[Paper Review] Gravitational wave signature of proto-neutron star convection: I. MHD numerical simulations

R Raynaud, P. Cerdá–Durán+1 more|arXiv (Cornell University)|Mar 23, 2021

Pulsars and Gravitational Waves ResearchPhysics and Astronomy108 references29 citations

TL;DR

This study computes gravitational wave (GW) signatures from proto-neutron star (PNS) convection using 3D MHD simulations in the anelastic approximation, focusing on early and late PNS phases. It identifies a low-frequency GW excess linked to strong-field dynamo action—characterized by an axisymmetric toroidal magnetic field—offering a potential observational probe for dynamo efficiency and magnetar formation mechanisms in neutron stars.

ABSTRACT

Gravitational waves provide a unique and powerful opportunity to constrain the dynamics in the interior of proto-neutron stars during core collapse supernovae. Convective motions play an important role in generating neutron stars magnetic fields, which could explain magnetar formation in the presence of fast rotation. We compute the gravitational wave emission from proto-neutron star convection and its associated dynamo, by post-processing three-dimensional MHD simulations of a model restricted to the convective zone in the anelastic approximation. We consider two different proto-neutron star structures representative of early times (with a convective layer) and late times (when the star is almost entirely convective). In the slow rotation regime, the gravitational wave emission follows a broad spectrum peaking at about three times the turnover frequency. In this regime, the inclusion of magnetic fields slightly decreases the amplitude without changing the spectrum significantly compared to a non-magnetised simulation. Fast rotation changes both the amplitude and spectrum dramatically. The amplitude is increased by a factor of up to a few thousands. The spectrum is characterized by several peaks associated to inertial modes, whose frequency scales with the rotation frequency. Using simple physical arguments, we derive scalings that reproduce quantitatively several aspects of these numerical results. We also observe an excess of low-frequency gravitational waves, which appears at the transition to a strong field dynamo characterized by a strong axisymmetric toroidal magnetic field. This signature of dynamo action could be used to constrain the dynamo efficiency in a proto-neutron star with future gravitational wave detections.

Motivation & Objective

• To compute gravitational wave (GW) emission from proto-neutron star (PNS) convection during the post-explosion phase, when neutrino-driven convection dominates.
• To investigate how magnetic fields generated by convective dynamos modulate GW amplitude and spectral features.
• To identify observable GW signatures—particularly low-frequency excess and inertial mode peaks—that could constrain dynamo efficiency and PNS rotation in future detections.
• To derive physical scaling laws for GW amplitude and frequency based on PNS properties such as rotation rate and Alfvén frequency.

Proposed method

• Post-processing 3D MHD simulations of the PNS convective zone in the anelastic approximation, using models representative of early (post-bounce) and late (several seconds after bounce) PNS states.
• Simulating both non-magnetized and magnetized convection with varying rotation rates to isolate the impact of magnetic fields on GW emission.
• Computing the quadrupole GW strain using the mass-current and mass-moment tensor formalism, decomposed into spherical harmonic modes (m = 1 and m = 2).
• Analyzing the GW spectrum to identify features such as peaks at three times the turnover frequency (slow rotation) and multiple peaks linked to inertial modes (fast rotation).
• Deriving analytical scaling laws for GW amplitude and frequency based on physical arguments involving buoyancy, rotation, and Alfvén wave dynamics.
• Identifying the m = 1 mode as the dominant source of low-frequency GW emission, with peak frequency scaling as (v_A² / Ω), where v_A is the Alfvén speed and Ω the rotation frequency.

Experimental results

Research questions

• RQ1 How does the gravitational wave emission from proto-neutron star convection depend on rotation rate and magnetic field strength?
• RQ2 What GW spectral features arise from convective motions in the presence of a strong-field dynamo, and can they be linked to specific physical modes?
• RQ3 Can the low-frequency excess in the GW spectrum be attributed to the growth of an axisymmetric toroidal magnetic field, and what does this imply for dynamo efficiency?
• RQ4 Do inertial modes in rapidly rotating PNSs produce distinct, resolvable peaks in the GW spectrum, and can their frequency be predicted from rotation rate?
• RQ5 What scaling laws govern the amplitude and frequency of GW emission in slow versus fast rotation regimes, and how well do they match numerical results?

Key findings

• In the slow rotation regime, the GW spectrum exhibits a broad peak centered at approximately three times the convective turnover frequency, with magnetic fields causing only a minor reduction in amplitude.
• For fast rotation, the GW amplitude increases by up to a factor of several thousand compared to non-rotating cases, with the spectrum showing multiple distinct peaks associated with inertial modes whose frequencies scale linearly with the rotation frequency.
• A low-frequency excess in the GW spectrum (≲100 Hz) appears during the transition to a strong-field dynamo, characterized by a dominant axisymmetric toroidal magnetic field, and is primarily emitted by the m = 1 quadrupole mode.
• The peak frequency of the m = 1 GW emission scales as the square of the Alfvén speed divided by the rotation frequency, suggesting a physical link to magnetized Rossby modes.
• Simple physical scaling laws derived from buoyancy, rotation, and Alfvén wave dynamics quantitatively reproduce the numerical results for both slow and fast rotation regimes.
• The low-frequency GW excess serves as a unique signature of strong-field dynamo action and could be used to constrain dynamo efficiency and magnetic field strength in proto-neutron stars via future gravitational wave detections.