👽Galaxies and the Universe Unit 11 – Gravitational Lensing & Dark Energy

Key Concepts and Definitions

• Gravitational lensing: The bending of light by massive objects due to the curvature of spacetime
• Einstein's theory of general relativity predicts that massive objects can bend the path of light
• Dark matter: Invisible matter that does not interact with electromagnetic radiation but has gravitational effects on visible matter
• Dark energy: Hypothetical form of energy that permeates all of space and accelerates the expansion of the universe
• Cosmological constant ($\Lambda$): A term in Einstein's field equations representing the energy density of the vacuum of space
  • Thought to be equivalent to dark energy
• Critical density: The average density of matter required for the universe to eventually stop expanding
• Hubble-Lemaître law: Describes the relationship between the distance to a galaxy and its recessional velocity due to the expansion of the universe

Historical Background

• In 1915, Albert Einstein published his theory of general relativity, which laid the foundation for gravitational lensing
• In 1919, Arthur Eddington observed the deflection of starlight during a solar eclipse, confirming Einstein's predictions
• Fritz Zwicky, in 1937, proposed that galaxies could act as gravitational lenses
• Yakov Zel'dovich, in 1964, discussed the possibility of observing gravitational lensing by galaxies
• The first gravitational lens, Twin QSO 0957+561, was discovered in 1979 by Dennis Walsh, Robert Carswell, and Ray Weymann
• In 1998, observations of Type Ia supernovae revealed that the expansion of the universe is accelerating, leading to the concept of dark energy
  • Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess were awarded the 2011 Nobel Prize in Physics for this discovery

Gravitational Lensing Explained

• Gravitational lensing occurs when a massive object (the lens) is located between the observer and a distant light source
• The lens can be a star, a galaxy, or a cluster of galaxies
• The gravitational field of the lens bends the light from the distant source, causing it to appear distorted or multiple images to form
• The amount of deflection depends on the mass of the lens and the relative positions of the source, lens, and observer
• Gravitational lensing is a consequence of Einstein's theory of general relativity
  • The presence of mass curves spacetime, and light follows the straightest possible path (geodesic) in this curved spacetime
• Gravitational lensing can magnify distant sources, allowing astronomers to study objects that would otherwise be too faint to observe
• Gravitational lensing provides a way to map the distribution of dark matter in the universe

Types of Gravitational Lensing

• Strong lensing: Occurs when the lens is massive enough and well-aligned with the source to create multiple images, arcs, or Einstein rings
  • Examples include the Horseshoe Einstein Ring and the Twin Quasar (QSO 0957+561)
• Weak lensing: Occurs when the lens is not perfectly aligned or is less massive, causing subtle distortions in the shape of background galaxies
  • Requires statistical analysis of many galaxies to detect
• Microlensing: Occurs when a compact object (star or planet) passes in front of a background star, causing a temporary brightening
  • Used to detect exoplanets and study the distribution of dark matter in the Milky Way galaxy
• Cosmic shear: The distortion of images due to the large-scale structure of the universe
  • Caused by the cumulative effect of all matter (dark and visible) along the line of sight
• Time delay: Occurs when light from a lensed source takes different paths, arriving at the observer at different times
  • Can be used to measure the Hubble constant and study the expansion of the universe

Observational Techniques

• Hubble Space Telescope (HST): High-resolution imaging has been crucial for studying gravitational lenses
• Ground-based telescopes with adaptive optics: Compensate for atmospheric distortions, allowing for sharp images of lensed systems
• Radio interferometry: Used to study lensed quasars and measure time delays between lensed images
• Spectroscopy: Helps confirm the lensing nature of a system by measuring the redshift of the lens and the source
• Gravitational lens modeling: Computational techniques used to reconstruct the mass distribution of the lens and the properties of the source
• Machine learning algorithms: Increasingly used to automatically detect and classify lensed systems in large astronomical datasets
• Upcoming facilities, such as the James Webb Space Telescope (JWST) and the Vera C. Rubin Observatory (LSST), will greatly enhance our ability to study gravitational lenses

Dark Energy: The Mysterious Force

• Dark energy is a hypothetical form of energy that permeates all of space and causes the universe's expansion to accelerate
• First proposed to explain observations of Type Ia supernovae, which indicated that the universe's expansion is accelerating
• Accounts for approximately 68% of the total energy density of the universe
• The nature of dark energy remains one of the greatest mysteries in modern cosmology
• The simplest explanation for dark energy is the cosmological constant ($\Lambda$) in Einstein's field equations
  • Represents the energy density of the vacuum of space
• Alternative theories include quintessence, phantom energy, and modified gravity
• Dark energy has a negative pressure, which causes the expansion of the universe to accelerate
• The presence of dark energy has implications for the ultimate fate of the universe (eternal expansion, Big Rip, etc.)

Applications in Cosmology

• Gravitational lensing provides a way to directly measure the mass of galaxies and clusters, including dark matter
• Weak lensing surveys can map the large-scale structure of the universe and constrain cosmological parameters
• Time delays in strongly lensed systems can be used to measure the Hubble constant independently of other methods
• Gravitational lensing can test alternative theories of gravity and the nature of dark matter
• Studying the evolution of gravitational lens systems over cosmic time can probe the growth of structure in the universe
• Gravitational lensing can magnify distant galaxies, allowing astronomers to study the early universe and galaxy formation
• Cosmic shear measurements can constrain the properties of dark energy and test theories of modified gravity

Current Research and Future Directions

• Ongoing and upcoming gravitational lensing surveys, such as the Dark Energy Survey (DES) and the Euclid mission, aim to constrain the properties of dark matter and dark energy
• Improved modeling techniques, such as machine learning algorithms, are being developed to analyze the growing amount of gravitational lensing data
• Gravitational waves, detected by LIGO and Virgo, can also be gravitationally lensed, opening a new avenue for studying the universe
• Future facilities, such as the James Webb Space Telescope (JWST) and the Vera C. Rubin Observatory (LSST), will greatly expand our ability to detect and study gravitational lenses
• Combining gravitational lensing with other cosmological probes (CMB, BAO, Type Ia supernovae) will provide tighter constraints on cosmological parameters and the nature of dark matter and dark energy
• Studying the microlensing of stars in the Milky Way can reveal the presence of compact dark matter objects, such as primordial black holes
• Investigating the strong lensing of gravitational waves can test general relativity and alternative theories of gravity in extreme environments