The Neutron Star Merger Delay-time Distribution, <i>R</i>-process “Knees,” and the Metal Budget of the Galaxy

Abstract For a sample of 18 currently known recycled millisecond pulsars (rMSPs) that are in double neutron star (DNS) systems, and 42 rMSPs with similar properties that are not in DNS pairs, we analyze the distributions of the characteristic age, τ c , and the time-until-merger of the double systems, τ gw . Based on the τ c distribution of non-DNS rMSPs, we argue that τ c is a reasonable estimator of true pulsar age and that rMSPs are active as pulsars for a long (≳Hubble) time. Among the DNSs there is an excess of young systems (small τ c ) with short life expectancy (small τ gw ) compared to model expectations for the distributions of τ c and τ gw if, at birth, DNSs have a delay-time distribution (DTD) of the form <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>∼</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">gw</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (expected generically for close binaries), or for that matter, from expectations from any single power-law DTD. A two-population DNS model solves the problem: the data are best fit by the combination of a “fast” population with DTD going as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">gw</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.9</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.4</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , and a “slow” population of DNSs, with DTD proportional to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">gw</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.1</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.15</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> . The fast population can be equivalently represented by a shallow power-law DTD with an exponential cutoff beyond τ gw ∼ 300 Myr. The fast population completely dominates, by a factor A ≈ 10–100, the numbers of DNSs that merge within a Hubble time, and that presumably lead to short gamma-ray bursts and kilonova explosions. Using a simple, empirically based, chemical-evolution calculation, we show that the fast/steep kilonova DTD, convolved with the measured star formation history of the Milky Way’s thick-disk population, naturally reproduces the “knee” structure seen in abundance-ratio diagrams of thick-disk stars, for europium and for two other r -process elements. As a corollary, we show, based again solely on empirical input concerning iron production by supernovae, that the Milky Way is nearly a “closed box” that has retained at least ∼70%–90% of the metals produced over the Galaxy’s lifetime.