XL-Calibur measurements of polarized hard X-ray emission from the Crab

ABSTRACT

1 INTRODUCTION

The Crab, comprising a rotation-powered pulsar and wind nebula (PWN), is one of the brightest persistent sources of celestial X-rays (Bühler & Blandford 2014). The pulsar is a highly magnetized (⁠$\sim {10}^{12}$ G) neutron star with a rotation period $\sim$33.8 ms. A small fraction of the rotational energy powers a relativistic leptonic wind, which illuminates the nebulous supernova remnant yielding synchrotron and inverse Compton emission across the electromagnetic spectrum (Gaensler & Slane 2006; Hester 2008). The Crab has been extensively studied using spectroscopy, timing, and imaging, but the addition of X-ray polarimetry allows the emission to be studied in a systematically new way. The linear polarization of the emission is described by a polarization degree (PD, per cent) and a polarization angle (PA, ${}^{\circ }$⁠).¹ In the soft X-ray band, 2–8 keV, the linear polarization of the X-ray emission was recently measured by the IXPE satellite mission (Bucciantini et al. 2023; Mizuno et al. 2023; Wong, Romani & Dinsmore 2023; Wong et al. 2024; González-Caniulef et al. 2025). Here, we present complementary measurements in the neighbouring hard X-ray band, $\sim$19–64 keV, from the balloon-borne mission XL-Calibur.

The pulsar X-ray light curve has two peaks, as is the case across the electromagnetic spectrum. The main pulse (P1) is separated from a second pulse (P2, also referred to as the interpulse) by a bridge region. The remaining off-pulse (OP) region is dominated by nebula emission. A fundamental understanding of the emission locale and field geometry for the pulsar is lacking (Harding 2019). The evolution of PD and PA across the light curve elucidates the geometry of regions where accelerated particles dissipate their energy, e.g. potentially discriminating between emission from just inside the light cylinder and proximate to the magnetospheric current sheet (Cerutti, Mortier & Philippov 2016; Harding & Kalapotharakos 2017), and that outside the magnetosphere in the inner nebula (Pétri 2013; Harding & Kalapotharakos 2017).

Spectroscopic and spectropolarimetric images of the Crab constrain the structure of the PWN, the process of particle acceleration at relativistic shocks, and the propagation of particles in the downstream plasma. Chandra images (Weisskopf et al. 2000) reveal complex structure in the inner nebula, including time-varying polar jets, an equatorial torus, and shock structures. Two concentric magnetic tori are centred on the pulsar. The inner torus lies in a plane perpendicular to the pulsar spin-axis, which has a sky-projected angle of (124.0$\pm 0.1{)}^{\circ }$ (Ng & Romani 2004).

In a phase-resolved analysis of IXPE data (300 ks), Wong et al. (2024) revealed a  + 40${}^{\circ }$ PA swing throughout P1, where the maximum PD$\sim$15  per cent is reached close to the peak phase. The phase-dependence of polarization parameters was found to differ significantly from the optical band, indicating that different mechanisms or locations are responsible for the polarized emission in the two bands. In contrast, González-Caniulef et al. (2025) present a phenomenological model connecting the polarization properties in the soft X-ray and optical bands. This suggests a common underlying emission mechanism for both bands.

In Bucciantini et al. (2023) (92 ks), IXPE reports PD = (19.0$\pm$0.2) per cent and PA = (145.5$\pm 0.3{)}^{\circ }$ for phase-integrated emission measured within 2.5 arcmin of the pulsar. Similar off-pulse values are found for the region. The polarization map follows expectations for synchrotron emission in the 100–150 $\mu$G toroidal magnetic field estimated in Mizuno et al. (2023). Local enhancement of the PD in several regions (up to 40–50 per cent to the north and south of the inner nebula) is attributed to variations in the amount of magnetic turbulence within the nebula. For the nebula-dominated off-pulse region measured within 20 arcsec of the pulsar, Bucciantini et al. (2023) reports PD = (24.1$\pm$0.8) per cent and PA = (133.6$\pm 1.0{)}^{\circ }$⁠. In the deeper IXPE observations reported in Wong et al. (2024), the polarization map of the inner nebula confirms the presence of a toroidal magnetic field. A spatial correlation is found between polarization parameters and photon spectral index, which informs the interpretation of XL-Calibur observations presented here, where the magnetic field orientations are sampled by higher energy electrons in the inner region of the PWN.

