EDP Sciences logo
Subscriber Authentication Point
Search
Menu
Home All issues Volume 711 (July 2026) A&A, 711 (2026) A208 Full HTML
Open Access
Issue
A&A
Volume 711, July 2026
Article Number A208
Number of page(s) 14
Section Stellar structure and evolution
DOI https://doi.org/10.1051/0004-6361/202659608
Published online 16 July 2026

© The Authors 2026

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe to Open model. This email address is being protected from spambots. You need JavaScript enabled to view it. to support open access publication.

1. Introduction

Weakly magnetized neutron stars in low-mass X-ray binaries (NS-LMXBs) are systems characterized by a neutron star accreting matter through Roche-lobe overflow, typically from a late main-sequence or evolved degenerate companion star. The accretion flow is stopped by the surface of the NS, creating a boundary (BL) or spreading layer (SL) between the accretion disk and the NS surface. Z-sources are a class of NS-LMXBs with typical X-ray luminosity LX > 1038 erg s−1 and exhibiting a three-branch track in their hardness-intensity (HID) or hard color-soft color diagrams (CCDs; Hasinger & van der Klis 1989; van der Klis 1989), characterized by the “horizontal branch” (HB), the “normal branch” (NB), and the “flaring branch” (FB).

Typical X-ray spectra of NS-LMXBs are generally well described by soft thermal emission produced by the accretion disk (Mitsuda et al. 1984, 1989) or the NS surface (White et al. 1988) plus a harder component related to the inverse Compton scattering of soft photons in a hot electron plasma. However, the exact nature and geometry of the Comptonizing region are still a matter of debate since the different models are spectroscopically degenerate. In contrast, X-ray polarization strongly depends on the geometry of the system (e.g., Gnarini et al. 2022, 2024b; Farinelli & Cocchi 2025) and is crucial to determining its physical characteristics. The reflection of X-ray photons above the surface of the accretion disk is another important component (see also the reviews by Di Salvo et al. 2024 and Ludlam 2024): reflection features have been detected in the spectra of most Z-sources (Smale 1998; D’Aì et al. 2009; Iaria et al. 2009; Cackett et al. 2010; Coughenour et al. 2018; Mazzola et al. 2021; Ludlam et al. 2022; Thomas et al. 2024), although not in all (e.g., GX 5–1; Homan et al. 2018; Fabiani et al. 2024). These reflected photons are expected to be highly polarized (Lapidus & Sunyaev 1985; Matt 1993), significantly contributing to the polarization despite the fact that their relative contribution to the total X-ray emission may be quite low (Ursini et al. 2023; Gnarini et al. 2024b; Anitra et al. 2025).

X-ray polarimetry performed with the Imaging X-ray Polarimetry Explorer (IXPE; Weisskopf et al. 2022) now represents a very powerful tool to study NS-LMXBs. In particular, the characteristics of the polarization signal are highly sensitive to the specific geometrical configuration and morphology of the Comptonizing region (Gnarini et al. 2022, 2024b; Farinelli et al. 2024; Bobrikova et al. 2025). For example, a polarization lower than 2% for a source observed at low inclination would rule out slab-like configurations, favoring spreading layer-like geometries; on the other hand, a high PD of 5–6% would suggest a slab-shaped geometry at a high inclination angle. Being very bright sources, NS-LMXBs are perfect targets for X-ray polarimetry, and IXPE has detected significant polarization in most of them (see Ursini et al. 2024b, for a detailed review).

In the first part of this work (Gnarini et al. 2025, G25 hereafter), we performed model-independent analysis for each Z-source using IXPEOBSSIM (Baldini et al. 2022) to measure polarization along the Z-track. We decided to restrict our sample to Z-sources for which IXPE data were publicly available before December 2024, namely Cyg X-2, XTE J1701–462, GX 5–1, Sco X-1, GX 340+0, and GX 349+2. In this second part, we report the results of the first branch-resolved spectropolarimetric analysis of the sample of Z-sources observed with IXPE as they move along their CCDs. These sources exhibit the highest polarization in the full 2–8 keV IXPE band when observed along the HB, up to about 4% (G25); however, when they move along the NB, the polarization decreases (≲2%) without any significant rotation of the polarization angle (PA). Although the FB was identified during the observations of all Z-sources, significant polarization was detected only for some of them (G25); in particular, the polarization seems to increase moving from the NB to the FB for Cyg X-2 and Sco X-1, while it remains consistent within the two branches at the 90% confidence level for GX 5–1 and GX 349+2.

Similarly to the first part of the work (G25), we considered the same procedure for data reduction and analysis for all Z-sources, to perform the spectropolarimetric analysis with XSPEC (Arnaud 1996) using the same baseline model for a uniform spectral fitting. Using the same model for all sources allows us to make direct comparisons between the various Z-sources observed and to study the evolution of their physical parameters, for example, the temperature and optical depth of the Comptonizing region or the location of the inner edge of the accretion disk, as the sources move along their CCDs. The paper is structured as follows: in Sect. 2, we report the data reduction to obtain the spectra for each observatory. In Sect. 3, we present the new X-ray spectropolarimetric analysis for each source; finally, in Sects. 4 and 5, we discuss the results obtained.

2. Observations and data reduction

All observations of the Z-sources with IXPE, NICER, and NuSTAR are introduced and listed in G25. In addition to the data reduction procedure for each instrument already described in G25, we extracted the spectra to analyze with XSPEC as follows.

2.1. IXPE

We extracted spectropolarimetric data for each detector unit (DU) using the standard dedicated FTOOLS procedure with the latest available calibration files (CALDB v.20250225). The spectra for each Z-source have been extracted using the same source circular regions found in G25, without applying any background rejection or subtraction (Di Marco et al. 2023b). The adopted radius of the extraction regions for each source and DU is derived using an iterative process to maximize the S/N in the 2–8 keV range. The resulting radii R are reported in Table 1. Only for GX 5–1, we used a fixed 60″ radius region to avoid the X-ray halo observed with Chandra (Smith et al. 2006; Clark 2018). We applied the weighted analysis method described in Di Marco et al. (2022) with the parameter stokes=Neff in XSELECT. For each DU, we produced the ancillary response file (ARF) and modulation response file (MRF) using the ixpecalcarf task, with the same source extraction radii. Then we rebinned all the IXPE I spectra using the standard ftgrouppha task and requiring a minimum S/N of 3 per bin. The Stokes Q and U spectra were then rebinned using the same energy binning as the I spectra.

Table 1.

Log of source extraction regions.

2.2. NICER

We derived NICER spectra with the nicerl3-spect task available in HEASARC, while the background was computed using the SCORPEON1 model. The spectra were then automatically rebinned with the ftgrouppha task, considering the optimal binning algorithm by Kaastra & Bleeker (2016) with the additional requirement of 10 counts per grouped bin. In most of the NICER spectra, we found some significant residuals, typically below 2 keV; these features are likely related to instrumental issues not considered in the NICER ancillary response file (ARF; see also Miller et al. 2018; Strohmayer et al. 2018). Therefore, we added a multiplicative absorption edge (edge) to remove these features from the residuals. The resulting threshold energy of this edge obtained from the best-fits is very close to the Al edge at 1.839 keV. If we fix the threshold energy to the same value of the Al edge, the fits improve. For the spectral analysis of NICER spectra, we adopted PGstat statistics since the background estimation for NICER observations is done with SCORPEON and results in a non-Poissonian background.

2.3. NuSTAR

We extracted the spectra for each focal plane module (FPM) using the nuproducts command, with the same source and background circular regions found in G25. Following the same approach adopted for IXPE, we derived the size of the extraction regions for each source and FPM by maximizing the S/N in the 3–79 keV range, while a fixed 60″ region is considered for the background. The resulting source radii R for each source and observation are reported in Table 1. Similarly to the IXPE spectra, the NuSTAR spectra were also rebinned using ftgrouppha, with the optimal binning algorithm by Kaastra & Bleeker (2016) and a minimum S/N of 3 per grouped bin.

