Mass-Radius Constraints for 2S 0918-549 from an RXTE Superexpansion Burst: A Direct Cooling-Tail Analysis

TL;DR

The authors apply the direct cooling-tail method to a rare superexpansion PRE burst from the ultracompact binary 2S 0918-549, using RXTE data to test atmospheric composition and extract neutron-star mass and radius. They find the cooling tail is best described by a pure-He atmosphere; metal-rich models are disfavored and no strong need for heavy-element absorption edges is found. The joint M–R constraint is $M=1-2\,M_\ extodot$, $R=9.7-11.9$ km at 99% confidence with distance $D=4.1-5.3$ kpc, allowing both gravity-bound and self-bound EOS within 1σ. The results are consistent with prior distance estimates and Gaia-based constraints, and illustrate the continued potential of cooling-tail analysis in constraining the dense-matter EOS, pending improvements in atmosphere modeling and independent distances.

Abstract

Thermonuclear (Type I ) X-ray bursts from accreting neutron stars offer a means to determine neutron-star (NS) mass ($M$) and radius ($R$) and thereby probe the properties of matter at supranuclear density. A subset of these events, photospheric radius-expansion (PRE) bursts, provide a particularly powerful tool to constrain the neutron-star $M$ and $R$. Here, we apply the direct cooling-tail method to 2S~0918$-$549, using a rare superexpansion burst observed by \emph{RXTE}. We fit only the post-touchdown data within \(F/F_{\rm td}\in[0.6,0.95]\), employing modern atmosphere models (pure He and metal-enriched). The pure-He atmosphere yields a good description of the cooling tail (\(χ^{2}/ν=18.12/14\)), whereas metal-rich models fail; information-criterion tests (AIC/BIC) disfavor adding a free absorption edge in every time bin, indicating that heavy-element ashes are unnecessary. The joint fit gives a distance \(d=4.1-5.3\) kpc and mass-radius constraints \(M=1-2\,M_\odot\) and \(R=9.7-11.9\) km (99\% confidence). These results suggest that representative families of both gravity-bound and self-bound equations of state remain viable at the $1σ$ confidence level.

Figures (5)

• Figure 1: The persistent emission spectrum of 2S 0918--549 (observation ID: 93416-01-05-00). The reduced $\chi^2$ is 0.45.
• Figure 2: From the top to the bottom, the panels show the bolometric flux, the blackbody temperature and radius (assuming a distance of 5 kpc), the absorption-edge energy, the absorption optical depth and the reduced $\chi^{2}$. The black dots are the fitting results using the TBABS*(BBODYRAD+POW) model, and the red dots are from the TBABS*(BBODYRAD*EDGE+POW) model. The shaded region highlights the range when the flux is between $0.95 F_{\rm td} - 0.6 F_{\rm td}$. The vertical dashed line marks the touchdown position.
• Figure 3: Dependence of blackbody normalization on flux for the PRE burst. Data are shown as circles with error bars. The solid red curve denotes the best-fit model for a pure He atmosphere, while the solid blue curve shows the best-fit metal-rich atmosphere model. Only the black points between the vertical dashed lines are used in the fit. Blue points indicate spectra with significant absorption edges and are excluded from the fit. Grey points denote data with fluxes outside the $0.95 F_{\rm td} - 0.6 F_{\rm td}$ range, which are not used in the fit.
• Figure 4: Mass--radius constraints for the neutron star in 2S 0918$-$549 using a pure-helium atmosphere model. The pink, blue, and gray contours show the 68%, 90%, and 99% confidence regions, respectively. The best fit yields $\chi^{2} = 18.12$ for 14 dof. The red solid line correspond to the constant Eddington temperature, $T_{\mathrm{Edd}}$, given by the equation of the best-fit pure-helium model. The solid green line correspond to the critical radius $R = 4GMc^2$. The black dotted curves correspond to constant distances of 4.5, 5, and 5.5 $\mathrm{kpc}$ for the pure-helium model.
• Figure 5: The pink, blue, and gray contours show the 68%, 90%, and 99% confidence regions, respectively. Also shown are representative theoretical mass–radius relations: the unified Skyrme model SLy42001AA...380..151D, the APR EOS 1998PhRvC..58.1804A, the Brussels–Montreal unified EOS BSk19, BSk20 (analytic representation from 2013AA...560A..48P), the self-bound strangeon star EOS lx01, lx02, lx05 and lx062009MNRAS.398L..31L and the self-bound strange-quark–matter model SQM32001ApJ...550..426L.These curves are shown for comparison only; the shaded contours reflect the statistical uncertainties of our pure-He model fit.