A review of Crab polarization measurements in the hard X-ray band is given in Chattopadhyay (2021). Results are generally weakly constrained. Hitherto, the most precise measurement was provided by PoGO +  (20–160 keV), where a phase integrated PD = (20.9$\pm$5.0) per cent and PA = (131.3$\pm 6.8{)}^{\circ }$ was found (Chauvin et al. 2017). In this paper, we report XL-Calibur results in the $\sim$19–64 keV range, averaged over the full pulsar phase as well as for phase selections, including the off-pulse emission, the two pulsar peaks, and the intervening bridge region. When combined with IXPE, our results provide a broad-band view of the polarization properties of Crab X-ray emission.

2 XL-CALIBUR

The XL-Calibur (Abarr et al. 2021) balloon-borne polarimeter comprises a 12 m long optical bench (truss), pointed with arcsecond precision by the Wallops ArcSecond Pointer (WASP) (Stuchlik 2017). A 45 cm diameter X-ray mirror (Tsunemi et al. 2014) is mounted at one end of the truss, with a polarimeter/anticoincidence-shield assembly at the other end. The mirror focuses X-rays by Bragg reflection from multilayer platinum and carbon foils. With a field-of-view of $\sim$5 arcmin, the effective area is $\sim$350 cm${}^2$ at 15 keV and $\sim$50 cm${}^2$ at 60 keV. A sharp reduction at 78 keV results from the K absorption edge of platinum. The half-power diameter of the point-spread function (PSF) is $\sim$2 arcmin, reaching 7.3 mm diameter in the focal plane of the mirror. Prior to the flight, the shape of the PSF was measured at the SPring-8 synchrotron beam facility (Kamogawa et al. 2022).

Focused X-rays pass through a tungsten collimator and impinge on a beryllium (Be) rod with diameter 12 mm and length 80 mm. A fraction of incident X-rays (⁠$\sim$85 per cent at 30 keV) will undergo Compton scattering from the Be rod into a circumadjacent assembly of 0.8 mm thick CdZnTe (CZT) detectors (each 20 mm $\times$ 20 mm area, 2.5 mm pixel pitch), arranged four-high around the rod in a square geometry. The energy resolution is $\sim$5.9 keV at 40 keV (full width at half-maximum). To mitigate measurement background from atmospheric X-/$\gamma$-rays and neutrons, the polarimeter is housed in a 3–4 cm thick Bi${}_4$Ge${}_3$O${}_{12}$ anticoincidence shield (Iyer et al. 2023), operated with a veto threshold of 50 keV. The polarimeter/shield assembly rotates around the viewing axis twice per minute to eliminate systematic errors arising from non-uniform CZT detector response.

The Klein–Nishina differential Compton-scattering cross-section depends on polarization as

where $\theta$ denotes the polar scattering angle, and $\varphi$ is the azimuthal angle between the photon scattering direction and the polarization (electric field) vector of the incident X-ray. By reconstructing the distribution of azimuthal scattering angles, the linear polarization of the incident beam can be estimated (Bernard et al. 2022; Del Monte, Fabiani & Pearce 2022). The resulting modulation curve, $C(\varphi )$⁠, is a harmonic function with 180${}^{\circ }$ periodicity:

where $\mu$ and $\zeta$ are the amplitude and phase of the modulation curve, respectively, and N is the mean. The modulation response to a 100  per cent polarized beam is ${\mu }_{100}$⁠, so that $\mathrm{PD}=\mu /{\mu }_{100}$⁠. Since X-rays preferentially scatter in a direction perpendicular to the orientation of the polarization vector, $\mathrm{PA}=\zeta +{90}^{\circ }$⁠.

Reconstructed polarization parameters are subject to a systematic error arising from movement of the focal point on the Be rod during observations, e.g. due to thermal or gravitational deformation of the truss (Aoyagi et al. 2024). For in-flight monitoring of the mirror alignment, an embedded back-looking camera (BLC) is used. Prior to flight, the direction of the mirror X-ray axis was determined at ISAS/JAXA and NASA Goddard Space Flight Center. At the launch site, the polarimeter-mirror alignment was confirmed using the BLC to image parallel beams of laser light focused by the mirror. X-rays that pass the Be rod impinge an imaging CZT. The profile of the X-ray beam reconstructed in this detector is used to determine the mean scattering position within the Be rod, which defines the interaction point assumed when calculating scattering angles.

