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X-Ray Polarization from the Atoll 4U 1735-44 Suggests a Low Inclination

This paper presents the first X-ray spectropolarimetric results for the atoll source 4U 1735-44 using coordinated IXPE, NICER, and NuSTAR observations, revealing a marginal polarization detection and a disk inclination of approximately 40° that suggests the source's low polarization is due to its low inclination.

Original authors: M. A. Díaz Teodori, A. Bobrikova, A. Gnarini, F. Ursini, S. V. Forsblom, J. Poutanen, A. Salganik, S. Bianchi, F. Capitanio, M. Cocchi, S. Fabiani, R. Farinelli, P. Kaaret, J. J. E. Kajava, G. Matt, M

Published 2026-04-21

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CC BY 4.0

Original authors: M. A. Díaz Teodori, A. Bobrikova, A. Gnarini, F. Ursini, S. V. Forsblom, J. Poutanen, A. Salganik, S. Bianchi, F. Capitanio, M. Cocchi, S. Fabiani, R. Farinelli, P. Kaaret, J. J. E. Kajava, G. Matt, M. Ng, S. Ravi, P. Soffitta, A. Tarana, S. Zane

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to figure out the shape of a spinning top, but you can't see it directly. You can only see the light it reflects. If you could see the direction in which the light waves are vibrating, you could deduce the top's shape and how it's tilted.

This is exactly what a team of astronomers did with a cosmic object called 4U 1735−44. They used a new "cosmic compass" to measure the polarization of X-rays coming from this object, which is a neutron star (the ultra-dense, dead core of a massive star) that is actively eating material from a companion star.

Here is the story of their discovery, broken down into simple concepts:

1. The Cosmic Setup: A Hungry Star

Think of 4U 1735−44 as a cosmic vacuum cleaner. It's a neutron star pulling gas off a nearby star. As this gas falls in, it doesn't just drop straight down; it swirls around like water going down a drain, forming a flat, spinning accretion disk.

The Problem: We know these disks exist, but we don't know exactly how they are tilted relative to us. Is the disk face-on (like looking at a plate from above) or edge-on (like looking at a coin from the side)?
The Tool: To solve this, the scientists used three space telescopes: IXPE (the new polarimeter), NICER, and NuSTAR. Think of IXPE as a pair of special sunglasses that can tell if light is vibrating horizontally, vertically, or at an angle.

2. The Experiment: Taking a Cosmic Snapshot

On August 31, 2024, these telescopes pointed at the star for about 10 hours. They collected X-rays (high-energy light) to see if the light was "polarized."

The Analogy: Imagine shining a flashlight through a picket fence. If the light waves are vibrating parallel to the fence slats, they pass through. If they are vibrating perpendicular, they get blocked. This filtering creates "polarized" light.
The Result: The team found a very faint hint of polarization. It wasn't a loud "Yes, it's polarized!" but more of a whisper: "Maybe it's polarized, but we aren't 100% sure yet."
- They measured a polarization degree of about 1.4%.
- To be safe, they said, "We are 99.7% sure the polarization is less than 3.5%."

3. The Detective Work: Why is the signal so weak?

Usually, when light bounces off a disk or gets scrambled by hot plasma, it becomes highly polarized. So, why was the signal from 4U 1735−44 so weak?

The scientists built a computer model to simulate the star's environment. They found that the best explanation for the weak signal is that we are looking at the disk from a low angle.

The Metaphor: Imagine a spinning pizza dough.
- If you look at it from above (high inclination), you see the whole surface, and the light bounces off in a way that creates a strong, clear polarization signal.
- If you look at it from the side (low inclination), the pizza looks like a thin line. The light bounces off in all sorts of mixed directions, canceling each other out. The result is a very weak, "smeared" polarization signal.

The model suggested the disk is tilted at about 40 degrees. This is a "low" angle compared to some other stars, which explains why the polarization signal was so faint. It's like trying to see the pattern on a spinning top when you are looking at it from the side rather than the top.

4. The Big Picture: Connecting the Dots

The team compared 4U 1735−44 to other similar stars (called "atoll sources").

Some of those stars showed strong polarization because they were tilted steeply toward us.
Others showed no polarization because they were tilted away (low inclination).
The Conclusion: 4U 1735−44 fits right in with the "low inclination" group. It has the same ingredients (a disk, hot plasma, and reflected light) as the others, but because of its specific tilt, the "cosmic compass" didn't pick up a strong signal.

Summary

In short, this paper is about using a new type of X-ray glasses to look at a hungry neutron star. The scientists found that the light coming from it is only slightly polarized. By analyzing this faint signal, they concluded that the star's accretion disk is tilted at a moderate angle (about 40 degrees) relative to Earth. This "low tilt" is the reason the polarization signal is so weak, helping us understand the 3D geometry of these mysterious cosmic objects.

It's a bit like trying to guess the shape of a spinning coin by looking at the blur of light it reflects; even a faint clue helps us figure out how it's sitting in space.

1. Problem and Scientific Context

Accreting weakly magnetized neutron stars (WMNSs) in low-mass X-ray binaries (LMXBs) are among the brightest X-ray sources, yet the geometry of the accretion flow—specifically the region between the neutron star (NS) surface and the inner accretion disk—remains poorly understood. While spectroscopy and timing have advanced significantly, they often yield model-dependent constraints on system inclination and geometry.