3. Spectral analysis

For each source, we performed a single joint fit of the IXPE, NuSTAR, and NICER spectra among the different branches of the Z-track with XSPEC (Arnaud 1996). The spectra are integrated along each branch and are derived using good time intervals (GTIs), as described in G25. For all sources, we considered the IXPE spectra in the 2–8 keV band, while for NICER the 1.5–10 keV energy range is considered. For NuSTAR, the adopted energy ranges differ between sources and branches because the background starts to dominate at different energies, but typically in the 20–30 keV range.

To have a direct comparison between the different Z-sources and a uniform spectral fitting, we decided to use the same two-component baseline model:

TBabs*(diskbb+thcomp*bbodyrad).

An energy-independent cross-calibration multiplicative constant has been introduced for each IXPE DU, each NuSTAR FPM and the NICER spectra. We modeled interstellar absorption using tbabs, considering vern cross section (Verner et al. 1996) and wilm abundances (Wilms et al. 2000). The baseline model includes a multicolor disk blackbody (diskbb; Mitsuda et al. 1984) and a harder Comptonized emission modeled with the convolution model thcomp (Zdziarski et al. 2020) applied to a bbodyrad component, associated with the NS emission. The covering fraction f of thcomp represents the fraction of Comptonized photons with respect to the total seed photon emission.

All observed Z-sources, with the exception of GX 5–1 (see also Homan et al. 2018; Fabiani et al. 2024), show evidence of an iron Kα line between 6–7 keV and a reflection component. We employed the relxillNS model to account for the reflected photons. The relxill models calculate the relativistic reflection from the innermost regions of the accretion disk (García et al. 2014; Dauser et al. 2014; García et al. 2022); relxillNS is a particular flavor of relxill assuming a single-temperature blackbody spectrum as the primary continuum illuminating the accretion disk at 45°, physically related to the emission from the NS surface or from the boundary or spreading layer. In each branch, we decided to tie the temperature of the seed photons of relxillNS to the blackbody temperature of bbodyrad. The reflection fraction is set to −1 for all sources in order to obtain only the reflected emission without the direct continuum. The shape of the reflection spectrum is characterized by several physical parameters: the emissivity index qem, the dimensionless spin a, the inner and outer radii of the accretion disk (Rin and Rout respectively), the inclination i of the system, the number density ne, the iron abundance AFe, and the ionization parameter ξ. For a standard NS, the dimensionless spin can be fixed to 0.1, consistent with the value that could be derived from the spin period obtained from quasi-periodic oscillations (Wijnands et al. 1998; Braje et al. 2000; see also Patruno et al. 2017 for a statistical analysis of the spin distributions of NS-LMXBs). Therefore, for all Z-sources, we fixed the value of a to 0.1, while the outer disk radius is always fixed to 1000 gravitational radii. As the sources move along their Z-tracks, we expect that some parameters such as the inclination of the system, the iron abundance, and the emissivity index should remain constant differently, for example, from the inner disk edge.

3.1. Cyg X-2

Cyg X-2 was the first Z-source observed by IXPE, simultaneously with NICER and NuSTAR. The two observations were made early in the mission, before in-flight adjustments were made to establish a good alignment between the mirror module and overall telescope optical axes2. This is not modeled in the response matrices, thus for each DU the slope of the IXPE spectra is slightly different and not compatible with those of NICER and NuSTAR (see also Capitanio et al. 2023; Farinelli et al. 2023). Therefore, spectral analysis was conducted using only these two observatories. It should be noted that since this issue impacts the Stokes parameters I, Q, and U in the same way, the PD and PA remain unaffected.

Cyg X-2 was found mainly in the NB with a rapid excursion in the FB (G25). We left most of the physical parameters of the disk and the Comptonization component free to vary as the source moves along the different branches, along with the ionization parameter ξ and the normalization of the reflection. The inclination i and the emissivity index qem of relxillNS are tied between the branches but left free to vary, while the values of iron abundance AFe and number density ne were fixed to those obtained by Ludlam et al. (2022). In both branches, we found that the covering fraction f is very close to 1, i.e., > 0.98 and > 0.95, for the NB and FB respectively; therefore, its value was fixed to 1 to better constrain the other physical parameters.

The deconvolved spectra with the resulting best-fit for each branch are reported in Fig. 1a and Table A.1. The best-fit models obtained for the NB and FB provide statistically acceptable results, with χ2/d.o.f. (degrees of freedom) of 350/309 and 318/275, respectively. The values of the disk and Comptonization parameters are consistent with the typical values for Cyg X-2 (Di Salvo et al. 2002; Farinelli et al. 2009, 2023), while the results obtained for relxillNS are similar to those obtained by Ludlam et al. (2022). The radius of the blackbody-emitting region Rbb and the apparent inner radius of the disk Rd are derived from the normalizations of bbodyrad and diskbb, considering a distance to the source of 7.2 kpc (Orosz & Kuulkers 1999). As the source moves from the NB to the FB, both the diskbb and bbodyrad temperatures decrease. Additionally, the thcomp electron temperature decreases, whereas the optical depth remains almost unchanged. In the 2–8 keV range, accretion disk emission is the main contribution to the photon flux in the NB, while the Comptonization and the reflection are significantly more important in the FB. Recently, Cyg X-2 was also observed in the HB by Gnarini et al. (2026). Because the spectropolarimetric analysis was performed with the same model and procedure, we can include those results in this analysis to obtain a complete coverage of the Z-track. In the HB, the total 2–8 keV flux is significantly dominated by Comptonized emission, characterized by an electron temperature slightly higher than the other branches but optical depth consistent within errors. On the other hand, the disk temperature is much lower than those of the NB and FB.

Thumbnail: Fig. 1. Refer to the following caption and surrounding text. Fig. 1.

Deconvolved spectra for each Z-source with the resulting best-fit model and the corresponding residuals in units of σ. The three branches are highlighted with different colors and markers. Main spectral components are highlighted with different line styles, i.e., diskbb (dash-dotted lines), thcomp*bbodyrad (dashed lines), and relxillNS (dotted lines). (a) Cyg X-2. (b) XTE J1701–462. (c) GX 5–1. (d) Sco X-1. (e) GX 340+0. (f) GX 349+2.

3.2. XTE J1701–462

XTE J1701–462 was observed twice by IXPE during its 2022 outburst (see also Cocchi et al. 2023; Yu et al. 2025). In the first observation, simultaneously with NICER, the source was identified in its HB, while in the second observation the source was tracking the NB and FB in its NuSTAR and IXPE HIDs (G25). For all the branches, we left the physical parameters of diskbb and thcomp*bbodyrad free to vary. Reflection features were well identified in the NuSTAR spectra, while in the NICER one there is a hint of the presence of the iron line between 6–7 keV. Therefore, we decided to characterize the properties of the reflection using the NuSTAR spectra of the second observation, leaving free to vary the inclination i, the inner disk radius Rin, and the ionization parameter ξ. Then, we linked all the physical parameters of relxillNS for the first observation to that obtained for the second one but with only the normalization free to vary.

The deconvolved spectra with the resulting best-fit for each branch are reported in Fig. 1b and Table A.2. The best-fit models obtained for the three branches yield statistically acceptable results, with χ2/d.o.f. values of 565/552 for the HB, 615/575 for the NB, and 625/571 for the FB. Both the diskbb and the bbodyrad temperature varies moving from the HB to the FB, while the electron temperature of thcomp remains consistent within the errors. On the other hand, the covering fraction f decreases significantly. In the HB, its value is always > 0.93, therefore all the seed photons are Comptonized; in the NB only about 20% of the blackbody photons result in Comptonization; in the FB, almost all the seed photons are observed since only about 2% of them get scattered in the Comptonizing region. Moreover, the optical depth τ of thcomp increases as the source moves to the FB, up to about 30 keV, although its value in the FB is not well constrained because of the low fraction of Comptonized photons. From relxillNS, we found an inclination of about 30°, consistent with the results obtained by Thomas et al. (2024), while only an upper limit for the inner disk radius is obtained in the HB and NB. In the FB, Rin results in being always unconstrained, and we decided to fix its value to the innermost stable circular orbit (ISCO) radius. The ionization parameter significantly decreases moving to the FB. In the HB, the major contribution to the total 2–8 keV flux comes from Comptonized photons (≈67%), while in the NB the disk contributes almost 70% of the emission. The situation is a bit peculiar in the FB: although the main contribution comes from the thcomp*bbodyrad component, since the covering fraction is only 2%, the 2–8 keV flux is dominated by the seed blackbody photons. For all the branches, the photon flux ratio of thcomp*bbodyrad significantly increases with energy, whereas the diskbb contribution decreases, as expected.