3 OBSERVATIONS AND DATA ANALYSIS

XL-Calibur was launched on a 1.1 million-cubic-metre helium-filled balloon from the Esrange Space Center, Kiruna, Sweden (68.89${}^{\circ }$N, 21.11${}^{\circ }$E), on 2024 July 9, at 03:04 ut. Crab observations were conducted on July 11th, 12th, and 13th, at a median altitude of $\sim$39.4 km (line-of-sight column density of $\sim$5.55 g cm⁻²). The black-hole X-ray binary Cygnus X-1 was also observed.² The flight followed a trajectory of approximately constant latitude before termination close to Kugluktuk, Nunavut, Canada, on 2024 July 14, at 22:34 ut.

During the commissioning phase, arcminute-level offsets were introduced to Crab pointing solutions to centre the focused X-ray beam on the Be rod, based on feedback from the imaging CZT. The resulting mean interaction-point offset, reconstructed within the perimeter of the 12 mm diameter Be rod, is (0.99, 0.21) mm (zenith, starboard) when averaged across all observations, corresponding to a net offset of 17 arcsec.

The pointing direction alternated between the Crab location (on-source observations) and background fields offset by 1${}^{\circ }$ (off-source observations). Off-source pointings were conducted in a cross-pattern around the source, with excursions in azimuth or elevation. An on/off ratio of 25 min/5 min was employed for the majority of observations.

The X-ray interaction time in the polarimeter is determined with microsecond precision relative to GPS Universal Time using an on-board oscillator synchronized to a GPS pulse-per-second (PPS) signal. A phase-folded light curve is obtained with a barycentre timing correction using the closest preceding ephemeris from the Jodrell Bank Observatory³ (Lyne et al. 2014): 2024 June 15. Phase selections are used when determining polarization parameters for the pulsar. The off-pulse emission is subtracted from the pulsar-peak phase range, along with measurement background. As the GPS timing system experienced thermal-management problems on July 11th and 13th, phase-dependent studies are only possible for $\sim$63  per cent of the total signal integration-time.

Events comprising an above-threshold energy deposit (median threshold $\sim$15.4 keV, standard deviation $\sim$4.7 keV) in a single CZT pixel and no coincident activity in the shield during a $\sim$3 $\mu$s window were used in the polarization analysis. Noisy pixels were removed from the data based on measured scaler rates and inspection of pixel-by-pixel spectra, individually calibrated prior to flight using X-ray lines from a ${}^{152}$Eu source. To maximize the signal-to-background ratio, events with detected energy in the range 15–60 keV were kept. At lower energies, the signal rate diminishes due to atmospheric attenuation and pixel-by-pixel energy thresholds, while at higher energies the source flux drops below the background level. The selected range corresponds to $\sim$18.5–63.5 keV incident energy, after taking into account the average energy loss in the Be rod upon Compton scattering. The energy response was determined using Geant4 (Agostinelli et al. 2003) Monte-Carlo simulations (Aoyagi et al. 2024), where a Crab spectrum is generated and folded through the atmospheric attenuation and mirror response.

For each valid detector event, the azimuthal scattering angle is first transformed from the rotating polarimeter frame to the non-rotating truss reference frame. Scattering angles are then converted to a coordinate system referenced to celestial north, using the truss orientation determined by the WASP system. The focal-point offset was accounted for by assuming scattering from the day-by-day-averaged interaction point, as measured with the imaging CZT. The endpoint was randomized within the 2.5-mm width of the hit wall-CZT pixel, as described in Aoyagi et al. (2024). Resulting scattering-angle distributions are shown in Fig. 1.

Figure 1.

Scattering-angle distributions for the XL-Calibur Crab observation. The modulation in the on-source distribution (top curve) arises from the polarization of the incident flux, as per equation (1). The off-source distribution (bottom curve) is shown when calculated the same way as for on-source, i.e. relative to celestial north and using offset correction. Without offset correction and in the non-rotating truss frame, the off-source distribution becomes flat, indicating that the background impinging on the polarimeter is isotropic. Subtracting the exposure-weighted off-source distribution from the on-source result gives the signal excess (middle curve). The signal distribution is well-described by a fitted modulation curve with 180${}^{\circ }$ periodicity, as well as a component with 360${}^{\circ }$ periodicity (relative amplitude $\sim$1 per cent), arising due to the small residual offset of the focused X-ray beam from the centre of the Be rod (Aoyagi et al. 2024). In the absence of an offset correction, the relative amplitude of the 360${}^{\circ }$ component becomes significantly higher (⁠$\sim$10 per cent relative amplitude). The polarization parameters determined from fitting the modulation curve are shown, where only fitting errors are quoted. Only the Stokes-parameter analysis described in Section 3 is used to produce the polarization results presented in Section 4.

