Numerical-relativity surrogate model for hyperbolic encounters of black holes: Challenges in parameter estimation

We present a surrogate numerical-relativity model for close hyperbolic black-hole encounters with equal masses and spins aligned with the orbital momentum. Our model, generated in terms of the Newman–Penrose scalar <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>ψ</a:mi></a:mrow><a:mrow><a:mn>4</a:mn></a:mrow></a:msub></a:mrow></a:math>, spans impact parameters <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>b</c:mi><c:mo>/</c:mo><c:mi>M</c:mi><c:mo>∈</c:mo><c:mo stretchy="false">[</c:mo><c:mn>11</c:mn><c:mo>,</c:mo><c:mn>15</c:mn><c:mo stretchy="false">]</c:mo></c:math> and spin components <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>χ</g:mi><g:mi>i</g:mi></g:msub><g:mo>∈</g:mo><g:mo stretchy="false">[</g:mo><g:mo>−</g:mo><g:mn>0.5</g:mn><g:mo>,</g:mo><g:mn>0.5</g:mn><g:mo stretchy="false">]</g:mo></g:math>, modeling the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mo stretchy="false">(</k:mo><k:mo>ℓ</k:mo><k:mo>,</k:mo><k:mi>m</k:mi><k:mo stretchy="false">)</k:mo><k:mo>=</k:mo><k:mo stretchy="false">(</k:mo><k:mn>2</k:mn><k:mo>,</k:mo><k:mn>0</k:mn><k:mo stretchy="false">)</k:mo></k:math>, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mo stretchy="false">(</q:mo><q:mn>2</q:mn><q:mo>,</q:mo><q:mo>±</q:mo><q:mn>2</q:mn><q:mo stretchy="false">)</q:mo></q:math>, <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mo stretchy="false">(</u:mo><u:mn>3</u:mn><u:mo>,</u:mo><u:mo>±</u:mo><u:mn>2</u:mn><u:mo stretchy="false">)</u:mo></u:math>, and <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mo stretchy="false">(</y:mo><y:mn>4</y:mn><y:mo>,</y:mo><y:mo>±</y:mo><y:mn>4</y:mn><y:mo stretchy="false">)</y:mo></y:math> emission multipoles. The model is faithful to numerical-relativity simulations, yielding mismatches lower than <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msup><cb:mn>10</cb:mn><cb:mrow><cb:mo>−</cb:mo><cb:mn>3</cb:mn></cb:mrow></cb:msup></cb:math>. We test the ability of our model to recover the parameters of numerically simulated signals. We find that, despite the high accuracy of the model, parameter inference struggles to correctly capture the parameters of the source even for SNRs as large as 50 due to the strong degeneracies present in the parameter space. This indicates that correctly identifying these systems will require extremely large signal loudness, which is only typical of third generation detectors. Nevertheless, we also find that, if one attempts to infer certain combinations of such degenerated parameters, there might be a chance to prove the existence of this type of event, even with the current ground-based detectors, as long as these combinations make sense astrophysically and cosmologically.