Image of a wormhole with an arbitrary throat profile
We investigate the observable signatures -- the shadow, the throat silhouette, and the image of a thin accretion disk -- for a family of static, spherically symmetric wormholes with an arbitrary throat profile. First, we derive expressions for the shadow radius, the throat silhouette radius, and the photon energy shift for a general static, spherically symmetric metric. Then we apply these results to a specific wormhole metric containing three free parameters: the throat radius~$a$, the throat length~$λ$, and the parameter~$u_0$ that controls the depth of the gravitational well. We numerically obtain the shadow and silhouette radii as functions of $λ$, $u_0$, and $a$, construct accretion disk images for three representative parameter sets, and compare the results with those for a Schwarzschild black hole. We find that there exist sets of parameters $a$, $λ$, $u_0$ such that the wormhole shadow and throat silhouette radii coincide with the shadow and event horizon silhouette of a Schwarzschild black hole of the same mass. Nevertheless, the accretion disk images of these objects differ substantially. In wormhole images, the Doppler effect plays a major role, not the gravitational redshift. As a result, the accreting wormhole images appear brighter.