Constraining the Abundance of Spinning Deformed Galactic Compact Objects with Continuous Gravitational Waves

Abstract Galactic spinning compact objects (COs) with nonzero ellipticity are expected to be sources of continuous gravitational waves (CGWs). Certain classes of hypothetical COs, such as neutron stars with quark cores (hybrid stars) and quark stars, are thought to be capable of sustaining large ellipticities from theoretical considerations. Such exotic COs (eCOs) with large ellipticities and spins should produce CGWs detectable by the current LIGO-Virgo-KAGRA GW detector network. Since no detections for CGWs from searches in LIGO-Virgo data have so far been reported, we place constraints on the abundance of highly elliptical, rapidly spinning eCOs in our Galaxy. We formulate a Bayesian framework to place upper limits on the number count N tot of highly deformed Galactic eCOs. We divide our constraints into two classes: an “agnostic” set of upper limits on N tot evaluated on a CGW frequency and ellipticity grid that depend only on the choice of spatial distribution of COs; and a model-dependent set that additionally assumes prior information on the distribution of frequencies. We find that COs with ellipticities ϵ ≳ 10 −5 have abundance upper limits at 90% confidence, of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">tot</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>90</mml:mn> <mml:mrow> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:mrow> </mml:msubsup> <mml:mo>≲</mml:mo> <mml:mn>100</mml:mn> </mml:math> , and those with ϵ ≳ 10 −6 have <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">tot</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>90</mml:mn> <mml:mrow> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:mrow> </mml:msubsup> <mml:mo>≲</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:math> . We additionally place upper limits on the ellipticity of Galactic COs informed by our choices of spatial distributions, given different abundances N tot .