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To constrain the equation of state of cold dense matter, astrophysical measurements are essential. These are mostly based on observations of neutron stars in the X-ray band, and, more recently, also on gravitational wave observations. Of particular interest are observations of unusually heavy or light neutron stars which extend the range of central densities probed by observations and thus permit the testing of nuclear-physics predictions over a wider parameter space. Here we report on the analysis of such a star, a central compact object within the supernova remnant HESS J1731-347. We estimate the mass and radius of the neutron star to be M=0.77−0.17+0.20M⊙\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M=0.7{7}_{-0.17}^{+0.20}\,{M}_{\odot }$$\end{document} and R=10.4−0.78+0.86\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R=10.{4}_{-0.78}^{+0.86}$$\end{document} km, respectively, based on modelling of the X-ray spectrum and a robust distance estimate from Gaia observations. Our estimate implies that this object is either the lightest neutron star known, or a ‘strange star’ with a more exotic equation of state. Adopting a standard neutron star matter hypothesis allows the corresponding equations of state to be constrained.
Equation of state predictions and observational constraints as a function of the radius and mass of the compact star The gray dashed contours show mass and radius constraints for PSR J0740+6620 and PSR J0030+0451 reported in refs. 51,55 based on the NICER data, and the black dotted line denotes constrains for 4U 1702-429 in ref. ²⁵. The black solid and dashed lines show constrains for the CCO in HESS J1731-347 obtained in this work. Here, the thick solid line corresponds to the case when only parallax priors and X-ray data are considered, whereas the thick dashed lines correspond to the joint fit including all prior information as discussed in the text. All contours are plotted for 68.3% and 95.4% credible intervals (including only statistical uncertainties). The collection of thin black lines represents the family of chiral EOSs considered in refs. 23,24, with red lines on top indicating the EOSs that are allowed by the combined analysis of priors in refs. 51,55, constraints based on the analysis of X-ray bursts from 4U 1702-429 in ref. ²⁵, and this work (both at 90% confidence). Two representative strange quark-matter EOSs are also plotted for completeness (red dashed lines). The error bars around 1.4M⊙ show the expected radius of a ‘standard’ neutron star allowed by EOS constraints in ref. ⁵¹ (black) and in this work (beige, both at 90% confidence level). The horizontal dashed line shows a lower limit on the expected astrophysical neutron star mass from ref. ²⁹.
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Nature Astronomy | Volume 6 | December 2022 | 1444–1451 1444
nature astronomy
Article
https://doi.org/10.1038/s41550-022-01800-1
A strangely light neutron star within a
supernova remnant
Victor Doroshenko , Valery Suleimanov , Gerd Pühlhofer and
Andrea Santangelo
To constrain the equation of state of cold dense matter, astrophysical
measurements are essential. These are mostly based on observations of
neutron stars in the X-ray band, and, more recently, also on gravitational
wave observations. Of particular interest are observations of unusually
heavy or light neutron stars which extend the range of central densities
probed by observations and thus permit the testing of nuclear-physics
predictions over a wider parameter space. Here we report on the analysis of
such a star, a central compact object within the supernova remnant HESS
J1731-347. We estimate the mass and radius of the neutron star to be
M077󰁜0󰅂20
󰁝0󰅂17 M
and
R104󰁜0󰅂86
󰁝0󰅂78
 km, respectively, based on modelling of
the X-ray spectrum and a robust distance estimate from Gaia observations.
Our estimate implies that this object is either the lightest neutron star
known, or a ‘strange star’ with a more exotic equation of state. Adopting a
standard neutron star matter hypothesis allows the corresponding
equations of state to be constrained.
Central compact objects (CCOs) are isolated, radio-quiet,
non-accreting, thermally emitting neutron stars found at the centres of
supernova remnants (SNRs)
13
. Their thermal X-ray emission is believed
to be associated with the cooling of young, weakly magnetized4,5 neu-
tron stars and comes from the atmosphere covering a large fraction of
the surface. Most CCOs exhibit no pulsations, which suggests a rather
uniform temperature distribution over the neutron star surface. This
implies that the uncertainties associated with the geometry of the
emission region, the details of the accretion physics and the radiative
transfer in strong magnetic fields, which are all typical of accreting
neutron stars, are irrelevant for CCOs. Such simplicity makes CCOs ideal
laboratories to investigate the equation of state (EOS) of dense matter6,7.
