Inferring the pair-instability mass gap from gravitational wave data

We use hierarchical Bayesian inference with nonparametric Gaussian process models to investigate the effective inspiral spin parameter, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>χ</a:mi><a:mi>eff</a:mi></a:msub></a:math>, as a function of primary black hole mass in the third gravitational-wave transient catalog (GWTC-3). Our analysis reveals a transition in the population at a primary mass of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msubsup><c:mrow><c:mn>46</c:mn></c:mrow><c:mrow><c:mo>−</c:mo><c:mn>5</c:mn></c:mrow><c:mrow><c:mo>+</c:mo><c:mn>7</c:mn></c:mrow></c:msubsup><c:msub><c:mrow><c:mi>M</c:mi></c:mrow><c:mrow><c:mo stretchy="false">⊙</c:mo></c:mrow></c:msub></c:mrow></c:math>. Beyond this mass, the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi>χ</f:mi><f:mi>eff</f:mi></f:msub></f:math> distribution broadens, becomes consistent with being symmetric around zero, and has a median of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mo>−</h:mo><h:mn>0.0</h:mn><h:msubsup><h:mn>3</h:mn><h:mrow><h:mo>−</h:mo><h:mn>0.59</h:mn></h:mrow><h:mrow><h:mo>+</h:mo><h:mn>0.36</h:mn></h:mrow></h:msubsup></h:math> (90% credibility). These results are consistent with the presence of a pair-instability mass gap that is repopulated by black holes that are the remnant of a previous merger, formed in dense star clusters. However, asymmetric distributions skewed toward positive <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi>χ</j:mi><j:mi>eff</j:mi></j:msub></j:math> are not excluded by current data. Below the inferred transition mass, we constrain the fraction of second-generation black holes to be <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mo>≲</l:mo><l:mn>10</l:mn><l:mo>%</l:mo></l:math>. These results provide model-independent support for a high-mass and high-spin population of black holes in the data, consistent with earlier work using parametric models. Imminent gravitational-wave data releases will be essential to sharpen constraints on spin symmetry and clarify the origin of the black holes.