X-Ray Polarized View of the Accretion Geometry in the X-Ray Binary Circinus X-1

Cir X-1 is a neutron star X-ray binary characterized by strong variations in flux during its eccentric ∼16.6 day orbit. There are also strong variations in the spectral state, and it has historically shown both atoll and Z state properties. We observed the source with the Imaging X-ray Polarimetry Explorer during two orbital segments, 6 days apart, for a total of 263 ks. We find an X-ray polarization degree in these segments of 1.6% ± 0.3% and 1.4% ± 0.3% at polarization angles of 37° ± 5° and −12° ± 7°, respectively. Thus, we observed a rotation of the polarization angle by 49° ± 8° along the orbit. Because variations of accretion flow, and then of the hardness ratio, are expected during the orbit, we also studied the polarization binned in hardness ratio and found the polarization angle differing by 67° ± 11° between the lowest and highest values of the hardness ratio. We discuss possible interpretations of this result that could indicate a possible misalignment between the symmetry axes of the accretion disk and the Comptonizing region caused by the misalignment of the neutron star’s angular momentum with respect to the orbital one.

1. INTRODUCTION X-ray binaries (XRBs) consist of a compact object with a stellar companion orbiting it, from which it accretes matter.Flux and spectral variations in XRBs are thought to correspond to different accretion configurations.The spectrum of each state can be interpreted as a superposition of different components having a different * Deceased relative flux: typically the accretion disk, emitting a soft nearly thermal spectrum described by a blackbody or a multicolor disk, and a corona of hot plasma, whose electrons up-scatter the low-energy ambient photons, generating a hard X-ray component.In neutron star (NS) X-ray binaries (NS-XRBs), the surface region, where the accreting matter is stopped, also contributes to the total emission.The interfacing region, which is coplanar to the accretion disk, is known as the boundary layer (BL; Shakura & Sunyaev 1988;Popham & Sunyaev 2001), while the gas layer at the NS surface, extending up to high latitudes, is known as the spreading layer (SL; Inogamov & Sunyaev 1999;Suleimanov & Poutanen 2006;Abolmasov et al. 2020).XRBs with a weakly magnetized NS are classified, according to their tracks on the hard/soft X-ray color diagram, as Z or atoll sources (van der Klis 1989;Hasinger & van der Klis 1989).
Cir X-1 is a weakly magnetized NS-XRB characterized by an eccentric (e ∼ 0.45) ∼16.5 d orbit (see e.g.Kaluzienski et al. 1976;Schulz et al. 2020), during which its flux and spectrum change significantly, very different from any other known XRB.Cir X-1 has historically been shown to go through all the different states for both Z and atoll sources (Schulz et al. 2019).On the basis of its spectral characteristics, it was for a long time suspected to host a black hole, but the discovery of type I bursts undoubtedly proved that the compact object is a NS (Tennant et al. 1986;Linares et al. 2010).During its orbit, the X-ray flux varies by two orders of magnitude, and there are also more irregular decades-long variations (D'Aì et al. 2012).
An extended emission from a supernova remnant has been found around Cir X-1 (Heinz et al. 2013) with an estimated age of 4600 years, implying that the source is the youngest known XRBs.The young age is consistent both with the eccentricity of the orbit and with its irregular variations.Another characteristic that sets Cir X-1 apart from other XRBs is the presence of both radio and -unique case identified so far for NS-XRBs -Xray jets, indicating the ejection of matter at relativistic speeds.The X-ray jets are clearly visible on both sides of the receding and the approaching radio jet (Heinz et al. 2007;Soleri et al. 2009).Their presence, observed by Chandra either as a Doppler shift of emission lines or by directly imaging a diffuse and elongated emission, is interesting for comparing this system with black holes, showing that jets can be produced despite the shallower gravitational potential of NSs (Fender et al. 2004).The orientation of the radio jets has been reported to change with time either because of the precession of the regions from which it is emitted, which is well-accepted that they must be close to the compact object, or because of the interaction with the interstellar matter (Coriat et al. 2019).
Several models have been proposed to account for the peculiar orbital and state variations of Cir X-1.A dip in the light curve -followed by a flaring phase -is seen every orbit.This dip could be caused by a cold absorber; however, this would work only for high inclinations (D'Aì et al. 2012).According to Johnston et al. (1999) the eccentric orbit causes orbital variations in the mass accretion rate, producing the modulation in the Xray luminosity.Schulz et al. (2019) suggested that the companion is a massive supergiant of a Be type, which would imply that Cir X-1 is a high-mass Be XRB.The available observations until now have not been sufficient to discriminate among the different models.
We report the first polarimetric study of Cir X-1 using IXPE, measuring the new observables of polarization degree (PD), and polarization angle (PA).With X-ray polarimetry we can discern, from different polarization signatures, the different emission mechanisms, and the geometry of the regions closer to the compact object.In the absence of relativistic effects the PA is expected to be either parallel or perpendicular to the main geometrical axis of the component; as a consequence, if two components (such as disk and Comptonized region) are aligned, we expect their PAs to be either the same or orthogonal.If this is not the case, it can indicate that there is a geometrical misalignment between them, or that relativistic effects rotate the polarization plane (e.g., Connors & Stark 1977;Connors et al. 1980;Dovčiak et al. 2004;Loktev et al. 2020Loktev et al. , 2022)).

