Gravitational wave radiation from rapidly deformed post-merger neutron star: perspective for the Milky way detection by LIGO-Virgo-KAGRA

Abstract Binary neutron star (BNS) merger events, detected by the LIGO-Virgo Collaboration, have ushered in the era of multi-messenger astronomy. If a rapidly spinning neutron star (NS) is formed post-merger, asymmetric explosions or ultra-strong magnetic fields (e.g., $$\sim 10^{15-16}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>15</mml:mn> <mml:mo>-</mml:mo> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> G) can induce non-axisymmetric deformation and a mass quadrupole moment, leading to continuous gravitational wave (GW) emission. To explore the detectability of such GWs by updated LIGO-Virgo-KAGRA (LVK) detectors, we derived the GW radiation properties and spin-down timescales of post-merger NS with an initial spin frequency of 1000 Hz (corresponding to an initial GW frequency of 2000 Hz). Our calculations show that signal duration strongly depends on magnetic field strength: for an ultra-strong field ( $$B \sim 10^{16}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>16</mml:mn> </mml:msup> </mml:mrow> </mml:math> G), magnetic dipole radiation dominates, causing rapid signal decay (e.g., the GW frequency drops from 2000 to 1000 Hz in $$\sim 20.48$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>20.48</mml:mn> </mml:mrow> </mml:math> s); for a weaker field ( $$B \sim 10^{14}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>14</mml:mn> </mml:msup> </mml:mrow> </mml:math> G), GW braking prevails, prolonging the signal to years. By comparing the expected GW strain with LVK sensitivity curves, we find that next-generation LVK detectors could detect such post-merger GW signals from sources within the Milky Way (distance $$\approx 10{,}000$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≈</mml:mo> <mml:mn>10</mml:mn> <mml:mo>,</mml:mo> <mml:mn>000</mml:mn> </mml:mrow> </mml:math> light-years), with a required NS ellipticity of $$\varepsilon \sim 10^{-4}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ε</mml:mi> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . This study identifies post-merger rapidly rotating NSs as potential high-frequency continuous GW sources, which in the favorable long-lived scenarios may open a new window for investigating compact binary merger products and advancing multi-messenger astronomy.