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For the polarization analysis, selected events are used to form exposure-weighted sums of intensity (I)-normalized Q and U Stokes parameters (⁠$\mathcal{Q}=Q/I$ and $\mathcal{U}=U/I$⁠), following the procedure detailed in Kislat et al. (2015). Reconstructed Stokes parameters ${\mathcal{Q}}_r$ and ${\mathcal{U}}_r$ additionally take the modulation response ${\mu }_{100}$ into account, e.g. ${\mathcal{Q}}_r=\mathcal{Q}/{\mu }_{100}$⁠. The additive nature of Stokes parameters makes it straightforward to account for measurement backgrounds using on-source and exposure-weighted off-source observations, whereby polarization parameters are defined as⁴

Since PD is a positive-definite quantity, the measurement may be subject to bias (Quinn 2012; Maier, Tenzer & Santangelo 2014; Mikhalev 2018). Equation (3) is therefore applicable only when PD $\gtrsim$ MDP, i.e. when the measured polarization degree exceeds the minimum detectable polarization (Weisskopf, Elsner & O’Dell 2010). Defined at 99 per cent confidence level and using the formalism of Kislat et al. (2015),

where $R_s$⁠, $R_b$⁠, and T are the signal rate, background rate, and observation time, respectively, and $f_{\mathrm{off}}$ is the fraction of time spent observing off-source (background) fields. For a simulated 100 per cent polarized Crab beam (Aoyagi et al. 2024), ${\mu }_{100}=(42.4\pm$0.1) per cent.

We use a Bayesian framework for the polarization analysis (see examples in Chauvin et al. 2017; Abarr et al. 2020; Kiss & Pearce 2024). The uninformative Jeffreys prior (uniform in Stokes Q and U) tends to overestimate the true PD (Maier et al. 2014). Following the reasoning in Quinn (2012), we instead assume a prior that is uniform in polar coordinates (PD, PA). Our posterior is evaluated in (PD, PA) space, as defined in Chauvin et al. (2017). The maximum a posteriori (MAP) estimate is the mode (most probable value) of the 2D Bayesian posterior, and corresponds to equations (3) and (4). While the MAP PD is a biased estimator, marginalizing over PA prevents the point-estimate for from becoming biased (Mikhalev 2018). Our reported PD and PA values, as well as their credible regions (uncertainties) are derived by marginalization over the posterior. The Bayesian method provides asymmetric credible regions ensuring that the physical requirement PD $\in$ [0, 1] is fulfilled.

4 RESULTS

The total on-source observation time was 49.7 ks, interspersed with 17.1 ks of off-source observations. On-source rates vary depending on the Crab elevation and observing altitude, with an average of $\sim$1.1 counts per second observed, while the background rate of $\sim$0.36 counts per second remained constant during observations. The resulting mean signal-to-background ratio of 3 is $\sim$20 times higher than PoGO +  (Chauvin et al. 2017). Observation statistics are summarized in Table 1. The XL-Calibur light curve is defined with the measured peak of P1 at phase 0. We then adopt the same phase intervals as IXPE for the off-pulse/bridge (Bucciantini et al. 2023) and P1/P2 (Wong et al. 2024). Marginalized polarization parameters are shown superimposed on the measured pulsar light curve in Fig. 2. The pulsed fraction is (14.6$\pm$1.0) per cent, matching Eckert et al. (2010). Results are summarized in Table 2.

Figure 2.

Marginalized polarization degree and polarization angle, superimposed on the phase-folded light curve as measured by XL-Calibur. Shaded regions indicate relevant phase intervals from Table 1. For the off-pulse PD and PA, exposure-weighted background has been subtracted, while for P1 and P2, the exposure-weighted off-pulse contribution has been subtracted together with the background, leaving only the pulsed contribution. Right-side panels show phase-integrated results. Corresponding IXPE results have been added from Bucciantini et al. (2023) and Wong et al. (2024). For the latter, error-bar colours indicate different levels of significance (⁠$>5\sigma$⁠, $>3\sigma$⁠, $>1.9\sigma$⁠, $<1.9\sigma$ for red, blue, green, and turquoise, respectively), and Wong et al. (2024) have remarked that marginally significant measurements have significant PD–PA covariance, whereby reported error bars are not fully representative.

