Spectroscopy
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Measuring the redshift of 3C 273 – The Brightest Quasar
3C 273 is a quasar located in the constellation of Virgo. It is the brightest quasar visible from Earth, and was the first quasar to have its spectral redshift identified as such, by Dr. Maarten Schmidt in 1963 with the Hale 200 inch reflector at the Palomar Observatory.
A quasar is an extremely luminous active galactic nucleus (AGN), powered by a supermassive black hole. Gas in the accretion disc surrounding the black hole falls inwards and releases enormous amounts of electromagnetic radiation. As a result, quasars are the most luminous objects in the Universe and outshine their host galaxies by many orders of magnitude.
The Universe is expanding equally in all directions and this makes distant objects recede from us with enormous velocities. In the case of quasars, their relative velocities amount to a significant fraction of the speed of light, and their spectra therefore appear heavily redshifted due to the Doppler-effect. This cosmological redshift is surprisingly easy to measure with amateur equipment.
For 3C 273 I acquired 13x 300s exposures through a StarAnalyzer spectral grating, mounted in the filter wheel of my QSI683 CCD camera. This relatively short exposure, taken under a first quarter Moon, was more than sufficient to capture the brightest Hydrogen emission lines in the spectrum.
How to measure the redshift and distance:
To measure the distance and redshift of the quasar we can use the following method: The quasar spectrum image is loaded into a spectral analysis program such as RSpec. Here the quasar spectrum is firstly calibrated against another spectrum of a nearby reference star (with negligible redshift). In my spectrum the Balmer lines for H-Alpha and H-Beta appear prominently as strong emission features and there is also a hint of the H-Gamma line. The observed peak wavelengths (λ) of the emission lines is then identified, and their offset relative to the true emitted wavelengths is calculated. In my spectrum image I measured the following wavelength shifts:H-Alpha: 7674Å(observed) - 6563Å(emitted) = 1111Å.
H-Beta: 5692Å(observed) - 4861Å(emitted) = 831Å.
H-Gamma: 5083Å(observed) - 4340Å(emitted) = 743Å.
To calculate the redshift z we can first use the classical formula:
z = λ(observed) - λ(emitted) / λ(emitted)
For the three emission line offsets we get an average z = 0.17. This number is significantly higher than the officially reported value of z = 0.158, but this is only because 3C 273 is moving away from us at such great velocity and the classical formula does not take relativistic speeds into account.
We can calculate the relativistic velocity of 3C 273 using the formula v = c * ((z+1)2-1) / ((z+1)2+1), and get 46,787 km/s.
This means that 3C 273 is receding from us at nearly 47,000 km/s, which is over 15% of the speed of light! Now we can use the relativistic velocity to calculate a proper relativistic redshift using z = v/c and we get z = 0.156 which is very close to the officially reported value of z = 0.158339 in the NASA/IPAC Extragalactic database.
Lastly, using Hubble's law, we can calculate the distance to 3C 273 as d = v / H0. Assuming the current best estimate for Hubble's constant H0 = 69.8(km/s)/Mpc we get 670.31 Mpc or roughly 2.186 billion light years!
Because of their incredible luminosity, quasars are some of the most distant objects visible to us on Earth. When we observe such distant objects we also see back in time, because their light has taken very long to reach us. So we are really viewing 3C 273 as it appeared over 2 billion years ago.
3C 273 is one of the most luminous quasars known, being 4 trillion times more luminous than the Sun and having an absolute magnitude of −26.7, meaning that if it were only 30 light years from us it would appear as bright in the sky as the Sun!
It is truly a remarkable object and it is fascinating that the distance to a remote quasar can be estimated quite accurately using a modest amateur telescope and a simple diffraction grating!
