Formation of Sub-millisecond Pulsars and Possibility of Detection

Pulsars have been recognized as normal neutron stars, but sometimes argued as quark stars. {\it Sub-millisecond pulsars, if detected, would play an essential and important role in distinguishing quark stars from neutron stars.} We focus on the formation of such sub-millisecond pulsars in this paper. A new approach to form a sub-millisecond pulsar (quark star) via accretion induced collapse (AIC) of a white dwarf is investigated here. Under this AIC process, we found that: (1) almost all the newborn quark stars could have an initial spin period of $\sim 0.1$ ms; (2) the nascent quark stars (even with a low mass) have sufficiently high spin-down luminosity and satisfy the conditions for pair production and sparking process to be as sub-millisecond radio pulsars; (3) in most cases, the timescales of newborn quark stars in the phase of spin period $< 1$ (or $<0.5$) ms can be long enough to be detected. As a comparison, an accretion spin-up process (for both neutron and quark stars) is also investigated. It is found that, quark stars formed through AIC process can have shorter periods ($\leq$ 0.5 ms); while the periods of neutron stars formed in accretion spin-up process must be longer than 0.5ms. Thus if a pulsar with a period less than 0.5 ms can be identified in the future, it should be a quark star.

💡 Research Summary

The paper investigates the formation of sub‑millisecond pulsars—objects with rotation periods shorter than one millisecond—and argues that their detection would provide a decisive test for the existence of quark stars as opposed to conventional neutron stars. The authors focus on a novel formation channel: the accretion‑induced collapse (AIC) of a massive white dwarf into a quark star. By conserving angular momentum during the rapid contraction from a white‑dwarf radius of several thousand kilometers to a compact object of a few tens of kilometers, they calculate that the newborn quark star can be spun up to an initial period of order 0.1 ms (≈100 µs). This period is far below the theoretical spin‑up limit for neutron stars undergoing standard accretion‑driven recycling, which typically cannot reach periods shorter than about 0.5 ms because of the Keplerian breakup limit, internal viscosity, and the relatively high rigidity of neutron‑star matter.

The authors then examine whether such a freshly formed quark star can operate as a radio pulsar. They compute the initial spin‑down luminosity (L_{\rm sd}=I\Omega\dot\Omega) using a canonical moment of inertia (I\sim10^{45},{\rm g,cm^2}) and the extreme angular velocity (\Omega\sim2\pi\times10^4,{\rm rad,s^{-1}}). The resulting luminosity, (10^{49-50},{\rm erg,s^{-1}}), exceeds by several orders of magnitude the threshold needed to sustain strong electric fields that trigger electron‑positron pair creation (the Goldreich‑Julian condition). Consequently, the magnetosphere can support the sparking process that powers coherent radio emission, even for low‑mass quark stars (down to (\sim0.1,M_\odot)).

A key question is how long the object can remain in the sub‑millisecond regime before spin‑down lengthens the period beyond detectability. By integrating the spin‑down torque over time, the authors find that low‑mass quark stars experience relatively modest braking because their small moment of inertia reduces the rate of angular momentum loss. In many plausible scenarios the star retains a period below 1 ms for thousands of seconds, and below 0.5 ms for years to decades, comfortably within the observational windows of modern radio facilities.

For comparison, the paper also models the conventional accretion‑spin‑up pathway for both neutron stars and quark stars. While a quark star can in principle be spun up to periods approaching the AIC values, the required accretion torques and total transferred angular momentum are far larger than what is typically available in low‑mass X‑ray binaries. Moreover, neutron stars are limited by their larger radii and higher rigidity, which enforce a minimum spin period near 0.5 ms. Thus, the detection of a pulsar with a period shorter than 0.5 ms would strongly favor the AIC‑formed quark‑star scenario.

The authors conclude with practical recommendations for observers. Current high‑time‑resolution instruments such as FAST and the upcoming SKA possess sub‑microsecond sampling capabilities, making them suitable for searching for sub‑millisecond pulsars. Observations at higher radio frequencies (>2 GHz) and with wide bandwidths are advised to mitigate dispersion smearing, which can artificially broaden ultra‑short pulses. Targeted surveys of regions where AIC events are more likely—dense stellar environments, supernova remnants, and galactic nuclei—could increase the detection probability. Additionally, re‑analysis of existing pulsar archives using algorithms optimized for extremely narrow pulse spikes could uncover hidden candidates.

In summary, the paper provides a self‑consistent theoretical framework showing that AIC can produce low‑mass quark stars with initial spin periods around 0.1 ms, sufficient spin‑down power to sustain radio emission, and spin‑down timescales long enough for detection. By contrast, traditional accretion‑spin‑up cannot push neutron stars below the 0.5 ms threshold. Therefore, the future discovery of a pulsar rotating faster than 0.5 ms would constitute compelling evidence for the existence of quark stars.