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The PD is constrained at $\sim 1\sigma$ level for P1. For P2, the marginalized PD peaks at 0 per cent. Upper limits at 99 per cent Confidence Level are 90.1 per cent and 78.5 per cent, respectively. As shown in Fig. 2, our observations are in line with IXPE, where (in the lower 2–8 keV band) the overall PD level for P1 appears to be higher than P2 (Wong et al. 2024).

XL-Calibur measures the polarization of the phase-averaged and off-pulse emissions with high statistical significances of 8.6$\sigma$ and 4.5$\sigma$⁠, respectively. The two results are compatible within the statistical accuracy of the measurements, as expected if the overall pulsar contribution is only weakly polarized. We do not find evidence for a change of the PD and PA between 15–31 keV and 31–60 keV (Table 3). Our phase-averaged results for PD and PA are compatible with PoGO + observations conducted in 2016 (Chauvin et al. 2017). This may indicate that the overall magnetic configuration of the inner emission region was similar when the two observations were made. Between these measurements, an excursion in soft X-ray on-pulse PD was reported by PolarLight (3.0–4.5 keV) (Feng et al. 2020; Long et al. 2021).

5 DISCUSSION

By combining a large-area X-ray mirror with a compact and well-shielded polarimeter, XL-Calibur measures the polarization of the $\sim$19–64 keV X-ray emission of the Crab pulsar and PWN with unprecedented sensitivity. The systematic error on our measurements stems from (i) the focal-point offset correction, (ii) the uncertainty on ${\mu }_{100}$⁠, and (iii) background subtraction. For (i), with no offset correction applied, the PD only changes by $\sim$0.7 percentage points. Since the uncertainty on ${\mu }_{100}$ from simulations is negligible, (ii) is dictated by knowledge of the PSF. For two independent PSF measurements, the simulated ${\mu }_{100}$ varies by only 0.2 percentage points. The systematic error arising from background subtraction (iii) is minimal since signal and background observations are interspersed. We therefore expect the overall systematic error to be significantly smaller than the statistical error.

Our observations indicate a low level of polarization when integrating across the pulsar peaks. As noted in Bucciantini et al. (2023), this contrasts with many inner magnetospheric models, where high-energy emission arises from accelerated particles emitting synchrotron emission within plasma-starved gaps in the magnetosphere. In the striped-wind picture of Pétri (2013), emission outside the light cylinder (LC) generates strong reductions in the PD at and following each pulse peak. The plasma simulations of Cerutti et al. (2016) at the current sheet inside the LC display a modest anticorrelation between PD and intensity, and can have large variations in PA. For a force-free magnetic geometry, Harding & Kalapotharakos (2017) demonstrate that synchrotron radiation from regions just outside the LC exhibit PDs at the measured levels, however the accompanying PA variations at various phases are strong. Higher significance PD measurements within the pulsar peaks are required to discriminate between these various scenarios.

For XL-Calibur this is not a straightforward proposition. Even when assuming fully efficient observations with purely on-source pointing during a week-long flight⁵, MDP$\sim$20 per cent is expected when integrating across P1 or P2. To accurately track the phase-dependence of polarization parameters, the MDP must be improved by an order of magnitude. Further reducing the already low measurement background is not a feasible approach. The signal rate can be enhanced by increasing the effective area of the X-ray mirror. To be practical, this would require multiple mirror assemblies – a significant engineering challenge, since XL-Calibur is already close to the payload mass-limit for the current balloon. Work is in progress to allow phase-folding of data from July 11th and 13th when GPS timing was unavailable. While this may lead to a modest reduction in the PD uncertainty for the pulsar peaks, our overall conclusions will not be affected.

A comparison to previous phase-integrated X-/$\gamma$-ray measurements is shown in Fig. 3. Our phase-averaged PD = (25.1$\pm$2.9) per cent and PA = (129.8$\pm 3.2{)}^{\circ }$ differ from the PD = (19.0$\pm$0.19) per cent and PA = (145.5$\pm 0.3{)}^{\circ }$ measured by IXPE within 2.5 arcmin of the pulsar (Bucciantini et al. 2023). While the regions viewed by both missions are comparable, the higher energy band of XL-Calibur (⁠$\sim$19–64 keV) compared to IXPE (2–8 keV) means that the emission originates closer to the central toroidal region of the PWN, since the synchrotron radiative lifetime for outflowing electrons is inversely proportional to energy. This is shown by NuSTAR, where 3–8 keV observations reveal inner nebula emission from a larger region (⁠$\sim 75\times$40 arcsec) than at 20–80 keV (⁠$\sim 60\times$25 arcsec) (Madsen et al. 2015). Hitomi HXT, 15–70 keV, confirms this trend (Morii et al. 2024). We note that IXPE off-pulse measurements for (i) an elliptical region extending $\sim$80 arcsec (⁠$\sim$40 arcsec) along the toroidal (jet) axis (Wong et al. 2024), referred to as ‘Region 1’, and (ii) within 20 arcsec of the pulsar (Bucciantini et al. 2023), are more compatible with XL-Calibur off-pulse results. This is illustrated in Fig. 4, showing that the XL-Calibur PA is aligned with the pulsar spin axis, indicating that the harder X-rays measured by XL-Calibur are dominated by the central region of the PWN. For OSO-8 measurements encompassing the full nebula (Weisskopf et al. 1978), the PA (155.79$\pm 1.37{)}^{\circ }$ at 2.6 keV and 5.2 keV combined lies even further away from the XL-Calibur PA.