IXPE
The Imaging X-ray Polarimetry Explorer (IXPE; Weisskopf et al. 2022;Soffitta et al. 2021) is the first observatory combining detectors sensitive to X-ray polarization in the 2-8 keV energy band with X-ray optics.This mission, a collaboration between NASA and the Italian Space Agency (ASI), consists of three X-ray polarization sensitive Gas Pixel Detectors (GPD; Costa et al. 2001;Bellazzini et al. 2006Bellazzini et al. , 2007;;Baldini et al. 2021) at the focus of three grazing incidence optics.Other than detecting polarization, IXPE simultaneously detects the energy, time of arrival and celestial position of each X-ray detected.
IXPE observed Cir X-1 in two different pointings (2023-08-02T11:24 to 2023-08-04T23:52, and 2023-08-11T10:17 to 2023-08-13T22:46, joint in the ObsID 02002699, see Table 1), to cover two different parts of the orbit, for a net total exposure time of 263 ks.NICER and NuSTAR observations were performed to simultaneously partially cover the IXPE observation.IXPE data are reduced and corrected by the standard pipeline running at the Science Operations Center in NASA/MSFC, and were downloaded from the IXPE public archive at HEASARC.1 In the following analysis, event-by-event Stokes parameters are calculated following an unweighted approach Kislat et al. (2015) and Di Marco et al. (2022a), and computed using ixpeob- (Bottom) Hardness ratio obtained from IXPE (Eq. 1) during the observations binned in 500 s time bins.There is a clear change in state from the hard to the soft at the beginning of the IXPE observation; based on this, we divide the analysis in the 3 phase intervals indicated in the plots by the colored regions.
sssim 30.6.3 (Baldini et al. 2022); they are provided to the user in a reference frame projected on the sky.We selected the source in a circular region of radius 90 ′′ centered on the source.Because of the high brightness of this source, the background is negligible (see Di Marco et al. 2023a).
The top panel of Figure 1 shows the IXPE light curve during these observations -overlaid with data from the Monitor of All-sky X-ray Image (MAXI; Matsuoka et al. 2009) telescope.MAXI is mounted on-board the International Space Station, and monitors X-ray sources continuously; therefore its light curve allows to study the flux variations in Cir X-1 over its entire orbit, even outside the IXPE observation.
To verify possible changes in the accretion flow of Cir X-1, we study its flux, and its Hardness-Ratio (HR) variations over the IXPE observing time.The bottom panel of Figure 1 shows the IXPE HR, defined as The same plots show a division of the overall observations in three phase intervals, which we will use in the following to study the polarization along the orbit of Cir X-1: P1 (phase from 0.21 to 0.22), P2 (phase from 0.22 to 0.36) and P3 (phase from 0.75 to 0.90).We clearly see during the first observation a transition from a low flux -hard -state, to a high flux -softstate.The IXPE observation starts just when the source is coming out from the dip, as shown by the MAXI light curve, so that the low-hard state corresponds to this part of the orbit.Figure 2 (left) shows the hardness-intensity diagram (HID) for the three phase intervals obtained from the IXPE data.We clearly see a variation in hardnessintensity between the low-hard and high-soft state when moving from the first to the second phase interval.We also see that the HR is on average slightly larger in the third phase interval, when the flux was lower, compared to the second phase interval.The same effect is also seen in the color-color diagram (right panel of Figure 2), which shows the evolution of the source in two colors defined for the low-and high-energy bands.Tominaga et al. (2023) studied Cir X-1 for an extended period and divided (figure 2 of their paper) the orbit in different phases: a dip phase, where the X-ray flux is low due to strong absorption, whose end corresponds to P1 in this paper; a flaring phase, with rapid changes, corresponding to P2 in this paper; and a stable phase, with a gradual decrease in X-ray flux, corresponding to P3 in this paper.

