# A Strong X-Ray Polarization Signal from the Magnetar 1RXS J170849.0-400910

Silvia Zane, Roberto Taverna, Denis González-Caniulef, Fabio Muleri, Roberto Turolla, Jeremy Heyl, Keisuke Uchiyama, Mason Ng, Toru Tamagawa, Ilaria Caiazzo, et al.

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Silvia Zane, Roberto Taverna, Denis González-Caniulef, Fabio Muleri, Roberto Turolla, et al. A Strong X-Ray Polarization Signal from the Magnetar 1RXS J170849.0-400910. The Astrophysical journal letters, 2023, 944, 10.3847/2041-8213/acb703. insu-04031688

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A Strong X-Ray Polarization Signal from the Magnetar 1RXS J170849.0-400910

Silvia Zane<fnref n="1" />, Roberto Taverna<fnref n="2" />, Denis González-Caniulef<fnref n="3" />,<fnref n="4" />,⁵⁶, Fabio Muleri<fnref n="5" />, Roberto Turolla<fnref n="1" />,<fnref n="2" />, Jeremy Heyl<fnref n="3" />, Keisuke Uchiyama<fnref n="6" />,<fnref n="7" />, Mason Ng<fnref n="8" />, Toru Tamagawa<fnref n="6" />,<fnref n="7" />,<fnref n="9" />, Ilaria Caiazzo<fnref n="10" />, Niccolò Di Lalla<fnref n="11" />, Herman L. Marshall<fnref n="8" />, Matteo Bachetti<fnref n="12" />, Fabio La Monaca<fnref n="5" />, Ephraim Gau<fnref n="13" />, Alessandro Di Marco<fnref n="5" />, Luca Baldini<fnref n="14" />,<fnref n="15" />, Michela Negro<fnref n="16" />,<fnref n="17" />,<fnref n="18" />, Nicola Omodei<fnref n="11" />, John Rankin<fnref n="5" />, Giorgio Matt<fnref n="19" />, George G. Pavlov<fnref n="20" />, Takao Kitaguchi<fnref n="9" />, Henric Krawczynski<fnref n="13" />, Fabian Kislat<fnref n="21" />, Ruth Kelly<fnref n="1" />, Iván Agudo<fnref n="22" />, Lucio A. Antonelli<fnref n="23" />,<fnref n="24" />, Wayne H. Baumgartner<fnref n="25" />, Ronaldo Bellazzini<fnref n="14" />, Stefano Bianchi<fnref n="19" />, Stephen D. Bongiorno<fnref n="25" />, Raffaella Bonino<fnref n="26" />,<fnref n="27" />, Alessandro Brez<fnref n="14" />, Niccolò Bucciantini<fnref n="28" />,<fnref n="29" />,<fnref n="30" />, Fiamma Capitanio<fnref n="5" />, Simone Castellano<fnref n="14" />, Elisabetta Cavazzuti<fnref n="31" />, Chieng-Ting Chen<fnref n="25" />,<fnref n="32" />, Stefano Ciprini<fnref n="23" />,<fnref n="33" />, Enrico Costa<fnref n="5" />, Alessandra De Rosa<fnref n="5" />, Ettore Del Monte<fnref n="5" />, Laura Di Gesu<fnref n="31" />, Immacolata Donnarumma<fnref n="31" />, Victor Doroshenko<fnref n="34" />, Michal Dovčiak<fnref n="35" />, Steven R. Ehlert<fnref n="25" />, Teruaki Enoto<fnref n="9" />, Yuri Evangelista<fnref n="5" />, Sergio Fabiani<fnref n="5" />, Riccardo Ferrazzoli<fnref n="5" />, Javier A. Garcia<fnref n="36" />, Shuichi Gunji<fnref n="37" />, Kiyoshi Hayashida<fnref n="38" />, Wataru Iwakiri<fnref n="39" />, Svetlana G. Jorstad<fnref n="40" />,<fnref n="41" />, Philip Kaaret<fnref n="25" />,<fnref n="42" />, Vladimir Karas<fnref n="35" />, Jeffery J. Kolodziejczak<fnref n="25" />, Luca Latronico<fnref n="27" />, Ioannis Liodakis<fnref n="43" />, Simone Maldera<fnref n="27" />, Alberto Manfreda<fnref n="14" />, Frédéric Marin<fnref n="44" />, Andrea Marinucci<fnref n="31" />, Alan P. Marscher<fnref n="40" />, Francesco Massaro<fnref n="26" />,<fnref n="27" />, Ikuyuki Mitsuishi<fnref n="45" />, Tsunefumi Mizuno<fnref n="46" />, C.-Y. Ng⁴⁷, Stephen L. O'Dell<fnref n="25" />, Chiara Oppedisano<fnref n="27" />, Alessandro Papitto<fnref n="24" />, Abel L. Peirson<fnref n="11" />, Matteo Perri<fnref n="23" />,<fnref n="24" />, Melissa Pesce-Rollins<fnref n="14" />, Pierre-Olivier Petrucci⁴⁸, Maura Pilia<fnref n="12" />, Andrea Possenti<fnref n="12" />, Juri Poutanen⁴⁹, Simonetta Puccetti<fnref n="23" />, Brian D. Ramsey<fnref n="25" />, Ajay Ratheesh<fnref n="5" />, Oliver J. Roberts<fnref n="25" />,<fnref n="32" />, Roger W. Romani<fnref n="11" />, Carmelo Sgró<fnref n="14" />, Patrick Slane⁵⁰, Paolo Soffitta<fnref n="5" />, Gloria Spandre<fnref n="14" />, Douglas A. Swartz<fnref n="25" />,<fnref n="32" />, Fabrizio Tavecchio⁵¹, Yuzuru Tawara<fnref n="45" />, Allyn F. Tennant<fnref n="25" />, Nicholas E. Thomas<fnref n="25" />, Francesco Tombesi<fnref n="33" />,⁵²,⁵³, Alessio Trois<fnref n="12" />, Sergey S. Tsygankov⁴⁹, Jacco Vink⁵⁴, Martin C. Weisskopt<fnref n="25" />, Kinwah Wu<fnref n="1" />, and Fei Xie<fnref n="5" />,⁵⁵¹⁰

<footnote n="1">¹ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK; s.zane@ucl.ac.uk</footnote>

<footnote n="2">²Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, Via Marzolo 8, I-35131 Padova, Italy</footnote>

<footnote n="3">³Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada</footnote>

<footnote n="4">⁴Institut de Recherche en Astrophysique et Planétologie 9 avenue du Colonel Roche BP 44346, F-31028 Toulouse CEDEX 4 France</footnote>

<footnote n="5">⁵INAF Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere 100, I-00133 Roma, Italy</footnote>

<footnote n="6">⁶RIKEN Nishina Center, 2-1 Hiroshima, Wako, Saitama 351-0198, Japan</footnote>

<footnote n="7">⁷Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan</footnote>

<footnote n="8">⁸MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA</footnote>

<footnote n="9">⁹RIKEN Cluster for Pioneering Research, 2-1 Hiroshima, Wako, Saitama 351-0198, Japan</footnote>

<footnote n="10">¹⁰Cahill Astrophysics, 1216 California Blvd, MC 350-17, Caltech, Pasadena, CA 91125, USA</footnote>

<footnote n="11">¹¹Department of Physics and Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA 94305, USA</footnote>

<footnote n="12">¹²INAF Osservatorio Astronomico di Cagliari, Via della Scienza 5, I-09047 Selargius (CA), Italy</footnote>

<footnote n="13">¹³Physics Department and McDonnell Center for the Space Sciences, Washington University in St. Louis, St. Louis, MO 63130, USA</footnote>

<footnote n="14">¹⁴Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy</footnote>

<footnote n="15">¹⁵Dipartimento di Fisica, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy</footnote>

<footnote n="16">¹⁶University of Maryland, Baltimore County, Baltimore, MD 21250, USA</footnote>

<footnote n="17">¹⁷NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA</footnote>

