The radioactive heating of neutron-rich ejecta from neutron star mergers powers kilonovae, and the inferred ejecta mass from a kilonova observation or upper limit depends sensitively on the adopted heating rate. Kawaguchi, Shibata and Tanaka (2020) showed, for the black hole–neutron star merger candidate S190814bv, that the dynamical ejecta-mass upper limit weakens by a factor of about 2–3 when the heating contribution of fission fragments from spontaneous fission of very heavy r-process nuclei (e.g. 266^{266}Cf, 259,262^{259,262}Fm) is omitted rather than included, because the beta-decay and spontaneous-fission lifetimes of these transuranic parent nuclides are highly uncertain. The subsequent literature leaves this open core standing: nuclear-input sensitivity studies still find order-of-magnitude uncertainty in the heating rate at one day and factor-of-eight uncertainty in inferred ejecta mass at 8–10 days; late-time heating remains strongly fission-dependent; new microscopic predictions of spontaneous-fission half-lives and beta-decay rates are only now arriving and still disagree; and no observational diagnostic of actinide production (the 254^{254}Cf mid-infrared bump or fission gamma-ray lines) has been detected. The problem — determining the spontaneous-fission heating contribution of very heavy r-process nuclei and thereby hardening kilonova-based ejecta-mass constraints — remains open.

Background

When two compact objects (binary neutron stars, or a black hole and a neutron star) merge, tidal forces and disk winds eject neutron-rich matter in which the rapid neutron-capture process (the r-process) synthesizes nuclei heavier than iron, including the lanthanides and the actinides (translead elements such as uranium, plutonium, californium, and fermium). The freshly synthesized nuclei are radioactive, and their decay energy, deposited thermally in the optically thick ejecta, powers a transient called a kilonova (historically "macronova"). The observed kilonova luminosity is the primary tool for inferring the mass and composition of the ejecta, which in turn constrains the neutron-star equation of state and the cosmic origin of the heavy elements.

The heating rate is usually taken from nucleosynthesis network calculations that follow thousands of unstable nuclei. For very neutron-rich ejecta (electron fraction YeY_e — the number of electrons per baryon, a measure of neutron richness — below about 0.1–0.2), the decay flow reaches the transuranic region, where nuclei decay by alpha decay, beta decay, and spontaneous fission (SF): the breakup of a heavy nucleus into two comparably massive fragments without external excitation. Wanajo et al. (2014) found that SF of nuclei such as 266^{266}Cf and 259,262^{259,262}Fm can contribute significantly to the radioactive heating at Ye<0.1Y_e<0.1, and Zhu et al. (2018) showed that a single isotope, 254^{254}Cf, with a half-life of about 61 days, can dominate the heating between roughly 15 and 250 days after merger. The energy released by fission is carried by the fission fragments, whose kinetic energy must thermalize (be shared with the ejecta plasma through Coulomb stopping) before it can power the light curve; Hotokezaka and Nakar (2020) computed this thermalization explicitly.

The difficulty is nuclear data: the neutron-rich transuranic nuclei involved are far from the valley of stability, and the most neutron-rich nuclei on the r-process path have never been produced in the laboratory, so their beta-decay and spontaneous-fission lifetimes are at best poorly constrained and their fission-fragment mass/charge distributions exist only as theoretical predictions, which disagree substantially because spontaneous-fission lifetimes depend exponentially on fission barriers and collective inertias. Kawaguchi, Shibata and Tanaka (2020), in their analysis of the black hole–neutron star merger candidate S190814bv (an event detected by the LIGO and Virgo gravitational-wave observatories in August 2019 at about 267 Mpc, with no kilonova counterpart found), adopted the Wanajo et al. (2014) heating prescription with the fission-fragment contribution included, and repeated the radiative-transfer calculation with it omitted. The resulting upper limit on the dynamical ejecta mass was weaker by a factor of about 2–3 without fission heating, so the constraint itself is hostage to the poorly determined nuclear physics of the transuranics. The same heating-rate uncertainty propagates into every kilonova-based ejecta-mass inference and, through analytical fits calibrated to numerical-relativity simulations (merger simulations that solve Einstein's equations of general relativity numerically), into neutron-star-radius constraints.

Problem Statement

Determine the contribution of spontaneous fission of very heavy r-process nuclei (neutron-rich transuranics such as 254,266^{254,266}Cf and 259,262^{259,262}Fm) to the radioactive heating rate of neutron-rich compact-object-merger ejecta, and quantify how this contribution and its uncertainty propagate into kilonova light curves and ejecta-mass constraints. Concretely, the open question posed by Kawaguchi, Shibata and Tanaka (2020) — and left standing by the subsequent literature — is: what is the magnitude and uncertainty of the spontaneous-fission (plus fission-fragment) heating term as a function of time since merger and electron fraction YeY_e, given that the beta-decay and spontaneous-fission lifetimes of the parent nuclides are highly uncertain? The answer must quantify the reduction that this determined contribution and its uncertainty allow in the factor-of-2–3 (and, across the full input-model range, up to order-of-magnitude) systematic in kilonova-based dynamical ejecta-mass limits, such as those derived for S190814bv.

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