Continuous gravitational waves from magnetized white dwarfs: Quantifying the detection plausibility by LISA

TL;DR

This work investigates continuous gravitational waves from magnetized white dwarfs whose strong internal fields create time-varying deformations when rotation is oblique to the magnetic axis. Using general-relativistic magneto-hydrostatic WD models (XNS) with a degenerate electron EOS, the authors compute GW strains, account for field decay and angular-momentum loss, and assess detectability with future space-based detectors via semi-coherent SNR. They show that a population of young, highly magnetized WDs could yield a few to a few dozen detections by LISA (and other missions), while individual targets like ZTF J1901+1458 could become detectable within a few years of integration under favorable geometry. The study also discusses distinguishing CGWs from binary foregrounds through frequency evolution and emphasizes the implications for WD magnetic-field structure and potential connections to overluminous Type Ia supernova progenitors.

Abstract

White dwarfs (WDs) are frequently observed to have strong magnetic fields up to $10^9$ G and expected to have a possible internal field as high as $\sim 10^{14}$ G. High internal fields can significantly deform a WD's equilibrium structure, generating a quadrupole moment. If the rotation axis is misaligned with the magnetic axis, the deformation can lead to the emission of continuous gravitational waves (CGWs). We examine the potential for detecting CGWs from magnetized WDs with future space-based detectors such as LISA, ALIA, DECIGO, Deci-Hz, BBO and TianQin. We model the field-induced deformation and compute the resulting GW strain, incorporating amplitude decay due to angular momentum loss from electromagnetic and gravitational radiation. This sets a timescale for detection -`active timescale' of $10^{5-6}$ yr, requiring observation while the object remains sufficiently young. Our results suggest that LISA could detect a few dozens of highly magnetized WDs across the Galaxy during its mission. As a specific case, we investigate ZTF J1901+1458- a compact, massive, fast-rotating, and strongly magnetized WD with spin period $\sim416$ s and inferred surface field $\sim10^{9}$ G. We find that this object would be detectable by LISA with four years of continuous data. This highlights the potential of CGW observations to probe magnetic field structure in WDs and their role in type Ia supernova progenitors.

Figures (14)

• Figure 1: A cartoon diagram of magnetized rotating WD with misalignment between the magnetic field axis with and the rotation axis. Here $i$ is the angle between the rotation axis of the source and detector, $\chi$ is the misalignment between magnetic and rotation axes
• Figure 2: Density (top panels) and magnetic field (bottom panels) are shown in colorbar for WD1 (of $M=1.83\,M_\odot$): toroidal (left panels) and WD2 (of $M=1.42\,M_\odot$): poloidal (right panels). The isocontour lines are drawn for density, toroidal magnetic field (having magnetic field perpendicular to the plane) and the poloidal magnetic field lines with arrow. The detailed properties of those WDs are mentioned in Table. \ref{['tab:tableblind']}
• Figure 3: Top panel: The decay of maximum magnetic $B_{max}=4\times 10^{13}$ G with time for WD1 and WD2 with radius $5708$ and $2815$ km, respectively. Middle: Magnetic field as a function of radius, before and after magnetic field decay for toroidal field (WD1). Bottom panel: Same as middle panel except for poloidal field (WD2)
• Figure 4: Top Panel: Decay of $\nu$ (red solid), $\chi$ (blue dashed) as functions of time for initial $\nu=0.05$ Hz, $\chi=3^\circ$ for toroidally dominated WD- WD1+$B_P$ ( $B_{max}^{Toroidal}=4\times10^{13}$ G, $B_{p}^{Poloidal}=8\times 10^{8}$ G) with magnetosphere. For the same WD, Middle panel shows variation of luminosities and bottom panel shows GW strain decay with time.
• Figure 5: Same as top panel of Figure \ref{['fig:wdtorpolmagsp']}, except with initial $\chi=30\degree$.