<footnote n="18">¹⁸Center for Research and Exploration in Space Science and Technology, NASA/GSFC, Greenbelt, MD 20771, USA</footnote>

<footnote n="19">¹⁹Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Via della Vasca Navale 84, I-00146 Roma, Italy</footnote>

<footnote n="20">²⁰Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802, USA</footnote>

<footnote n="21">²¹University of New Hampshire Department of Physics & Astronomy Space Science Center Morse Hall, Rm 311 8 College Rd Durham, NH 03824, USA</footnote>

<footnote n="22">²²Instituto de Astrofísica de Andalucía-CSIC, Glorieta de la Astronomía s/n, E-18008, Granada, Spain</footnote>

<footnote n="23">²³Space Science Data Center, Agenzia Spaziale Italiana, Via del Politecnico snc, I-00133 Roma, Italy</footnote>

<footnote n="24">²⁴INAF Osservatorio Astronomico di Roma, Via Frascati 33, I-00078 Monte Porzio Catone (RM), Italy</footnote>

<footnote n="25">²⁵NASA Marshall Space Flight Center, Huntsville, AL 35812, USA</footnote>

<footnote n="26">²⁶Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria 1, I-10125 Torino, Italy</footnote>

<footnote n="27">²⁷Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via Pietro Giuria 1, I-10125 Torino, Italy</footnote>

<footnote n="28">²⁸INAF Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, I-50125 Firenze, Italy</footnote>

<footnote n="29">²⁹Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy</footnote>

<footnote n="30">³⁰Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy</footnote>

<footnote n="31">³¹Agenzia Spaziale Italiana, Via del Politecnico snc, I-00133 Roma, Italy</footnote>

<footnote n="32">³²Universities Space Research Association (USRA), USA</footnote>

<footnote n="33">³³Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma, Italy</footnote>

<footnote n="34">³⁴Institut für Astronomie und Astrophysik, Universität Tübingen, Sand 1, D-72076 Tübingen, Germany</footnote>

<footnote n="35">³⁵Astronomical Institute of the Czech Academy of Sciences, Bočňík II 1401/1, 14100 Praha 4, Czech Republic</footnote>

<footnote n="36">³⁶California Institute of Technology, Pasadena, CA 91125, USA</footnote>

<footnote n="37">³⁷Yamagata University, 1-4-12 Kojirakawa-machi, Yamagata-shi 990-8560, Japan</footnote>

<footnote n="38">³⁸Osaka University, 1-1 Yamadaoka, Suita, Osaka 565-0871, Japan</footnote>

<footnote n="39">³⁹International Center for Hadron Astrophysics, Chiba University, Chiba 263-8522, Japan</footnote>

<footnote n="40">⁴⁰Institute for Astrophysical Research, Boston University, 725 Commonwealth Avenue, Boston, MA 02215, USA</footnote>

<footnote n="41">⁴¹Department of Astrophysics, St. Petersburg State University, Universitetsky pr. 28, Petrodvoretz, 198504 St. Petersburg, Russia</footnote>

<footnote n="42">⁴²University of Iowa Department of Physics and Astronomy, Van Allen Hall, 30 N. Dubuque Street, Iowa City, IA 52242, USA</footnote>

<footnote n="43">⁴³Finnish Centre for Astronomy with ESO, FI-20014 University of Turku, Finland</footnote>

<footnote n="44">⁴⁴Université de Strasbourg, CNRS, Observatoire Astronomique de Strasbourg, UMR 7550, F-67000 Strasbourg, France</footnote>

<footnote n="45">⁴⁵Graduate School of Science, Division of Particle and Astrophysical Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan</footnote>

<footnote n="46">⁴⁶Hiroshima Astrophysical Science Center, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan</footnote>
Received 2022 December 27; revised 2023 January 23; accepted 2023 January 28; published 2023 February 15

## Abstract

Magnetars are the most strongly magnetized neutron stars, and one of the most promising targets for X-ray polarimetric measurements. We present here the first Imaging X-ray Polarimetry Explorer observation of the magnetar 1RXS J170849.0-400910, jointly analyzed with a new Swift observation and archival NICER data. The total (energy- and phase-integrated) emission in the 2–8 keV energy range is linearly polarized, at a ~35% level. The phase-averaged polarization signal shows a marked increase with energy, ranging from ~20% at 2–3 keV up to ~80% at 6–8 keV, while the polarization angle remains constant. This indicates that radiation is mostly polarized in a single direction. The spectrum is well reproduced by a combination of either two thermal (blackbody) components or a blackbody and a power law. Both the polarization degree and angle also show a variation with the spin phase, and the former is almost anticorrelated with the source counts in the 2–8 and 2–4 keV bands. We discuss the possible implications and interpretations, based on a joint analysis of the spectral, polarization, and pulsation properties of the source. A scenario in which the surface temperature is not homogeneous, with a hotter cap covered by a gaseous atmosphere and a warmer region in a condensed state, provides a satisfactory description of both the phase- and energy-dependent spectro-polarimetric data. The (comparatively) small size of the two emitting regions, required to explain the observed pulsations, does not allow to reach a robust conclusion about the presence of vacuum birefringence effects.

Unified Astronomy Thesaurus concepts: Polarimetry (1278); Magnetars (992)

## 1. Introduction

The launch of the NASA-Agenzia Spaziale Italiana Imaging X-ray Polarimetry Explorer (IXPE; Weisskopf et al. 2022) in 2021 December opened a new window to our view of the X-ray sky by adding polarimetry to the spectroscopy, timing, and imaging as a tool to interpret astrophysical X-ray sources. IXPE has been in operation for nearly 1 yr now, and already observed more than 30 X-ray sources belonging to different classes.

Particularly interesting for IXPE observations are magnetars, a class of isolated neutron stars (NSs) that are powered by their huge magnetic field (Duncan & Thompson 1992; Thompson & Duncan 1993). They are characterized by an X-ray luminosity $L \approx 10^{31}-10^{36}$ erg s⁻¹, spin period $P \approx 1-12$ s, and period derivative $\dot{P} \approx 10^{-13}-10^{-11}$ s s⁻¹, implying a dipole field $B \approx 10^{14}-10^{15}$ G. Magnetars are extremely active sources over different ranges of luminosities and timescales, from the short-lived X-ray bursts and powerful giant flares to outbursts, during which their persistent X-ray flux suddenly increases by a factor of ≈10–1000 and then gradually decays over months–years (e.g., Rea & Esposito 2011; Coti Zelati et al. 2018).

Magnetar X-ray spectra below 10 keV are typically well reproduced by a two-component model, comprising either two thermal (blackbody, hereafter BB) components or a thermal component plus a nonthermal (power-law, hereafter PL) one. While the BB component(s) is believed to originate from

(regions of) the cooling star surface, the PL one is usually interpreted as due to resonant cyclotron scattering (RCS) of thermal photons off magnetospheric currents flowing in a twisted magnetic field. In addition, magnetars exhibit a powerful and highly pulsed nonthermal emission at higher energies, up to ~100–200 keV, first discovered by International Gamma-Ray Astrophysics Laboratory (INTEGRAL; see, e.g., Turolla et al. 2015; Kaspi & Beloborodov 2017, for reviews).

Strongly magnetized sources, which electromagnetic emission is expected to be highly polarized, are ideal targets for X-ray polarimetry. Emission from highly magnetized NSs is expected to be linearly polarized in two normal modes, the ordinary (O) and extraordinary (X) ones, with the polarization electric vector either parallel or perpendicular to the plane of the photon direction and the (local) magnetic field. The degree of polarization depends on the properties of the emission region, its geometry, magnetic field strength and orientation, and the dominant radiative processes. This makes X-ray polarimetry a new, powerful tool to probe the magnetospheric topology of the magnetar, the state of matter in the star crust, including whether the star has a bare, condensed surface or is surrounded by a gaseous atmosphere (see, e.g., Taverna et al. 2020; Caiazzo et al. 2022, and references therein), and even to test the properties of the QED magnetized vacuum around the star, such as its birefringence (Heyl & Shaviv 2000, 2002).