On the other hand, CCOs are only observed as faint X-ray sources
and often lack reliable distance and luminosity estimates, which trans-
lates to large uncertainties in the emission area and neutron star radius
estimates
810
. Furthermore, the lack of detected pulsations does not
necessarily imply that the entire surface emits uniformly, and could
be simply due to an unfavourable orientation of the observer’s line of
sight with respect to the spin and magnetic dipole axes of the neutron
star
11,12
. The composition of the atmosphere also strongly influences
the estimated neutron star parameters. In particular, atmospheres
composed of carbon, or even heavier elements, have been suggested
for a large fraction of CCOs1315.
We emphasize, however, that the caveats outlined above are now
largely sorted out. With regard to atmosphere composition, hydrogen
atmospheres yield unreasonably small neutron star radii9,10, whereas
emission from atmospheres with even heavier compositions strongly
deviates from the observed black-body-like spectra13. Instead of deduc-
ing unreasonably small neutron star radii, one could assume that the
emission originates from a fraction of the neutron star surface and
pulsations are not observed only because of an unfavourable viewing
orientation. This is, however, in conflict with the existing limits on the
amplitude of potential pulsations (~8% for the CCO in HESS J1731-347
(ref.
12
) and less than ~12% for the CCO in Cas A
1618
, and in the range
3–50% for other objects). Note that although probabilities quoted
above for individual objects, including the CCO in HESS J1731-347, are
not negligible, missing pulsations from all non-pulsating CCOs are
highly unlikely, with a chance probability estimated to be ≤10
−6
(ref.
16
).
Considering that there are currently no other ideas to explain
the observed thermal non-pulsed emission, uniformly emitting car-
bon atmospheres appear to be the only viable option to explain the
observed spectra of CCOs. The largest remaining source of uncertainty
Received: 31 March 2022
Accepted: 1 September 2022
Published online: 24 October 2022
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Institut für Astronomie und Astrophysik, Tübingen, Germany. e-mail: doroshv@astro.uni-tuebingen.de
Content courtesy of Springer Nature, terms of use apply. Rights reserved
... From the astrophysical point of view, a tremendous progress was done in the last decade. As such, NS masses in the range 0.8 ≲ M/M ⊙ ≲ 2.1 (Antoniadis et al. 2013;Arzoumanian et al. 2018;Brodie & Haber 2023;Cromartie et al. 2020;Demorest et al. 2010;Doroshenko et al. 2022;Fonseca et al. 2021) have been measured with unprecedented precision. Measurements of massive NSs are informative of the NS EOS stiffness and of utmost relevance for the onset of non-nucleonic particle degrees of freedom (Oertel et al. 2017;Sedrakian et al. 2023). ...
... At the other extremity, NS masses lower than 1 M ⊙ challenge our understanding of NS formation in core-collapse supernovae (Suwa et al. 2018). This is, in particular, the case of the NS in the supernova remnant (SNR) HESS J1731-347, whose mass was recently estimated to be M = 0.77 +0.20 −0.17 M ⊙ (or M = 0.83 +0.17 −0.13 M ⊙ ) (Brodie & Haber 2023;Doroshenko et al. 2022). Moreover, its very low radius R = 10.4 +0.86 −0.78 km (or R = 11.25 +0.53 −0.37 km) (Brodie & Haber 2023;Doroshenko et al. 2022) triggers questions about the composition of low mass NS cores or the behavior of NS EOS at low densities. ...
... This is, in particular, the case of the NS in the supernova remnant (SNR) HESS J1731-347, whose mass was recently estimated to be M = 0.77 +0.20 −0.17 M ⊙ (or M = 0.83 +0.17 −0.13 M ⊙ ) (Brodie & Haber 2023;Doroshenko et al. 2022). Moreover, its very low radius R = 10.4 +0.86 −0.78 km (or R = 11.25 +0.53 −0.37 km) (Brodie & Haber 2023;Doroshenko et al. 2022) triggers questions about the composition of low mass NS cores or the behavior of NS EOS at low densities. In relation with the first aspect, the occurrence of quark matter (Di Clemente et al. 2022) and ∆-resonances ) has been speculated. ...
