B What is the Maximum Mass of a Neutron Star?

[Grinkle]

TL;DR Summary

Is there a link between general relativity math becoming singular and the maximum mass of a neutron star?

I read this -

https://www.sciencedaily.com/releases/2018/01/180116093650.htm

And I see this -

"However, there are indications that a neutron star with a maximum mass would collapse to a black hole if even just a single neutron were added."

And I think the maximum mass of a neutron star is calculated by understanding the fundamental forces, while the mass density to require to cause a black hole is calculated by understanding GR.

Do these two calculations (which to my uninformed mind seem to come from very different approaches) independently end up with the same answer for the maximum mass of a non-singular / observable neutron star?

 

[jedishrfu]

A neutron star is basically balancing the strong nuclear force against gravity. The notion of adding one more neutron tips the scales in the favor of gravity and the eventual collapse of the star into a black hole.

Of course, we need GR to compute the gravitational piece and we need quantum mechanics to compute the strong nuclear force.

 

[PAllen]

Just a note that Rezzolla is a top expert in gravitational collapse, and two independent groups got the same result (with significant input from observation as well as theory). Thus, the 2.16 solar mass upper limit for slow spinning neutron star seem reliable. At the present time, there is no upper limit with similar confidence for rapidly spinning neutron stars. These would have a larger upper mass limit, that is not currently precisely known.

 

[Grinkle]

the eventual collapse of the star into a black hole

I see - so its not that one more neutron increases the mass density enough to cause a black hole. I was reading too much into that snip from the article.

There is some shrinking that needs to happen to increase the density further, and assuming there is another force that takes over at some point, this shrinking results in a kind of star we don't have any theory to model that is dense enough to form an EH around itself.

 

[ohwilleke]

Is there a link between general relativity math becoming singular and the maximum mass of a neutron star?

Yes. But, there is a fair amount of uncertainty (about 15%) in the estimated threshold from different groups investigating the question theoretically and with observations.

The theoretical uncertainty comes almost entirely from uncertainty about the condensed matter physics of neutron stars (i.e. the Neutron Star (NS) equation of state (EOS)) that is hard to test in Earth based experiments. Basically, it isn't entirely clear just precisely how strongly the strong force in a neutron star is pushing back against gravitational collapse, because there is uncertainty in the precise way that neutrons behave when crushed up against each other (and over whether exotic kinds of matter other than neutrons with different properties form in that extremely high pressure environment).

Also, factors like whether the neutron star is spinning or not (and how fast) influence the theoretical threshold value by up to about 20%.

Observational efforts to determine the cutoff empirically comes predominantly from uncertainty in the mass measurements of edge case objects.

One of the edge cases which has not been definitively resolved either way is a "compact object" with a mass of 2.6 stellar masses. See LIGO Scientific Collaboration and Virgo Collaboration, "GW190814: Gravitational Waves from the Coalescence of a 23 M Black Holewith a 2.6 M Compact Object" arXiv (June 24, 2020), and also, discussing the same compact object: here, and here. The first of these references states that:

Either way, this is an unprecedented source because the secondary’s well-constrained mass of 2.50– 2.67 M makes it either the lightest BH or the heaviest NS ever observed in a double compact-object system. . . .

An analysis of the theoretical considerations and observational constraints on the maximum mass of a neutron star follows in the paper:

It is heavier than the most massive pulsar in the Galaxy (Cromartie et al. 2019), and almost certainly exceeds the mass of the 1.61–2.52 M primary component of GW190425, which is itself an outlier relative to the Galactic population of BNSs (Abbott et al. 2020a). On the other hand, it is comparable in mass to two BH candidates: the ' 2.7 M merger remnant of GW170817 (Abbott et al. 2019b) and the 2.6– 6.1 M compact object (95% confidence interval) discovered by Thompson et al. (2019). It is also comparable to the millisecond pulsar PSR J1748−2021B (Freire et al. 2008), whose mass is claimed as 2.74+0.21 −0.21M at 68% confidence. However, this estimate, obtained via measurement of the periastron advance, could be inaccurate if the system inclination is low or the pulsar’s companion is rapidly rotating (Freire et al. 2008). In sum, it is not clear if GW190814’s secondary is a BH or a NS. . . .

6.2. Nature of the Secondary Component

The primary mass measurement of 23.2 +1.1 −1.0 M securely identifies the heavier component of GW190814 as a BH, but the secondary mass of 2.59+0.08 −0.09 M may be compatible with either a NS or a BH depending on the maximum mass supported by the unknown NS equation of state (EOS). The source’s asymmetric masses, the non-detection of an electromagnetic counterpart and the lack of a clear signature of tides or spin-induced quadrupole effects in the waveform do not allow us to distinguish between a BBH or a NSBH. Instead, we rely on comparisons between m₂ and different estimates of the maximum NS mass, Mmax, to indicate the source classification preferred by data: if m₂ > Mmax, then the NSBH scenario is untenable.

