) -5 -5 -5 -5 -5 -5 a Here the beam width were asymmetric, with σ b1 =45 ◦ and σ b2 =60 ◦ . Brumback et al. obs_elev = -5 obs_elev = -5
Figure 8.
Observed hard (blue) and soft (red) pulse profiles compared with simulated (black) pulse profiles from the warpeddisk model with a fan beam for the three Her X-1 observations. The disk precession angles ( φ ) correspond to the 35 daysuperorbital phase. For each disk precession angle, we calculate the goodness of fit with the parameter r ( r = (cid:80) ( P obs ( φ spin ) − P sim ( φ spin )) /P obs , where P obs is the observed pulse profile and P sim is the simulated pulse profile). For the soft pulses, a disk precession of φ SO = 0 .
25 (highlighted in green) best describes the observed pulse profiles ofObservations H1 and H4, while a disk precession of φ SO = 0 .
75 best describes Observation R3. odeling disk precession in Her X-1 obs_elev = -5 φ SO =0.25 φ SO =0.25 φ SO =0.75 Figure 9.
The simulated disk that best reproduces the observed pulse profiles from Observation H1, R3, and H4 for both thefan beam and pencil beam models. The orange shaded section of the disk represents the illuminated side of the disk, while blacklines indicate the back of the disk which is not illuminanted by the pulsar beam. Units are 10 cm. Figure 10.
Energy resolved light curves centered around the onset of the pre-eclipse dip in Observation H4 and binned with30 second bins. The transition is abrupt in the soft X-rays (0.5–1 keV, red) and more gradual in the mid (7–12 keV, green) andhard (15–60 keV, blue) curves. The black arrow marks a re-brightening event during the onset of the dip that is visible in thehigher energy bands. The count rates for each light curve have been arbitrarily offset for clarity. We cleaned the
XMM-Newton light curves using the SAS tool epiclccorr to remove bins with low exposure fraction due to Counting Mode. Brumback et al.
Time since MJD 58556.3 (s) N o r m a li z e d C o un t R a t e NuSTAR 15-60 keVXMM 7-12 keV
Figure 11.
The same middle (7–12 keV, green) and hard (15–60 keV, blue) light curves from Figure 10, but shifted in time tofocus on the dip, rather than its onset. The onset of the dip starts at 12000 s in this plot. The black dashed lines are placed at108 minute intervals, starting at the first re-brightening event during the onset of the dip. The activity seen in this pre-eclipsedip does not appear to follow a 108 minute period.
XMM-Newton and
NuSTAR spec-tral analysis we do see similarities between ObservationsH1 and H4, particularly in the high energy continuum(photon index, power law cutoff and folding energies),the shape of the CRSF, and the size of the soft bump fea-ture (e.g. Jimenez-Garate et al. 2002; F¨urst et al. 2013).We do find some differences in the blackbody temper-ature and normalization between Observations H1 andH4, which is likely due to a combination of the short pre-dip exposure time for Observation H4 and small changesin the spectral continuum shape with superorbital phase(e.g., F¨urst et al. 2013).We see significantly different spectral shapes in Ob-servations H2 and H3 than we do in H1 and H4. Whilesome spectral differences with superorbital phase are tobe expected, the low flux and lack of strong pulsationsduring Observations H2 and H3 indicate that these ob-servations are somewhat unusual for Her X-1. We sug-gest that the neutron star and central accretion regionwere obscured during these observations because of thereduced flux and lack of pulsations.Using the same warped disk model from B20, we wereable to simulate a simple warped disk irradiated by ei-ther a pencil or a fan beam emission geometry and cal-culate the simulated pulse profiles that would be ob-served for different precession angles of the disk. Weused the previous disk modeling of Scott et al. (2000)and Leahy (2002) to guide our choice of disk geometry. We ultimately found that both the pencil and fan beamemission models, which were fit independently, were ca-pable of reproducing the observed pulse profiles and thatthe simulated disk precession phase was in good agree-ment with the superorbital phase of our observations.However, the pencil beam emission geometry provides aslightly better fit to the observed pulse profiles, whichcan be seen by the smaller values of r for each observa-tion in Figures 7 and 8. However, we would like to notethat the geometries used in this model are simplistic forthe purpose of highlighting the contribution of the pre-cessing disk. It is likely that the accretion geometry ofHer X-1 is more complex than this model suggests.In both the fan and pencil beam emission geometrieswe find that the preferred beam geometry is stronglynon-antipolar. We demonstrate this conclusion by show-ing a simulated pulse profile from antipodal pencilbeams in Figure 4. The shape of the simulated pulseprofile from antipodal beams is not a good fit to ourobserved pulse profiles. Kraus et al. (1995) identifieddistortions in the dipolar field of neutron stars as a possi-ble cause of asymmetry in pulse profiles. Blum & Kraus(2000) found that the energy-resolved pulse profiles fromHer X-1 suggested a slightly distorted dipolar field. B20and Hickox & Vrtilek (2005) also found this preferencefor non-antipolar beams. This preference may suggestthat the structure of magnetized accretion flows aremore complex than the current scope of our warpeddisk model. Future modeling efforts would benefit fromconsidering more complex emission geometries (e.g., Ko-liopanos & Vasilopoulos 2018; Iwakiri et al. 2019), physi-cally motivated accretion column models (e.g., Sokolova- odeling disk precession in Her X-1 XMM-Newton and