Figure 3.

Comparison of phase-integrated Crab results, from soft X-rays to gamma-rays, for polarization degree (top) and angle (bottom). Missions are listed in chronological order, with data points centred on the corresponding energy range. References: Weisskopf et al. (1976), Forot et al. (2008), Chauvin et al. (2015), Chauvin et al. (2017), Vadawale et al. (2018), Aharonian et al. (2018), Jourdain & Roques (2019), Feng et al. (2020), Bucciantini et al. (2023). The spin axis from Ng & Romani (2004) has also been indicated.

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Figure 4.

Off-pulse polarization results from OSO-8 Weisskopf et al. (1978) (nebula only, 2.6 and 5.2 keV combined), IXPE Bucciantini et al. (2023) (⁠$<$2.5 arcmin, $<$20 arcsec), Wong et al. (2024) (‘Region 1’) and XL-Calibur, superimposed on a Chandra image of the inner region of the Crab nebula (approximately 200$\times$200 arcsec). Arrow lengths are proportional to PD. For XL-Calibur, the $1\sigma$ error on PA has been indicated. Corresponding errors for the remaining measurements are small compared to the arrow widths. The pulsar spin-axis from Ng & Romani (2004) is shown by the dashdotted line. Image credit: Chandra X-ray: NASA/CXC/SAO.

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As discussed by Madsen et al. (2015), the imaging-spectroscopic NuSTAR observations of the Crab PWN are compatible with downstream leptons propagating sub-relativistically mostly through advection (Kennel & Coroniti 1984a, b) rather than through diffusion (Gratton 1972; Wilson & Shakeshaft 1972). Detailed 3D modelling of the combined Chandra, IXPE, NuSTAR, and XL-Calibur data with magnetohydrodynamics (e.g. Porth, Komissarov & Keppens 2013) and Particle in Cell (e.g. Cerutti & Giacinti 2021) codes is outside of the scope of this paper but could give new constraints on the structure of PWN, and their relativistic shocks, for the Crab and more generally.

ACKNOWLEDGEMENTS

XL-Calibur is funded in the US by the NASA APRA (Astrophysics Research and Analysis) program through grants 80NSSC20K0329 and 80NSSC24K0205. FK acknowledges funding from NASA ADAP award 80NSSC24K0636 and NASA IXPE GO Cycle 1 award 80NSSC24K1762. The Japanese Society for the Promotion of Science (JSPS) has supported this work through KAKENHI Grant Numbers 19H01908, 19H05609, 20H00175 (HM), 20H00178 (HM), 21K13946 (YU), 22H01277 (YM), 23H00117, and 23H00128 (HM). KTH authors are supported by the Swedish National Space Agency (2022-00178). MP also acknowledges funding from the Swedish Research Council (2021-05128). We thank the NASA-WASP team for campaign support and pointing operations. We are very grateful to colleagues at NASA-CSBF and Esrange Space Center who provided balloon launch, operations, and recovery services. H. Tsunemi and A. Furuzawa are thanked for their role in the construction of the mirror. T. Enoto, Y. Fukazawa, S. Gunji, T. Mizuno, and Y. Saito are thanked for advice and discussions. M. Aoyagi, K. Ishiwata, W. Kamogawa, H. Matake, N. Sakamoto are thanked for work on previous mirror calibration activities. J. Wong is thanked for providing tabulated IXPE results for reference. No AI was used in the data analysis presented here, nor for the writing of this paper.

DATA AVAILABILITY

The XL-Calibur data underlying this article will be made available via the NASA HEASARC data archive, at https://heasarc.gsfc.nasa.gov/docs/xlcalibur/.

Footnotes

REFERENCES