3.3. GX 5–1

IXPE observed GX 5–1 twice simultaneously with NICER and NuSTAR in 2023. The source remained in the HB throughout the first observation, while it moved along the NB and FB during the second (G25). Unlike the other Z-sources, we do not detect any reflection features in the GX 5–1 spectra. Following Fabiani et al. (2024), we considered an additional hard tail component modeled with a powerlaw with a low-energy exponential rolloff (expabs*powerlaw; see also Paizis et al. 2006). The energy of expabs is set equal to the temperature of bbodyrad since the powerlaw emission originates from the seed distribution of the Comptonized emission. The powerlaw photon index α is set to the best-fit value obtained by Fabiani et al. (2024), while normalization Npl is considered a free parameter. In the FB, we do not observe any excess in the high-energy part of NuSTAR spectra: including the powerlaw, the fit statistic does not significantly improve and we obtain an upper limit of 0.02 for the normalization of expabs*powerlaw. Therefore, we removed this component in the FB. Along the different branches, we left the physical parameters of the disk and Comptonization free to vary during the fit, while we tied the value of the hydrogen column density NH.

The deconvolved spectra with the resulting best-fit for each branch are reported in Fig. 1c and Table A.3. The best-fit models obtained for the three branches yield statistically acceptable results, with χ2/d.o.f. values of 976/881 for the HB, 906/814 for the NB, and 871/708 for the FB. During the first observation with the source in the HB, the covering fraction f result is > 0.97, therefore we decided to fix its value to 1. For the second observation, differently from Fabiani et al. (2024) in which the best-fit was performed using time-averaged spectra with a best-fit value for f ranging between 2.7% and 11.2%, we obtained a covering fraction > 0.98 and < 0.01 for NB and FB, respectively. Similarly to the HB, we fixed the value of f to 1 for the NB to better constrain the other physical parameters of thcomp. For the FB, we noticed that the fit improves by fixing the covering fraction to 0 or removing the thcomp component. We tried also to apply thcomp to the disk emission to verify if the fit would improve; in this case also the covering fraction result is < 0.02 and the fit is statistically very similar to that with thcomp*bbodyrad. Therefore, in the FB, the spectra are well modeled by a combination of the disk emission and a simple blackbody. As the source moves from the HB to the NB, both the temperature of the disk and of the seed blackbody component decrease, while they increase again in the FB. In addition, the temperature and the optical depth of the Comptonizing region also decrease from the HB to the NB. Unlike Cyg X-2 and XTE J1701–462, for GX 5–1, the main contribution to the total 2–8 keV flux comes from the disk emission for both the HB and the FB (up to 60%), while only in the NB does Comptonization represent the major component. On the other hand, the contribution of thcomp*bbodyrad, or only of bbodyrad in the FB, increases significantly with energy for all branches, while that of diskbb decreases.

3.4. Sco X-1

Sco X-1 was observed in 2023 by IXPE using the gray filter to reduce its X-ray flux, simultaneously with both NICER and NuSTAR (La Monaca et al. 2024b). In particular, NuSTAR identified the source moving between the NB and the FB during IXPE exposure (G25). For the spectral analysis, we considered only the NICER and NuSTAR spectra, since the IXPE spectra exhibit significant residuals in the entire 2–8 keV energy band, likely related to the use of the gray filter. To correct for this issue, during the polarimetric analysis, in addition to the cross-calibration constant, we multiplied the model by a powerlaw difference (E−ΔΓ), following a similar procedure to Ludlam et al. (2022).

The deconvolved spectra with the resulting best-fit for each branch are reported in Fig. 1d and Table A.4. The best-fit models obtained for the NB and FB provide statistically acceptable results, with χ2/d.o.f. of 440/367 and 474/367, respectively. The physical parameters of the disk and Comptonized emission are left free to vary during the fit, as long as the inclination i, the emissivity index qem, the iron abundance AFe, and the ionization parameter ξ of relxillNS. The values of the disk and electron temperature are consistent within errors between the NB and FB, while the optical depth and the temperature of bbodyrad significantly increases in the FB. Since in the NB the covering fraction is very close to 1, i.e., > 0.99, its value is fixed to 1 to find better constraints for the other physical parameters. However, in the FB, the covering fraction f ranges between 48% and 54%; therefore, not all the seed photons of bbodyrad are Comptonized. The parameters of the Comptonized component are also consistent with the results obtained by Mazzola et al. (2021), while the diskbb parameters are slightly different, probably due to the different value of NH. Unlike La Monaca et al. (2024b), we left the inclination free to vary and its measured value (46° ±3°) is consistent with the results obtained by Fomalont et al. (2001a,b), while we were able to constrain the value of the inner disk radius in the NB (≈2.2 RISCO), but only an upper limit of 1.8 RISCO is found for the FB. These results for the inner disk radius represent an improvement with respect to the upper limit obtained by La Monaca et al. (2024b), while the best-fit values for the ionization parameters are slightly different, probably as a result of the different spectral model and the assumptions for the reflected component. It should also be noted that the spectral analysis in La Monaca et al. (2024b) was performed using time-averaged spectra, rather than fitting the different branches separately. In the 2–8 keV energy band, the main contribution to the total flux comes from the Comptonization in both branches, about 45% in the NB and 55% in the FB, whereas the contribution of both the disk and reflection decreases from the NB to the FB. For both branches, both the photon flux ratios of thcomp*bbodyrad and relxillNS increase with energy, while the contribution of diskbb decreases from about 55% to less than 10%.

3.5. GX 340+0

IXPE observed GX 340+0 twice during the first cycle of the Guest Observing (GO) program in 2024 (see also Bhargava et al. 2024a,b; La Monaca et al. 2024a, 2025b). During the second IXPE observation, NICER also simultaneously observed the source; while no NuSTAR observation was strictly simultaneous to the IXPE ones, they were performed a few days after the IXPE ones. For each branch, we verified that the NuSTAR spectra were consistent with those of IXPE and, therefore, can be used for spectral modeling. To account for some residuals in the NuSTAR spectra, in addition to the baseline model and the relxillNS component, we applied the same ionized emission plasma model apec used by Ludlam et al. (2025), which analyzed the same NuSTAR spectra along with XRISM data. Since the parameters of apec are not constrained using only NuSTAR, NICER, and IXPE, we decided to fix the plasma temperature and the metal abundances to the same value reported by Ludlam et al. (2025). Similarly, we also fixed the value of the emissivity index qem and the iron abundance AFe to the results obtained with XRISM.

The deconvolved spectra with the resulting best-fit for each branch are reported in Fig. 1e and Table A.5. The best-fit models obtained for the three branches yield statistically acceptable results, with χ2/d.o.f. values of 763/675 for the HB, 808/750 for the NB, and 785/682 for the FB. Although the temperatures of bbodyrad and diskbb remain consistent within errors as the source moves along the Z-track, there is a clear evolution of the physical parameters of thcomp. In the HB, the covering fraction f is > 0.99 and we fixed its value to 1 to better constrain the other parameters. In the NB, the covering fraction decreases, ranging between 30% and 40%, while it reduces again in the FB, with only about 1% Comptonized photons with respect to total blackbody emission. The optical depth τ increases significantly from HB to FB, while the electron temperature kTe is consistent within the errors between the HB and the NB; in the FB, the electron temperature reaches about 15 keV, which is much higher than the results obtained for other Z-sources. However, the results for the FB of GX 340+0 are poorly constrained with respect to the other branches or other Z-sources, likely related to the very small fraction of Comptonized photons. The inclination i can be well constrained and results are consistent with the results obtained by Ludlam et al. (2025), while only upper limits are obtained for the inner disk radius. For each branch, the main contribution to the 2–8 keV flux is the direct accretion disk emission, about 50% in the HB and FB, and up to 67% in the NB. Comptonization contributes roughly to about 45% of the flux in the HB and FB, but only about 30% in the NB. As for the other Z-sources, for all branches, the contribution of diskbb significantly decreases with energy, whereas that of thcomp*bbodyrad and relxillNS increases.

