Observations of a GX 301-2 Apastron Flare with the X-Calibur Hard X-Ray Polarimeter Supported by NICER, the Swift XRT and BAT, and Fermi GBM
Q. Abarr, M. Baring, B. Beheshtipour, M. Beilicke, G. deGeronimo, P. Dowkontt, M. Errando, V. Guarino, N. Iyer, F. Kislat, M. Kiss, T. Kitaguchi, H. Krawczynski, J. Lanzi, S. Li, L. Lisalda, T. Okajima, M. Pearce, L. Press, B. Rauch, D. Stuchlik, H. Takahashi, J. Tang, N. Uchida, A. West, P. Jenke, H. Krimm, A. Lien, C. Malacaria, J. M. Miller, C. Wilson-Hodge
DDraft version January 13, 2020
Typeset using L A TEX twocolumn style in AASTeX62
Observations of a GX 301 − X-Calibur
Hard X-Ray PolarimeterSupported by
NICER , the
Swift
XRT and BAT, and
Fermi
GBM
Q. Abarr, M. Baring, B. Beheshtipour, M. Beilicke, G. de Geronimo, P. Dowkontt, M. Errando, V. Guarino, N. Iyer,
7, 8
F. Kislat, M. Kiss,
7, 8
T. Kitaguchi, H. Krawczynski, J. Lanzi, S. Li, L. Lisalda, T. Okajima, M. Pearce,
7, 8
L. Press, B. Rauch, D. Stuchlik, H. Takahashi, J. Tang, N. Uchida, A. West, P. Jenke, H. Krimm, A. Lien,
17, 18
C. Malacaria,
19, 20
J. M. Miller, and C. Wilson-Hodge Washington University in St. Louis, 1 Brookings Dr., CB 1105, St. Louis, MO 63130 Rice University, Department of Physics & Astronomy Department, 6100 Main Street, Houston TX 77251-1892 Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Leibniz Universit¨at Hannover, formely: WashingtonUniversity in St. Louis, 1 Brookings Dr., CB 1105, St. Louis, MO 63130 Former affiliation: Washington University in St. Louis, 1 Brookings Dr., CB 1105, St. Louis, MO 63130 DG CIrcuits, 30 Pine Rd, Syosset, NY 11791 Guarino Engineering, 1134 S Scoville Ave Oak Park, IL 60304 KTH Royal Institute of Technology, Department of Physics, 106 91 Stockholm, Sweden The Oskar Klein Centre for Cosmoparticle Physics, AlbaNova University Centre, 106 91 Stockholm, Sweden University of New Hampshire, Morse Hall, 8 College Rd, Durham, NH 03824 RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan NASA Wallops Flight Facility, 32400 Fulton St, Wallops Island, VA 23337 Brookhaven National Laboratory, 98 Rochester St, Upton, NY 11973 NASA’s Goddard Space Flight Center, Greenbelt, MD 20771 Hiroshima University, Department of Physical Science, 1-3-1, Kagamiyama, Higashi-Hiroshima, 739-8526, Japan University of Alabama in Huntsville, Huntsville, AL 35899, USA National Science Foundation, 2415 Eisenhower Ave., Alexandria, VA 22314 USA Center for Research and Exploration in Space Science and Technology (CRESST) and NASA Goddard Space Flight Center, Greenbelt,MD 20771, USA Department of Physics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA ST12 Astrophysics Branch, NASA Marshall Space Flight Center, Huntsville, AL 35812, USA Universities Space Research Association, NSSTC, Huntsville, AL 35805, USA University of Michigan, Department of Astronomy, 1085 S. University, Ann Arbor, MI 48109
ABSTRACTThe accretion-powered X-ray pulsar GX 301 − X-Calibur hardX-ray polarimeter during late December 2018, with contiguous observations by the
NICER
X-raytelescope, the
Swift
X-ray Telescope and Burst Alert Telescope, and the
Fermi
Gamma-ray BurstMonitor spanning several months. The observations detected the pulsar in a rare apastron flaringstate coinciding with a significant spin-up of the pulsar discovered with the
Fermi
GBM. The
X-Calibur , NICER , and
Swift observations reveal a pulse profile strongly dominated by one main peak,and the
NICER and
Swift data show strong variation of the profile from pulse to pulse. The
X-Calibur observations constrain for the first time the linear polarization of the 15-35 keV emission from a highlymagnetized accreting neutron star, indicating a polarization degree of (27 +38 − )% (90% confidence limit)averaged over all pulse phases. We discuss the spin-up and the X-ray spectral and polarimetric resultsin the context of theoretical predictions. We conclude with a discussion of the scientific potentialof future observations of highly magnetized neutron stars with the more sensitive follow-up mission XL-Calibur . Corresponding author: Henric Krawczynski, [email protected], Fabian Kisklat, [email protected], and Manel Errando, [email protected] a r X i v : . [ a s t r o - ph . H E ] J a n The X-Calibur team:
Abarr et al.
Keywords: hard X-ray polarimetry, accreting X-ray pulsars, strong-field quantum electrodynamics INTRODUCTIONIn this paper, we report on phase-resolved spectro-polarimetric observations of the accretion-powered,highly-magnetized X-ray pulsar GX 301 − X-Calibur baloon-borne mission (see Fig. 1) (Krawczynskiet al. 2011a; Guo et al. 2013; Beilicke et al. 2014, 2015;Kislat et al. 2017, 2018) in late December 2018. Theobservations were accompanied by spectro-temporal ob-servations in overlapping and adjacent periods by the
Neil Gehrels Swift Observatory (Swift)
Burst Alert Tele-scope (BAT) (Barthelmy et al. 2005), the
Swift
X-rayTelescope (XRT) (Burrows et al. 2007), the
Neutronstar Interior Composition Explorer Mission (NICER)
X-ray telescope (Gendreau et al. 2012), and the
Fermi
Gamma-ray Burst Monitor (GBM) (Meegan et al.2009). The observations covered a particularly inter-esting epoch in which the pulsar exhibited rare flaringactivity associated with a substantial pulsar spin-up.The pulsar is in an orbit of period ∼ . +0 . − . kpc (Gaia Collaboration 2018).Wray 977 has an estimated mass of ∼ (cid:12) , a ra-dius of ∼ R (cid:12) ∼ . ∼ × L (cid:12) (Kaper et al. 2006; Clarket al. 2012). The pulsar has a spin period of ∼
680 sec(White et al. 1976) and a 2-10 keV luminosity of 10 -10 erg/s (Liu et al. 2018). The pulsar displays brightflares prior to periastron at an orbital phase of ∼ . − ∼ − ◦ and 78 ◦ .GX 301 − r m ∼ − Figure 1.
