Strong lensing interferometry for compact binaries

We propose a possibility to improve the current precision measurements on compact binaries. When the orbital axis is almost perpendicular to our line of sight, a pulsar behind its companion can form two strong lensing images. These images cannot be resolved, but we can use multiwavelength interferometry to accurately determine the passage through superior conjunction. This method does not depend strongly on the stability of the pulse profile and applies equally well to both slow and fast pulsars. We discuss the possible improvement this can bring to the bound on stochastic gravitational wave background and to determine black hole spin. We also discuss the possibility of discovering a suitable binary system by the Square Kilometer Array to which our method can apply.

Figure 1

The binary orbit in the rest frame of the lens and viewed from a small inclination angle. When the source goes behind the lens and approaches the Einstein radius (the dotted circle), we can see both a far image (blue) and a close image (red). When far from the Einstein radius, the interior image becomes very faint.

Figure 2

The amplitude profile as a function of orbital phase ${\varphi }_{\text{orbit}}$. The orbital parameters are $R_{\text{orb}}={10}^9\mathrm{m}$, $R_{\text{lens}}={10}^6\mathrm{m}$, and ${\theta }_{\text{tilt}}=0.5(R_{\text{lens}}/R_{\text{orb}})$. We chose $\lambda =50\mathrm{m}$, which is about $f=6\mathrm{MHz}$, such that both the magnification envelope and the interference pattern are visible. The GHz observation will have a denser interference pattern (by a factor of hundreds).

Figure 3

The top panel is the standard two-dimensional interference pattern. White regions are peaks. The vertical axis is the wavelength in meters, which scans over frequency channels $(1\pm {10}^{-3})\mathrm{GHz}$. The horizontal axis is the orbital phase ${\varphi }_{\text{orb}}$. Its range is 10% of the full magnification envelope $\mathrm{\Delta }{\varphi }_{\text{amp}}$, which is about 0.1 sec, given the orbital parameters of the Hulse–Taylor binary. The middle panel shows how a long pulse illuminates a segment near the center. The bottom panel shows how multiple short pulses illuminate different vertical lines, along which we will get several one-dimensional interference patterns. We assume a uniform intensity across channels.