IXPE first observed a magnetar source, the bright anomalous X-ray pulsar (AXP) 4U 0142 + 61, in 2022 February. The polarization signal was clearly detected at ~13% level, with both the polarization degree and angle exhibiting a strong dependence on the energy (Taverna et al. 2022). In this paper, we report on the IXPE observation of a second magnetar, the AXP 1RXS J170849.0-400910.

<figure><img src="image_2.png" /></figure>

<footnote n="47"><sup>47</sup>Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong</footnote>

<footnote n="48"><sup>48</sup>Université Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France</footnote>

<footnote n="49"><sup>49</sup>Department of Physics and Astronomy, FI-20014 University of Turku, Finland</footnote>

<footnote n="50"><sup>50</sup>Center for Astrophysics, Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA</footnote>

<footnote n="51"><sup>51</sup>INAF Osservatorio Astronomico di Brera, Via E. Bianchi 46, I-23807 Merate (LC), Italy</footnote>

<footnote n="52"><sup>52</sup>Dipartimento di Fisica, Università degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma, Italy</footnote>

<footnote n="53"><sup>53</sup>Department of Astronomy, University of Maryland, College Park, MD 20742, USA</footnote>

<footnote n="54"><sup>54</sup>Anton Pannekoek Institute for Astronomy & GRAPPA, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands</footnote>

<footnote n="55"><sup>55</sup>Guangxi Key Laboratory for Relativistic Astrophysics, School of Physical Science and Technology, Guangxi University, Nanning 530004, People's Republic of China</footnote>

<footnote n="56"><sup>56</sup> CITA National Fellow.</footnote>

<footnote>Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Left: phase- and energy-averaged linear polarization of 1RXS J1708, in terms of the normalized Stokes parameters. Uncertainties are shown at the 68.3% (1σ) confidence level. Circles with center in the origin and increasing radii correspond to increasing values of the polarization degree while different values of the azimuth to different polarization angles. Right: polarization of 1RXS J1708 in different energy bands, computed with IXPEOBSSIM. Contours identify the 50% confidence regions for the joint measurement of the polarization degree and angle (which are not independent variables), accounting for statistical fluctuations only. Orange stars and green crosses show, for the same energy bins, the prediction of the belt+cap and cap+cap models, respectively (see Section 5 for details).</figcaption></figure>

## 2. Source Properties and Observations

1RXS J170849.0-400910 (1RXS J1708 hereafter) was first identified in the ROSAT All Sky Survey (Voges et al. 1999), but only a few years later, ~11 s pulsations were discovered by ASCA (Sugizaki et al. 1997). Both the large period derivative ($\dot{P} \sim 2 \times 10^{-11}$ s s$^{-1}$) and the upper limits inferred for a possible optical counterpart confirmed the source to be a member of the magnetar class (Israel et al. 1999). The value of the period derivative, if interpreted as due to a rotating dipole in vacuum, yields a dipole magnetic field strength of ~4–5 × 10¹⁴ G. The source presents an erratic timing behavior, characterized by frequent glitching activity that interrupts periods of steady spin-down (Dib & Kaspi 2014). The X-ray spectrum has been fitted with an absorbed BB+PL model, with (slightly variable) photon index Γ ~ 2.6, and BB temperature $kT \sim 0.45$ keV (Rea et al. 2003, 2007; Krawczynski et al. 2022). The source is radio-quiet. Hard, strongly pulsed X-ray emission extending up to ~150 keV has been detected from 1RXS J1708 with INTEGRAL (Kuiper et al. 2006); a marked variability in the hardness ratio is also observed (Gotz et al. 2007).

The distance of the source is uncertain. 1RXS J1708 lies in the Galactic plane, and the large column density inferred from X-ray data, $n_H \sim 1.36 \times 10^{22}$ cm$^{-2}$, suggests a distance in the 5–10 kpc range (Israel et al. 1999; Rea et al. 2007), although a smaller value cannot be ruled out, as hinted from spectral fits with atmospheric models or from reddening measures based on Two Micron All Sky Survey stars (Perna et al. 2001; Durant & van Kerkwijk 2006). In this paper, we present the results from the IXPE observation of 1RXS J1708 performed from 2022 September 19 05:08 UTC to 2022 September 29 12:00 UTC and from 2022 September 30 12:52:02 UTC to 2022 October 8 11:17:40 UTC. We complemented the analysis with data from a Swift X-Ray Telescope (XRT; Burrows et al. 2005) target of opportunity observation, performed on 2022 October 20 for a

total of 1020 s, and with the most recent NICER (Arzoumanian et al. 2014) data publicly available (see Appendix A for details). Our observations and the methods used for data processing are described in Appendix A.

## 3. Phase-integrated Polarimetric and Spectropolarimetric Analysis

No variations in either the source or background were found during the two IXPE observations (see Appendix A.1); therefore the combined data are used in the following analysis. The phase-integrated and energy-integrated polarization in the 2.0–8.0 keV interval, which is the nominal IXPE energy range, is shown in Figure 1 (left panel) for each detector unit (DU), and for their combination. The values of the Stokes parameters were derived with the IXPEOBSSIM suite (Baldini et al. 2022),<fnref n="57" /> and they are weighted by the (energy-dependent) effective area of the instrument. This allows us to correct the measured polarization, which is convolved with the spectral response of the instrument, and to obtain the polarization of the incoming radiation. The circles and the radial lines in Figure 1 mark the loci of constant polarization degree, $PD = \sqrt{Q^2 + U^2}/I$, and polarization angle, $PA = \arctan(U/Q)/2$, respectively. Since the Stokes parameters are (quasi) normally distributed, we report the one-dimensional uncertainties at 68.3% confidence level (1σ).

The measured polarization angle is ~60° west of north, and the phase- and energy-integrated polarization degree is remarkably high, ~35%, that is more than 2.5 times the average X-ray polarization of the only other magnetar observed to date (Taverna et al. 2022).

Even higher polarization degrees are detected by binning the data in five energy intervals, as reported in the right panel of Figure 1; here the contours show the 50% confidence regions in

<footnote n="57">⁵⁷ https://github.com/lucabaldini/ixpeobssim</footnote>
<table><caption>**Table 1**
Values of the Measured Polarization Degree and Angle, Obtained with the IXPEOBSSIM Software Suite</caption><thead><tr><th></th><th>2–3 keV</th><th>3–4 keV</th><th>4–5 keV</th><th>5–6 keV</th><th>6–8 keV</th><th>2–8 keV</th></tr></thead><tbody><tr><td>PD—sum [%]</td><td>21.7<sup>+1.7</sup><sub>-1.7</sub></td><td>41.3<sup>+2.0</sup><sub>-2.0</sub></td><td>58.6<sup>+3.7</sup><sub>-3.7</sub></td><td>57.7<sup>+6.8</sup><sub>-6.8</sub></td><td>85<sup>+15</sup><sub>-15</sub></td><td>35.1<sup>+1.6</sup><sub>-1.6</sub></td></tr><tr><td>PD S/N</td><td>12.9σ</td><td>20.2σ</td><td>15.8σ</td><td>8.5σ</td><td>5.8σ</td><td>22.5σ</td></tr><tr><td>PA—sum [deg]</td><td>-62.6<sup>+2.2</sup><sub>-2.2</sub></td><td>-62.4<sup>+1.4</sup><sub>-1.4</sub></td><td>-61.8<sup>+1.8</sup><sub>-1.8</sub></td><td>-60.7<sup>+3.3</sup><sub>-3.3</sub></td><td>-60.8<sup>+4.7</sup><sub>-4.7</sub></td><td>-62.1<sup>+1.3</sup><sub>-1.3</sub></td></tr></tbody></table>

**Note.** Reported values correspond to the sum of the three DUs (the measures of the single DUs are consistent with each other within errors). Uncertainties are obtained at 68.3% confidence level, assuming that the polarization degree and angle are independent. Signal-to-noise ratio (S/N) is calculated by dividing the polarization degree obtained by combining the results of the three telescopes on board IXPE by its uncertainty.