The
X-Calibur hard X-ray polarimeter duringintegration in McMurdo (Antarctica) in December 2018. The
InFOC µ S X-ray mirror is used to focus the X-rays onto ascattering polarimeter at the front (right) and back (left)ends of the 8 m long telescope. the neutron star surface (Basko & Sunyaev 1975, 1976;Becker et al. 2012; Mushtukov et al. 2015a). The X-rayemission is believed to form through the Comptoniza-tion of black body, bremstrahlung, and cyclotron seedphotons emitted in and nearby the shocked plasma lead-ing to a power law at low energies with an exponentialcutoff in the 10-20 keV energy range (Becker & Wolff2007; Farinelli et al. 2012; Postnov et al. 2015; West etal. 2017; Wolff et al. 2019).The literature on accreting X-ray pulsars distinguishesbetween two idealized radiation patterns associated withthe different locales for the energy dissipation, as illus-trated in Fig. 2. The dissipation in a radiative shockfurther up in the accretion column is believed to leadto a fan-shaped radiation pattern with most photonsleaving the accretion column perpendicular to the flowdirection (Davidson 1973). Emission associated with ahydrodymnamic shock close to the neutron star surfaceis expected to lead to a more narrowly focussed emissionpattern resembling a pencil beam (Burnard et al. 1991;Nelson et al. 1993). Discriminating between these twoscenarios is a prime goal of studies of X-ray Binaries,and X-ray polarimetry stands to play a decisive role.GX 301 − NuSTAR revealed twocyclotron resonant scattering features (CRSFs) withline centroids E CRSF and Gaussian widths σ CRSF of( E CRSF , σ
CRSF )= (37 keV, 5 keV) and (50 keV, 8 keV)(F¨urst et al. 2018; Nabizadeh et al. 2019). The CRSFenergies and widths depend on time and on the pul-sar phase (Kreykenbohm et al. 2006; F¨urst et al. 2018;Nabizadeh et al. 2019). In XRBs, CRSFs are associated -Calibur
Observations of GX 301 − Figure 2.
Schematic views of the fan-beam (left) and pencil-beam (right) emission geometries. (Adapted from Sch¨onherr etal. (2007).) with electrons transitioning between quantized Landaulevels, the transverse energy discretization relative tothe magnetic field direction that emerges from the Diracequation in quantum electrodynamics (QED). The ob-servation of an electron CRSF at energy E CRSF con-strains the magnetic field to be: B ≈ (1 + z ) n E CRSF .
57 keV 10 G . (1)Here, the positive integer n is the harmonic numberof the cyclotron transition. This relation applies toline features at energies significantly lower than m e c ,i.e. when B is much smaller than the quantum criticalfield B cr = m c e (cid:126) ≈ . × G , so that the harmon-ics are evenly spaced.For a neutron star of mass M and an emission fromradius r em (measured from the center of the neutronstar), the redshift z is approximately given by: z = 1 (cid:113) − GMr em c − ≈ . MM (cid:12) (cid:16) r em
10 km (cid:17) − . (2)If the absorption features are interpreted as coming fromone region, then the natural n = 3 , B = 1 . × (1 + z ) Gauss, while an n = 2 , B ∼ . × (1 + z ) Gauss. In such a case,the absence of a prominent n = 1 fundamental at lowerenergies poses an issue. Thus, F¨urst et al. (2018) inter-pret the two features as being fundamentals from dis-tinct regions, in which case they possess higher fields,namely ∼ × G and ∼ . × G (for z = 0),corresponding to cyclotron absorption radii differing byonly around 12%. These fields are substantially abovethe values inferred from accretion torque models (seeTable 1 of Staubert et al. 2019), the converse of whatis usually obtained when comparing these two field es-timates for X-ray binary pulsars. Some CRSFs are ob-served to depend on pulse phase, time, and luminosity (Staubert et al. 2019, and references therein). Thesevariations are sometimes attributed to a movement ofthe radiative shock along the accretion column, or bychanges in the magnetic field geometry (e.g. Becker etal. 2012; Mushtukov et al. 2015b).The polarimetric capability of X-Calibur opens up anew degree of freedom in diagnosing the physical envi-ronment of GX 301 −
2. Observations of the linear polar-ization fraction and angle can provide qualitatively newinformation on the origin of X rays in the accretion col-umn or at its impact locale on the neutron star surface,on their birefringent propagation in the magnetosphere,and on the photon interaction cross sections.The predictions of the polarization of the X-rays fromhighly magnetized neutron stars depend strongly on thestrong-field Quantum Electrodynamic (QED) predic-tions of the birefringence of the magnetized vacuum Eu-ler & Kockel (1935); Heisenberg & Euler (1936); Weis-skopf (1936); Schwinger (1951); Toll (1952); Gnedin &Pavlov (1974); Chanan et al. (1979); Heyl & Shaviv(2000) and the mode dependence of the scattering crosssections and absorption coefficients (e.g. Adler et al.1970; Canuto et al. 1971; Adler 1971; M´esz´aros & Ven-tura 1978; Ventura 1979; Arons et al. 1987; M´esz´aros1992; Harding & Lai 2006). Kii et al. (1986); Kii (1987)and M´esz´aros et al. (1988) used polarization-dependentradiation transfer calculations to predict the polariza-tion fractions of accreting X-ray pulsars. They foundthat the mode-dependent scattering cross-sections leadto high polarization fractions in certain pulse intervals.M´esz´aros et al. (1988) determined that the models ro-bustly predict that the phase-resolved flux and polar-ization fraction should be correlated (anti-correlated) inthe fan beam (pencil beam) models. The detection ofsuch a correlations can therefore discriminate betweenthe fan beam and pencil beam models. This is a design
The X-Calibur team:
Abarr et al. driver for an upgraded version of
X-Calibur , as describedin Sect. 6.The rest of the paper is structured as follows. The
X-Calibur mission and experiment is described in Sect. 2.The
X-Calibur , NICER , Swift , and
Fermi observationsand data analysis methods are described in Sects. 3 and4, respectively. We present the results of the observa-tions in Sect. 5 and conclude with a summary and anoutlook for the scientific potential of follow-up flightsin Sect. 6. The appendices include a description of the
X-Calibur
Stokes parameter analysis (Appendix A), ourestimates of the systematic errors on the
X-Calibur po-larization parameters (Appendix B), and a summary ofthe spectral results (Appendix C).All errors and uncertainties are quoted at 1 σ -level(68.27% confidence level), unless noted otherwise. THE
X-CALIBUR
EXPERIMENT
X-Calibur combines an 8 m long X-ray telescopewith arc-second pointing and a scattering polarimeter(Fig. 1). The telescope uses an aluminum-carbon fiberoptical bench (Kislat et al. 2017), which is pointed withthe Wallops Arc Second Pointer (WASP) with a point-ing stability of ∼
1” Root Mean Square and a pointingknowledge of <
15” (3 σ ) (Stuchlik 2015). X-Calibur’s en-ergy range is limited to >
15 keV by the absorption in theresidual atmosphere at a float altitude of 125,000 feet,and to <
60 keV by the mirror reflectivity. The mirrorachieves an angular resolution of 2.5 arcmin Half-PowerDiameter and effective areas of 93 cm at 20 keV and 46cm at 35 keV (Okajima et al. 2002; Berendse et al. 2003;Tueller et al. 2005; Ogasaka et al. 2008). Grazing inci-dence mirrors reduce the polarization of cosmic X-raysignals by less than 1% of the true polarization owing tothe shallow scattering angles (Sanchez Almeida & Mar-tinez Pillet 1993; Katsuta et al. 2009). The polarimeteris shown in Fig. 3 and is made of a Be scattering el-ement inside an assembly of Cadmium Zinc Telluride(CZT) detectors (each 2 mm thick, 2 × footprint,64 pixels). Photons preferentially scatter perpendicularto the angle of the electric field of the beam with anazimuthal scattering angle distribution of: dNdψ ∝ π [1 + µ p cos (2( ψ − ψ − π/ , (3)with p and ψ being the true polarization fractionand angle, ψ the measured azimuthal scattering angle,and µ = 51 .