3.6. GX 349+2

GX 349+2 was observed for the first time by IXPE in September 2024 during the first GO cycle (see also Kashyap et al. 2025a; La Monaca et al. 2025a). NuSTAR also observed the source twice simultaneously with IXPE, indicating that it was moving between the NB and the FB (Gnarini et al. 2025). All the physical parameters of disk and Comptonization are left free to vary between the branches, while we tied the hydrogen column density of TBabs. Similarly, the inclination i and the iron abundance AFe are also tied between the NB and FB, and we fixed the emissivity index qem and the number density to a reasonable value to better constrain the other parameters. The inclination of the source can be well constrained with the NuSTAR data, while only an upper limit can be obtained for the inner disk radius in the NB. Due to the short exposure of the FB, the inner disk radius is unconstrained and we fixed its value to 1 RISCO.

The deconvolved spectra with the resulting best-fit for each branch are reported in Fig. 1f and Table A.6. The best-fit models obtained for the NB and FB provide statistically acceptable results, with χ2/d.o.f. of 683/647 and 657/632, respectively. Moving from the NB to the FB, the temperatures of the diskbb and bbodyrad decrease, while the temperature and the optical depth of the Comptonizing region results are consistent within errors between the branches. In both branches, the covering fraction f is very close to 1, i.e., > 0.99 and > 0.97, for the NB and FB respectively; therefore, we decided to fix its value to 1 to better constrain the other parameters. The best-fit values for the physical parameters of diskbb and thcomp*bbodyrad differ slightly from those reported by Kashyap et al. (2025a) and La Monaca et al. (2025a), likely as a consequence of the different model adopted, but they are in line with the typical values of Z-type NS-LMXBs. From the reflection component, we found an inclination of 37° ±5°, which is consistent with the results obtained by Coughenour et al. (2018) and La Monaca et al. (2025a). However, we obtained only an upper limit in the NB for the inner disk radius of 1.6 RISCO, while it is not constrained in the FB and its value was fixed at 1 RISCO. The ionization parameter is consistent within the errors between the two branches. In both NB and FB, the main contribution to the total 2–8 keV flux is due to Comptonized photons (about 50%). The contribution of the disk decreases from about 44% to 33% moving from the NB to the FB, whereas the photon flux ratio of reflection increases from 9% to 17%. Similarly to the other sources, we found an increasing contribution of thcomp*bbodyrad and relxillNS with energy, while a decreasing behavior with energy is observed for the contribution of diskbb.

4. Spectropolarimetric analysis

Once we obtained the best-fit models for each source and each branch of the Z-track, we performed the spectropolarimetric analysis fixing all spectral parameters to their best-fit values and using only the IXPE Stokes spectra. We first applied the multiplicative polconst component, describing a constant polarization with energy, to the entire best-fit models. The results for the polarization are consistent with those obtained using PCUBE (G25). We then switched polconst with the multiplicative pollin model in order to test the linear dependence of the polarization with energy. In this case, we also recovered the same results obtained with the linear fit applied to the PCUBE results (G25). Then, we applied the polconst component separately to each spectral component. Unlike previous spectropolarimetric studies of Z-sources (Farinelli et al. 2023; Cocchi et al. 2023; La Monaca et al. 2024b, 2025b; Kashyap et al. 2025a), in which either a full reflection model was not used or reflection was not appropriately included in the spectropolarimetric analysis, we included the contribution of reflection to the polarization, as reflected photons can be highly polarized, up to about 10% or 20%, depending on the geometry and the ionization state of the disk (Matt 1993; Podgorný et al. 2026). However, it is difficult to estimate the PD and PA for each component due to the limited bandpass of IXPE and the degeneracy of some components; for example, the contribution of the Comptonized and reflected radiation is not well constrained without some theoretical and observational expectations, since they peak at similar energies.

For all Z-sources and branches, we decided to fix the PD of relxillNS at 10% (Matt 1993; Poutanen et al. 1996), while the PA is tied to that of thcomp*bbodyrad. This assumption is reasonable for a typical configuration with an optically thick boundary or spreading layer characterized by H ≫ ΔR, where H is its vertical height and ΔR its radial extension (Poutanen et al. 1996; Schnittman & Krolik 2009). For most sources, the reflection fraction is relatively small; therefore, fixing the PD does not significantly influence the results. In some cases, following the same assumption, we also decided to fix the value of the PA of diskbb to be perpendicular to that of thcomp*bbodyrad and relxillNS to obtain a constraint for the PD of the disk component. For GX 5–1, since the powerlaw component is related to the same seed distribution as the Comptonized component, we also linked the polarimetric parameters of expabs*powerlaw to those of thcomp*bbodyrad. For sources in which one or more Gaussian components were included to model an emission line, the polarization of those components was fixed to zero.

The results of the spectropolarimetric analysis applying polconst to each spectral component are reported in Table 2 and Fig. 2. Compared with previous studies reporting spectropolarimetric results for Z-sources (Farinelli et al. 2023; Cocchi et al. 2023; Fabiani et al. 2024; La Monaca et al. 2024b,a, 2025b,a), we performed the analysis by fitting the three individual branches separately. A similar approach was adopted only by Kashyap et al. (2025a) for GX 349+2, although using a three-component model that includes direct disk and NS emission, plus Comptonized disk photons, and without adopting a full reflection model. The resulting PD of the disk is generally lower with respect to the results obtained for Comptonization and reflection, with typical values ranging between 2–3%. Only for Cyg X-2 are the measured values consistent with the “classical” results for an electron scattering-dominated semi-infinite plane-parallel atmosphere (Chandrasekhar 1960; Sobolev 1963) observed at the specific inclination derived from relxillNS. However, for all other sources, the disk polarization obtained from spectropolarimetric analysis is higher compared to the PD calculated by Chandrasekhar (1960) considering the measured inclination. A PD exceeding that of a pure-scattering atmosphere can be achieved when accounting for absorption and considering an atmospheric ionization far from complete (Taverna et al. 2021; Marra et al. 2026). When measurable, in most cases, the PA of the disk emission is significantly misaligned and not perpendicular to that of Comptonization, as expected for a typical geometrically thin but optically thick accretion disk.

Thumbnail: Fig. 2. Refer to the following caption and surrounding text. Fig. 2.

Polarization degree of Comptonized (top) and disk (middle) emission, and the difference of the polarization angle of the two components (ΔPA; bottom) for each Z-source as a function of the branch (see Table 2). Empty markers correspond to values frozen during the fits. Errors are at the 90% confidence level; upper limits are reported at the 99% confidence level for one interesting parameter.

Table 2.

Polarization degree and angle of each spectral component for each source with the corresponding branch of the Z-track.