<figure><img src="image_4.png" /></figure>

**Figure 2.** Joint spectropolarimetric fit of IXPE, Swift/XRT, and NICER data. The Stokes *I*, *Q*, and *U* energy spectra are obtained by binning the event-by-event Stokes parameters, calculated following Kislat et al. (2015), according to the measured energy of the event. *Q* and *U* are given by the source flux multiplied by the polarization degree and either the cosine or the sine of twice the polarization angle, respectively. The Stokes *I*, *Q*, and *U* energy spectra convolved with the instrument response are shown in the left, central, and right panels, respectively. The best-fit model of the form TBABS*(BBODY * POLCONST + POWERLAW * POLCONST) is shown by the solid lines. Fit residuals are shown in the bottom panels; see Table 2 in Appendix B for the fit parameters. Light colored curves are the background of IXPE detectors.

the polarization degree versus polarization angle plane (see also Table 1). The polarization degree increases from ~20% between 2 and 3 keV to ~80% in the 6–8 keV energy range. The polarization angle remains roughly constant in all energy bins.

We performed a spectropolarimetric analysis making use of the IXPE, Swift-XRT, and NICER observations (the latter performed within a month; see Appendix A). We extracted Swift and NICER energy spectra with the standard data analysis tools and used IXPEOBSSIM to derive the IXPE *I*, *Q*, and *U* energy spectra. We use XSPEC (version 12.13.0, Arnaud 1996) for a joint spectropolarimetric fit of the *I* spectra from all three observatories and the *Q* and *U* spectra from IXPE.

We tested two models commonly used to interpret magnetar soft X-ray spectra, i.e., an absorbed BB+PL and a BB+BB.<fnref n="58" /> We started with the BB+PL model, multiplying the BB and PL components with a polarization factor constant in energy; the corresponding XSPEC model is TBABS*(BBODY * POLCONST + POWERLAW * POLCONST), with abundances from Wilms et al. (2000). We include multiplicative constant factors for each IXPE DU and for each observatory, except for IXPE DU1, which is used as reference. The fit gives a statistically acceptable $\chi^2 = 410.4$ for 408° of freedom (Figure 2). The best-fit parameter values are reported in Table 2 in Appendix B.

<footnote n="58">⁵⁸ Although BB radiation is not polarized, we assume that the shape of the thermal (polarized) spectra can be approximated by the Planck function.</footnote>
<table><caption>**Table 2**
Model Parameters for the Joint Spectropolarimetric Fit of IXPE Swift/XRT and NICER Data</caption><thead><tr><th>Model Parameters</th><th>Value</th><th>Model Parameters</th><th>Value</th></tr></thead><tbody><tr><td>DU1 normalization</td><td>1.0 (frozen)</td><td>DU1 normalization</td><td>1.0 (frozen)</td></tr><tr><td>TBabs nH [10<sup>22</sup> cm<sup>-2</sup>]</td><td>2.085<sup>+0.055</sup><sub>-0.050</sub></td><td>TBabs nH [10<sup>22</sup> cm<sup>-2</sup>]</td><td>1.391<sup>+0.039</sup><sub>-0.038</sub></td></tr><tr><td>kT<sub>bbody</sub> [keV]</td><td>0.4546<sup>+0.0077</sup><sub>-0.0058</sub></td><td>kT<sub>bbody1</sub> [keV]</td><td>0.4354<sup>+0.0076</sup><sub>-0.0078</sub></td></tr><tr><td>norm<sub>bbody</sub></td><td>0.0002293<sup>+0.0000179</sup><sub>-0.0000096</sub></td><td>norm<sub>bbody1</sub></td><td>0.0005440<sup>+0.0000097</sup><sub>-0.0000091</sub></td></tr><tr><td>PD<sub>bbody</sub></td><td>1.0 (U.L.)<sup>a</sup></td><td>PD<sub>bbody1</sub></td><td>0.060<sup>+0.036</sup><sub>-0.037</sub></td></tr><tr><td>PA<sub>bbody</sub> [deg]</td><td>30.5<sup>+3.4</sup><sub>-3.3</sub></td><td>PA<sub>bbody1</sub> [deg]</td><td>-69.0<sup>+16.7</sup><sub>-18.2</sub></td></tr><tr><td>PowLaw photon index</td><td>2.9672<sup>+0.0092</sup><sub>-0.0567</sub></td><td>kT<sub>bbody2</sub> [keV]</td><td>1.073<sup>+0.031</sup><sub>-0.029</sub></td></tr><tr><td>norm<sub>PowLaw</sub></td><td>0.04101<sup>+0.00059</sup><sub>-0.00382</sub></td><td>norm<sub>bbody2</sub></td><td>0.0002324<sup>+0.0000082</sup><sub>-0.0000079</sub></td></tr><tr><td>PD<sub>powerlaw</sub></td><td>0.768<sup>+0.041</sup><sub>-0.040</sub></td><td>PD<sub>bbody2</sub></td><td>0.728<sup>+0.038</sup><sub>-0.037</sub></td></tr><tr><td>PA<sub>powerlaw</sub> [deg]</td><td>-60.8<sup>+1.0</sup><sub>-1.2</sub></td><td>PA<sub>bbody2</sub> [deg]</td><td>-61.0<sup>+1.4</sup><sub>-1.4</sub></td></tr><tr><td>DU2 normalization</td><td>0.9567<sup>+0.0051</sup><sub>-0.0049</sub></td><td>DU2 normalization</td><td>0.9568<sup>+0.0053</sup><sub>-0.0052</sub></td></tr><tr><td>DU3 normalization</td><td>0.8921<sup>+0.0048</sup><sub>-0.0046</sub></td><td>DU3 normalization</td><td>0.8922<sup>+0.0049</sup><sub>-0.0049</sub></td></tr><tr><td>Swift/XRT normalization</td><td>0.922<sup>+0.032</sup><sub>-0.032</sub></td><td>Swift/XRT normalization</td><td>0.934<sup>+0.032</sup><sub>-0.032</sub></td></tr><tr><td>NICER normalization</td><td>1.062<sup>+0.013</sup><sub>-0.011</sub></td><td>NICER normalization</td><td>1.075<sup>+0.013</sup><sub>-0.013</sub></td></tr><tr><td>χ<sup>2</sup></td><td>410.4 with 408 d.o.f.</td><td>χ<sup>2</sup></td><td>405.8 with 408 d.o.f.</td></tr><tr><td>Null prob</td><td>45.7%</td><td>Null prob</td><td>52.2%</td></tr></tbody></table>

Notes. Uncertainties are calculated at the 68.3% confidence level for one parameter of interest. The two leftmost columns refer to the model TBABS*(BBODY * POLCONST + POWERLAW * POLCONST). The normalization of the BB components is defined as $L_{39}/D_{10}^2$, where $L_{39}$ is the BB luminosity in units of $10^{39}$ erg s⁻¹, and $D_{10}$ is the distance to the source in units of 10 kpc. The PL normalization is in units of counts keV⁻¹ cm⁻² s⁻¹ at 1 keV. The rightmost two columns are for the model TBABS*(BBODY * POLCONST + BBODY * POLCONST).

a In this case, the confidence level for the polarization degree of the BB component is not closed, and it was only possible to set an upper limit (U.L.). The value of this parameter is poorly constrained: by freezing the value of PD<sub>bbody1</sub> to 0.2 also returns an acceptable fit (see the text for details).