3% is
X-Calibur’s modulation factor. A rearCZT detector is positioned behind the scattering slab formonitoring the source location in the field-of-view. Thetiming resolution is ∼ µ s. The energy resolution in-creases from ∼ Figure 3.
X-Calibur detection principle: the X-ray mirrorfocuses photons onto a Be scattering element. The scatteredphoton is detected in the surrounding assembly of CZT de-tectors. The distribution of the azimuthal scattering anglesdepends on the linear polarization fraction and angle. A rearCZT detector behind the scattering element (at the right sideof the detector assembly) is used to monitor the position ofthe source in the field of view. at 35 keV. The detector assembly is shielded by a fullyactive CsI(Na) shield, and the polarimeter/shield assem-bly rotates at 1 rpm around the optical axis to minimizesystematic errors. Detailed descriptions of the polarime-ter and the in-flight performance of all components aregiven in (Beilicke et al. 2014; Kislat et al. 2018; Abarret al. 2019a). OBSERVATIONS
X-Calibur was launched at 20:45 on Dec. 29, 2018 (alltimes and dates are UTC) and reached a float altitude of39.6 km (130,000 feet) roughly 3 hours later. Followingthe checkout of the pointing system and the in-flightoptimization of the anti-coincidence shield settings,
X-Calibur observed the accreting X-ray pulsars GX 301-2and Vela X-1 until the flight was aborted owing to aHe leak of the balloon at 10 pm on Jan. 1, 2019. Thestarting times and durations of the
X-Calibur on-sourceobservations windows are listed in Table 2. The high-balloon-altitude GX 301 − ◦ away from the source).The NICER
X-ray Timing Instrument (XTI, Gen-dreau et al. 2016) observed GX 301 − Swift
X-rayTelescope (XRT) observed GX 301-2 from MJD 58,480through MJD 58,488 in nine individual pointings be-tween 0.5 ks and 1.1 ks for a total of 8.1 ks. Detailsabout the
NICER and
Swift observations are summa-rized in Appendix C, Table 2. Observing windows arelabeled
X-I - X-XXXIV for
X-Calibur , N − I to N − V for NICER and S − I to S − IX for Swift -XRT. The
Swift
BAT and
Fermi
GBM observe GX 301 − -Calibur Observations of GX 301 − DATA ANALYSIS4.1.
X-Calibur Data Analysis
The
X-Calibur data analysis uses single-pixel CZTevents without shield veto. The energy deposited inthe CZT is estimated based on the calibration of thepolarimeter with a
Eu source with low-energy linesat 39.52 keV (K α ), 40.12 keV (K α ), 45.7 keV, and121.78 keV.An event consists of the pixel number i (located at po-sition (cid:126)x i = ( x, y, z ) i in the detector reference frame with x and y being the coordinates in the focal plane and z pointing towards the source), the energy E deposited inthe CZT detectors, and the GPS event time t . Consis-tent with the exponential cutoff of the energy spectrum(e.g. F¨urst et al. 2018), X-Calibur does not detect a sig-nificant excess of photons with >
35 keV energy deposits,and we thus only use
E <
35 keV events. The events en-ter the analysis with weights that were optimized basedon the detector response as inferred from Monte Carlosimulations (Appendix A). For light curves, we normal-ize the weights so that the weighted event rate equalsthe true source rate.The polarization analysis uses the Stokes parameters I (total flux), Q (the linearly polarized flux along theNorth-South direction), and U (the linearly polarizedflux along the direction rotated 45 ◦ counterclockwisefrom the North-South direction when looking at thesource) which are the weighted sums of the correspond-ing Stokes parameters of individual events (Kislat et al.2015; Strohmayer 2017). The main results are given interms of the normalized Stokes parameters: Q = Q/I (4) U = U/I (5)so that Q ( U ) equals 1 for a beam 100% linearly polar-ized along the North-South (Northeast-Southwest) di-rection. The reconstructed polarization fraction p r isgiven by: p r = (cid:112) Q + U (6)and the reconstructed polarization angle ψ r is given by: ψ r = 12 arctan ( U / Q ) = 12 arctan ( U/Q ) . (7)During the observations, we switch every 15 minutesbetween observations targeting GX 301 − ◦ away from the source in pitch andin yaw (OFF observations). As the Stokes parametersare additive, we can infer the Stokes parameters of thesource beam by calculating the Stokes parameters for the ON-observations and OFF observations, and sub-tracting the OFF values from the ON values after scalingthe OFF values according to the ON and OFF observa-tion time ratio. Details of the Stokes parameter analy-sis and background subtraction procedure are given inAppendix A. The systematic error on a measured polar-ization fraction p r is (Appendix B):∆ p r = 7 . × p r . (8)The error ∆ p r is our best estimate of the maximum pos-sible error.We fit the X-Calibur energy spectrum with
XSPEC (Arnaud 1996, 2018) using Response Matrix Files(RMFs) and Auxiliary Response Files (ARFs) derivedfrom Monte Carlo simulations.4.2.
