π What is Redshift?
Redshift is a phenomenon where electromagnetic radiation (like light) from an object undergoes an increase in wavelength. This means the light shifts toward the red end of the spectrum. It's usually caused by the object moving away from the observer (Doppler effect) or by the expansion of the universe (cosmological redshift).
π History and Background
The concept of redshift emerged from astronomical observations in the early 20th century. Vesto Slipher's measurements of the redshifts of spiral galaxies provided crucial evidence for the expanding universe. Edwin Hubble later connected these redshifts with the distances to the galaxies, formulating Hubble's Law.
β¨ Key Principles
- π Wavelength Shift:
Redshift ($z$) is defined as the fractional change in wavelength: $z = (\lambda_{observed} - \lambda_{emitted}) / \lambda_{emitted}$, where $\lambda_{observed}$ is the observed wavelength and $\lambda_{emitted}$ is the emitted wavelength.
- π¨ Doppler Effect:
For relatively small velocities, the Doppler redshift is given by: $z \approx v/c$, where $v$ is the velocity of the object and $c$ is the speed of light.
- π Cosmological Redshift:
In an expanding universe, the cosmological redshift is related to the scale factor $a$ of the universe: $1 + z = a_{observed} / a_{emitted}$.
π’ Calculating Redshift: Step-by-Step
- π Obtain Spectra:
Acquire the spectrum of the object (e.g., a galaxy) you want to study.
- π§ͺ Identify Spectral Lines:
Look for recognizable spectral lines (e.g., Hydrogen-alpha at 656.3 nm) in the observed spectrum.
- π Measure Observed Wavelength:
Measure the observed wavelength ($\lambda_{observed}$) of a specific spectral line.
- π Determine Emitted Wavelength:
Find the rest-frame (emitted) wavelength ($\lambda_{emitted}$) of the same spectral line from laboratory measurements.
- β Calculate Redshift (z):
Use the formula: $z = (\lambda_{observed} - \lambda_{emitted}) / \lambda_{emitted}$.
- π‘ Interpret the Result:
A positive $z$ indicates redshift (object moving away), while a negative $z$ indicates blueshift (object moving towards).
π Real-world Examples
Example 1: A hydrogen-alpha line is observed at 660 nm from a distant galaxy. The rest-frame wavelength is 656.3 nm. Calculate the redshift.
Solution:
$z = (660 - 656.3) / 656.3 = 0.0056$
Example 2: A quasar has a redshift of $z = 2$. What was the scale factor of the universe when the light was emitted compared to now?
Solution:
$1 + z = a_{observed} / a_{emitted}$
$1 + 2 = a_{observed} / a_{emitted}$
$a_{emitted} = a_{observed} / 3$
The universe was 3 times smaller when the light was emitted.
Π·Π°ΠΊΠ»ΡΡΠ΅Π½ΠΈΠ΅
Understanding redshift is fundamental in astronomy and cosmology. It allows us to measure the velocities and distances of celestial objects, study the expansion of the universe, and probe the distant past. By following the steps outlined above, you can calculate redshift and gain insights into the cosmos!