Gravitational Lens

Joachim Köppen Kiel/Strasbourg March 2013

This is a simple applet to show how a background star appears when seen through a gravitational lens, and to compute the gain in the flux from the stellar image.

On the left hand side we see the star, represented by the blue circle in its position relative to the gravitational lens, which is marked by its centre (cross) and whose actions are indicated by the Einstein ring (the black circle). You can grab with the mouse the star and drag it to the new position of its centre. Likewise the lens centre can be moved by grabbing any position inside the Einstein ring (except the area covered by the star). The right hand side shows the corresponding image via the lens.

The angular radius of the star can be specified in a text field near the top. It is given in units of the radius of the Einstein ring. For graphical reasons there are limits for this value. The radius of the Einstein ring (in radians) can be computed from

R_E = sqrt[(4 G M / cē) * (d_S-d_L)/(d_L d_S)]
with the lensing mass M and the distances d_L and d_S from the observer to the lens and the star, respectively. The fields at the top allow to enter these data. Hitting the enter key will display the ring's radius.

The field on the upper right displays the gain in the flux from the star as seen through the lens, with respect to the one seen without the lens.

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last update: Apr. 2013 J.Köppen