NICER, Swift, and Fermi Data Analysis
The
NICER data were processed using
NICERDASv2018-11-19 V005a included in
HEASOFT v6.25 . Datawere calibrated, cleaned, and combined using the nicerl2 script with default screening filters. Forspectral analysis, channels corresponding to energies2-10 keV were selected.The
Swift
XRT data were taken entirely in win-dowed timing mode analyzed with the CALDBversion 20180710 and with
HEASOFT v6.25 , using s wxwt0to2s6 20131212v015 response function. The ab-sorption models were fit within the xspec command.The Swift
BAT data analysis uses the
HEASOFTv6.23 software and BAT CALDB version 20171016. The BATlight curves in eight energy bands (14-20, 20-24, 24-35,35-50, 50-75, 75-100, 100-150, and 150-195 keV) are cre-ated from the BAT survey data with the same method-ology that was used for the previous BAT survey cat-alogs (Oh et al. 2018; Baumgartner et al. 2013). The15-50 keV light curve is from the BAT transient moni-tor (Krimm et al. 2013).The
Fermi
GBM results were taken from the NationalSpace, Science, and Technology Center (NSSTC) webpage. The results are derived from the GBM NaI de-tectors binned in 0.256 s time bins and use the 12-25 keV and 25-50 keV energy channels (NSSTC GBMWeb Page 2019). The spin-frequencies are extracted us-ing techniques described in (Finger et al. 1999; Jenke etal. 2012). 4.3.
Orbital and Pulsar Phases
We compute the orbital phase with the parametersfrom Doroshenko et al. (2010), with the last recordedperiastron passage on MJD 53531.65 ± P = 41.472 days, and a period derivative of˙ P = ( − . ± . × − sec/sec. The X-Calibur team:
Abarr et al.
350 400 450 500 550 600 650 Date [MJD-58000]0.050.10.150.2 - k e V F l u x [ c t s c m - s - ] Figure 4.
GX 301 − Swift
BAT instrument (Lien & Krimm 2019). The time in-terval of the
X-Calibur observations is marked by the solidblue vertical lines. The periastron passages are marked bythe dashed black vertical lines.
Figure 5.
Average GX 301 − Swift
BAT 15-50 keV fluxin the 11 orbital cycles before the apastron flare (red his-togram), and in the orbital cycle of the apastron flare (greyhistogram). The time interval of the
X-Calibur observationsis marked by two vertical blue lines.
We calculate the pulsar phase with the following phasemodel derived from
Fermi -GBM data: φ ( t ) = ˙ φ ( t − t )+ ¨ φ t − t ) + ... φ t − t ) + .... φ
24 ( t − t ) (9)with t being the barycentered time. The model param-eters are given in Table 3. RESULTS5.1.
Timing Results
Figure 4 shows the 15-50 keV fluxes measured withthe Swift BAT. The graph clearly shows the 41.5 dayorbital period. The
X-Calibur observations fromMJD 58,482.1521-58,483.3912 (orbital phases 0.37-0.40) fall into a rare period of a flare close to apastron.Figure 5 compares the
Swift
BAT 15-50 keV count ratemeasured during the orbit covering the apastron flarewith the average count rates measured during the pre-vious eleven orbits. The activity was enhanced duringthe orbit of the apastron flare, with a pronounced peakat an orbital phase around 0.4. -1 -0.5 0 0.5 1 1.5 2 2.5 30.0050.010.0150.02 BA T R a t e [ c t s c m - s - ] H a r d . R a t i o Figure 6.
GX 301 − X-Calibur observations is marked by two vertical blue lines.
350 400 450 500 550 600 650 Date [MJD-58000]1.461.471.481.49 P u l s a r F r equen cy [ H z ] -3 Figure 7.
GX 301 − Fermi
GBM from 12-50 keV observations between 20 th Au-gust 2018 and 16 th June 2019 (from the NSSTC GBM WebPage 2019). The time period of the
X-Calibur observationsis shown by two vertical blue solid lines. The periastronpassages are marked by vertical dashed lines.
The
Swift
BAT data allows us to scrutinize the hardX-ray emission for spectral variability. Figure 6 presentsthe 14-20 keV, 20-24 keV, and 24-35 keV light curves andthe 24-35 keV to 14-20 keV hardness ratios. The RMS ofthe hardness ratios is 0.103 corresponding to a RMS ofthe photon indices Γ (from dN/dE ∝ E − Γ ) of ∆Γ ≈ Fermi
GBMin the 12-50 keV band (Fig. 7) show a spectacularspin-up coinciding with the exceptionally bright orbit.During the orbit (41.5 days) covering the
X-Calibur observations, the spin frequency (period) increased -Calibur
Observations of GX 301 −
470 480 490 500 510 520 530 540 550 Date [MJD-58000]00.050.10.150.2 - k e V F l u x [ c t s c m - s - ]
470 480 490 500 510 520 530 540 550 Date [MJD-58000]1.461.471.481.49 P u l s a r F r equen cy [ H z ] -3
470 480 490 500 510 520 530 540 550 Date [MJD-58000]-50510 S p i n - up r a t e [ H z s - ] -12 Figure 8.
The
Swift
BAT GX 301 − X-Calibur observations is shown by two vertical bluelines. The periastron passages are marked by dashed verticallines. from 1.461 mHz (spin period 684 s) on MJD 58,471.2to 1.482 mHz (spin period 675 s) on MJD 58,512.9 ata rate of 5.8 × − Hz s − (see also Nabizadeh etal. 2019). The next orbit saw a much slower spin-upfrom 1.482 mHz on MJD 58,512.9 to 1.490 mHz on MJD58,553.2 at a rate of 2.3 × − Hz s − . The spin-uprate is clearly correlated with an enhanced X-ray flux(Fig. 8), bolstering the hypothesis that a change of theaccretion rate or accretion mode is causing the spin-up. Interesting features include the simultaneous dipof the X-ray flux and spin-up rate at MJD 58,492, thedecrease of the spin-up rate between MJD 58,502 andMJD 58,510 during a phase of rather constant elevatedX-ray flux levels, and the factor two lower spin-up dur-ing MJD 58,546 and MJD 58,548 when compared to thespin up one orbit earlier (MJD 58,503-MJD 58,510) atsimilar flux levels. − − − − − − y [ mm ] − − × R a t e [ H z ] Figure 9.
X-Calibur focal plane image of the X-ray pulsarGX 301 − Date [MJD 58482] R a t e [ H z ] Figure 10.
X-Calibur
Koh et al. (1997) and Bildsten et al. (1997) reportedsimilar spin-up phases detected with the BATSE gammaray detectors. At the time, the spin frequency increasedover 23 days (MJD 48,440-48,463) from 1.463 mHz to1.473 mHz at a rate of 4.5 × − Hz s − and over 15days (MJD 49,245-49,230) from 1.474 mHz to 1.478 mHzat a rate of 3.0 × − Hz s − . All rapid spin-up periodswere accompanied by heightened apastron activity. The X-Calibur team:
Abarr et al. t [MJD]58480 58482 58484 58486 58488 ] s e r g c m × F ( k e V ) [ ] X C a li bu r R a t e [ s X Calibur (15 35 keV)BAT (20 24 keV), a.u.NICER (2 10 keV)Swift XRT (2 10 keV)
Figure 11.