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... These masses were computed using the orbital parameters and photometric information. To identify systems with possible neutron star companions, when masses are available, we kept systems with M 1 < M 2 and M 2 1.1 M e (see Doroshenko et al. 2022;Chamel et al. 2013, for a discussion of the minimum (0.77 M e ) and maximum (2.5 M e ) neutron star masses, respectively). In the present analysis, we will, however, consider 1.3 M e as the typical neutron star mass. ...
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PSR J0740+6620 has a gravitational mass of 2.08 ± 0.07 M o˙, which is the highest reliably determined mass of any neutron star. As a result, a measurement of its radius will provide unique insight into the properties of neutron star core matter at high densities. Here we report a radius measurement based on fits of rotating hot spot patterns to Neutron Star Interior Composition Explorer (NICER) and X-ray Multi-Mirror (XMM-Newton) X-ray observations. We find that the equatorial circumferential radius of PSR J0740+6620 is 13.7-1.5+2.6 km (68%). We apply our measurement, combined with the previous NICER mass and radius measurement of PSR J0030+0451, the masses of two other ∼2 M o˙ pulsars, and the tidal deformability constraints from two gravitational wave events, to three different frameworks for equation-of-state modeling, and find consistent results at ∼1.5-5 times nuclear saturation density. For a given framework, when all measurements are included, the radius of a 1.4 M o˙ neutron star is known to ±4% (68% credibility) and the radius of a 2.08 M o˙ neutron star is known to ±5%. The full radius range that spans the ±1σ credible intervals of all the radius estimates in the three frameworks is 12.45 ± 0.65 km for a 1.4 M o˙ neutron star and 12.35 ± 0.75 km for a 2.08 M o˙ neutron star. © 2021. The American Astronomical Society. All rights reserved.
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We present analysis of multiple Chandra and XMM-Newton spectra, separated by 9–19 years, of four of the youngest central compact objects (CCOs) with ages <2500yr: CXOU J232327.9+584842 (Cassiopeia A), CXOU J160103.1−513353 (G330.2+1.0), 1WGA J1713.4−3949 (G347.3−0.5), and XMMU J172054.5−372652 (G350.1−0.3). By fitting these spectra with thermal models, we attempt to constrain each CCO’s long-term cooling rate, composition, and magnetic field. For the CCO in Cassiopeia A, 14 measurements over 19 years indicate a decreasing temperature at a ten-year rate of 2.2 ± 0.2 or 2.8 ± 0.3 percent (1σ error) for a constant or changing X-ray absorption, respectively. We obtain cooling rate upper limits of 17 percent for CXOU J160103.1−513353 and 6 percent for XMMU J172054.5−372652. For the oldest CCO, 1WGA J1713.4−3949, its temperature seems to have increased by 4 ± 2 percent over a ten year period. Assuming each CCO’s preferred distance and an emission area that is a large fraction of the total stellar surface, a non-magnetic carbon atmosphere spectrum is a good fit to spectra of all four CCOs. If distances are larger and emission areas are somewhat smaller, then equally good spectral fits are obtained using a hydrogen atmosphere with B ≤ 7 × 1010G or B ≥ 1012G for CXOU J160103.1−513353 and B ≤ 1010G or B ≥ 1012G for XMMU J172054.5−372652 and non-magnetic hydrogen atmosphere for 1WGA J1713.4−3949. In a unified picture of CCO evolution, our results suggest most CCOs, and hence a sizable fraction of young neutron stars, have a surface magnetic field that is low early in their life but builds up over several thousand years.
Article
The second data release of Gaia revealed a parallax zero-point offset of −0.029 mas based on quasars. The value depended on the position on the sky, and also likely on magnitude and colour. The offset and its dependence on other parameters inhibited improvement in the local distance scale using for example the Cepheid and RR Lyrae period–luminosity relations. Analysis of the recent Gaia Early Data Release 3 (EDR3) reveals a mean parallax zero-point offset of −0.021 mas based on quasars. The Gaia team addresses the parallax zero-point offset in detail and proposes a recipe to correct for it based on ecliptic latitude, G -band magnitude, and colour information. This paper presents a completely independent investigation into this issue focusing on the spatial dependence of the correction based on quasars and the magnitude dependence based on wide binaries. The spatial and magnitude corrections are connected to each other in the overlap region in the range 17 < G < 19. The spatial correction is presented at several spatial resolutions based on the HEALPix formalism. The colour dependence of the parallax offset is unclear and in any case secondary to the spatial and magnitude dependence. The spatial and magnitude corrections are applied to two samples of brighter sources, namely a sample of approximately 100 stars with independent trigonometric parallax measurements from Hubble Space Telescope data, and a sample of 75 classical cepheids using photometric parallaxes. The mean offset between the observed GEDR3 parallax and the independent trigonometric parallax (excluding outliers) is about −39 μas, and after applying the correction it is consistent with being zero. For the classical cepheid sample the analysis presented here suggests that the photometric parallaxes may be underestimated by about 5%.
