Finding earth like planets from the comfort of our own planet

Gravitational lensing results from the fact that General Relativity describes our universe: mass bends light and can function in effect like a lens, bending light in ways that can be used to infer the mass distribution itself. Gravitational microlensing is due to this same effect, but refers to the detection of objects which are of much smaller size than those objects typically able to be detected by observational astronomers.  If a distant powerful light source has a massive object in the way along our line of sight  we can detect the object in the way independent of its luminosity, and in fact in a wavelength independent manner.  If the object doing the lensing is massive enough, we can resolve the actual displacement of the lens. If the object  doing the lensing is small in mass however as in the microlensing scenario (a planet for example), we can only detect an apparent brightening of the source of the light as the position of the object doing the lensing changes. Thus the position of the lens must change over time, and we must observe this as a function of time, for us to be able to use the microlensing technique, meaning it must be applied to objects that move on a human time scale (seconds to years) .

This technique is influenced by

• the size of the light source equations are more easily analyzed if we approximate it as a point, but this approximation gets worse and worse for larger sources-a problem called the finite-source effect
• parallax for longer lasting events, we have to consider the fact that the Earth is moving around the Sun
• the mass distribution of the object doing the lensing

In the short paper Reevaluating of the Feasibility of Ground-based Earth-mass Microlensing Planet Detections  Jung et. al. 2014 recap in Figure 2, the fact that bigger sources of light actually result in a decreased magnification of the object lensing their light in simulation. The top and bottom of this Figure have three numbered plots decreasing in size of the source for the same lens: Giant, Subgiant, and Main sequence stars from top to bottom respectively. I’ve included a cutout here, credit to the Jung et. al. 2014

The bump for the Giant stars  is lower than the subgiant is lower than the main sequence. This is due to the finite-source effect the giant stars are further from the point-source approximation. Previously these results alone were used to argue that detection of earth like planets (objects on the order of the mass of the earth) from the earth itself would be infeasible given the sensitivity of earth based instruments and the signal strength.

However, this paper revises that result by considering that there is a competing effect, going in the opposite direction, in which they consider the fact that larger source stars result in increased photometric precision. This ends  up more than compensating for the finite-source effect, depicted in Figure 3 which shows the probability of detecting Earth-mass planets for sources of light including giant, subgiant, and main sequence stars. We see that considering this, the giant and subgiant light sources actually do offer the possibility to lens Earth mass planets in a manner detectable from Earth. Cutout included here, credit again to Jung et. al. 2014.