X-Calibur (15-35 keV),
Swift XRT
BAT (20-24 keV),
NICER (2-10 keV), and
Swift XRT (2-10 keV) GX301 − phase X Calibur (15 35 keV)
Swift XRT (2 10 keV)
NICER (0.2 10 keV) N o r m a li z ed i n t en s i t y [ a . u .] Figure 12.
NICER (0.2-12 keV),
Swift XRT (0.2-10 keV),and
X-Calibur (15-35 keV) time-averaged GX 301 − Figure 9 shows the GX 301 − X-Calibur rear CZT detector. The image allows us toverify and refine the X-ray mirror alignment calibration(see also Appendix B). Figure 10 presents the 15-35 keVON and OFF light curves from the polarimeter sec-tion of the detector (without the rear CZT detector).Note that each data point corresponds to one 15-minuterun covering slightly more than one pulsar period.
X-Calibur detected the source with a mean 15-35 keV rateof 0.23 Hz. Figure 11 compares the X-ray light curvesfrom
X-Calibur , Swift
BAT,
Swift
XRT and
NICER taken around the time of the
X-Calibur campaign. Theflux level increased as the observation campaign un-folded and peaked a day after the
X-Calibur observa-tions ended. phase
MJD 58488.5S IX
MJD 58487.4S VIII
MJD 58486.4S VII
MJD 58485.5S VI
MJD 58484.0S V
MJD 58483.2S IV
MJD 58482.7S III
MJD 58481.2S II
MJD 58480.1S I ] R a t e ( k e V ) [ s Figure 13.
Individual
Swift XRT (0.2-10 keV) GX 301 − -Calibur Observations of GX 301 − Swift
XRT (0.2-10 keV),
NICER (0.2-12 keV),and
X-Calibur (15-35 keV). All three pulse profiles showone peak strongly dominating over the other. Theshape of the
X-Calibur
NuSTAR . Whereas the
NuSTAR pulse profiles showtwo pulses with approximately equal fluences (flux in-tegrated over time, see Figs. 3 and 4 of Nabizadeh etal. 2019), the fluence of the main
X-Calibur peak (phase0.8-1.14) exceeds that of the secondary peak 1/2 periodlater by a factor of ≈ NICER (notshown here) and
Swift data sets have sufficiently highsignal-to-noise ratios to reveal significant variations ofthe pulse profiles from pulse to pulse (Fig. 13). Suchpulse profile variations can be caused by alterations inthe accretion rate and by changes of the accretion andemission geometries.5.2.
Spectral Results
The large absorption column observable in the
NICER and
Swift energy spectra reduces the count rate dramat-ically below 2 keV. We select channels with energies be-tween 2 and 10 keV for spectral analysis, and fit themwith a power law continuum going through a partially-covered absorber, and an additional Gaussian line: N galH × (cid:18)(cid:16) cN H , + (1 − c ) N H , (cid:17) × power law + Line (cid:19) (10)where N galH was fixed to the galactic equivalent columndensity of 1 . × cm − reported in (Kalberla et al.2005).The results are reported in Tables 4-5. Given thewide variation of the signal-to-noise ratios of the dif-ferent data sets, some of the energy spectra do not con-strain some of the parameters of the model from Equ. 10.In those cases, the parameters without errors in Ta-bles 4-5 were fixed to the reported values during thefitting process. For example, in observation SI (Fig-ure 14, top, and Table 5) the data do not allow us toconstrain the second absorption component, so we fitthe spectrum using Equ. 10 with c = 1 . N H , = 0.For the main absorbing component we find N H valuesof between ∼ × cm and ∼ × cm . The N H of the main component decreases through the apastronflare until MJD 58,485.52 (observation S VI ). Most ofour values are higher than the pre-periastron columndensities of between ∼ × cm and ∼ × cm F l u x [ c m − s − k e V − ]
102 5−10−50510 ∆ χ Energy (keV)0.11 F l u x [ c m − s − k e V − ]
102 5−505 ∆ χ Energy (keV) F l u x [ c m − s − k e V − ]
105 20−505 ∆ χ Energy (keV)
Figure 14.
Top:
NICER
GX 301 − N-IV from Table 2).Middle:
Swift -XRT spectra from observation
S I (in blue)and
S V in red (see Tables 2 and 4 for details). Bottom:Joint
Swift XRT (observations
S III and
S IV from Table2) and
X-Calibur
GX 301 − from Suchy et al. (2012); F¨urst et al. (2018), and lowerthan the periastron values of between ∼ × cm and ∼ × cm of F¨urst et al. (2011).The NICER energy spectra show a clear Fe K α lines,and some marginally significant deviations of the data0 The X-Calibur team:
Abarr et al. from the best-fit model between 2 keV and 3 keV (Fig-ure 14, top). The
Swift -XRT spectra also show the pres-ence of the Fe K α line (Figure 14, middle) throughoutthe whole observation period.The X-Calibur . +1 . − . ) × − erg cm − s − and a power law index of4.2 ± σ errors). The photon index agrees withinstatistical errors with the energy spectrum measuredwith NuSTAR on 3/3/2019 which exhibits a rolloverfrom a photon index of Γ = 2 at 20 keV to Γ = 4 at30 keV (Fig. 6 of Nabizadeh et al. 2019).We study the broadband 2 −
35 keV energy spectrumby simultaneously fitting the
Swift -XRT (observations
SIII and
S IV ) and
X-Calibur data (Figure 14, bottom)with a power-law model with an exponential cutoff, apartially-covered absorber, and an additional Fe-K α flu-orescence line: N galH × (cid:18)(cid:16) cN H , + (1 − c ) N H , (cid:17) ×× E − Γ exp ( − E/E fold ) + Line (cid:19) . (11)A model with Γ = 0 . ± . E fold = 7 . ± .