Article
We present a detailed spectroscopic and timing analysis of X-ray observations of the bright pulsar PSR B0656+14. The observations were obtained simultaneously with eROSITA and XMM-Newton during the calibration and performance verification phase of the Spektrum-Roentgen-Gamma mission (SRG). The analysis of the 100 ks deep observation of eROSITA is supported by archival observations of the source, including XMM-Newton, NuSTAR , and NICER. Using XMM-Newton and NICER, we first established an X-ray ephemeris for the time interval 2015 to 2020, which connects all X-ray observations in this period without cycle count alias and phase shifts. The mean eROSITA spectrum clearly reveals an absorption feature originating from the star at 570 eV with a Gaussian σ of about 70 eV that was tentatively identified in a previous long XMM-Newton observation. A second previously discussed absorption feature occurs at 260–265 eV and is described here as an absorption edge. It could be of atmospheric or of instrumental origin. These absorption features are superposed on various emission components that are phenomenologically described here as the sum of hot (120 eV) and cold (65 eV) blackbody components, both of photospheric origin, and a power law with photon index Γ = 2 from the magnetosphere. We created energy-dependent light curves and phase-resolved spectra with a high signal-to-noise ratio. The phase-resolved spectroscopy reveals that the Gaussian absorption line at 570 eV is clearly present throughout ~60% of the spin cycle, but it is otherwise undetected. Likewise, its parameters were found to be dependent on phase. The visibility of the line strength coincides in phase with the maximum flux of the hot blackbody. If the line originates from the stellar surface, it nevertheless likely originates from a different location than the hot polar cap. We also present three families of model atmospheres: a magnetized atmosphere, a condensed surface, and a mixed model. They were applied to the mean observed spectrum, whose continuum fit the observed data well. The atmosphere model, however, predicts distances that are too short. For the mixed model, the Gaussian absorption may be interpreted as proton cyclotron absorption in a field as high as 10 ¹⁴ G, which is significantly higher than the field derived from the moderate observed spin-down.
Article
Gaia Early Data Release 3 (EDR3) provides trigonometric parallaxes for 1.5 billion stars, with reduced systematics compared to Gaia Data Release 2 and reported precisions better by up to a factor of 2. New to EDR3 is a tentative model for correcting the parallaxes of magnitude-, position-, and color-dependent systematics for five- and six-parameter astrometric solutions, Z 5 and Z 6. Using a sample of over 2000 first-ascent red giant branch stars with asteroseismic parallaxes, I perform an independent check of the Z 5 model in a Gaia magnitude range of 9 ≲ G ≲ 13 and color range of 1.4 μm-1 ≲ ν eff ≲ 1.5 μm-1. This analysis therefore bridges the Gaia team's consistency check of Z 5 for G > 13 and indications from independent analysis using Cepheids of a ≈15 μas overcorrection for G < 11. I find overcorrection sets in at G ≲ 10.8, such that Z 5-corrected EDR3 parallaxes are larger than asteroseismic parallaxes by 15 3 μas. For G ⪆ 10.8, EDR3 and asteroseismic parallaxes in the Kepler field agree up to a constant consistent with expected spatial variations in EDR3 parallaxes after a linear, color-dependent adjustment. I also infer an average underestimation of EDR3 parallax uncertainties in the sample of 22% 6%, consistent with the Gaia team's estimates at similar magnitudes and independent analysis using wide binaries. Finally, I extend the Gaia team's parallax spatial covariance model to brighter magnitudes (G < 13) and smaller scales (down to ≈0. 1), where systematic EDR3 parallax uncertainties are at least ≈3-4 μas. © 2021. The American Astronomical Society. All rights reserved.