Redshift is a fundamental concept in astronomy describing the stretching of light waves toward the red end of the electromagnetic spectrum. This phenomenon occurs when a light source moves away from an observer, causing the light’s wavelength to increase and its frequency to decrease. Quantifying this shift allows astronomers to determine the movement of stars, galaxies, and the overall expansion of the universe. Analyzing the light from distant celestial objects provides information about the object’s velocity and distance, which is the primary method used to map the cosmos.
The Physics Behind Wavelength Shift
The physical mechanism responsible for most observed redshift is the Doppler effect, which applies to all waves, including light. When a light source moves away from an observer, the waves are stretched out, resulting in a longer wavelength and a shift toward the red end of the spectrum. This is similar to the sound of a siren dropping in pitch as an ambulance drives away. Conversely, an object moving toward the observer causes the wavelengths to compress, resulting in a blueshift toward shorter wavelengths.
The Doppler effect for light relates directly to the relative speed between the source and the observer. Greater recession velocity results in more stretched light waves and a larger redshift. This wavelength change is measured by observing the distinct spectral lines created by elements like hydrogen and helium in a star’s or galaxy’s light. Scientists compare the observed, shifted lines with the known, unshifted lines measured in a laboratory on Earth, as every element has a unique spectral signature.
The Primary Formula for Calculating Redshift
Redshift is quantified using a dimensionless value denoted by the letter \(z\), which represents the fractional change in the light’s wavelength. The primary formula for calculating redshift from wavelengths is:
$\(z = \frac{\lambda_{observed} – \lambda_{rest}}{\lambda_{rest}}\)$
In this equation, \(\lambda_{observed}\) is the wavelength of a specific spectral line measured by the observer. \(\lambda_{rest}\) is the known, unshifted wavelength of that same spectral line measured in a lab on Earth. The difference between the observed and rest wavelengths represents the total shift. Dividing this shift by the rest wavelength provides the fractional change \(z\).
For example, if a hydrogen line has a rest wavelength (\(\lambda_{rest}\)) of 656.3 nanometers (nm) but is observed from a distant galaxy at 721.9 nm (\(\lambda_{observed}\)), the calculation is straightforward. Subtracting the rest wavelength from the observed wavelength yields a shift of 65.6 nm. Dividing this 65.6 nm shift by the original 656.3 nm rest wavelength gives a redshift \(z\) of approximately 0.10. A positive \(z\) value indicates a redshift (movement away), while a negative \(z\) value indicates a blueshift (movement toward the observer).
The calculated \(z\) value is independent of the specific spectral line used, as the ratio of the observed wavelength to the rest wavelength remains constant for a given object. The accuracy of \(z\) relies on precisely identifying and measuring multiple spectral lines. Once calculated, \(z\) serves as the foundation for determining the object’s velocity and distance.
Interpreting the Result: Velocity and Distance
The calculated redshift value (\(z\)) is immediately translatable into the object’s recession velocity. For objects moving significantly slower than the speed of light (small \(z\) values, typically \(z < 0.1[/latex]), a simplified non-relativistic Doppler formula can be used: [latex]v \approx z \times c[/latex], where [latex]v[/latex] is the velocity and [latex]c[/latex] is the speed of light. This approximation allows for a quick estimate; for instance, a [latex]z[/latex] of 0.10 implies a recession velocity equal to 10% of the speed of light. For galaxies with high redshift values, the velocity approaches the speed of light, and the simpler formula becomes inaccurate. In these cases, the full relativistic Doppler formula, which accounts for special relativity, must be used. For very distant galaxies, the redshift is primarily a result of the expansion of space itself, known as cosmological redshift, rather than simple motion. For these cosmologically distant objects, the [latex]z[/latex] value determines distance through Hubble's Law. This law states that a galaxy's recession velocity is proportional to its distance from us: [latex]v = H_0 \times d[/latex]. [latex]H_0[/latex] is the Hubble constant, representing the current expansion rate of the universe. By combining the velocity (derived from [latex]z[/latex]) with the Hubble constant, astronomers calculate the distance ([latex]d[/latex]) to the galaxy, mapping the large-scale structure of the cosmos.
Types of Redshift and Their Distinct Causes
Astronomers recognize three distinct physical origins for redshift, even though the calculation of the [latex]z\) value remains consistent.
Doppler Redshift
This results from the relative motion of a light source through space, such as a star orbiting a galactic center. This is the classic wave-stretching effect caused by physical movement away from the observer.
Cosmological Redshift
This is the most common type for distant galaxies and arises from the expansion of the universe itself. As light travels across space, the fabric of space expands, stretching the light wave along with it. This is stretching of space between the source and the observer, not motion through space.
Gravitational Redshift
This is a prediction of Einstein’s theory of general relativity. This shift occurs when light attempts to escape a strong gravitational field, such as that near a black hole or a massive star. The light loses energy as it climbs out of the gravity well, manifesting as an increase in wavelength.