Detection of magnetic galactic binaries in quasicircular orbit with LISA

Laser Interferometer Space Antenna (LISA) will observe gravitational waves from galactic binaries (GBs) of white dwarfs or neutron stars. Some of these objects are among the most magnetic astrophysical objects in the Universe. Magnetism, by secularly disrupting the orbit, can eventually affect the gravitational waves emission and could then be potentially detected and characterized after several years of observations by LISA. Currently, the data processing pipeline of the LISA Data Challenge (LDC) for GBs does not consider either magnetism or eccentricity. Recently, it was shown [Bourgoin et al., [Phys. Rev. D 105, 124042 (2022)]] that magnetism induces a shift on the gravitational wave frequencies. Additionally, it was argued that, if the binary’s orbit is eccentric, the presence of magnetism could be detected by LISA. In this work, we explore the consequences of a future data analysis conducted on quasicircular and magnetic GB systems using the current LDC tools. We first show that a single eccentric GB can be interpreted as several GBs and this can eventually bias population studies deduced from LISA’s future catalog. Then, we confirm that for quasicircular orbits, the secular magnetic energy of the system can be inferred if the signal-to-noise ratio of the second harmonic is high enough to be detected by traditional quasimonochromatic source searching algorithms. LISA observations could therefore bring new insights on the nature and origin of magnetic fields in white dwarfs or neutron stars.

Figure 1

Orientation of $({\widehat{\mathbf{e}}}_{\vartheta },{\widehat{\mathbf{e}}}_{\phi },\widehat{\mathbf{N}})$, the transverse frame (in green), in the source frame (in red), namely $({\widehat{\mathbf{e}}}_X,{\widehat{\mathbf{e}}}_Y,{\widehat{\mathbf{e}}}_Z)$. The primary is shown at the center-of-mass of the binary system in order to simplify the drawing—this corresponds to the case where the mass of the secondary is negligible with respect to primary’s. The orbital motion of the binary system is described at any time $t$ by making use of the radial separation ($r$), the inclination ($\iota$), the longitude of the node ($\mathrm{\Omega }$), the argument of the pericenter ($\omega$), and the true anomaly ($\nu$). The orientation of the transverse frame with respect to the source frame is parameterized by the following triple of angles: $(\vartheta ,\phi ,\chi )$. The magnetic moments of the primary and secondary (in blue) are denoted by ${\mathit{\mu }}_1$ and ${\mathit{\mu }}_2$, respectively.

Figure 2

Schematic representation of the expected frequency spectrum of the “$+$” GW polarization for a magnetic GB in quasicircular orbit up to second-order in eccentricity. The spectrum for the “$\times$” polarization is similar than the one for the $+$ polarization. The zeroth, first, and second-order contributions in eccentricity to the GW signal are depicted in black, red, and green, respectively. The plain and dashed signals represent the frequency spectrum for a nonmagnetic and a magnetic GB, respectively. Hence, a frequency peak occurring at pulsation $k{n}_0$ with $k\in \mathbb{N}$ is shifted by $(k+2){\dot{\varpi }}_{\mathrm{M}}$ with respect to a configuration where magnetism is neglected.

Figure 3

Optimistic () and pessimistic () studies for the main frequency after a 1-year LISA mission. Except for amplitude and inclination in the pessimistic case and the amplitude for the optimistic case, the parameters are well estimated as shown by the gaussian distributions. The dotted lines and the square marker represent the value injected during the simulation.

Figure 4

Optimistic () and pessimistic () studies for both frequencies and a 4-years mission. Except for amplitude and inclination in the pessimistic case and the amplitude for the optimistic case, the parameters are well estimated as shown by the gaussian distributions. The dotted lines and the square marker represent the value injected during the simulation.

Figure 5

Optimistic () and pessimistic () studies for the both frequencies and a 8-years mission.

Figure 6

Estimate of the magnetic energy over its theoretical definition as a function of the symmetric mass ratio. The computation is realized for a 4-years LISA mission scenario. The black dot represents the input value of the magnetic energy while the blue curve is the estimate inferred from data analysis. The light blue area, blue area and dark blue area represent respectively the magnetic energy uncertainty associated to a 10%, 5% and 0% uncertainty levels on the knowledge of the symmetric mass ratio.