Our fit parameters are in approximate agreement with those reported in Rea et al. (2007). The different neutral hydrogen column densities ($n_H \sim 2 \times 10^{22} \text{ cm}^{-2}$ instead of $\sim 1.4 \times 10^{22} \text{ cm}^{-2}$) largely result from the use of a different absorption model and elemental abundances, TBABS and Wilms et al. (2000) in our case instead of PHABS and Anders & Grevesse (1989). We find however a significantly steeper PL than that from Rea et al. (2007). The PL component dominates over the BB component at all energies, the latter contributing only $\sim 20\%$ in the 2–8 keV energy range (see Figure 2).

The simultaneous fit of the *Q* and *U* energy spectra provides further insights. We find that the PA associated to the BB component turns out to be different by $\sim 90^\circ$ with respect to that of the PL. This is similar to what IXPE observed in 4U 0142 + 61 (Taverna et al. 2022), and it supports a scenario in which thermal and nonthermal photons are polarized, one in the X and the other in the O mode. The changing polarization degree with energy can be then explained as due to the different relative contributions of the two orthogonally polarized components. However, the polarization degree turns out to be much higher in 1RXS J1708 than that in 4U 0142 + 61. Taken at face value, the best fit gives a 100% polarized BB component (see Table 2 in Appendix B). However, the polarization properties of this component are not well constrained, and for instance, fixing the polarization degree of the BB component to 20% still gives an acceptable fit ($\chi^2 = 434.2$ for 408 degrees of freedom). We infer that the PL component is linearly polarized to $\sim 65\%–75\%$, depending on the polarization of the BB component. This polarization degree is much higher than predicted by the resonant scattering scenario (Taverna et al. 2022). It should be noted that the assumptions of constant thermal and PL polarization degrees lead to a significant contribution of the thermal component. The data can be fit with a single PL component if we allow for a polarization degree with a linear energy dependence (we get a

$\chi^2 = 454.3$ for 410 degrees of freedom for a PL fit with a photon index of $3.43 \pm 0.02$; the probability for getting higher $\chi^2$ values by chance is $\sim 6$.

In the next step, we fitted the data with an absorbed BB+BB model, again assuming a constant polarization for each additive component; the correspondent XSPEC model is TBABS*(BBODY * POLCONST + BBODY * POLCONST). The result of the fit is shown in Figure 3 (see again Appendix A, Table 2). Also in this case, the fit is acceptable ($\chi^2 = 405.8$ for 408 degrees of freedom), and the high-energy BB component is highly polarized, $\sim 70\%$. The low-energy component is polarized parallel to the high-energy component. The best-fit model exhibits low polarization in the cold BB component, and by fixing the polarization degree to $\sim 20\%$ also provides an acceptable fit with $\chi^2 = 422.5$ for 409 degrees of freedom. It is worth noting that requiring a low-energy polarization angle orthogonal to the high-energy polarization angle gives a low-energy polarization degree consistent with zero. Therefore, in this scenario, the observed increase of polarization with energy stems from the superposition of two parallel polarized components, a weakly polarized component dominating at low energies and a strongly polarized component dominating at high energies, in the IXPE range.

## 4. Phase-resolved Spectropolarimetric Analysis

The first step of our phase-resolved analysis involved the determination of an accurate timing solution of the count rate data (see Appendix C). Using epoch MJD 59850.84175 in the Barycentric Dynamical Time (TDB) as a reference, this provided $f = 0.090795742(5)$ Hz, $\dot{f} = -1.87(25) \times 10^{-13}$ Hz s⁻¹. The addition of the second frequency derivative did not improve the fit significantly. We then used this timing solution to perform the phase-resolved analysis. To this aim, we selected photons coming from different rotational phases, and repeated the procedures of Section 3 with the event files of the
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Same as in Figure 2, for the TBABS(BBODY * POLCONST + BBODY * POLCONST) model. See Table 2 in Appendix B for the fit parameters.</figcaption></figure>

different phase bins. Rotational phases were ascribed to single events starting from their arrival times using the IXPEOBSSIM tool *xpphase*, and the events in the same phase bins were then added together with the tool *xppselect*. Results are shown in Figure 4 for the total (2–8 keV), low (2–4 keV) and high (4–8 keV) energy bands. The source flux exhibits a single-peaked, nearly sinusoidal profile, as already reported by Rea et al. (2003); the pulse shape and the pulsed fraction change with energy. The polarization degree and angle also vary with phase, and their pulse profiles are different in different energy bands. The pulse of the polarization degree is broadly anticorrelated with that of the flux both in the total (2–8 keV) and low (2–4 keV) energy bands.

On the other hand, in the high-energy interval (4–8 keV), the modulation of the signal is less significant, and no robust conclusion can be reached whether this anticorrelation holds at these energies as well.

## 5. Discussion

1RXS J1708 and the Vela Pulsar Wind Nebula (PWN; Xie et al. 2022) are the most strongly polarized IXPE sources detected so far. The polarization degree of the phase-integrated emission of 1RXS J1708 increases from ~20% around 2 keV to ~80% at 7–8 keV. The polarization angle, on the other hand, stays roughly constant at ~60° (counted west of north). The polarimetric properties of 1RXS J1708 are quite at variance with those of the other magnetar observed by IXPE. For both sources, a BB+PL and a BB+BB model provide a satisfactory fit of the IXPE spectrum (see Section 3). However, 4U 0142+61 exhibits a lower polarization degree, which decreases to approximately 0 at ~5 keV, where the polarization

angle swings by 90°, and then increases to ~35% around 8 keV (Taverna et al. 2022).

The swing of polarization angle by 90° and the presence of a PL tail at higher energies with a value of polarization degree close to 30% led Taverna et al. (2022) to suggest that the X-ray emission from 4U 0142+61 is in two different normal modes below and above ~5 keV. One possibility that has been suggested is that the low-energy photons are mostly polarized in the O mode and come from either a heated equatorial belt on the condensed NS surface or an atmospheric zone that is hit by back-flowing, bombarding magnetospheric currents (Gonzalez-Caniulef et al. 2019), while the high-energy ones are mainly in the X mode being reprocessed by magnetospheric RCS.

The picture for 1RXS J1708 is different. The very high degree of polarization observed at higher energies cannot be reproduced by the RCS mechanism, which indicates that RCS is not present, or, at least, that it does not affect primary photons much in the IXPE energy range. The lack of a swing in the polarization angle points to the emission in the 2–8 keV range being dominated by a single mode. The relative contribution of the other mode is larger at lower energies, explaining the lower polarization degree at lower energies. If we assume that radiation comes from the magnetar surface, a polarization degree as large as ~70%–80% (as that observed at high energies) can be obtained if the star is covered (at least in part) by an atmosphere (e.g., Gonzalez Caniulef et al. 2016; Taverna et al. 2020; Caiazzo et al. 2022). Emission, then, would be thermal, and so the most likely spectral model, among those compatible with the data (see Section 3), is the BB+BB one. Standard atmospheric emission, however, is hard to reconcile with a polarization degree as low as ~20% (unless
<figure><img src="image_6.png" /><figcaption>**Figure 4.** 1RXS J1708 IXPE observation (blue circles with error bars) for the source counts (panels (A)–(C)) and polarization degree (panels (D)–(F)), plotted as a function of the rotational phase (in each row, the three panels from the left to the right show the data integrated over the 2–8, 2–4, and 4–8 keV bands, respectively). Panels (G) and (H) show: (left) the phase averaged spectrum (solid lines) together with the contributions of the condensed zone (dashed lines) and atmospheric zone (dotted lines); (right) the polarization angle as a function of the rotational phase, integrated over the 2–8 keV band. Errors are shown at the 1σ level assuming the polarization degree and polarization angle are not correlated. In all panels, the orange and green lines represent the model expectation within the belt+cap and cap +cap scenarios (solid lines for the total model, dotted and dashed lines in panel (G) only for the two separate components); the red solid line in panel (H) shows the RVM (see the text for the parameter values and other details). Note that data points in the phase-resolved analysis are obtained with IXPEOBSSIM, and therefore independent on the spectral decomposition.</figcaption></figure>

the viewing geometry is very particular), as it is observed in 1RXS J1708 at low energies. It is nevertheless possible that, because of a nonhomogeneous temperature distribution, some regions of the star surface are cold enough to undergo a phase transition that turns the atmosphere into a magnetic condensate. Emission from the condensed surface can be either in the X or in the O mode, but the PD is always modest, ≲20%, and, if the condensate coexists with a hotter region that has an atmosphere on top, this could explain the IXPE observation of 1RXS J1708.