NICER
The Neutron Star Interior Composition Explorer (NICER; Gendreau et al. 2016), mounted on-board the International Space Station, observed Cir X-1 during part of the IXPE observations.Obsid 6689030104right at the end of the first IXPE observation -and obsid 6689030203 -during the second IXPE observation (see Table 1) -were used to study the spectral components of Cir X-1 (see Section 3).NICER, consists of 56 co-aligned concentrator X-ray optics, each with a silicon drift detector at its focus, and, although it does not have imaging capabilities, it has a large collecting area in the energy interval of 0.2-12 keV.These observations were obtained in the framework of the GO Cycle 5 (proposal 6189); data were processed with the NICER Data Analysis Software v010a released on 2022 December 16 provided under HEASoft v 6.31.1 with the CALDB version released on 2022 October 30.The Nuclear Spectroscopic Telescope Array (NuS-TAR; Harrison et al. 2013) consists of two focal plane modules (FPMA and FPMB), providing broadband Xray imaging, spectroscopy, and timing in the energy range of 3-79 keV with an angular resolution of 18 ′′ (FWHM) and spectral resolution of 400 eV (FWHM) at 10 keV, and it is the only observatory employing multi-layer X-ray optics capable of focusing hard Xrays.We used the Cir X-1 observations at the end of the first IXPE observation (ObsID 30902037002) and during the second one (ObsID 30902037004, see Table 1), performed in the framework of GO cycle 9 (proposal 9212).

NuSTAR
NuSTAR data were processed by using the standard Data Analysis Software (nustardas v2.1.2from 2022 Feb 12) provided under HEASoft v 6.31.1 with the CALDB version released on 2023 April 4. The source was selected from a circular 150 ′′ radius region centered on the source position; the background was extracted in a similar region, but in a position of the field of view out of the source.

SPECTROSCOPIC ANALYSIS
Aiming to constrain the spectral model, and understand the different components, we analyzed NICER (in 1-10 keV) and NuSTAR (in 3-25 keV) data: the Obsid are these reported above, and were selected to overlap and have a short duration, so that there would be no HR variations.Previous spectral fits, such as in the broad-band BeppoSAX spectra (Iaria et al. 2002(Iaria et al. , 2005)), reported the presence of two components: a blackbody disk and a Comptonization component.However the temperature of one of the components -the disk -has been reported to be low (∼0.5 keV, Iaria et al. 2008) and so the disk is not expected to contribute significantly to the IXPE energy band.
We attempted to fit the continuum with the two components reported in literature: diskbb (Mitsuda et al. 1984;Makishima et al. 1986) associated with the disk or NS surface, and comptt (Titarchuk 1994) associated to the Comptonization in the BL/SL.We saw an excess in the residuals around 6 keV -associated with a broad iron line due to reflection from the disk -and around 1.7 keV -associated with a silicon line, suspected to be an instrumental NICER feature due to an incorrect calibration of the response, which becomes visible at the high flux observed from Cir X-1.To estimate the absorption from the interstellar medium, we set the abundances at the wilm values (Wilms et al. 2000); we started with a tbabs model, but found there were residuals better taken into account using tbfeo.The resulting model is written in xspec as tbfeo*(diskbb+comptt+gauss+gauss).We started by leaving free all the parameters, but found the temperature of the disk to be degenerate with its norm.We then fixed the disk temperature to a value minimizing the χ 2 and left the norm free in the subsequent fit: the resulting best-fit models are shown in Figure 3 and the parameters are given in Table 2.We see that the flux during P3 is lower than in P2, and the spectrum is harder.This is also reflected in a significantly higher optical depth τ p during P3, while the electron temperature is nearly the same.We left a free constant between NICER and NuSTAR, and also between the different NuSTAR modules: the two NuSTAR modules, normalized to NICER, have values 1.16 and 1.14 in P2, and 1.39 and 1.37 in P3.Since NuSTAR shows calibration uncertainties (Madsen et al. 2022), we left free a gain offset in the fit.No systematic errors were added to the fits (a known systematic error <1.5% is already applied to NICER data by the NICER pipeline nicerl3-spect).From the relative fluxes of the components in the nominal IXPE energy band of 2-8 keV we see that, even if both components are present, the dominant component is comptt.One of the Gaussians is an instrumental NICER feature, while the other is not visible due to a low IXPE energy resolution with respect to NICER and NuSTAR.Therefore in the following spectropolarimetric analysis of the IXPE data we only considered the comptt component.