In contrast, the Comptonization component exhibits a systematically higher PD, with values also reaching about 6% in the HB, up to 6.7%±1.4% for XTE J1701–462. For GX 5–1 and GX 340+0, the PD of thcomp*bbodyrad in the NB is lower with respect to the HB values, while the PD is consistent within the errors between the HB and the NB for Cyg X-2 and XTE J1701–462. Despite the results in the FB exhibiting larger errors or upper limits due to the shorter exposures of the FB intervals, there is a hint of a scenario with variations in the geometry of the Comptonizing region throughout the Z-track providing a significant difference in the average 2–8 keV PD but without strong rotation of the PA. Typical spreading layer configurations are characterized by a polarization lower than about 2% (Gnarini et al. 2022, 2024b; Farinelli et al. 2024; Bobrikova et al. 2025), while the results obtained for thcomp*bbodyrad from spectropolarimetric analysis are generally significantly higher. The only exceptions are XTE J1701–462 (FB), Sco X-1 (NB and FB), and GX 349+2 (NB and FB), for which the PD of thcomp*bbodyrad is less than 2% and consistent with the results for an optically thick spreading layer. Therefore, for other sources and branches, the Comptonizing region is expected to differ from typical spreading layer geometries to reproduce the high PD measured. For example, if we consider a boundary layer configuration characterized by a small opening angle, covering only the equatorial part of the NS surface, but which extends more radially from the NS to the inner edge of the accretion disk, the geometry of the Comptonizing region is less spherically symmetric, and the resulting PD could be higher than typical spreading layers. Nevertheless, it must be noted that there is a clear variation in the covering fraction parameter f along the Z-track for XTE J1701–462, GX 5–1, Sco X-1, and GX 340+0 (see Tables A.2, A.3, A.4, and A.5); therefore, the measured PD for thcomp*bbodyrad represents the total contribution to the polarization of Comptonized photons plus the fraction of seed blackbody photons, which are expected to be unpolarized. For all Z-sources, the PA of thcomp*bbodyrad is consistent with the value derived with the model-independent analysis in the 2–8 keV band (G25), as expected, being the main contribution to the polarized signal. Therefore, considering Cyg X-2, the PA of Comptonization is still aligned with the direction of the radio jet (Spencer et al. 2013), while for Sco X-1 results rotated by approximately 40° (Fomalont et al. 2001a,b; Long et al. 2022).

In Fig. 3, we report the average PD derived with the model-independent analysis described in G25 and the photon flux ratios for the Comptonized, disk, and reflected emission for each Z-source as a function of the branch (see also Tables A.1, A.2, A.3, A.4, A.5, and A.6). The contribution of the disk seems to be more important in the NB with respect to the other two branches, whereas the photon flux ratio of reflection is generally lower than 10% for most of the sources and branches. Although no evident dependence between the polarization and the contribution of reflected photons among different branches can be claimed, there is a hint of correlation with the other two components: while the photon flux ratios of Comptonization seem to decrease from the HB to the NB, the contribution of the disk generally increases, and the polarization decreases. Therefore, the different contribution of the spectral components seems to be one of the mechanisms responsible for the variation of the polarization throughout the CCD. Completing the sample of Z-sources observed in each branch would be crucial to confirm this behavior.

Thumbnail: Fig. 3. Refer to the following caption and surrounding text. Fig. 3.

Average polarization in the 2–8 keV range (top) and photon flux ratios of Comptonized, disk, and reflected emission for each Z-source as a function of the branch. Errors are at the 90% confidence level; upper limits are reported at the 99% confidence level for one interesting parameter.

In Fig. 4, we also reported the PD of the Comptonized and disk emission as a function of the inclination derived from the reflection component during spectral analysis for each source and each branch. For GX 5–1, no reflection features are observed (see also Homan et al. 2018; Fabiani et al. 2024); however, the absence of these features may be due to a highly ionized accretion disk with low iron abundance observed at high inclination (≳60°; Kuulkers et al. 1994; Homan et al. 2018). For the Comptonization, the results do not show any significant correlation between the polarization and the inclination. As for the disk emission, the PD is relatively stable with the inclination for the HB and the NB with values consistent within the errors, whereas in the FB only upper limits are found. Differing from the expectation of an increasing polarization with inclination, some sources at intermediate inclinations (≈30 − 40°, i.e., XTE J1701–462 and GX 340+0) are characterized by a PD comparable to or even higher than other sources at higher inclination. These results may suggest a possible break in the axial symmetry of these systems: if the configuration is not axially symmetric, the dependence of the PD with inclination may differ from the increasing trend. In addition, the disk and Comptonized components would not be orthogonally polarized, as observed for some Z-sources (e.g., XTE J1701–462, GX 5–1, and GX 340+0). We note that it may be possible that the value of the inclination derived during the best-fits with relxillNS could be underestimated: Cyg X-2 is the only source exhibiting an inclination higher than 50° and the result is consistent with previous measurements obtained with the same methodology (Ludlam et al. 2022) and using optical observations (Orosz & Kuulkers 1999); for other Z-sources, the inclination is lower, but typically consistent with the results obtained from the spectral fitting of the reflection component. Sco X-1 is the only Z-source considered for which the inclination obtained with relxillNS is in perfect agreement with the results obtained from radio observation with very long baseline interferometry (VLBI) by Fomalont et al. (2001a,b). However, no other estimates of the inclination using different methodologies are available for the other sources. Therefore, we cannot exclude the possibility that some of these Z-sources could be observed at higher inclinations than the measured ones, although the absence of eclipses suggests that their inclinations are not extremely high.

Thumbnail: Fig. 4. Refer to the following caption and surrounding text. Fig. 4.

Polarization degree of Comptonized (left) and disk (right) emission for each Z-source as a function of the inclination. Empty markers correspond to values frozen during the fits. Errors are at the 90% confidence level; upper limits are reported at the 99% confidence level for one interesting parameter.

In addition, we did not find any significant differences between Cyg X-2-like and Sco X-1-like sources; considering the average PD in the 2–8 keV energy band (Fig. 3; see also G25), the values for Cyg X-2-like and Sco X-1-like sources are very similar, but we cannot exclude any differences in the HB since no Sco X-1-like sources were observed in this branch. From the spectropolarimetric analysis of the different spectral components (Fig. 2), we notice that in the NB and FB, only upper limits are obtained for the PD of Comptonization of Sco X-1-like sources, while for the disk the results are always consistent for every source and branch. Although every source is observed in the FB, the polarization is typically less constrained compared to the other branches, and we cannot draw robust conclusions about the two subclasses; since the FB exhibits markedly different properties in Cyg X-2-like and Sco X-1-like sources (see Church et al. 2012), improved constraints on the polarization in this branch could provide valuable insight into the physical processes underlying this difference between the two types of Z-sources. Recently, Kashyap et al. (2025b) reported the first polarimetric results for the Sco X-1-like Z-source GX 17+2: the X-ray emission of GX 17+2 is characterized by a PD = 1.9% ± 0.3% and PA = 11° ± 4° as the source moves along the NB. The measured PD is in line with other Z-sources in the NB, and both the PD and PA are consistent with the radio polarization measured with the Very Large Array at 10 GHz (Kashyap et al. 2025b). Similarly to other Z-sources discussed in this work, the spectra of GX 17+2 are well described by a combination of soft accretion disk emission, a harder Comptonized component, and reflection off the accretion disk surface. Further observations of the source in the HB and FB are crucial in determining whether its behavior is consistent with that of other Z-sources.

5. Conclusions

In this work, we performed a new branch-resolved spectropolarimetric analysis of the Z-sources observed by IXPE, after the energy- and branch-resolved model-independent polarimetric analysis with IXPEOBSSIM reported by G25. In particular, differently from previous spectral analyzes, we employed the same model for all sources to directly compare the spectropolarimetric results. Comparing the best-fit obtained for different Z-sources along each branch, we do not observe any significant trends for the physical parameters of diskbb and thcomp*bbodyrad; see also Tables A.1, A.2, A.3, A.4, A.5, and A.6. The best-fit values for the election temperature and optical depth of the Comptonizing region are very similar for all sources and branches, except for XTE J1701–462 and GX 340+0 in the FB, which are characterized by a covering fraction f of thcomp*bbodyrad very close to zero, which also leads to higher uncertainties for kTe and τ. In contrast, the physical parameters of the disk and the blackbody seed photons vary moderately across different branches, although not in the same way for all sources. Consequently, the relative contributions of the two spectral components to the total photon flux differ significantly (see Fig. 3). As in the case of the inclination, no clear or significant correlation is found between the observed polarization and any physical parameter of diskbb or thcomp*bbodyrad. In most of the cases, Comptonization represents the main contribution to the total 2–8 keV flux, whereas disk emission typically dominates at lower energies (≲4 keV). Although the contribution of reflection generally ranges between 5% and 20%, its contribution to polarization is not negligible, since reflected photons are expected to be highly polarized (Matt 1993; Poutanen et al. 1996). The only exception is GX 5–1 for which we have not observed any reflection features (see also Homan et al. 2018; Fabiani et al. 2024). However, we note that the polarimetric properties of this source do not differ significantly from the other Z-sources, suggesting that reflection does not have a dominant role in any case. A detailed study on the contribution of reflection was performed by Liu et al. (2026) for Cyg X-2, also adopting different reflection models during spectral analysis but without resolving the different branches. Although there is strong degeneracy between the Comptonized and reflected components, as expected, the upper limits derived for the reflection are consistent with the assumption that we adopted for each Z-source.