To explore this scenario, we ran a number of simulations assuming that the star surface comprises a hot atmospheric patch at temperature $T_{\text{hot}}$ and a warm condensed region at $T_{\text{warm}}$; the rest of the surface is again condensed but at a much colder temperature $T_{\text{cold}}$.<fnref n="59" /> We tried several different geometries, leaving as free parameters the inclination of the line of sight, $\chi$, and of the magnetic axis, $\xi$, with respect to the spin axis. This, necessarily oversimplified, picture is mostly meant to suggest possibilities on how the main feature of a complex

thermal map may look, and not to provide a diagnostics of the shape and location of the emitting regions.

The emission from the condensate is treated in the free-ion limit and for a Fe composition, following Potekhin et al. (2012). The lack of observed spectral features in the soft X-rays argues against the presence of a heavy-elements atmosphere (see the models by Mori & Ho 2007, for $B = 10^{12}-10^{13}$ G). On the other hand, a light elements composition (mostly hydrogen) may be expected if the star experienced episodes of accretion–fallback. We computed emission from a pure hydrogen, completely ionized atmosphere using the numerical setup described in Lloyd (2003).<fnref n="60" /> No mode conversion is assumed at the vacuum resonance (see, e.g., Ho & Lai 2003). Photons were then propagated to the observer by using a ray-tracing method. The effects of vacuum birefringence as photons cross the star magnetosphere are accounted for.

We tested various configurations and found that there exist at least two geometrical setups, within the scenario outlined above, that match well most of the observed properties of 1RXS J1708. The first one (model (A), or “belt plus cap”) is a variation of the geometry envisaged for 4U 0142+61.

<footnote n="59">⁵⁹ This was done to ensure a physically consistent picture, and in the actual modeling, $T_{\text{cold}} = 0.15$ keV was assumed. However, the contribution of the colder zone does not affect the observed spectral and polarization properties.</footnote>

<footnote n="60">⁶⁰ We have a caveat that this is an approximation, because strictly speaking these models can be applied only for $B \lesssim 10^{14}$ G.</footnote>
(Taverna et al. 2022), in which the warm (condensed) region corresponds to an equatorial belt, and the hot (atmospheric) region corresponds to a circular, polar cap; the belt, however, needs to be limited in azimuth in order to reproduce the X-ray pulse profile. In this case, calculations have been performed using the general relativistic ray-tracing code discussed in Zane & Turolla (2006; see also Taverna et al. 2015). In the second model (model (B), or “cap plus cap”), the warm and hot regions are two circular spots, with the warm (condensed) one located about 150° from the spin axis, and a hot (atmospheric) spot located in the opposite hemisphere and displaced in longitude by about 90° with respect to the warm one. For this latter scenario, we used the spectro-polarimetric magnetar model discussed in Caiazzo et al. (2022), properly extended to account for different circular regions. We refer to the original papers for a detailed description of the models and the meaning of the various parameters.

We found that the values of the parameters that best match the data are similar in the two cases: $T_{\text{hot}} \sim 0.8$ keV, $T_{\text{warm}} \sim 0.6$ keV (all values are referred to the star surface), and a magnetic field of $\sim 10^{14}$ G (model (B)) or $\sim 5 \times 10^{14}$ G (model (A)). Also the values of the geometrical viewing angles are comparable, $\chi \sim 30^\circ$, and $\xi \sim 10^\circ$. The size of the emitting regions turns out to be somewhat smaller for model (B), semiaperture $\sim 5^\circ$ versus $\sim 10^\circ$ for the atmospheric cap and semiaperture $\sim 22^\circ$ of the warm cap as compared to $\sim 30^\circ \times 270^\circ$ of the belt. The observed pulsations require the size of the emitting regions to be relatively small, and this places an upper limit on the source distance to about 5 kpc.

QED vacuum birefringence can strongly affect the polarization properties at infinity, leading to an enhancement in the polarization degree of the observed signal. However, the extent to which QED effects are measurable is actually quite sensitive to the size of the radiating region on the star surface. As discussed in van Adelsberg & Perna (2009), if emission comes from a small polar cap, the depolarization due to geometrical effects is not present, so that the expectations from models computed with or without vacuum birefringence are quite the same. In the case of 1RXS J1708, the small size of the two emitting regions (in particular that of the hot, highly polarized spot) does not allow for a robust test of vacuum birefringence.

Both these models can reproduce the main spectropolarimetric features observed in 1RXS J1708 by IXPE: namely the spectrum; the energy dependence of the phase-averaged polarization degree and angle across the 2–8 keV band (see Figure 1); the pulse profile in the entire IXPE range (2–8 keV), and in the 2–4 and 4–8 keV bands; the energy-integrated polarization degree as a function of phase in the total, 2–4 and 4–8 keV ranges, including the anticorrelation in phase of the polarization degree and the flux in the total and low-energy bands (see Figure 1). As it can be seen in panel (H) of Figure 4, the observed amount of swing in the polarization angle with the phase can also be explained by both models; the red curve depicts the best-fit simple rotating vector model (RVM; with unbinned likelihood analysis, e.g., González-Caniulef et al. 2023). In both the proposed configurations, the model spectra show no features, in agreement with data (see Figure 4). In principle absorption features are expected in the spectrum of a pure hydrogen atmosphere or in that of the magnetic condensate. However, the strong proton cyclotron line in the atmospheric component is $\sim 0.6$ keV in model (B), and is drowned out by the dominant contribution from the colder belt

in model (A). Emission from the condensate component predicts spectral features at low energies ($\sim 0.6$ keV), but at least for these model parameters, they are too faint to be detectable in the currently available spectra.

The observed anticorrelation in the phase of the polarization degree and the flux is due to the relative dominance of two regions, and to the fact that the (less polarized) condensed zone is contributing to much of the counts below $\sim 4$ keV.

There are, however, some caveats. The surface temperature of the warm condensed region is very close to that of the hotter atmospheric patch. Although the conditions for a phase transition in a strongly magnetized medium are still largely uncertain, assuming a dipolar magnetic field with polar strength $\sim 5 \times 10^{14}$ G, condensation is expected at $T \lesssim 0.5$ and $T \lesssim 0.9$ keV at the equator and the pole, respectively, for a Fe composition (Medin & Lai 2007; see also Figure 1 in Taverna et al. 2020). This may indicate that, if the hot and warm regions at the star surface, which are in different phases, have the same chemical composition, they are very close to the phase transition. Alternatively, it may indicate that the chemical composition varies across the surface (as in our models, which assume a pure hydrogen atmosphere and an iron condensate), that the real surface temperature map is more complicated than what is caught in our, necessarily, oversimplified model, or that there may be departures of the local magnetic field from the (overall) dipole topology.

As mentioned before, the spectro-polarimetric analysis indicates that the data are also compatible with a scenario in which emission is dominated by a nonthermal (PL) component. Would that be the case, the fact that the polarization degree decreases at low energies may be due either to the presence of a second subdominant spectral component with emission in the opposite polarization mode (e.g., a thermal emission from a condensed part of the crust) or to the fact that the nonthermal emission has an intrinsic variation of the polarization properties with energy. The main reason why we have not attempted to explore this scenario is that the very high degree of polarization observed at high energy ($\sim 70\%–80\%$) cannot be reconciled with the physical models commonly proposed to explain the nonthermal emission from magnetars in the soft X-ray band, e.g., RCS (saturated RCS only predicts a $\sim 30\%$ level of polarization). However, it is worth noticing that 1RXS J1708 exhibits a strong nonthermal emission at high energies, as detected in the INTEGRAL band, with extreme variations in phase and energies, whose origin is still unexplained in terms of detailed physical models (Kuiper et al. 2006). It could therefore be possible that this nonthermal component and that observed in the IXPE band could be similar in origin (but with varying degrees of manifestation).

