How to measure distance to black hole?

Measuring distances to astronomical objects helps us understand the location of the object in the space. The Space is very vast. The distance of an object from Earth helps us define the object in one of the many ways. An astronomical object can be identified by us by defining its mass, shape, size and distance (location). We saw how the distance of planets and stars that are fairly close to us can be found out by using simple geometry i.e; the parallax method!
Below is the parallax Method-


However such methods like parallax or other methods to find distance of distant stars can be applied only to shining or visible objects!
Black Hole as we know is Black(reflects or emits no light; only absorbs). Also, Black hole has no defined size! Black hole by definition is the mass confined in a singularity or single point. The distance from singularity where an object just escapes its pull is called the EVENT HORIZON. Within the event horizon, no object can escape the pull of black hole; not even light.
Astronomers use several methods to find distance to objects in space by determining the amount and intensity of light coming from them or using their size. But such methods cannot be applied to Black holes.

As seen above the parallax triangle made by Earth and Sun, for a black hole, the base of the triangle is the distance between the the black hole and the dust cloud surrounding it. We know black holes suck matter. Hence, gases near the event horizon of black holes suffer huge pull and hence have high temperatures which makes them glow at such temperatures, When the gas just near the event horizon glows, it emits light. This initial pulse at the event horizon is noted. This light then travels through the dust clouds around black holes that makes the clouds light up. The final signal is also noted from these clouds.

The time lag between initial pulse and final signal gives us the base of this triangle! This technique is called Reverberation Mapping.

The angular size or the angle subtended by clouds to Earth can be found easily by devices called interferometers that determine even small angles.

By solving this triangle, the distance to Black Hole can be found out.

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