microlensing

The Basics of Microlensing

In microlensing, the light bending occurs through the effect predicted by Einstein's theory of General Relativity. When a massive object passes near a line of sight to a more distant star, it creates a momentary increase in the star's apparent brightness. This is often detectable even though the lensing star itself is too faint to be seen. The fundamental concept can be explained as follows:

To understand this better, consider the lens equation in gravitational lensing, given as:\[\theta = \theta_S + \frac{4GM}{c^2}\frac{\theta - \theta_L}{|\theta - \theta_L|^2}\]Where:

• \(\theta\) is the observed angular position of the source.
• \(\theta_S\) is the actual angular position of the source.
• \(\theta_L\) is the angular position of the lens.
• \(G\) is the gravitational constant.
• \(M\) is the mass of the lens.
• \(c\) is the speed of light.

Applications and Observations

Microlensing has become a powerful tool in the field of astrophysics for several reasons. It is especially useful in the study of compact dark objects, like black holes or planets, because it does not depend on the light emitted by the lens itself. Instead, it relies on the gravitational effects produced by the intervening mass. This has led to several key applications, such as:

Gravitational Microlensing Explained

At its core, gravitational microlensing is a celestial event that harnesses the power of gravity to alter the path of light. This phenomenon takes place when a massive object, such as a star or planet, aligns with a distant background source and an observer, causing the light from the source to be deflected and magnified. This results in a temporary increase in the source's brightness as seen from Earth.

How Microlensing Works

Microlensing is an application of Einstein’s General Relativity, which posits that massive objects can warp spacetime. When a lens, like a star, moves near the line of sight between Earth and a distant star, its gravitational field bends the light. This creates a ring-shaped image when viewed through a telescope, depending on the alignment.

Mathematical Representation

The lensing effect can be described using the lens equation:\[\theta = \theta_S + \frac{4GM}{c^2}\frac{\theta - \theta_L}{|\theta - \theta_L|^2}\]In this equation:

• \(\theta\) is the observed angle of the source.
• \(\theta_S\) is the true position angle of the source.
• \(\theta_L\) denotes the lens position angle.
• \(G\) is the gravitational constant, \(6.674 \times 10^{-11} m^3 kg^{-1} s^{-2}\).
• \(M\) is the mass of the lensing object.
• \(c\) is the speed of light, \(2.998 \times 10^8 m/s\).

Microlensing Technique in Astrophysics

In the vast expanse of the universe, microlensing serves as a crucial technique in understanding celestial bodies and their interactions. It leverages the gravitational field of massive objects to act as a lens, bending and focusing light from more distant sources.

Understanding Microlensing in Astrophysics

When a massive object, such as a star or planet, passes near the line of sight between an observer and a distant star, its gravity bends and magnifies the light of the background star. This temporary increase in brightness can be detected from Earth, allowing astronomers to study objects that might otherwise be invisible.

Mathematics Behind Microlensing

The mathematical framework of microlensing can be grasped through the lens equation, which describes how light is deflected by gravity:\[\theta = \theta_S + \frac{4GM}{c^2}\frac{\theta - \theta_L}{|\theta - \theta_L|^2}\]Where:

• \(\theta\) is the observed angle of the light source.
• \(\theta_S\) is the true angle of the source.
• \(\theta_L\) is the angle of the lensing object.
• \(G\) is the gravitational constant \(6.674 \times 10^{-11} m^3 kg^{-1} s^{-2}\).
• \(M\) represents the lens mass.
• \(c\) is the speed of light \(2.998 \times 10^8 m/s\).

Astrometric Microlensing Basics

Astrometric microlensing is a sophisticated phenomenon in astrophysics that allows for the study of celestial bodies through gravitational lensing effects. It is part of the broader category of gravitational lensing, which bends light from distant stars due to the gravitational field of a foreground mass.

Principles of Astrometric Microlensing

Unlike traditional microlensing, which measures changes in brightness, astrometric microlensing measures the shift in position of a star caused by the gravitational influence of a massive object passing in front of it. This method provides crucial insights into mass distribution and distances between celestial objects.

Mathematical Framework

The changes in the angular position of the light source during microlensing can be predicted by the lens equation, modified for astrometric shifts: \[\delta\theta = \frac{\theta_E^2}{\theta_S} \]Where:

• \(\delta\theta\) is the shift in the observed position.
• \(\theta_E\) is the Einstein radius, describing the ring's angular radius in perfect alignment.
• \(\theta_S\) denotes the angular separation between the observer, lens, and source.