POLARIZATION ANALYSIS
We studied the polarization of Cir X-1 in the three different phase and HR intervals.We first performed a study independent of any spectral model using the pcube algorithm of the ixpeobsssim software (Baldini et al. 2022).Then we also studied the polarization applying the spectro-polarimetric analysis in xspec (Arnaud 1996) by fitting the I, Q, and U spectra.Following the spectral models reported in literature (see e.g., D'Aì et al. 2012), we describe the I spectrum with the model: tbabs*comptt, setting the abundances to the values of Wilms et al. (2000), for the comptt model the geometry assumed is a disk (Titarchuk 1994), the hydrogen column density is fixed at the values found in the fit from the previous section for P2 and P3, and for the intermediate value for the HR bins.We did not fit P1 data since it is too short, has too few counts for polarimetric studies, and it has no contemporaneous NuSTAR data (however we still studied this data using pcube).To take into account IXPE calibration uncertainties (Di Marco et al. 2022b;Rankin et al. 2023), we left free the gain slope and offset, obtaining values of the order respectively of 95% for the slope, and in the 0.005 to 0.2 keV range for the offset.The results for the spectral modeling in the two phase intervals and in the three HR intervals are reported in Table 3.For the spectro-polarimetric analysis, we use the best-fit spectral fits from Table 3) and then fit Q and U using model polconst in xspec (see Table 4 for the obtained results).We also attempted fitting with the pollin model, but this gave no improvement over polconst.We considered fitting with a double polconst model ( tbabs*(comptt*polconst + diskbb*polconst)).However in this case, due to the low flux of diskbb, not all bins under consideration provide an acceptable fit with all parameters constrained and we are not able to separate the two components.

Polarization Along the Orbital Phase Intervals
We first studied the polarization degree (PD) and angle (PA) into each single phase interval in the whole IXPE 2-8 keV energy band: Figure 4-top shows a polar plot representing the PD and PA confidence regions in the three phase intervals defined in Figure 1.The polarization in the first phase interval (P1) -the lowhard state -is unconstrained, as expected due to the low counts; the polarization in the remaining two phase intervals -P2 and P3 -is significantly detected at Note-Uncertainties are at 68% confidence level.
Table 5. Polarization for different phase intervals and for different hardness ratios using pcube.
a confidence level (CL) higher than 99%.We also observe a clear rotation of the PA by 49  results obtained in these phase intervals using xspec are summarized in Table 4.We also attempted to measure the polarization properties in different energy bands (bottom panels of Figure 4).No evidence for an energy dependence at 90% CL is observed in any energy band; however, there are low significance hints of PD energy dependence in P2 and P3.There is also a low significance indication of a PA rotation with energy in P1: the PA at lower energies is consistent with the PA measured in P3, while at higher energies it is similar to that of P2.

