Probing the solar interior with lensed gravitational waves from known pulsars

When gravitational waves (GWs) from a spinning neutron star arrive from behind the Sun, they are subjected to gravitational lensing that imprints a frequency-dependent modulation on the waveform. This modulation traces the projected solar density and gravitational potential along the path as the Sun passes in front of the neutron star. We calculate how accurately the solar density profile can be extracted from the lensed GWs using a Fisher analysis. For this purpose, we selected three promising candidates (the highly spinning pulsars J1022+1001, J1730-2304, and J1745-23) from the pulsar catalog of the Australia Telescope National Facility. The lensing signature can be measured with $3 \sigma$ confidence when the signal-to-noise ratio (SNR) of the GW detection reaches $100 \, (f/300 {\rm Hz})^{-1}$ over a one-year observation period (where $f$ is the GW frequency). The solar density profile can be plotted as a function of radius when the SNR improves to $\gtrsim 10^4$.