78 keVand N H , = (56 ± × cm gives a good fitto the broadband data, with χ / NDF = 159 . / NuSTAR observations, with the exception of the softer photonindex of Γ ∼ . X-Calibur Polarization Analysis
All polarization results are given in the 15-35 keVband for three data sets (see lower panel in Fig. 12):(i) the entire data set, (ii) the main pulse (pulsar phase0.8-1.14), and for (iii) the bridge and secondary pulseemission (pulsar phase 0.14-0.8). Figure 15 presents themodulation curves (azimuthal scattering angle distribu-tions) for the ON and OFF observations. Neither theON nor the OFF distributions show obvious modula-tions.Figure 16 presents the results in the Q - U plane for allthree data sets. The statistical significance for a polar-ization detection can be calculated with Q and U whichhave slightly smaller relative errors than Q and U . Theoverall results deviate by (cid:112) ( Q/σ Q ) + ( U/σ U ) = 1.41(entire emission), 1.47 (main pulse), and 0.78 (bridgeand secondary pulse) standard deviations from zero po-larization ( Q = 0 and U = 0). The X-Calibur obser-vations thus did not lead to a significant detection of anon-zero polarization. ° [ ψ r a t e [ a . u .] ° [ ψ r a t e [ a . u .] ° [ ψ r a t e [ a . u .] Figure 15.
Distribution of the azimuthal scattering anglesfor the entire emission (top panel), the main pulse (phase 0.8-1.14, center panel), and for the bridge and secondary pulseemission (phase 0.14-0.8, bottom panel) for the ON (red) andOFF (black) data. Individual events enter the analysis witha weight, and we thus give the rate per bin (i.e. the weightednumber of events per unit time per bin) in arbitrary units(a.u.).
For the pulse-integrated emission, Fig. 17 shows the Q and U parameters for the background-subtracted ON-data and the OFF background data as a function oftime. It can be seen that the Q and U parameters ofthe ON and OFF observations are consistent with zeropolarization for all time intervals. The same applies tothe Q and U parameters of the entire OFF data set.Figure 18 presents the observational constraints on thepolarization fraction p and angle ψ . We use a Bayesiananalysis with a flat prior of the polarization fraction p between 0% and 100% and the polarization angle ψ -Calibur Observations of GX 301 − Table 1.
X-Calibur p and ψ are on 90% Confidence Level. The polarization angleof the third data set is unconstrained on the 90% confidence level. Phase Interval Q [%] U [%] Deviation from p = 0 [ σ ] p [%] ψ [ ◦ ] Upp. Lim. p (90% CL) [%]All (0-1) 18.4 ± ± +38 − ±
43 46.9Main Pulse (0.8-1.14) 26.6 ± ± +41 − ±
40 52.3Bridge and Sec. Pulse (0.14-0.8) 8.3 ± ± +55 −
10 62.2 between 0 and π (Quinn 2012; Kislat et al. 2015): dP ( p , ψ ) = const dp dψ (12) ∝ / (cid:112) Q + U d Q d U . The most likely true parameter combination p and ψ is shown by a cross mark, and the confidence regionsare shown by contours and the color scales. Table 1lists the most likely values of p and ψ together withthe confidence intervals derived from the distributions inFig. 18. The table includes the 90% confidence intervalupper limits on the polarization fraction p calculated bymarginalizing the probability density function P ( p , ψ )over ψ . SUMMARY AND OUTLOOKThis paper presents the results of the observations ofthe accretion-powered X-ray pulsar GX 301 − X-Calibur , NICER , the
Swift
XRT, and BAT, and
Fermi
GBM. The observations reveal a rare flaring period be-tween the periastron flares associated with a spin-up ofthe pulsar similar to earlier events (Koh et al. 1997; Bild-sten et al. 1997). Historically, the spin of GX 301 − X-Calibur observations lasted for two orbits witha marked decline of the spin-up rate after the first orbit.The spin-up events start briefly after periastron (Fig. 7in this paper, and Fig. 11 of Koh et al. 1997).A possible interpretation of these signatures is thatthe neutron star acquires a temporary accretion disk(Koh et al. 1997) shortly after periastron passage. Thetemporary disk provides fuel for one orbit during whichthe pulsar spins up continuously, and is destroyed duringthe next periastron passage. The disk may form for ex-ample when the neutron star crosses the plasma stream − − 𝒬 − − 𝒰 Figure 16.
X-Calibur constraints on the linear polariza-tion of the 15-35 keV GX 301 − σ statistical errors. Polarization fractions of0%, 30% (for illustrative purposes), and 100% correspond to Q = U = 0 point at the center of the graph, the red circle,and the black circle, respectively. − − − 𝒬 , 𝒰 Figure 17. Q (filled circles) and U (open circles) param-eters for the background-subtracted ON-data (red) and theOFF-data (black) as a function of time. The X-Calibur team:
Abarr et al. p020406080100120140160180 ] ° [ ψ C on f i den c e Le v e l p020406080100120140160180 ] ° [ ψ C on f i den c e Le v e l p020406080100120140160180 ] ° [ ψ C on f i den c e Le v e l Figure 18.
X-Calibur p and polarization angle ψ plane for theentire emission (top), the main pulse (pulsar phase 0.8-1.14, center), and the bridge emission and the secondary pulse (pulsarphase 0.14-0.8, bottom). The most likely p - ψ combination is marked by a cross. The color scale shows the results for differentconfidence levels, and the contours delineate the 68.27% (1 σ ) and 90% confidence regions. The analysis only accounts forstatistical errors. -Calibur Observations of GX 301 − ∼ ≈ X-Calibur observationsdid not yield a definitive polarization detection, but didoffer constraints on the polarization fraction and the po-larization angle plane. The results can be compared tothe predictions from M´esz´aros et al. (1988). The authorsfind that the propagation of the radiation in the ordi-nary and extraordinary mode and the strongly mode-dependent scattering cross-sections can lead to very high( ∼ X-Calibur observations constrain the po-larization fraction in the 15-35 keV band, somewhat be-low the centroids of the CRSFs at 35 keV and 50 keV.The calculations of M´esz´aros et al. (1988) were car-ried out for a cyclotron resonance at 35 keV. At 25 keVthe pencil-beam (fan-beam) model predicts polarizationfractions of ∼
20% ( < X-Calibur
GX 301 − p r = 27 +38 − % cannot distinguish between the twomodels. Doing so with high statistical certainty will re-quire future observations with a one-sigma error of < X-Calibur follow-up mission called
XL-Calibur (Abarr etal. 2019b) which promises hard X-ray polarimetric ob-servations with one to two orders of magnitude improvedsignal-to-background ratio. The mission uses the 12 mfocal length mirror fabricated for the Formation FlightAstronomical Survey Telescope (FFAST) (Tsunemi etal. 2014) which offers more than three times larger ef-fective areas than the current mirror (Awaki et al. 2014;Matsumoto et al. 2018). We furthermore expect morethan one order of magnitude lower background rates ow-ing to the use of thinner (0.8 mm thick) CZT detectors,improved shielding, and flights closer to solar minimumrather than solar maximum (see Shaw et al. 2003; Pot-gieter 2008). Simulated
XL-Calibur observations of GX301 − Imaging X- ] s e r g c m [ E E f XL Calibur 300ksec X Calibur 2018/19 0.20.40.60.81 X C a li bu r [ a r b . un i t s ] P o l . F r a c t i on Fan beam Pencil beamMin. Det. Polarization
Figure 19.