The disk emission results are generally lower polarized compared to the harder components but only for Cyg X-2 is the resulting PD consistent with the prediction for a plane-parallel atmosphere above the accretion disk dominated by electron scatterings (Chandrasekhar 1960; Sobolev 1963) for the corresponding inclination obtained from the best-fit models, while for other sources the PD is generally higher than expected. The PD of Comptonized photons varies between branches: for most sources, its values are higher than expected for typical spreading or boundary layer configurations (Farinelli et al. 2024; Bobrikova et al. 2025). Such high polarization levels would necessitate low optical depths, which is inconsistent with the properties of Z-sources, or with different geometries of the Comptonizing region. This leaves open the possibility of an additional component contributing to the polarized signal, despite not influencing the continuum spectrum significantly enough to be appreciably detectable through current spectroscopy, such as a sub-relativistic wind intercepting a significant fraction of the Comptonized radiation (Rogantini et al. 2025) or a completely ionized wind. We want to remark that we cannot exclude the possibility that disk photons are also Comptonized, as in the case of extended accretion disk corona systems (ADC; e.g., White & Holt 1982; Parmar & White 1988; Miller et al. 2016; Ludlam et al. 2025; Mizumoto et al. 2026). However, this configuration would be characterized by a PD that is typically higher than the measured values for Atolls and Z-sources (e.g., Gnarini et al. 2024b).

The average polarization, as well as the polarization of the different components, seems to be correlated neither with the inclination, as could be expected for axially symmetric systems, nor with the variations of the reflected contribution throughout the CCD. On the other hand, the contribution of the disk is generally higher moving from the HB to the NB (see also Psaltis et al. 1995); since the PA of the disk emission is misaligned with that of the Comptonization component, an increase in the flux of the disk inevitably leads to a decrease in the net polarization. As reported in Fig. 2, the PAs of the two components are not necessarily orthogonal: for some Z-sources, they differ by as little as 30°. Furthermore, for statistical reasons, the PA of reflection was tied to that of the Comptonized emission. Although this assumption holds for a strictly axis-symmetric geometry, a warped disk would require the reflection component to rotate, following the local surface normal to the disk. We also note the difficulty in drawing definitive conclusions about FB, mostly due to short exposure. Indeed, only for XTE J1701–462 is a clear trend observed, where the PD associated with the Comptonized component progressively decreases along the Z-track, while for the remaining sources, we obtain either upper limits only or associated uncertainties that are too large to be conclusive. Consequently, a complete mapping of the polarimetric behavior of Z-sources in the 2–8 keV band along the entire track would be achievable with the upcoming eXTP mission (Zhou et al. 2025).

Although the properties of Z-sources are not yet fully understood, IXPE is offering unprecedented insight into this class of NS-LMXBs. Compared to Atolls, Z-sources are significantly more polarized in the HB, while in the NB their PD is similar to that measured for Atoll sources (≲2%; Capitanio et al. 2023; Ursini et al. 2023; Di Marco et al. 2023a; Ursini et al. 2024a; Gnarini et al. 2024a; Tarana et al. 2025). Moreover, for both classes of NS-LMXBs, the polarization increases with energy, while the PA remains typically constant. On the other hand, recently IXPE observed two highly inclined NS-LXMBs exhibiting the highest PD measured so far. The transient source AX J1745.6–2901 (Mikušincová et al. 2025) was serendipitously detected during the observation of MAXI J1744–294 (Marra et al. 2025) with a PD of 14.7%±4.0%, obtained after a detailed analysis of contamination due to the Galactic center and the MAXI J1744–294 emission; 2S 0921–630 (=V395 Car; Tomaru et al. 2025) is characterized by a polarization of 8.8%±1.4% and PD increasing with energy. These sources are typical ADC systems, in which the outer vertically extended region of the accretion disk obscures the central region of the system due to the high inclination (≳80°; Ashcraft et al. 2012; Ponti et al. 2015, 2018). For these sources, the extremely high PD seems to be related to the presence of an accretion disk wind. Therefore, a similar effect applied to Z-sources observed at lower inclinations may reproduce the high PD measured in the HB but having a lower polarization for the Comptonized emission. These results on Z-sources emphasize the need for improved spectropolarimetric models, in order to move beyond the purely phenomenological approach, which is crucial also for future polarimetric missions with higher sensitivity and broader energy coverage than IXPE. An initial step in this direction was provided by Farinelli & Cocchi (2025) with a spectropolarimetric tabular model based on Monte Carlo simulations for high-soft state NS-LMXBs, including Comptonization within the SL and direct and disk-reflected emission, and by Podgorný et al. (2026) with a detailed spectropolarimetric model for the reflected thermal emission, taking into account scattering, absorption, and spectral lines for a slab in photoionization equilibrium above the accretion disk. These improved theoretical models, supported by new X-ray spectropolarimetric observations, will provide an answer to understanding the geometry of these accreting sources.

Acknowledgments

AG was supported by an appointment to the NASA Postdoctoral Program at the Marshall Space Flight Center (MSFC), administered by Oak Ridge Associated Universities under contract with NASA. This research was supported by the Italian Space Agency (Agenzia Spaziale Italiana, ASI) through the contract ASI-INAF-2022-19-HH.0. AT, FC, and SF acknowledge financial support by the Istituto Nazionale di Astrofisica (INAF) grant 1.05.24.02.04: “A multi frequency spectro-polarimetric campaign to explore spin and geometry in Low Mass X-ray Binaries”. SF and LM have been supported by the project PRIN 2022 – 2022LWPEXW – “An X-ray view of compact objects in polarized light”, CUP C53D23001180006. This work reports observations obtained with the Imaging X-ray Polarimetry Explorer (IXPE), a joint US (NASA) and Italian (ASI) mission, led by MSFC. The research uses data products provided by the IXPE Science Operations Center (MSFC), using algorithms developed by the IXPE Collaboration (MSFC, Istituto Nazionale di Astrofisica – INAF, Istituto Nazionale di Fisica Nucleare – INFN, ASI Space Science Data Center – SSDC), and distributed by the High-Energy Astrophysics Science Archive Research Center (HEASARC). This research has made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by NASA. Data analysis was performed using the NuSTAR Data Analysis Software (NuSTARDAS), jointly developed by the ASI Science Data Center (SSDC, Italy) and the California Institute of Technology (USA).