X-ray polarimetry offers a new diagnostic tool to probe these geometries. Previous IXPE observations of "atoll" sources (a subclass of WMNSs characterized by lower luminosity) have shown mixed results: some exhibit high polarization degrees (PD) linked to reflection features, while others show no detection. The paper aims to investigate the atoll source 4U 1735−44 to determine its polarization properties, constrain its system inclination, and understand why it might differ from other atoll sources with similar reflection features.

2. Methodology

The authors conducted coordinated multi-mission observations of 4U 1735−44 using three space-based observatories:

IXPE (Imaging X-ray Polarimetry Explorer): Provided polarimetric data in the 2–8 keV range. Observations occurred on August 31, 2024, with a total exposure of ~39 ks per detector unit.
NuSTAR (Nuclear Spectroscopic Telescope Array): Provided high-energy spectral coverage (3–79 keV) on August 31, 2024 (~34 ks).
NICER (Neutron Star Interior Composition Explorer): Provided soft X-ray timing/spectral data (0.2–12 keV) on August 28–30, 2024.

Data Analysis Approach:

Model-Independent Polarimetry: Used the pcube algorithm to derive Stokes parameters ( $q, u$ ), Polarization Degree (PD), and Polarization Angle (PA) without assuming a spectral model.
Spectral Modeling: Performed joint spectral fitting of NuSTAR and IXPE data (NICER data was excluded due to spectral state mismatches).
- Model 1: A phenomenological model consisting of a thermal disk (diskbb), Comptonized emission (comptt), and a Gaussian iron line (gauss).
- Model 2: A physically motivated model replacing the Gaussian line with a relativistic reflection component (relxillNS), which self-consistently models the disk reflection, ionization, and inclination.
Spectro-Polarimetric Modeling: Applied the polconst and pollin models to the spectral components to constrain the PD and PA of individual emission mechanisms (disk, Comptonized, and reflection).

3. Key Results

A. Polarimetric Detection

Overall Detection: The study achieved a marginal (2 $\sigma$ ) detection of X-ray polarization in the 2–8 keV band.
- Polarization Degree (PD): $1.4\% \pm 0.7\%$ .
- Polarization Angle (PA): $-29^\circ \pm 14^\circ$ .
- Upper Limit: The 3 $\sigma$ upper limit on the PD is 3.5%.
Energy Dependence: A potential signal was detected in the 6–7 keV bin (PD $\approx$ 8.5%), but the significance was insufficient to draw firm conclusions about energy dependence. No significant spectral hardness variations were observed during the observation.

B. Spectral Analysis and Inclination

Best-Fit Model: The relxillNS model (Model 2) provided a superior fit compared to the phenomenological model.
Inclination Constraint: The relativistic reflection model inferred a disk inclination of $\sim 39^\circ$ ( $39^{+3}_{-2}$ $3 9_{- 2}^{+ 3}$ degrees).
- This is lower than previous X-ray estimates ( $\sim 42^\circ$ – $60^\circ$ ) but consistent with the broader optical constraint range ( $27^\circ$ – $60^\circ$ ).
Disk Geometry: The inner disk radius derived from relxillNS is $R_{in} \approx 3.7 R_{ISCO} \approx 45$ km, suggesting the disk extends significantly beyond the innermost stable circular orbit.

C. Component Polarization

Spectro-polarimetric analysis attempted to isolate polarization from the disk, Comptonized, and reflection components.
Results suggest the disk emission may be polarized nearly orthogonally ( $\sim 90^\circ$ difference in PA) to the Comptonized and reflection components, though statistical uncertainties remain large.
The reflection component (relxillNS) showed a tentative PD of $5.6^{+4.0}_{-2.8}\%$ , but this is not statistically significant given the large error bars.

4. Significance and Discussion

Low Inclination as the Primary Factor:
The paper concludes that the low polarization detection (or lack thereof) in 4U 1735−44 is likely due to its low system inclination ( $\sim 39^\circ$ ).

In high-inclination systems, the accretion disk is viewed edge-on, enhancing polarization signatures from scattering and reflection.
In low-inclination systems (face-on), these polarization signatures are washed out due to symmetry.
This finding aligns 4U 1735−44 with other non-detection cases like Ser X-1, GX 3+1, and GX 9+1, which also exhibit reflection features but show no significant polarization due to low inclinations.

Comparison with Other Atolls:
The results contrast with high-polarization atoll sources like GX 9+9 and 4U 1820−303, where strong reflection and higher inclinations likely drove the high PD. The study reinforces the hypothesis that the presence of reflection features alone does not guarantee high polarization; the viewing angle is a critical determinant.

Future Outlook:
The authors note that the current detection is marginal. They suggest that future, longer IXPE observations combined with event-based maximum likelihood estimation (Bayesian Nested Sampling) could significantly improve the detection significance, allowing for tighter constraints on the geometry of the boundary layer and the Comptonization region.

Summary of Contributions

First Polarimetric Study: Provides the first X-ray spectro-polarimetric results for the atoll source 4U 1735−44.
Inclination Constraint: Derives a robust inclination of $\sim 39^\circ$ using relativistic reflection modeling, resolving discrepancies in previous estimates.
Geometric Insight: Establishes a link between low inclination and low polarization in atoll sources, even when reflection features are present, refining the understanding of accretion geometry in WMNSs.
Methodological Benchmark: Demonstrates the utility of joint IXPE/NuSTAR analysis for constraining both spectral and polarimetric parameters simultaneously.