NuSTAR . Examiningthe pulsed fractions (Figure 2) and energy-resolved lightcurves (Figure 10) both show strong absorption of thesoft X-ray emission consistent with obscuration by partof the accretion disk. The data do not show evidenceof a periodic spiking signal previously seen by Vrtilek &Halpern (1985). CONCLUSIONIn this work we performed a broad-band X-ray tim-ing analysis of Her X-1 during its 35 day superorbitalcycle. Our series of four joint
XMM-Newton and
NuS-TAR observations sampled a single superorbital cycle;however, we focus on the first and fourth observationsin this series which had sufficient signal to noise to cre-ate energy-resolved pulse profiles in narrow energy band-passes. We supplemented our missing coverage of the su-perorbital phase with an archival
XMM-Newton obser-vation at φ SO =0.60. We found that the soft ( < > NuSTAR
Software:
HEAsoft (v6.26.1; HEASARC 2014), NuS-TARDAS, SAS (Gabriel et al. 2004), Stingray (Hup-penkothen et al. 2019), Xspec (v12.10.1; Arnaud 1996),MaLTPyNT (Bachetti 2015)APPENDIX A. EXTENDED TIMING ANALYSISAlthough we could not use our warped disk model on Observation H3 due to the lack of
XMM-Newton pulsations,we were able to extract a
NuSTAR
NuSTAR data which were most strongly pulsed and followed the method described in Section 3. We show the
NuSTAR pulse profile of Observation H3 in Figure 12. The pulse profile shows a single broad peak that is atypical forhard pulses from Her X-1.When selecting the energy bands to be used in our hard and soft pulse profiles, we found it necessary to examinethe energy dependence of the pulse profile to make an appropriate selection. This decision was motivated heavily byRamsay et al. (2002), who examined the energy dependence of their
XMM-Newton observations and found changes inthe soft pulse profile beginning around 0.8 keV (see Figure 2 in Ramsay et al. (2002). We created similar figures byfiltering the
XMM-Newton data for Observations H1 and H4 into the following energy bins: 0.3–0.7 keV, 0.8–1.2 keV,1.5–3 keV, 3–6 keV, 6.2-6.6 keV, and 7–12 keV. We also filtered the
NuSTAR data for Observations H1 and H4 intoenergy bins consisting of 3–6 keV, 6.2–6.6 keV, 7-12 keV, 12.4-30 keV, 30.4–60 keV. We based these energy bins onthose used by Ramsay et al. (2002), but adjusted the energy ranges slightly to suit joint
XMM-Newton and
NuSTAR observations. We also filtered the pulsed portion of the
NuSTAR data from Observation H3 into the same energy0
Brumback et al.
Observation H3 ( φ SO =0.74) Figure 12.
The
NuSTAR bands used for the
NuSTAR data of Observations H1 and H4. As mentioned in Section 2, we were unable to extractcoherent energy-resolved pulse profiles from the
XMM-Newton data of Observation H3.We folded the energy-resolved data by the best fit period for the corresponding observation. We varied the resolutionwith which we plotted the pulse profiles to match the effective exposure of the pulsed emission from each observation:Observation H1 profiles contain 128 phase bins, Observation H3 profiles contain 20 phase bins, and Observation H4profiles contain 70 phase bins. We have also shifted the profiles of Observations H3 and H4 so that the hard pulsepeak aligns in phase with the peak from H1. We show the resulting pulse profiles in Figure 13.Figure 13 shows that the soft pulse profiles are highly energy dependent and that the sharp, notched peak thatdefines the hard pulse profile begins to emerge around 0.8 keV. In order to isolate the soft, reprocessed emission, wetherefore selected the energy range of 0.3–0.7 keV for our soft energy band in this work.While the pulse profiles of Observations H1 and H4, and their energy dependence, are almost identical (as we expectfrom the precessing disk scenario), the pulse profiles from Observation H3 differ significantly. The pulsations aregenerally weaker and the pulse is much broader than the pulses in Observations H1 and H4, and lacks the distinctivenotch. Some differences in pulse shape can be expected from the processing disk scenario, in which different parts ofthe accretion column are visible at this superorbital phase.Interestingly, we note that the energy resolved pulse profiles shown by Ramsay et al. (2002) are significantly differentin shape than those from our series, despite the similar energy bins used. Some of these changes may be expectedfrom the differences in superorbital phase (Ramsay et al. (2002) observations fall at superorbital phases 0.17, 0.26,and 0.60, compared to the phases of Observations H1, H3, and H4 of 0.20, 0.74, and 1.14). However, the magnitudeof these differences imply that the pulse shape has changed between these two series. The pulse profiles shown in thiswork show more similarity to the pulse profiles presented in Staubert et al. (2009). odeling disk precession in Her X-1 Figure 13.
Energy resolved pulse profiles for Observations H1, H3, and H4. Red profiles are
XMM-Newton and blue profilesare
NuSTAR . In order to show the pulse profiles in detail while maintaining high signal-to-noise, we varied the resolution withwhich we produced these profiles to match the effective exposure of the pulsed emission: Observation H1 profiles contain 128phase bins, Observation H3 profiles contain 20 phase bins, and Observation H4 profiles contain 70 phase bins. We have alsoshifted the profiles of Observations H3 and H4 so that the hard pulse peak aligns in phase with the peak from H1, for clarity.We note that there is strong energy dependence in the soft band, which is illustrated by the emergence of the primairy pulsepeak as early as 0.8 keV. The softest energy band (0.3–0.7 keV) shows a smooth, single peaked profile that we expect fromreprocessed emission (e.g., Hickox et al. 2004). The 0.8–1.2 keV band appears to be a mix of the reprocessed emission and theharder, sharply pulsed profiles that dominates at energies above 1.5 keV. In Observation H3 we are unable to produce energyresolved pulse profiles from the
XMM-Newton data.
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