Polarization as a function of the Hardness Ratio
Since HR varies during the orbit -even inside the phase intervals we considered above -we studied the polarization in different HR states.This analysis is also useful to have an idea, given the difficulties in the determination of the spectral components, for the polarization of the different emission regions/components.We used the HR values in the time bins of Figure 1-bottom to define three different HR intervals: HR1 in the range 0.5-0.6,HR2 in the range 0.6-0.7 and HR3 in the range 0.7-0.8.Given the large uncertainty on each HR value -at a level of ∼0.05 -we used the average HR in larger time bins of 2000 s each to populate the three HR intervals in the polarimetric analysis.This average curve is reported in Figure 5-top.
The polarization computed from events in these HR bins is shown in Figure 5; the numerical values are reported in Table 5, while these obtained with xspec are in Table 4.The two estimates are compatible.In the 2-8 keV energy band the PD is compatible in the three HR intervals, while the PA shows a gradual rotation as the HR changes, with a total rotation of the PA by 67 • ±11 • between the lowest and the highest hardness-ratio bins; a 90 • rotation is not consistent with this result at 68.2% CL.
The polarization in different energy bands is reported in Figure 5-bottom.No evidence for an energy trend at 90% CL is observed in any energy band, but there are only hints of an increase of PD with energy.

DISCUSSION AND CONCLUSIONS
We studied for the first time the X-ray polarization of the NS-XRB Cir X-1.With the available statistics, there is no significant variation with energy (see lower panels of Figures 4 and 5).In other X-ray binaries observed by IXPE, an increase of the PD with energy was observed, but in this case we only have hints of such an increase; we also find low significance hints of a rotation of the PA with energy in the hard state at the beginning of the IXPE observation (P1 of Figure 4), which is the state where the Comptonization component is stronger.Comparing with Poutanen et al. (2023) and Gnarini et al. (2022), we find that the energy trend in polarization for Cir X-1 observation is compatible with a shell or sandwich/wedge coronal geometry (with an inclination < 80 • ), but not with a slab geometry -for which a pronounced increase with energy would be expected.However, none of these two scenarios can fully explain our observation, where a change of the polarization is observed as a function of time and HR.This can be explained in terms of a scenario as the one of Figure 6 which we present below, where a spreading layer and a boundary layer are present, but currently no such model is available in literature allowing for a deeper analysis capable to estimate the system inclination and the inclination of the NS axis with respect to the disk.
Along Cir X-1 orbit, we observe a rotation of the PA by 49 • ± 8 • between different phase intervals (Figure 4), while the PD stays constant within the same observing phase intervals.Being the accretion flow expected to be related to the orbital variations of Cir X-1, we performed an analogous study in HR intervals: we observe also in this case a constant PD with a rotation of the PA by 67 • ± 11 • (Figure 5).The rotation between phase intervals is compatible with the rotation between HRs within 68% CL.
From a spectral point of view, comptt dominates in the IXPE energy band.However, at least two components are present, as reported in Section 3. Thus the variations along the orbit can be due to a superimposition of two different components contributing in a different way along the phase intervals.Looking at the top panel of Figure 5 we see that all the phase intervals are dominated by HR2 (∼ 60%), with a contribution from HR1 (∼ 35%) in P2, and from HR3 (∼ 35%) in P3.This confirms a scenario where the accretion flow -and the HR -varies along the orbit, with the harder state gradually becoming dominant as we are further away from the end of the dip (close to the beginning of the first IXPE observation).This is compatible with a model in which the accretion disk changes during the orbit due to its eccentricity (Johnston et al. 1999).In this model the modulation in the X-ray luminosity is due to orbital variations in the mass accretion of the compact star; during the periastron passage, the companion star overfills its Roche lobe, and the accretion disk is perturbed, through both tidal interaction and a sudden surge of material inflow, triggering an X-ray outburst.
We can interpret variations of the PA as due to two spectral components with significantly different PAs: a lower energy one dominating at low HR, and a harder one dominates at higher HR.In the intermediate HRs the two components are mixed.Such a two-component model, composed e.g. of a multicolor blackbody from the accretion disk and a Comptonized component, is the obvious candidate to explain two components in the polarization, and so has been proposed for the other IXPE observations of weakly magnetized accreting NSs (Ursini et al. 2023a;Capitanio et al. 2023;Farinelli et al. 2023;Cocchi et al. 2023;Di Marco et al. 2023b).From simple geometrical considerations, and in the absence of relativistic effects, each component can be expected to be polarized either parallel or orthogonal to its symmetry axis.The PA of the optically thick accretion disk is expected to be perpendicular to the position angle of the rotation axis.Relativistic effects may cause a small decrease (for counterclockwise rotation) of the PA by 5 • -10 • (Loktev et al. 2022).The Comptonization component can be associated either with the BL (which is coplanar with the accretion disk), or with the SL at the NS surface.The PA of the BL is likely nearly aligned with the PA of the accretion disk.In the absence of relativistic effects, the PA of the optically thick SL emission is parallel to the rotation axis.Due to aberration and Doppler boosting, the emission is expected to be dominated by the part of the SL moving towards the observer, breaking the symmetry and causing a decrease (also for counterclockwise rotation) of the PA by up to ∼20 • -30 • depending of the parameters (Bobrikova et al., in prep.).If the SL is optically thin, the PA may rotate by an additional 90 • (Sunyaev & Titarchuk 1985;Viironen & Poutanen 2004).However, it is clear from this consideration that the difference in the PA by 50 • -60 •as found for Cir X-1 -is impossible to produce.
