The special point on the hybrid star mass–radius diagram and its multi–messenger implications

Abstract

We show the existence and investigate the location of the special point (SP) in which hybrid neutron star mass-radius (M-R) curves have to cross each other when they belong to a class of hybrid equation of state (EoS) constructed with generic constant–speed–of–sound (CSS) quark matter models for which the onset deconfinement is varied. We demonstrate that for a three-parameter CSS model the position of the SP in the M-R diagram is largely independent of the choice of the hadronic EoS, but in dependence on the stiffness of the quark matter EoS it spans a region that we identify. We find that the difference between the maximum mass and the SP mass depends on the mass at the onset of deconfinement so that an upper limit of 0.19 M⊙ for this difference is obtained from which a lower limit on the radius of hybrid stars is deduced. Together with a lower limit on the radius of hadronic stars, derived from a class of reasonably soft hadronic EoS including hyperons, we identify a region in the M-R diagram which can be occupied only by hybrid stars. Accordingly, we suggest that a NICER radius measurement on the massive pulsar PSR J0740 + 6620 in the range of 8.6-11.9 km would indicate that this pulsar is a hybrid neutron star with deconfined quark matter in the inner core.

Hybrid neutron stars in the mass‐radius diagram

“…By exploring a more radical construction from Shahrbaf et al (2020), depicted in Figure 2, we arrive at a somewhat unconventional mass–radius relation (shown in Figure 5), motivated by the recent developments in multimessenger astronomy, specifically the interplay between the likelihood of rather compact range neutron stars (Abbott et al 2018) and the likely low‐compactness of PSR J0740 (Miller et al 2021; Riley et al 2021). By exploring a transition from a borderline soft hadronic EoS (APR) compared to the stiff DD2p40, we immediately notice that the discrepancy in the SP mass and radius remains consistent with the findings in Cierniak & Blaschke (2020), thus reaffirming the approximate invariance of the SP to the choice of hadronic EoS, as well as demonstrating an insensitivity to the phase transition construction.…”

“…This tool makes use of a property that is unique to two–phase models, namely, the existence of a stationary point for hybrid star sequences in the mass–radius plot with respect to variations of the onset density of the second phase. It has been demonstrated in Cierniak & Blaschke (2020) that this point is insensitive to the other phase chosen. Additionally, a precise relation between this point's mass and the maximum mass was derived, thus demonstrating the capability of this feature in estimating model parameters based on observational constraints.…”

“…In Cierniak & Blaschke (2020), the region in the M–R diagram has been explored where the SP point (Yudin et al 2014) can be located, while appearing on the stable part of the hybrid neutron star branch. We further improve the systematics of this study by taking into account a lower bound on the A parameter, corresponding to a RIM mixed phase for which the onset density is equal to the nuclear saturation density .…”

“…As a next step, we revise the initial observation from Cierniak & Blaschke (2020), that the SP is insensitive to the choice of hadronic EoS, by introducing a variation of the phase transition construction. As seen in Figure 4, a simple interpolated mixed phase (Figure 1) results in a meaningful change of the mass–radius relation only in the area closest to the onset mass.…”

“…In this manuscript, we will analyze the possibility of a phenomenological constant–speed–of–sound (CSS) model to consistently explain all of the current multimessenger observations. For that purpose, we will employ the “Special Point” interface, a heuristic tool discovered in Yudin et al (2014) and recently studied in Cierniak & Blaschke (2020) and Blaschke & Cierniak (2021). This tool makes use of a property that is unique to two–phase models, namely, the existence of a stationary point for hybrid star sequences in the mass–radius plot with respect to variations of the onset density of the second phase.…”