The Power of Tiny Distortions: Weak Lensing I
“Not only are we in the Universe, the Universe is in us” -Niel deGrasse Tyson.
As we have discussed earlier, a significantly heavy mass can divert the path of light and create lens-like imaging. Still, the only difference in this effect is that the distortion is due to the gravitational influence of the heavier body. This creates a distortion or shearing effect in the object's shape, helping us determine whether it's gravitationally lensed. This phenomenon is called gravitational lensing, which can be considered an accidental discovery as it was discovered while Eddington and his team were verifying Einstein's theory of general relativity in 1919. Gravitational lensing has since then been one of the most potent tools for cosmologists and astrophysicists in determining the existence of celestial objects that may be unobserved or not recognized to come into the foresight.
As we already know the categories of gravitational lensing (in case you forgot or need more reference, check GL I, II, III ), I would save time and directly dive into the introduction to weak lensing today.
Weak Lensing
Light sources: elliptic galaxies
Deflector: dark matterThe distribution of ellipticities of distant galaxies is statistically evaluated to obtain information on the surface density of intervening (dark) masses. 1989, the first observation of weak lensing by matter in galaxy clusters was made. 2000, the first sign of weak lensing by large-scale structure, or "cosmic shear," was discovered.
Weak Lensing refers to a subtle effect in which the light from distant galaxies is slightly deflected due to the gravitational influence of intervening matter along its path. This slight deflection leads to the distortion or shearing of the shape of the galaxies, providing valuable information about the distribution of mass in the universe. To understand the mathematics behind weak lensing, we need to consider the concept of gravitational potential. Gravitational potential is a scalar field that describes the gravitational influence at every point in space. We can approximate the gravitational potential in weak lensing as a small perturbation to the background geometry. Weak lensing can be mathematically described using the concept of linear approximation. In the linear approximation, we assume that the gravitational potential is small enough that we can neglect higher-order terms in the equation. This allows us to simplify the mathematical equations and make them more manageable for analysis. The shear tensor is one of the main mathematical tools used in weak lensing. The shear tensor is a mathematical quantity that describes the stretching and compression of an object caused by gravitational lensing. The shear tensor is the derivative of the displacement field, which measures the change in position due to gravitational lensing. The weak lensing mathematics involves applying the sudden-deflection approximation, where the continuous deflection along the light path is approximated by a series of discrete deflections at various points along the path. This approximation allows us to simplify the integral form of the lens equation and calculate the effects of weak lensing on the observed galaxy shapes. The weak lensing mathematics also involves using statistical techniques to analyze the distortion patterns in a large sample of galaxies. By studying the statistical properties of the distortions, we can extract valuable information about the underlying mass distribution and cosmological parameters.
Weak lensing involves the statistical analysis of distorted images due to matter's gravitational influence along the light path. To quantify this statistical distortion, researchers use various mathematical techniques. Some commonly used techniques include measuring the ellipticity of galaxies, which is a measure of their shape, and analyzing the power spectrum of the measured distortions.
Can Weak lensing probe dark matter existence?
Weak lensing has proven to be a powerful tool for probing the existence of dark matter. By measuring the gravitational effects of weak lensing on the shapes and positions of galaxies, scientists can infer the presence and distribution of dark matter in the universe (Huterer, 2010). Weak lensing has emerged as a valuable tool for studying dark matter. It allows us to directly observe the effects of dark matter on the observed galaxy shapes and infer its distribution in the universe. Weak lensing surveys are a promising avenue for distinguishing between General Relativity and alternative gravity theories, such as those incorporating extra dimensions. Weak lensing surveys play a crucial role in our understanding of the nature of dark matter and its distribution in the universe. Weak lensing surveys have the potential to provide strong evidence for the existence of dark matter.
Did You Know?
Professor Priyamvada Natarajan developed a groundbreaking framework for mapping dark matter on small scales within galaxy clusters using a combination of strong and weak lensing observations. This allowed for more precise and detailed measurements of dark matter distribution, offering valuable insights into its structure and formation. I remember I once stumbled upon her video on black holes, and her presence is something one can’t replace. Dr. Nataranjan proposed innovative methods for analyzing weak lensing data, including techniques for measuring galaxy shapes and accounting for intrinsic alignment effects. These methodologies improved the accuracy and sensitivity of weak lensing measurements, leading to more reliable constraints on cosmological parameters like dark matter and energy. Through her research and advocacy, Natarajan played a crucial role in establishing weak lensing as a vital tool for probing the Universe and understanding its evolution. Her work helped demonstrate the potential of weak lensing for constraining cosmological models and uncovering fundamental mysteries like the nature of dark matter and energy. Dr. Natarajan’s methodologies and insights have influenced the design and analysis of major ongoing and planned weak lensing surveys, such as LSST and Euclid. These surveys will collect vast amounts of data, further advancing our understanding of the Universe through weak lensing observations.
That’s it for today! Next week, I will try to bring up some research problems and talk about them here. I am attaching a few exciting reads. Till then, bye!!