The coexistence of two components with such a large difference in the PA may be explained if their symmetry axes are not aligned.This can be related, for example, to a misalignment of the NS angular momentum with respect to the orbital axis, this way causing a shift of the symmetry axis of the Comptonization region (associated with the SL) with respect to the disk (Abolmasov et al. 2020).We note here that Cir X-1 is not the only source for which such a misalignment might be present, but there are other hints: in Cyg X-2 the PAs of the two components are 66 • apart (see Fig. 7 in Farinelli et al. 2023), while in XTE J1701−462 and GX 5−1 the difference is ∼40 • (Cocchi et al. 2023;Fabiani et al. 2023).Also, X-ray polarimetry provided evidence for a misalignment in the X-ray pulsar Her X-1 (Doroshenko et al. 2022).Such a misalignment is in fact more likely for Cir X-1, than for other NS systems, as the system is younger than 4600 years (Heinz et al. 2013): if the newly-formed NS spins out of plane with respect to the binary system, there was not enough time to come to the alignment of the spinning axes.
At the same time, the accretion disk itself has a lower temperature compared to the Comptonization components (Iaria et al. 2008), and does not contribute significantly to the IXPE band.Thus the only other option for the second component is the BL.At low accretion rates (Figure 6-left), the disk is terminated at the innermost stable orbit of ∼3 Schwarzschild radii (i.e. about 13.5 km for a 1.5M ⊙ NS) which is likely larger than the NS radius of ∼12 km (e.g., Nättilä et al. 2017;Annala et al. 2022).In this situation, the BL does not exist at all and matter freefalls on the NS surface, forming a SL.Thus, the PA would correspond to the orientation of the NS rotation axis on the sky.At high accretion rates (Figure 6-right), the thickness of the SL grows, connecting it to the accretion disk through the BL.In this case, the PA would be related to the symmetry axis of the disk.Tominaga et al. (2023) modeled Cir X-1 as an accretion disk covered by a partially covering media, and interpreted the different phases of the orbit as changes in these two components.Their observations cover the dip for much longer than the IXPE polarimetric ones, where there is no significant polarimetric information for this phase; if we had observed the dip for longer with IXPE, we might have expected a high polarization degree due to obscuration, as observed in black hole systems (Veledina et al. 2023;Ursini et al. 2023b).It is interesting to note how their model is very good at predicting observational features such as lines, while to interpret the polarization we need a geometric model dealing with different features -such as the model we outlined in this paper.
In order to understand the geometry of the inner accretion flow in Cir X-1, it is now worth relating the observed PAs to the orientation of the jet.Cir X-1 is among the few NS-XRB showing jets both in the radio and the X-rays.The position angle of the (approaching) jet measured in the radio lies in the range 110 • -140 • (Fender et al. 1998;Tudose et al. 2008;Sell et al. 2010;Calvelo et al. 2012;Miller-Jones et al. 2012).Also in the X-rays the signatures of the (receding) jet is found in the north-west direction at position angles of about −70 • and −35 • (Heinz et al. 2007;Soleri et al. 2009), while the approaching jet is seen in the PA interval of 90 • -150 • (Soleri et al. 2009).Thus the average jet direction seems to be nearly orthogonal to the direction of the X-ray polarization in P2 (and at H1 and H2; see Table 5), which we associate with the BL emission.On the other hand, the X-ray polarization at the highest hardness ratio (HR3) is ∼ 1.3σ apart the the jet direction (−35 • or 140 • -150 • ).Finally, the X-ray PA of −12 • during P3 is clearly neither parallel, nor perpendicular to the jet.Associating the observed PA with the SL implies a misalignment of the NS's angular momentum from the orbital axis by about 30 • (Figure 6).Because the PA in this case is larger than the jet position angle, the rotation of the SL (and of the disk) has to be clockwise, corresponding to an inclination exceeding 90 • .
Although a large spread in the position angles measured for the jet can be explained by precession (Calvelo et al. 2012;Sell et al. 2010), such an interpretation does not work for the variations of the X-ray PAs, because of much shorter time scales involved and detection of different PAs at different HRs.This gives further support to the interpretation that variations of the PA are caused by different spectral components (accretion disk, BL, and SL) dominating at different times.With the data at hand it is impossible to extract those components from the spectra; variations of the PA, however, strongly support the idea that the NS angular momentum is misaligned from the orbital one, which is a necessary requirement for the precession to operate.The X-ray polarimetric data, thus, provide a unique view of the geometry of the accreting NS Cir X-1.

