Redshift, a key concept in cosmology, occurs when light from distant objects shifts towards longer wavelengths. This phenomenon, caused by the Doppler effect and cosmic expansion, provides crucial evidence for our expanding universe.
Measuring redshift allows astronomers to calculate galaxy distances and velocities, revealing the universe's structure and evolution. Hubble's law, linking redshift to distance, laid the foundation for modern cosmology and the Big Bang theory.
Redshift and Cosmological Expansion
Redshift causes and definition
- Redshift occurs when spectral lines shift towards longer wavelengths (red end of the spectrum) in the electromagnetic spectrum
- Observed wavelength is longer than the emitted wavelength
- Observed frequency is lower than the emitted frequency
- Causes of redshift include:
- Doppler effect
- Occurs when the light source moves away from the observer
- Emitted light wavelength stretches due to the relative motion (ambulance siren pitch change)
- Cosmological expansion
- Caused by the expansion of the universe itself
- Space expansion stretches the wavelength of light traveling through it
- Not due to relative motion between the source and observer, but rather the expansion of space itself (rubber sheet analogy)
Redshift-distance relationship
- Redshift directly relates to the distance of celestial objects
- Farther objects have greater redshifts (distant galaxies vs. nearby stars)
- Hubble's law describes the relationship between redshift and distance
- $v = H_0 \times d$
- $v$ represents the galaxy's recessional velocity
- $H_0$ represents the Hubble constant, the current expansion rate of the universe
- $d$ represents the distance to the galaxy
- The redshift-distance relationship results from the expansion of the universe
- As the universe expands, farther galaxies recede faster, resulting in greater redshifts (Andromeda vs. Abell 2744)
Galaxy recessional velocity calculations
- Calculate a galaxy's recessional velocity using the redshift formula
- $z = \frac{\Delta \lambda}{\lambda_0} = \frac{\lambda_{obs} - \lambda_0}{\lambda_0}$
- $z$ represents the redshift
- $\Delta \lambda$ represents the change in wavelength
- $\lambda_0$ represents the emitted (rest) wavelength
- $\lambda_{obs}$ represents the observed wavelength
- For small redshifts ($z << 1$), approximate the recessional velocity using the non-relativistic Doppler formula
- $v = c \times z$
- $v$ represents the recessional velocity
- $c$ represents the speed of light
- $z$ represents the redshift
- For large redshifts ($z \geq 1$), use the relativistic Doppler formula
- $v = c \times \frac{(1 + z)^2 - 1}{(1 + z)^2 + 1}$
Evidence for universe expansion
- Redshift measurements of galaxies show a consistent relationship between distance and redshift
- Farther galaxies have higher redshifts, indicating faster recession (Hubble Deep Field)
- The observed redshift-distance relationship is consistent with the predictions of an expanding universe
- In a static universe, there would be no systematic relationship between redshift and distance
- Edwin Hubble's discovery of the redshift-distance relationship provided the first observational evidence for the expansion of the universe
- This discovery led to the development of the Big Bang theory, describing the universe's origin and evolution
- Other observations further confirm the expansion of the universe, as evidenced by redshift measurements
- Cosmic microwave background radiation (CMB)
- Abundance of light elements in the universe (primordial nucleosynthesis)
- Large-scale structure of the universe (galaxy clusters and superclusters)