The Imaging X-ray Polarimetry Explorer (IXPE) is a joint US and Italian mission. The US contribution is supported by the National Aeronautics and Space Administration (NASA) and led and managed by its Marshall Space Flight Center (MSFC), with industry partner Ball Aerospace (contract NNM15AA18C). The Italian contribution is supported by the Italian Space Agency (Agenzia Spaziale Italiana; ASI) through contract ASI-OHBI-2017-12-I.0, agreements ASI-INAF-2017-12-H0 and ASI-INFN-2017.13-H0, and its Space Science Data Center (SSDC) with agreements ASI-INAF-2022-14-HH.0 and ASI-INFN 2021-43-HH.0, and by the Istituto Nazionale di Astrofisica (INAF) and the Istituto Nazionale di Fisica
Nucleare (INFN) in Italy. This research used data products
provided by the IXPE Team (MSFC, SSDC, INAF, and INFN).
We thank K. C. Gendreau and Z. Arzoumanian for their help in
scheduling NICER observations of the source. We acknowl-
edge the use of public data from the Swift data archive, and we
thank the Swift team for promptly scheduling a target of
opportunity (ToO) observation. R.T. and R.T. acknowledge
financial support from the Italian Ministry of University and
Research (MUR) through grant PRIN 2017LJ39LM. D.G.-C.,
J.H., and I.C. acknowledge support from the Natural Sciences
and Engineer Council of Canada and the Canadian Space
Agency. M.N. acknowledges the support by NASA under
award number 80GSFC21M0002. T.T. was supported by
grant JSPS KAKENHI JP19H05609. H.K. and E.G.
acknowledge NASA support under grants 80NSSC18K0264,
80NSSC22K1291, 80NSSC21K1817, and NNX16AC42G. We
thank an anonymous referee for a careful reading of the paper.

Facilities: IXPE, Swift (XRT), NICER.

# Appendix A
## Observational Data and Data Processing

A.1. IXPE

IXPE observed 1RXS J1708 in two segments close in time,
from 2022 September 19 05:08 UTC to 2022 September 29
12:00 UTC and from 2022 September 30 12:52:02 UTC to
2022 October 8 11:17, for a total livetime of ~837 ks. Level 2
(LV2) data, processed to produce suitable inputs for science
analysis, were downloaded from the IXPE archive at
HEASARC.<fnref n="61" /> One file for each of the three IXPE telescopes
was generated, and they were further processed independently.
Photons' arrival times are corrected to the solar system
barycenter in TDB scale, with the FTOOL/BARYCORR tool,
included in HEASOFT 6.31, using the object coordinates
stored in the LV2 file, the Jet Propulsion Laboratory
Development Ephemeris 421, and the International Celestial
Reference System reference frame. Background events in the
LV2 files are at first partially rejected. They are identified
starting from topological characteristics of the event, e.g., the
number of hit pixels and the fraction of the energy in the main
track with respect to the total collected for the event. The
events falling outside predefined intervals are tagged as
background and removed. This approach allows to reduce the
background counting rate by more then 30%, at the cost of a
reduction of the source count rate by ~0.5%, which is deemed
negligible for the subsequent analysis (see A. Di Marco et al.
2023, in preparation, for a more detailed description).

The source region is then defined with SAOImage Deep
Space 9 (DS9; Joye & Mandel 2003) as a circle with radius of
1.5. The background is extracted from an annulus centered on
1RXS J1708 with inner and outer radii of 2.5 and 4.0,
respectively. The response to polarization is extracted from
LV2 data with the IXPEOBSSIM package (Baldini et al. 2022),
which implements the algorithms in Kislat et al. (2015) and is

publicly available.<fnref n="62" /> The spectro-polarimetric analysis is
carried out by feeding the Stokes spectra, generated with the
IXPEOBSSIM tool XPBIN, into XSPEC (Arnaud 1996) and
exploiting the appropriate response matrices available at
HEASARC for modeling the polarization as suggested by
Strohmayer (2017). The lightcurve of 1RXS J170849.0-400910
and of the background during the two IXPE observations is
shown in Figure 5. Note that the first segment is split in two
pointings, the first between 2022 September 19 5:00–7:20 UTC
and the second starting at 2022 September 19 17:30 and ending
at 2022 September 29 12:00. Both components did not show
any indication of either a spectral or polarization variation with
time. To test this, we binned the lightcurves of the Stokes
parameters and background in bins of 20 ks, and we checked
that the variations are compatible with statistical fluctuations
only (the null probability for a fit with a constant is acceptable).
Therefore, we proceeded with the analysis by summing all
the data.

A.2. NICER

In order to complement the IXPE data, we requested a set of
new NICER observations, which have been awarded and
performed a week after the end of the last IXPE observation.
However, all these observations suffered from high optical
loading (resulting from a low Sun angle), and thus were
unusable for our analysis. We therefore resorted to the use of
the NICER archival data, using the most recent available
observations (closest in time to the IXPE observation).
Specifically, for the contemporaneous spectral fitting with
IXPE and Swift spectra, we made use of the observations from
2022 August 21 (observation ID 5593051301).

The data were processed using version 9 of the NICER Data
Analysis Software (NICERDAS) on version 6.30.1 of HEA-
Soft. We applied standard filtering criteria as per the default
cuts with nicer12, resulting in 972 s of filtered exposure. The
spectrum was then binned with optimal binning (Kaastra &
Bleeker 2016) and with a minimum of 25 counts per bin. The
background spectrum was generated using version 7 of the
3C50 model (Remillard et al. 2022). The Response Matrix
Files (RMFs) and Ancillary Response Files (ARFs) were
generated from nicerrmf and nicerarf, respectively.

A.3. Swift

A Swift-XRT target of opportunity observation was
performed on 2022 October 20 for a total of 1020 s in
windowed timing mode. The data were processed using the
standard HEASoft tools, extracting the spectra using xse-
lect, after generating ancillary response file using
xrtmkarf and the latest calibration files available in the
Swift-XRT CALDB. The source was extracted from the
cleaned event file using a centered circular region with a radius
of 17 pixels. The background region was extracted using an off-
centered circular region of the same radius. The extracted source

<footnote n="61">⁶¹ https://heasarc.gsfc.nasa.gov/docs/ixpe/archive/</footnote>

<footnote n="62">⁶² https://github.com/lucabaldini/ixpeobssim</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Top panel: 1RXS J1708 lightcurve, averaged over the three IXPE telescopes, for the source and the background. The count rate is averaged over 500 s and integrated over the IXPE nominal energy band, 2.0–8.0 keV. Middle and bottom panels: lightcurve of normalized Stokes parameters; the time bin is 20 ks. In all panels, variations are compatible with statistical fluctuations only: the null probability for a fit with a constant is acceptable.</figcaption></figure>

spectra were binned, requiring each spectral channel to have at least 25 counts.

# Appendix B

## Model Parameters from the Spectro-polarimetric Analysis

As discussed in Section 3, there are two possible spectral decompositions that are both compatible with the data: one consists of a thermal (BB) component plus a nonthermal (PL), and the second consists of two blackbodies. The best fitting model parameters, for the two cases, are listed in Table 2.