Figure 1 .
Figure1.Evolution of the X-ray properties of Cir X-1.(Top) Rate obtained by MAXI (2-20 keV) and IXPE over two orbits binned in 180 s time bins.(Bottom) Hardness ratio obtained from IXPE (Eq. 1) during the observations binned in 500 s time bins.There is a clear change in state from the hard to the soft at the beginning of the IXPE observation; based on this, we divide the analysis in the 3 phase intervals indicated in the plots by the colored regions.

Figure 2 .
Figure 2. Hardness-intensity (left) and color-color (right) diagrams during the IXPE observations, binned in time bins of 180 s, with color highlighted the three phase intervals chosen for the subsequent analysis.

Figure 3 .
Figure 3. Spectral energy distribution of Cir X-1 during P2 (left) and P3 (right) in EFE representation using NICER and NuSTAR (FPMA and FPMB) data and showing the different model components.

Figure 4 .
Figure 4. Polar plot of polarization, computed using the pcube algorithm from the ixpeobsssim software (Baldini et al. 2022), for the three phase intervals defined in Figure 1.(Top) Polarization in the entire IXPE energy band is reported.The shaded region indicates the direction of the jet (see discussion), and the black lines indicate this direction and its orthogonal direction.Contours are reported at the 68%, 95%, and 99% confidence levels.(Bottom) polarization in different energy bands for the three phase intervals, with contours showing 90% confidence level.

Figure 5 .
Figure 5. Study of polarization binned in hardness ratio.(Top) HR trend along time (2000 s time binning), the colored bands identify the chosen binning for HR.(Middle) Polar plot of polarization, computed using the model-independent pcube algorithm from the ixpeobsssim software(Baldini et al. 2022), for events in different intervals of HR reported in the top panel, in the energy band 2-8 keV where the shaded region indicates the direction of the jet (see discussion), and the black lines indicate this direction and its orthogonal direction.Contours are reported at 68%, 95%, and 99% confidence levels.(Bottom) Polarization in different energy band.Contours are reported at 90% confidence level.

Figure 6 .
Figure 6.Illustration of a possible accretion geometry in Cir X-1.(Left) Low accretion-rate case, when there is a gap between the disk and the NS surface, and the full SL is developed.(Right) High accretion-rate case, where the disk touches the NS surface, and the BL is emitting (with a PA almost perpendicular to the symmetry axis of the disk).

Table 1 .
Observational data used in this paper, reporting for each mission the observation IDs, the livetime and the start and end times of each observation.