Weak gravitational lensing: A compact object with arbitrary quadrupole moment immersed in plasma

We study weak gravitational lensing around a compact object with arbitrary quadrupole moment in the presence of plasma. The studied compact objects are considered to be spherically symmetric. The additional parameter $\epsilon$ regulating the quadrupole moment in the metric alters the deflection angle of light rays along with the plasma parameters. In the vacuum, the number of images due to the presence of the parameter $\epsilon$ increases and causes the increase of the magnification of the image source. The effects of uniform and nonuniform plasma on gravitational lensing around the compact object are also studied.

Figure 1

The dashed line corresponds to deflection for nonuniform plasma with power-law electron density $N(r)=N_0/r^3$. The electron density at the radial coordinate $r=3M$ is set at ${10}^{-4}{\mathrm{cm}}^{-3}$. The dotted line corresponds to a uniform plasma distribution with the electron density $1.3\times {10}^{-4}{\mathrm{cm}}^{-3}$. In all cases, the photon frequency is $4\times {10}^{10}\mathrm{Hz}$. The solid line corresponds to deflection without plasma and quadrupole correction (Schwarzschild limit).

Figure 2

The dashed line corresponds to deflection for nonuniform plasma with power-law electron density $N(r)=N_0/r^3$. The electron density at the radial coordinate $r=3M$ is set at ${10}^{-4}{\mathrm{cm}}^{-3}$. The dotted line corresponds to a uniform plasma distribution with the electron density $1.3\times {10}^{-4}{\mathrm{cm}}^{-3}$. The photon frequency is always $4\times {10}^{10}\mathrm{Hz}$. The solid line corresponds to deflection without plasma.

Figure 3

The solid lines correspond to the total magnification under the effects of quadrupole correction parameter $\epsilon$.

Figure 4

The solid lines correspond to the total magnification under the effects of quadrupole correction parameter $\epsilon$.