Simulated outcome of a 300 ksec GX 301 − XL-Calibur , assuming a 20-50 keV flux of700 mCrab, an energy spectrum similar to those from F¨urstet al. (2018), and an atmospheric depth of 7 g/cm (equalto the mean depth of the 2018/2019 GX 301 − X-Calibur
XL-Calibur results (black data points). Bottom:Expected polarization fractions for the fan beam (green line)and pencil beam (blue line) models of M´esz´aros et al. (1988)(model 45/45). The black data points show the simulated
XL-Calibur polarization fraction results for the fan beammodel, and the dark red lines show the Minimum DetectablePolarizations (MDPs), i.e. the polarization fractions that
XL-Calibur could detect with a 99% confidence level.
Ray Polarimetry Explorer ( IXPE , 2 keV-8 keV, launchin 2021) (Weisskopf 2016) and
XL-Calibur (launches in2022, 2023, and 2025), will enable detailed comparisonsof predicted and observed signatures.APPENDIX A - STOKES PARAMETER ANALYSISOF THE
X-CALIBUR
DATAThe analysis of the
X-Calibur events starts with thede-rotation of the x and y coordinates of the energydeposition in the detector reference frame into the ref-erence frame of the telescope truss. Subsequently, wecorrect for the offset of the focal spot of the X-ray mir-ror from the center of the scattering element as deter-mined from the excess recorded in the rear CZT detector(Fig. 9). Finally, the coordinates are referenced to thecelestial North pole based on the truss orientation mea-sured by the pointing system. Choosing a coordinatesystem with the y -coordinate pointing North and the x -coordinate pointing East, the azimuthal scattering angleis given by: ψ = arctan ( y/x ) (13)4 The X-Calibur team:
Abarr et al. so that ψ = 0 corresponds to scatterings along theNorth-South direction, and 0 < ψ < π/ k th event: i k = 1 (14) q k = − µ cos (2 ψ k ) (15) u k = − µ sin (2 ψ k ) (16)The factor µ is the modulation factor (see Equation (3)).The minus signs in the expressions of q k and u k accountfor the 90 ◦ offset between the electric field vector of thephotons and the preferred scattering direction.The fac-tor 2 /µ normalizes q k ( u k ) so that its average is 1 fora beam 100% linearly polarized along the North-Southdirection (looking into the sky, 45 ◦ anti-clockwise fromthe North-South direction).The k th event enters the analysis with weight w k thatis proportional to the expected signal-to-background ra-tio, and is the product of two functions (spectral anal-ysis) or three functions (light curves) optimized withMonte Carlo simulations of the detector. The first func-tion f ( z ) depends on the position of the energy de-position along the optical axis (the z coordinate) andaccounts for the approximately exponential distributionof the depths of the Compton scattering in the scatter-ing element. As a consequence, most source photons aredetected near the front of the polarimeter. The secondfunction f ( x, y ) depends on the position of the trig-gered pixel relative to the scattering element and is pro-portional to the azimuthal scattering angle interval ∆ ψ that the pixel covers as seen from the axis of the scat-tering element. The function weighs events close to themiddle of the side walls of the rectangular detector as-sembly more heavily than those close to the edges, asthose pixels achieve a better signal-to-background ratio.The third function f ( E ) (only for light curves) weighsevents according to the energy E deposited in the CZTdetectors and is proportional to the expected source de-tection rate as a function of energy accounting for thesource spectrum, atmospheric absorption, and the mir-ror effective area.With t ON and t OFF being the ON and OFF obser-vation times and α = t ON /t OFF , we define the total background-subtracted Stokes parameters as: I = (cid:88) ON w k i k − α (cid:88) OF F w k i k (17) Q = (cid:88) ON w k q k − α (cid:88) OF F w k q k (18) U = (cid:88) ON w k u k − α (cid:88) OF F w k u k , (19)where the sums run over the ON and OFF events.Compared to the unweighted analysis, the weightedanalysis improves the signal-to-background ratio of theGX 301 − ∼ I , Q , U , Q and U from error propagation. Each event contributes withthe following RMS-values to the analysis (Kislat et al.2015): σ i k = 1 (20) σ q k = √ µ (21) σ u k = √ µ (22)The estimates of σ q k and σ u k are conservatively chosenfor p = 0. For p > Q ( U ), we assume that the errorson I and Q ( I and U ) are statistically independent. Atoy simulation shows that this is indeed an excellentassumption.APPENDIX B - SYSTEMATIC ERRORS ON THE X-CALIBUR
POLARIZATION RESULTSWe calibrated the polarimeter at the Cornell High En-ergy Synchrotron Source using a 40 keV beam with a ∼
90% polarization (Beilicke et al. 2014). The measure-ments were carried out with different polarimeter orien-tations allowing us to simulate an unpolarized beam bycombining data taken at orientations differing by 90 ◦ .It is important to note that the rotation of the detectorand shield assembly removes systematic errors due todetector non-uniformities (e.g. dead pixels, noisy pix-els) and geometrical effects (including uncertainties inthe distances between the center of the scattering ele-ment and the CZT detectors and gaps between the de-tectors). Based on the calibration data, we estimate thatwe know the modulation factor µ within an uncertaintyof ± µ introduces a relative sys-tematic error on the measured polarization fraction p r of ∆ p r = 2% p r . -Calibur Observations of GX 301 − − d = 1 . d , the uncertainty in d leads to a residual systematic polarization fraction errorof < . Q OFF = − . ± .
011 (23) U OFF = 0 . ± .
011 (24)where the errors are given for a 1 σ confidence interval(see also Fig. 17). The fact that the background looksunpolarized implies that an under- or over-subtractionof the background (owing for example to a time variablebackground) does not create a spurious polarization de-tection. We estimate that the background subtractionintroduces a relative 5% error on measured polarizationfractions.Adding all systematic errors linearly, we get a totalsystematic error on the polarization fraction quoted inEquation (8).APPENDIX C - DATA TABLES6 The X-Calibur team:
Abarr et al.
Table 2.
Summary of
X-Calibur , NICER and
Swift -XRT obser-vations.