While some candidate EOSs from nuclear theory can support nonrotating NSs with masses of up to ∼ 3 M (e.g., M¨uller & Serot 1996), such large values of Mmax are disfavored by the relatively small tidal deformabilities measured in GW170817 (Abbott et al. 2017a, 2019b), which correlate with smaller internal pressure gradients as a function of density and hence a lower threshold for gravitational collapse. By adopting a phenomenological model for the EOS, conditioning it on GW170817, and extrapolating the constraints to the high densities relevant for the maximum mass, Lim & Holt (2019) and Essick et al. (2020) place Mmax . 2.3 M. Similarly, the EOS inference reported in Abbott et al. (2018), based on an analysis of GW170817 with a spectral parameterization (Lindblom 2010; Lindblom & Indik 2012, 2014) for the EOS, implies a 90% credible upper bound of Mmax ≤ 2.43 M, with tenuous but non-zero posterior support beyond 2.6 M. We calculate the corresponding Mmax posterior distribution, shown in the right panel of Figure 3, from the GW170817- informed spectral EOS samples used in Abbott et al. (2018) by reconstructing each EOS from its parameters and computing its maximum mass. Comparison with the m₂ posterior suggests that the secondary component of GW190814 is probably more massive than this prediction for Mmax: the posterior probability of m₂ ≤ Mmax, marginalized over the uncertainty in m₂ and Mmax, is only 3%. Nevertheless, the maximum mass predictions from these kinds of EOS inferences come with important caveats: their extrapolations are sensitive to the phenomenological model assumed for the EOS; they use hard Mmax thresholds on the EOS prior to account for the existence of the heaviest Galactic pulsars, which is known to bias the inferred maximum mass distribution towards the threshold (Miller et al. 2020); and they predate the NICER observatory’s recent simultaneous mass and radius measurement for J0030+0451, which may increase the Mmax estimates by a few percent (Landry et al. 2020) because it favors slightly stiffer EOSs than GW170817 (Raaijmakers et al. 2019; Riley et al. 2019; Miller et al. 2019; Jiang et al. 2020).

NS mass measurements also inform bounds on Mmax independently of EOS assumptions. Fitting the known population of NSs in binaries to a double-Gaussian mass distribution with a high-mass cutoff, Alsing et al. (2018) obtained an empirical constraint of Mmax ≤ 2.6 M (one-sided 90% confidence interval). Farr & Chatziioannou (2020) recently updated this analysis to include PSR J0740+6620 (Cromartie et al. 2019), which had not been discovered at the time of the original study. Based on samples from the Farr & Chatziioannou (2020) maximum-mass posterior distribution, which is plotted in the right panel of Figure 3, we find Mmax = 2.25+0.81 −0.26 M. In this case, the posterior probability of m₂ ≤ Mmax is 29%, again favoring the m₂ > Mmax scenario, albeit less strongly because of the distribution’s long tail up to ∼ 3 M. However, the empirical Mmax prediction is sensitive to selection effects that could potentially bias it (Alsing et al. 2018). In particular, masses are only measurable for binary pulsars, and the mass distribution of isolated NSs could be different. Additionally, the discovery of GW190425 (Abbott et al. 2020a) should also be taken into account in the population when predicting Mmax.

Finally, the NS maximum mass is constrained by studies of the merger remnant of GW170817. Although no postmerger gravitational waves were observed (Abbott et al. 2017g, 2019f), modeling of the associated kilonova (Abbott et al. 2017b; Kasen et al. 2017; Villar et al. 2017; Cowperthwaite et al. 2017; Abbott et al. 2017d) suggests that the merger remnant collapsed to a BH after a brief supramassive or hypermassive NS phase during which it was stabilized by uniform or differential rotation. Assuming this ultimate fate for the merger remnant immediately implies that no NS can be stable above ∼ 2.7 M, but it places a more stringent constraint on NSs that are not rotationally supported. The precise mapping from the collapse threshold mass of the remnant to Mmax depends on the EOS, but by developing approximate prescriptions based on sequences of rapidly rotating stars for a range of candidate EOSs, Mmax has been bounded below approximately 2.2–2.3 M (Margalit & Metzger 2017; Rezzolla et al. 2018; Ruiz et al. 2018; Shibata et al. 2019; Abbott et al. 2020c). Although the degree of EOS uncertainty in these results is difficult to quantify precisely, if we take the more conservative 2.3 M bound at face value, then m₂ is almost certainly not a NS: the m₂ posterior distribution has negligible support below 2.3 M.

Overall, these considerations suggest that GW190814 is probably not the product of a NSBH coalescence, despite its preliminary classification as such. Nonetheless, the possibility that the secondary component is a NS cannot be completely discounted due to the current uncertainty in Mmax.

There are two further caveats to this assessment. First, because the secondary’s spin is unconstrained, it could conceivably be rotating rapidly enough for m₂ to exceed Mmax without triggering gravitational collapse: rapid uniform rotation can stabilize a star up to ∼ 20% more massive than the nonrotating maximum mass (Cook et al. 1994), in which case only the absolute upper bound of ∼ 2.7 M is relevant. However, it is very unlikely that a NSBH system could merge before dissipating such extreme natal NS spin angular momentum.

Second, our discussion has thus far neglected the possibility that the secondary component is an exotic compact object, such as a boson star (Kaup 1968) or a gravastar (Mazur & Mottola 2004), instead of a NS or a BH. Depending on the model, some exotic compact objects can potentially support masses up to and beyond 2.6 M (Cardoso & Pani 2019). Our analysis does not exclude this hypothesis for the secondary.

Since the NSBH scenario cannot be definitively ruled out, we examine GW190814’s potential implications for the NS EOS, assuming that the secondary proves to be a NS. This would require Mmax to be no less than m₂, a condition that severely constrains the distribution of EOSs compatible with existing astrophysical data. The combined constraints on the EOS from GW170817 and this hypothetical maximum mass information are shown in Figure 8. Specifically, we have taken the spectral EOS distribution conditioned on GW170817 from Abbott et al. (2018) and reweighted each EOS by the probability that its maximum mass is at least as large as m₂. The updated posterior favors stiffer EOSs, which translates to larger radii for NSs of a given mass. The corresponding constraints on the radius and tidal deformability of a canonical 1.4 M NS are R1.4 = 12.9 +0.8 −0.7 km and Λ1.4 = 616+273 −158.