# Appendix C

## Timing Solution

A timing solution of the count rate data has been obtained by following the procedure from Bachetti et al. (2022). We first determined an approximate solution and then used the Pletsch & Clark (2015) maximum likelihood method to refine it. We determined an approximate first solution with the tool HENzsearch, running a $Z_3^2$ search (Buccheri et al. 1983)

around the known pulse frequency from Dib & Kaspi (2014). The pulsar was detected with extremely high significance, with $Z_3^2 \sim 16,000$ ($\sim 126\sigma$, considering 10,000 trials), at $f=0.09079575$ Hz, and $\dot{f} = -2.28 \times 10^{-13}$ Hz s$^{-1}$. Then, we used the tool ell1fit$^{63}$ v. 0.2 to run a maximum likelihood fit of the spin solution, using a template for the pulse profile obtained by a Fourier analysis with 4 harmonics, and letting only the spin frequency and its first spin derivative vary. The resulting solution, using epoch MJD 59850.84175 (TDB) as a reference, is $f=0.090795742(5)$ Hz, $\dot{f} = -1.87(25) \times 10^{-13}$ Hz s$^{-1}$. The addition of the second frequency derivative did not improve the fit significantly: the $3\sigma$ upper limit on the second derivative in our observation is $\sim 2 \times 10^{-19}$ Hz s$^{-2}$.

## ORCID iDs

Silvia Zane https://orcid.org/0000-0001-5326-880X

Roberto Taverna https://orcid.org/0000-0002-1768-618X

<footnote>$^{63}$ https://github.com/matteobachetti/ell1fit</footnote>
Denis González-Caniulef https://orcid.org/0000-0001-5848-0180

Fabio Muleri https://orcid.org/0000-0003-3331-3794

Roberto Turolla https://orcid.org/0000-0003-3977-8760

Jeremy Heyl https://orcid.org/0000-0001-9739-367X

Keisuke Uchiyama https://orcid.org/0000-0002-7752-9389

Mason Ng https://orcid.org/0000-0002-0940-6563

Toru Tamagawa https://orcid.org/0000-0002-8801-6263

Ilaria Caiazzo https://orcid.org/0000-0002-4770-5388

Niccolò Di Lalla https://orcid.org/0000-0002-7574-1298

Herman L. Marshall https://orcid.org/0000-0002-6492-1293

Matteo Bachetti https://orcid.org/0000-0002-4576-9337

Fabio La Monaca https://orcid.org/0000-0001-8916-4156

Ephraim Gau https://orcid.org/0000-0002-5250-2710

Alessandro Di Marco https://orcid.org/0000-0003-0331-3259

Luca Baldini https://orcid.org/0000-0002-9785-7726

Michela Negro https://orcid.org/0000-0002-6548-5622

Nicola Omodei https://orcid.org/0000-0002-5448-7577

John Rankin https://orcid.org/0000-0002-9774-0560

Giorgio Matt https://orcid.org/0000-0002-2152-0916

George G. Pavlov https://orcid.org/0000-0002-7481-5259

Henric Krawczynski https://orcid.org/0000-0002-1084-6507

Ruth Kelly https://orcid.org/0000-0002-5004-3573

Iván Agudo https://orcid.org/0000-0002-3777-6182

Lucio A. Antonelli https://orcid.org/0000-0002-5037-9034

Wayne H. Baumgartner https://orcid.org/0000-0002-5106-0463

Ronaldo Bellazzini https://orcid.org/0000-0002-2469-7063

Stefano Bianchi https://orcid.org/0000-0002-4622-4240

Stephen D. Bongiorno https://orcid.org/0000-0002-0901-2097

Raffaella Bonino https://orcid.org/0000-0002-4264-1215

Alessandro Brez https://orcid.org/0000-0002-9460-1821

Niccolò Bucciantini https://orcid.org/0000-0002-8848-1392

Fiamma Capitanio https://orcid.org/0000-0002-6384-3027

Simone Castellano https://orcid.org/0000-0003-1111-4292

Elisabetta Cavazzuti https://orcid.org/0000-0001-7150-9638

Chieng-Ting Chen https://orcid.org/0000-0002-4945-5079

Stefano Ciprini https://orcid.org/0000-0002-0712-2479

Enrico Costa https://orcid.org/0000-0003-4925-8523

Alessandra De Rosa https://orcid.org/0000-0001-5668-6863

Ettore Del Monte https://orcid.org/0000-0002-3013-6334

Laura Di Gesu https://orcid.org/0000-0002-5614-5028

Immacolata Donnarumma https://orcid.org/0000-0002-4700-4549

Victor Doroshenko https://orcid.org/0000-0001-8162-1105

Michal Dovčiak https://orcid.org/0000-0003-0079-1239

Steven R. Ehlert https://orcid.org/0000-0003-4420-2838

Teruaki Enoto https://orcid.org/0000-0003-1244-3100

Yuri Evangelista https://orcid.org/0000-0001-6096-6710

Sergio Fabiani https://orcid.org/0000-0003-1533-0283

Riccardo Ferrazzoli https://orcid.org/0000-0003-1074-8605

Javier A. Garcia https://orcid.org/0000-0003-3828-2448

Shuichi Gunji https://orcid.org/0000-0002-5881-2445

Wataru Iwakiri https://orcid.org/0000-0002-0207-9010

Svetlana G. Jorstad https://orcid.org/0000-0001-6158-1708

Philip Kaaret https://orcid.org/0000-0002-3638-0637

Vladimir Karas https://orcid.org/0000-0002-5760-0459

Jeffery J. Kolodziejczak https://orcid.org/0000-0002-0110-6136

Luca Latronico https://orcid.org/0000-0002-0984-1856

Ioannis Liodakis https://orcid.org/0000-0001-9200-4006

Simone Maldera https://orcid.org/0000-0002-0698-4421

Alberto Manfreda https://orcid.org/0000-0002-0998-4953

Frédéric Marin https://orcid.org/0000-0003-4952-0835

Andrea Marinucci https://orcid.org/0000-0002-2055-4946

Alan P. Marscher https://orcid.org/0000-0001-7396-3332

Francesco Massaro https://orcid.org/0000-0002-1704-9850

Tsunefumi Mizuno https://orcid.org/0000-0001-7263-0296

C.-Y. Ng https://orcid.org/0000-0002-5847-2612

Stephen L. O'Dell https://orcid.org/0000-0002-1868-8056

Chiara Oppedisano https://orcid.org/0000-0001-6194-4601

Alessandro Papitto https://orcid.org/0000-0001-6289-7413

Abel L. Peirson https://orcid.org/0000-0001-6292-1911

Matteo Perri https://orcid.org/0000-0003-3613-4409

Melissa Pesce-Rollins https://orcid.org/0000-0003-1790-8018

Pierre-Olivier Petrucci https://orcid.org/0000-0001-6061-3480

Maura Pilia https://orcid.org/0000-0001-7397-8091

Andrea Possenti https://orcid.org/0000-0001-5902-3731

Juri Poutanen https://orcid.org/0000-0002-0983-0049

Simonetta Puccetti https://orcid.org/0000-0002-2734-7835

Brian D. Ramsey https://orcid.org/0000-0003-1548-1524

Ajay Ratheesh https://orcid.org/0000-0003-0411-4243

Oliver J. Roberts https://orcid.org/0000-0002-7150-9061

Roger W. Romani https://orcid.org/0000-0001-6711-3286

Carmelo Sgró https://orcid.org/0000-0001-5676-6214

Patrick Slane https://orcid.org/0000-0002-6986-6756

Paolo Soffitta https://orcid.org/0000-0002-7781-4104

Gloria Spandre https://orcid.org/0000-0003-0802-3453

Douglas A. Swartz https://orcid.org/0000-0002-2954-4461

Fabrizio Tavecchio https://orcid.org/0000-0003-0256-0995

Allyn F. Tennant https://orcid.org/0000-0002-9443-6774

Nicholas E. Thomas https://orcid.org/0000-0003-0411-4606

Francesco Tombesi https://orcid.org/0000-0002-6562-8654

Alessio Trois https://orcid.org/0000-0002-3180-6002

Sergey S. Tsygankov https://orcid.org/0000-0002-9679-0793

Jacco Vink https://orcid.org/0000-0002-4708-4219

Martin C. Weisskopf https://orcid.org/0000-0002-5270-4240

Kinwah Wu https://orcid.org/0000-0002-7568-8765

Fei Xie https://orcid.org/0000-0002-0105-5826

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