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Cosmology
Table of Contents
Unit 6 Overview: The Expanding Universe and Hubble's Law
6.1 Hubble's discovery and the expansion of the universe
6.2 The cosmic distance ladder and measuring cosmic distances
6.3 Redshift and its relationship to expansion
6.4 The Hubble-Lemaître law and its implications

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6.2 The cosmic distance ladder and measuring cosmic distances

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Measuring cosmic distances is a crucial task in cosmology, using various methods like parallax, Cepheid variables, and Type Ia supernovae. Each technique works for different distance ranges, building upon one another to create a cosmic distance ladder.

This ladder allows astronomers to gauge distances from nearby stars to the farthest galaxies. Understanding these measurement techniques is essential for grasping the universe's vast scale and structure, from our local neighborhood to the observable universe's limits.

Measuring Cosmic Distances

Rungs of cosmic distance ladder

  • Parallax
    • Measures distances to nearby stars within the Milky Way galaxy up to about 1,000 light-years
    • Relies on the apparent shift in a star's position as Earth orbits the Sun (Proxima Centauri, Alpha Centauri)
  • Main sequence fitting
    • Determines distances to star clusters within the Milky Way galaxy up to about 50,000 light-years
    • Compares the observed properties of stars in a cluster to well-studied nearby clusters (Pleiades, Hyades)
  • Cepheid variables
    • Measures distances within the Local Group of galaxies up to about 20 million light-years
    • Utilizes the period-luminosity relationship of pulsating stars (Delta Cephei, Polaris)
  • Type Ia supernovae
    • Determines distances to galaxies beyond the Local Group up to billions of light-years
    • Relies on the consistent peak luminosity of exploding white dwarf stars (SN 1972E, SN 1006)
  • Hubble's law and redshift
    • Measures distances to the most distant galaxies and quasars up to the observable universe limit of about 46 billion light-years
    • Uses the relationship between a galaxy's recession velocity and its distance (GN-z11, ULAS J1342+0928)

Principles of cosmic distance measurement

  • Parallax
    • Measures the apparent angular shift in a star's position as Earth moves around the Sun
    • Larger parallax angles indicate closer stars while smaller angles suggest more distant stars
    • The parallax angle ($p$) in arcseconds and the distance ($d$) in parsecs are related by the equation $d = 1/p$
  • Cepheid variables
    • Pulsating stars that exhibit a well-defined relationship between their pulsation period and intrinsic luminosity
    • Longer pulsation periods correspond to higher intrinsic luminosities
    • By comparing the observed brightness to the intrinsic luminosity derived from the period, the distance can be calculated using the inverse square law
  • Type Ia supernovae
    • Exploding white dwarf stars that reach a consistent peak luminosity
    • Serve as "standard candles" due to their uniform intrinsic brightness regardless of distance
    • The distance is determined by comparing the observed brightness to the known intrinsic luminosity using the inverse square law

Limitations of distance measurement methods

  • Parallax
    • Limited to nearby stars as parallax angles become too small to measure accurately for distant objects
    • Requires precise measurements of tiny angular shifts, which can be affected by the proper motion of stars and the presence of unseen companion stars
  • Main sequence fitting
    • Assumes that star clusters have similar ages and compositions to well-studied nearby clusters, which may not always be the case
    • Affected by interstellar dust absorption and uncertainties in stellar evolution models
  • Cepheid variables
    • Requires the identification and monitoring of Cepheid stars in distant galaxies, which can be challenging
    • Affected by uncertainties in the period-luminosity relationship and variations in metallicity
    • Limited by the ability to resolve individual stars in distant galaxies
  • Type Ia supernovae
    • Relies on the assumption that all Type Ia supernovae have similar peak luminosities, which may not be strictly true
    • Affected by dust absorption along the line of sight and possible variations in supernova properties
    • Limited by the rarity of Type Ia supernova events in distant galaxies
  • Hubble's law and redshift
    • Assumes that the universe is homogeneous and isotropic on large scales, which is an approximation
    • Affected by peculiar velocities of galaxies and uncertainties in measuring precise redshifts
    • Limited by the difficulty in measuring redshifts for extremely distant and faint objects

Scale of universe via distance ladder

  • Each rung of the cosmic distance ladder builds upon the previous one, providing a foundation for measuring greater distances
    1. Parallax measurements calibrate the distances to nearby stars
    2. Main sequence fitting extends the distance scale to star clusters within the Milky Way
    3. Cepheid variables, calibrated using nearby stars, allow distance measurements to galaxies in the Local Group
    4. Type Ia supernovae, calibrated using Cepheid variables, extend the distance scale to distant galaxies beyond the Local Group
  • The overlapping distance ranges of the various methods ensure a continuous and consistent distance scale across the universe
  • By combining distance measurements from multiple methods, astronomers can determine distances to objects throughout the observable universe
  • The cosmic distance ladder enables the measurement of the Hubble constant, which relates the expansion velocity of the universe to its size and age
  • Ultimately, the cosmic distance ladder allows astronomers to comprehend the vast scale and structure of the universe, from nearby stars to the most distant galaxies and quasars