The Maximum Offsets of Binary Neutron Star Mergers from Host Galaxies

Abstract We analytically derive, and illustrate with a population synthesis model, the maximum offset of binary neutron star mergers ejected from their host galaxies. This approximate maximum offset is 300 kpc <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>×</mml:mo> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">esc</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:mn>500</mml:mn> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">km</mml:mi> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:msup> </mml:math> , where v esc is the escape velocity from the host galaxy. Massive hosts with high escape velocities are unlikely to yield very large offsets. This maximum offset should inform the host associations of mergers that are not coincident with galaxies. We also discuss potential correlations between offsets and system masses, and possibly the duration of the gamma-ray burst accompanying the merger.