Instrument Label ObsID Start [MJD] Exposure [s]
X-Calibur
X-I 1 58482.158310 1080
X-Calibur
X-II 2 58482.168337 653
X-Calibur
X-III 3 58482.188979 925
X-Calibur
X-IV 4 58482.211214 923
X-Calibur
X-V 5 58482.233435 925
X-Calibur
X-VI 6 58482.255660 925
X-Calibur
X-VII 7 58482.277879 925
X-Calibur
X-VIII 8 58482.300110 924
X-Calibur
X-IX 9 58482.322312 928
X-Calibur
X-X 10 58482.344555 924
X-Calibur
X-XI 11 58482.366783 925
X-Calibur
X-XII 12 58482.389004 924
X-Calibur
X-XIII 13 58482.411225 925
X-Calibur
X-XIV 14 58482.433447 916
X-Calibur
X-XV 15 58482.455664 926
X-Calibur
X-XVI 16 58482.477913 923
X-Calibur
X-XVII 17 58482.500132 923
X-Calibur
X-XVIII 18 58482.522364 922
X-Calibur
X-XIX 19 58482.544571 926
X-Calibur
X-XX 20 58482.566831 918
X-Calibur
X-XXI 21 58482.589033 928
X-Calibur
X-XXII 22 58483.117441 219
X-Calibur
X-XXIII 23 58483.135091 757
X-Calibur
X-XXIV 24 58483.151973 986
X-Calibur
X-XXV 25 58483.174523 931
X-Calibur
X-XXVI 26 58483.193260 328
X-Calibur
X-XXVII 27 58483.218975 932
X-Calibur
X-XXVIII 28 58483.241197 930
X-Calibur
X-XXIX 29 58483.263374 925
X-Calibur
X-XXX 30 58483.285587 925
X-Calibur
X-XXXI 31 58483.307799 925
X-Calibur
X-XXXII 32 58483.330011 925
X-Calibur
X-XXXIII 33 58483.352284 936
X-Calibur
X-XXXIV 34 58483.374538 931
NICER
N-I 1010220101 58,480.09 400
NICER
N-II 1010220101 58,480.16 230
NICER
N-II 1010220101 58,480.28 310
NICER
N-IV 1010220101 58,480.34 1015
NICER
N-V 1010220102 58,481.26 230
Swift -XRT S-I 00031256019 58,480.10 1055
Swift -XRT S-II 00031256020 58,481.15 1010
Swift -XRT S-III 00031256021 58,482.73 960
Swift -XRT S-IV 00031256022 58,483.66 960
Swift -XRT S-V 00031256023 58,484.00 760
Swift -XRT S-VI 00031256024 58,485.52 895
Swift -XRT S-VII 00031256025 58,486.39 990
Swift -XRT S-VIII 00031256026 58,487.38 540
Swift -XRT S-IX 00031256027 58,488.51 920 -Calibur
Observations of GX 301 − Table 3.
GX 301 − Parameter Value t φ − ¨ φ − ... φ -0.00868925 day − .... φ − Table 4.
Spectral results from
NICER observations. The errors are on 1 σ confidence level. Observation: N-I N-II N-III N-IV N-V F −
10 keV [ × − erg cm − s − ] 1 . ± .
06 0 . ± .
10 1 . ± .
08 1 . ± .
02 2 . ± . H , [10 cm − ] 78 . ± . . ± . . ± . . ± . . ± . H , [10 cm − ] 2 . ± . . ± . . ± . . ± . . ± . . ± .
001 0 . ± .
003 0 . ± .
001 0 . ± .
001 0 . ± . Norm [cm − s − keV − ] 0 . ± .
10 0 . ± .
09 0 . ± .
13 0 . ± .
04 0 . ± . Γ . ± .
08 1 . ± .
14 1 . ± .
09 0 . ± .
06 0 . ± . α A [10 − s − cm − ] 3 . ± . . ± . . ± . . ± . . ± . α E [keV] 6 . ± .
01 6 . ± .
01 6 . ± .
01 6 . ± .
01 6 . ± . α σ [keV] 0 . ± .
02 0 .
02 0 . ± .
011 0 . ± .
007 0 . ± . χ / NDF 0.97 1.00 0.93 1.14 1.06
Table 5.
Spectral results from the
Swift XRT . The errors are on 1 σ confidence level. Observation: S-I S-II S-III S-IV S-V S-VI S-VII S-VIII S-IX F −
10 keV [10 − − −
1] 1 . ± .
20 1 . ± .
12 2 . ± .
15 2 . ± .
11 3 . ± .
15 2 . ± .
12 1 . ± .
09 1 . ± .
20 1 . ± . , −
2] 63 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . , −
2] 0 . . ± . . . ± . . . . . . ± . . . ± .
045 1 . . ± .
031 0 . ± .
002 1 . . . . ± . − − −
1] 0 . ± .
17 0 . ± .
41 0 . ± .
07 0 . ± .
34 0 . ± .
09 0 . ± .
09 0 . ± .
06 0 . ± .
07 0 . ± . . ± .
36 1 . ± .
22 1 . ± .
24 1 . ± .
17 0 . ± .
12 1 . ± .
09 0 . ± .
12 0 . ± .
26 1 . ± . α A [10 − − −
2] 9 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . α E [keV] 6 . ± .
07 6 . ± .
05 6 . ± .
05 6 . ± .
04 6 . ± .
05 6 . ± .
04 6 . ± .
03 6 . ± .
06 6 . ± . α σ [keV] 0 . ± .
082 0 . ± .
085 0 . ± .
070 0 . ± .
073 0 . ± .
061 0 . ± .
058 0 . ± .
048 0 . ± .
078 0 . χ / NDF 1.58 1.53 1.07 0.90 1.28 1.13 0.75 0.66 1.20 The X-Calibur team:
Abarr et al.
ACKNOWLEDGEMENTSWe thank A. Awaki (Ehime Uniersity), K. Hayashida(Osaka University, Project Research Center for Fun-damental Sciences, ISAS), Y. Maeda (ISAS), H. Mat-sumoto (Osaka University, Project Research Center forFundamental Sciences), T. Tamagawa (RIKEN), and K.Tamura (Nagoya University) for fruitful discussions andfor their comments on this paper. We thank V. Mikhalevfor contributing the code for barycentring the
X-Calibur event times and Rakhee Kushwah (KTH, Oskar KleinCentre) for contributing to the flight monitoring shifts.
X-Calibur is funded by the NASA APRA program un-der contract number 80NSSC18K0264. We thank theMcDonnell Center for the Space Sciences at WashingtonUniversity in St. Louis for funding of an early polarime-ter prototype, as well as for funds for the developmentof the ASIC readout. Henric Krawczynski acknowl-edges NASA support under grants 80NSSC18K0264and NNX16AC42G. KTH authors acknowledge supportfrom the Swedish National Space Agency (grant num-ber 199/18). MP also acknowledges support from theSwedish Research Council (grant number 2016-04929).Hans Krimm acknowledges support from the NationalScience Foundation under the Independent Researchand Development program.REFERENCES
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