References

  1. Anitra, A., Gnarini, A., Di Salvo, T., et al. 2025, A&A, 697, A83 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  2. Arnason, R. M., Papei, H., Barmby, P., Bahramian, A., & Gorski, M. D. 2021, MNRAS, 502, 5455 [NASA ADS] [CrossRef] [Google Scholar]
  3. Arnaud, K. A. 1996, ASP Conf. Ser., 101, 17 [Google Scholar]
  4. Ashcraft, T. A., Hynes, R. I., & Robinson, E. L. 2012, MNRAS, 424, 620 [Google Scholar]
  5. Baldini, L., Bucciantini, N., Lalla, N. D., et al. 2022, SoftwareX, 19, 101194 [NASA ADS] [CrossRef] [Google Scholar]
  6. Bhargava, Y., Ng, M., Zhang, L., et al. 2024a, ApJ, submitted [arXiv:2405.19324] [Google Scholar]
  7. Bhargava, Y., Russell, T. D., Ng, M., et al. 2024b, ApJ, submitted [arXiv:2411.00350] [Google Scholar]
  8. Bobrikova, A., Poutanen, J., & Loktev, V. 2025, A&A, 696, A181 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  9. Braje, T. M., Romani, R. W., & Rauch, K. P. 2000, ApJ, 531, 447 [Google Scholar]
  10. Cackett, E. M., Miller, J. M., Ballantyne, D. R., et al. 2010, ApJ, 720, 205 [Google Scholar]
  11. Capitanio, F., Fabiani, S., Gnarini, A., et al. 2023, ApJ, 943, 129 [NASA ADS] [CrossRef] [Google Scholar]
  12. Chandrasekhar, S. 1960, Radiative Transfer (New York: Dover Publications) [Google Scholar]
  13. Church, M. J., Gibiec, A., Bałucińska-Church, M., & Jackson, N. K. 2012, A&A, 546, A35 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  14. Clark, G. W. 2018, ApJ, 852, 121 [NASA ADS] [CrossRef] [Google Scholar]
  15. Cocchi, M., Gnarini, A., Fabiani, S., et al. 2023, A&A, 674, L10 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  16. Coughenour, B. M., Cackett, E. M., Miller, J. M., & Ludlam, R. M. 2018, ApJ, 867, 64 [CrossRef] [Google Scholar]
  17. D’Aì, A., Iaria, R., Di Salvo, T., Matt, G., & Robba, N. R. 2009, ApJ, 693, L1 [CrossRef] [Google Scholar]
  18. Dauser, T., Garcia, J., Parker, M. L., Fabian, A. C., & Wilms, J. 2014, MNRAS, 444, L100 [Google Scholar]
  19. Di Marco, A., Costa, E., Muleri, F., et al. 2022, AJ, 163, 170 [NASA ADS] [CrossRef] [Google Scholar]
  20. Di Marco, A., La Monaca, F., Poutanen, J., et al. 2023a, ApJ, 953, L22 [NASA ADS] [CrossRef] [Google Scholar]
  21. Di Marco, A., Soffitta, P., Costa, E., et al. 2023b, AJ, 165, 143 [CrossRef] [Google Scholar]
  22. Di Salvo, T., Farinelli, R., Burderi, L., et al. 2002, A&A, 386, 535 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  23. Di Salvo, T., Papitto, A., Marino, A., Iaria, R., & Burderi, L. 2024, in Handbook of X-ray and Gamma-ray Astrophysics, eds. C. Bambi, & A. Santangelo (Singapore: Springer), 4031 [Google Scholar]
  24. Fabiani, S., Capitanio, F., Iaria, R., et al. 2024, A&A, 684, A137 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  25. Farinelli, R., & Cocchi, M. 2025, A&A, 702, A272 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  26. Farinelli, R., Paizis, A., Landi, R., & Titarchuk, L. 2009, A&A, 498, 509 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  27. Farinelli, R., Fabiani, S., Poutanen, J., et al. 2023, MNRAS, 519, 3681 [NASA ADS] [CrossRef] [Google Scholar]
  28. Farinelli, R., Waghmare, A., Ducci, L., & Santangelo, A. 2024, A&A, 684, A62 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  29. Fender, R. P., & Hendry, M. A. 2000, MNRAS, 317, 1 [NASA ADS] [CrossRef] [Google Scholar]
  30. Fomalont, E. B., Geldzahler, B. J., & Bradshaw, C. F. 2001a, ApJ, 553, L27 [NASA ADS] [CrossRef] [Google Scholar]
  31. Fomalont, E. B., Geldzahler, B. J., & Bradshaw, C. F. 2001b, ApJ, 558, 283 [Google Scholar]
  32. García, J., Dauser, T., Lohfink, A., et al. 2014, ApJ, 782, 76 [Google Scholar]
  33. García, J. A., Dauser, T., Ludlam, R., et al. 2022, ApJ, 926, 13 [CrossRef] [Google Scholar]
  34. Gnarini, A., Ursini, F., Matt, G., et al. 2022, MNRAS, 514, 2561 [NASA ADS] [CrossRef] [Google Scholar]
  35. Gnarini, A., Farinelli, R., Ursini, F., et al. 2024a, A&A, 692, A123 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  36. Gnarini, A., Lynne Saade, M., Ursini, F., et al. 2024b, A&A, 690, A230 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  37. Gnarini, A., Ursini, F., Matt, G., et al. 2025, A&A, 699, A230 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  38. Gnarini, A., Ravi, S., Kaaret, P., et al. 2026, ApJ, 997, 299 [Google Scholar]
  39. Grimm, H. J., Gilfanov, M., & Sunyaev, R. 2002, A&A, 391, 923 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  40. Hasinger, G., & van der Klis, M. 1989, A&A, 225, 79 [NASA ADS] [Google Scholar]
  41. Homan, J., Steiner, J. F., Lin, D., et al. 2018, ApJ, 853, 157 [NASA ADS] [CrossRef] [Google Scholar]
  42. Iaria, R., D’Aí, A., di Salvo, T., et al. 2009, A&A, 505, 1143 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  43. Kaastra, J. S., & Bleeker, J. A. M. 2016, A&A, 587, A151 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  44. Kashyap, U., Maccarone, T. J., Ng, M., et al. 2025a, ApJ, 986, 207 [Google Scholar]
  45. Kashyap, U., Maccarone, T. J., Pattie, E. C., et al. 2025b, ApJ, 994, 221 [Google Scholar]
  46. Kuulkers, E., van der Klis, M., Oosterbroek, T., et al. 1994, A&A, 289, 795 [NASA ADS] [Google Scholar]
  47. La Monaca, F., Di Marco, A., Ludlam, R. M., et al. 2024a, A&A, 691, A253 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  48. La Monaca, F., Di Marco, A., Poutanen, J., et al. 2024b, ApJ, 960, L11 [NASA ADS] [CrossRef] [Google Scholar]
  49. La Monaca, F., Bobrikova, A., Poutanen, J., et al. 2025a, A&A, 702, A40 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  50. La Monaca, F., Di Marco, A., Coti Zelati, F., et al. 2025b, A&A, 702, A101 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  51. Lapidus, I. I., & Sunyaev, R. A. 1985, MNRAS, 217, 291 [NASA ADS] [CrossRef] [Google Scholar]
  52. Lin, D., Homan, J., Remillard, R., & Wijnands, R. 2007, ATel, 1183, 1 [NASA ADS] [Google Scholar]
  53. Liu, H., Jiang, J., Ingram, A., et al. 2026, J. High Energy Astrophys., 51, 100548 [Google Scholar]
  54. Long, X., Feng, H., Li, H., et al. 2022, ApJ, 924, L13 [NASA ADS] [CrossRef] [Google Scholar]
  55. Ludlam, R. M. 2024, Ap&SS, 369, 16 [NASA ADS] [CrossRef] [Google Scholar]
  56. Ludlam, R. M., Cackett, E. M., García, J. A., et al. 2022, ApJ, 927, 112 [NASA ADS] [CrossRef] [Google Scholar]
  57. Ludlam, R. M., Ballhausen, R., Chakraborty, P., et al. 2025, PASJ, 77, S117 [Google Scholar]
  58. Marra, L., Mikušincová, R., Vincentelli, F. M., et al. 2025, ApJ, submitted [arXiv:2506.17050] [Google Scholar]
  59. Marra, L., Podgorný, J., Taverna, R., et al. 2026, A&A, 705, A8 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  60. Matt, G. 1993, MNRAS, 260, 663 [NASA ADS] [CrossRef] [Google Scholar]
  61. Mazzola, S. M., Iaria, R., Di Salvo, T., et al. 2021, A&A, 654, A102 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  62. Mikušincová, R., Marra, L., Manikantan, H., et al. 2025, ApJ, submitted [arXiv:2512.13182] [Google Scholar]
  63. Miller, J. M., Raymond, J., Cackett, E., Grinberg, V., & Nowak, M. 2016, ApJ, 822, L18 [NASA ADS] [CrossRef] [Google Scholar]
  64. Miller, J. M., Gendreau, K., Ludlam, R. M., et al. 2018, ApJ, 860, L28 [NASA ADS] [CrossRef] [Google Scholar]
  65. Mitsuda, K., Inoue, H., Koyama, K., et al. 1984, PASJ, 36, 741 [NASA ADS] [Google Scholar]
  66. Mitsuda, K., Inoue, H., Nakamura, N., & Tanaka, Y. 1989, PASJ, 41, 97 [NASA ADS] [Google Scholar]
  67. Mizumoto, M., Takahashi, H., Behar, E., et al. 2026, ApJ, 996, 49 [Google Scholar]
  68. Orosz, J. A., & Kuulkers, E. 1999, MNRAS, 305, 132 [Google Scholar]
  69. Paizis, A., Farinelli, R., Titarchuk, L., et al. 2006, A&A, 459, 187 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  70. Parmar, A. N., & White, N. E. 1988, Mem. Soc. Astron. It., 59, 147 [NASA ADS] [Google Scholar]
  71. Patruno, A., Haskell, B., & Andersson, N. 2017, ApJ, 850, 106 [NASA ADS] [CrossRef] [Google Scholar]
  72. Podgorný, J., Dovčiak, M., Goosmann, R., et al. 2026, A&A, 711, A175 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  73. Ponti, G., Bianchi, S., Muñoz-Darias, T., et al. 2015, MNRAS, 446, 1536 [NASA ADS] [CrossRef] [Google Scholar]
  74. Ponti, G., Bianchi, S., Muñoz-Darias, T., et al. 2018, MNRAS, 473, 2304 [NASA ADS] [CrossRef] [Google Scholar]
  75. Poutanen, J., Nagendra, K. N., & Svensson, R. 1996, MNRAS, 283, 892 [NASA ADS] [CrossRef] [Google Scholar]
  76. Psaltis, D., Lamb, F. K., & Miller, G. S. 1995, ApJ, 454, L137 [NASA ADS] [Google Scholar]
  77. Rogantini, D., Homan, J., Plotkin, R. M., et al. 2025, ApJ, 986, 41 [Google Scholar]
  78. Schnittman, J. D., & Krolik, J. H. 2009, ApJ, 701, 1175 [CrossRef] [Google Scholar]
  79. Smale, A. P. 1998, ApJ, 498, L141 [NASA ADS] [CrossRef] [Google Scholar]
  80. Smith, R. K., Dame, T. M., Costantini, E., & Predehl, P. 2006, ApJ, 648, 452 [CrossRef] [Google Scholar]
  81. Sobolev, V. V. 1963, A Treatise on Radiative Transfer [Google Scholar]
  82. Spencer, R. E., Rushton, A. P., Bałucińska-Church, M., et al. 2013, MNRAS, 435, L48 [NASA ADS] [CrossRef] [Google Scholar]
  83. Strohmayer, T. E., Gendreau, K. C., Altamirano, D., et al. 2018, ApJ, 865, 63 [NASA ADS] [CrossRef] [Google Scholar]
  84. Tarana, A., Capitanio, F., Gnarini, A., et al. 2025, A&A, 698, A245 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  85. Taverna, R., Marra, L., Bianchi, S., et al. 2021, MNRAS, 501, 3393 [NASA ADS] [Google Scholar]
  86. Thomas, N. T., Jirawala, K., Gudennavar, S. B., & Bubbly, S. G. 2024, MNRAS, 531, 2237 [Google Scholar]
  87. Tomaru, R., Done, C., & Odaka, H. 2025, MNRAS, submitted [arXiv:2509.26147] [Google Scholar]
  88. Ursini, F., Farinelli, R., Gnarini, A., et al. 2023, A&A, 676, A20 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  89. Ursini, F., Gnarini, A., Bianchi, S., et al. 2024a, A&A, 690, A200 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  90. Ursini, F., Gnarini, A., Capitanio, F., et al. 2024b, Galaxies, 12, 43 [NASA ADS] [CrossRef] [Google Scholar]
  91. van der Klis, M. 1989, ARA&A, 27, 517 [NASA ADS] [CrossRef] [Google Scholar]
  92. Verner, D. A., Ferland, G. J., Korista, K. T., & Yakovlev, D. G. 1996, ApJ, 465, 487 [Google Scholar]
  93. Weisskopf, M. C., Soffitta, P., Baldini, L., et al. 2022, JATIS, 8, 1 [Google Scholar]
  94. White, N. E., & Holt, S. S. 1982, ApJ, 257, 318 [NASA ADS] [CrossRef] [Google Scholar]
  95. White, N. E., Stella, L., & Parmar, A. N. 1988, ApJ, 324, 363 [NASA ADS] [CrossRef] [Google Scholar]
  96. Wijnands, R., Homan, J., van der Klis, M., et al. 1998, ApJ, 493, L87 [NASA ADS] [CrossRef] [Google Scholar]
  97. Wilms, J., Allen, A., & McCray, R. 2000, ApJ, 542, 914 [Google Scholar]
  98. Yu, W., Bu, Q., Doroshenko, V., et al. 2025, A&A, 695, A108 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  99. Zdziarski, A. A., Szanecki, M., Poutanen, J., Gierliński, M., & Biernacki, P. 2020, MNRAS, 492, 5234 [NASA ADS] [CrossRef] [Google Scholar]
  100. Zhou, P., Mao, J., Zhang, L., et al. 2025, Sci. China: Phys. Mech. Astron., 68, 119507 [Google Scholar]

