Observing black hole mergers beyond the pair-instability mass gap with next-generation gravitational wave detectors

Stellar evolution predicts the existence of a mass gap for black hole remnants produced by pair-instability supernova dynamics, whose lower and upper edges are very uncertain. We study the possibility of constraining the location of the upper end of the pair-instability mass gap, which is believed to appear around <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>m</a:mi><a:mi mathsize="small">min</a:mi></a:msub><a:mo>∼</a:mo><a:mn>130</a:mn><a:msub><a:mi>M</a:mi><a:mo stretchy="false">⊙</a:mo></a:msub></a:math>, using gravitational wave observations of compact binary mergers with next-generation ground-based detectors. While high metallicity may not allow for the formation of first-generation black holes on the “far side” beyond the gap, metal-poor environments containing population III stars could lead to such heavy black hole mergers. We show that, even in the presence of contamination from other merger channels, next-generation detectors will measure the location of the upper end of the mass gap with a relative precision close to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="normal">Δ</e:mi><e:msub><e:mi>m</e:mi><e:mi mathsize="small">min</e:mi></e:msub><e:mo>/</e:mo><e:msub><e:mi>m</e:mi><e:mi mathsize="small">min</e:mi></e:msub><e:mo>≃</e:mo><e:mn>4</e:mn><e:mo>%</e:mo><e:mo stretchy="false">(</e:mo><e:msub><e:mi>N</e:mi><e:mi mathsize="small">det</e:mi></e:msub><e:mo>/</e:mo><e:mn>100</e:mn><e:msup><e:mo stretchy="false">)</e:mo><e:mrow><e:mo>−</e:mo><e:mn>1</e:mn><e:mo>/</e:mo><e:mn>2</e:mn></e:mrow></e:msup></e:math> at 90% CL, where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>N</m:mi><m:mi mathsize="small">det</m:mi></m:msub></m:math> is the number of detected mergers with both members beyond the gap. These future observations could reduce current uncertainties in nuclear and astrophysical processes controlling the location of the gap.