Appendix A: Best-fit tables

Table A.1.

Best-fitting model parameters for Cyg X-2.

Table A.2.

Best-fitting model parameters for XTE J1701–462.

Table A.3.

Best-fitting model parameters for GX 5–1.

Table A.4.

Best-fitting model parameters for Sco X-1.

Table A.5.

Best-fitting model parameters for GX 340+0.

Table A.6.

Best-fitting model parameters for GX 349+2.

All Tables

Table 1.

Log of source extraction regions.

In the text
Table 2.

Polarization degree and angle of each spectral component for each source with the corresponding branch of the Z-track.

In the text
Table A.1.

Best-fitting model parameters for Cyg X-2.

In the text
Table A.2.

Best-fitting model parameters for XTE J1701–462.

In the text
Table A.3.

Best-fitting model parameters for GX 5–1.

In the text
Table A.4.

Best-fitting model parameters for Sco X-1.

In the text
Table A.5.

Best-fitting model parameters for GX 340+0.

In the text
Table A.6.

Best-fitting model parameters for GX 349+2.

In the text

All Figures

Thumbnail: Fig. 1. Refer to the following caption and surrounding text. Fig. 1.

Deconvolved spectra for each Z-source with the resulting best-fit model and the corresponding residuals in units of σ. The three branches are highlighted with different colors and markers. Main spectral components are highlighted with different line styles, i.e., diskbb (dash-dotted lines), thcomp*bbodyrad (dashed lines), and relxillNS (dotted lines). (a) Cyg X-2. (b) XTE J1701–462. (c) GX 5–1. (d) Sco X-1. (e) GX 340+0. (f) GX 349+2.
In the text
Thumbnail: Fig. 2. Refer to the following caption and surrounding text. Fig. 2.

Polarization degree of Comptonized (top) and disk (middle) emission, and the difference of the polarization angle of the two components (ΔPA; bottom) for each Z-source as a function of the branch (see Table 2). Empty markers correspond to values frozen during the fits. Errors are at the 90% confidence level; upper limits are reported at the 99% confidence level for one interesting parameter.
In the text
Thumbnail: Fig. 3. Refer to the following caption and surrounding text. Fig. 3.

Average polarization in the 2–8 keV range (top) and photon flux ratios of Comptonized, disk, and reflected emission for each Z-source as a function of the branch. Errors are at the 90% confidence level; upper limits are reported at the 99% confidence level for one interesting parameter.
In the text
Thumbnail: Fig. 4. Refer to the following caption and surrounding text. Fig. 4.

Polarization degree of Comptonized (left) and disk (right) emission for each Z-source as a function of the inclination. Empty markers correspond to values frozen during the fits. Errors are at the 90% confidence level; upper limits are reported at the 99% confidence level for one interesting parameter.
In the text

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.