8-April-2011: Quasar 3C273: determination of redshift

Jan Preuss, Manfred Rudolf

In the context of a seminar paper at school Jan Preuss has analyzed the spectra of QSOs (Quasi-stellar objects, formerly known as quasars). These spectra were obtained from SDSS data.
SDSS (Sloan Digital Sky Survey) is a survey carried out over 8 years in several steps. SDSS has identified more than one hundred thousand quasars and has analyzed and published the spectral data. Jan's work mainly concerns the correlation of emission lines using software based on Mathematica. Manfred Rudolf has photographed a spectrum of the QSO 3C273 for comparison. We analyze this spectrum in order to determine its redshift.

Unfortunately, SDSS has not published a spectrum for 3C273. Hence, comparison data could only be taken from NTT/EMMI http://isdc.unige.ch/www/3c273#emmi.

3C273, also known as PGC41121, is one of the nearest and brightest quasars, located in the constellation of Virgo, at R.A. 12h 29m 07s, Decl. +0203'11", and having a brightness of 12.8 mag. The sky map (Guide 8) shows the region around 3C273. The rectangular frame corresponds to the field of view of the imaging camera.

CCD image showing the quasar. Nothing special can be seen, the object looks like an ordinary star. 7 April 2011, ca. 22:30 UT, Telescope C11, Camera SBIG ST10, 20 exposures 30s. The field of view is ca. 18x12 arcmin.

Spectra of 3C273 and nearby stars have been obtained by placing a transmission grating with 200 grooves/mm just before the CCD camera. The camera has been rotated 90 counterclockwise (north is to the left) so that the spectrum of the quasar is in parallel to the long axis of the image and does not interfere with other star images. The brightest star near the bottom, marked with "S" (PPM 158889, 10.3 mag, spectral class F5) can be used as reference star for calibrating the spectrum.
8. April 2011, C11, ST10, 10x180s.

The spectrum of 3C273 has been cut out, and the "sky background", a portion of the image immediately below the spectrum, subtracted from the spectrum of 3C273. This eliminates the signal of the background sky, and also the brightening in the image near the right border which was caused by the grating.

In the graph below showing the intensity of the spectrum, some peaks of emission lines can be recognized: hydrogen-alpha, marked with "2", hydrogen beta and oxygen (3), and a weak emission of hydrogen gamma (4). The oversaturated peak to the far left is the zero order image of the quasar.

For evaluation, the spectrum of 3C273, the spectrum of the reference star S in the same image as the quasar, and a spectrum of Vega (alpha Lyrae) have been arranged so that the center points of the zero-order images of the "stars" are on a vertical line. The spectrum of Vega has been recorded with the same equipment, but one day later. As Vega shows prominent hydrogen lines, its spectrum can assist to identify the lines in the other spectra.

Turning to the spectrum of Vega, we see - to the far right - the dark absorption band of atmospheric oxygen (Fraunhofer A-band), marked with "1". Then, from right to left, the absorbtion lines of hydrogen (balmer series) can clearly be seen, starting with hydrogen alpha (2) up to hydrogen epsilon (6). The same lines, also far weaker and blurred, can be seen in the spectrum of the reference star S.

Now, by correlating the wavelength of those lines to their position in the reference spectra, a scale can be determined. Since the correlation is almost perfectly linear, the scale factor is equal to the quotient of wavelength and pixel number subtracted by the center of the zero-order image. The median value of the most prominent Balmer lines (no. 2 – 6), approximately 10.714 ngstrms per pixel is applied to the spectrum of 3C273.

The redshift value z is defined as the relative difference between observed and emitted wavelength:
    λobs – λemit
z = ———————————
The emitted wavelength is assumed equal to the laboratory-measured wavelength. As line center we take the wavelength assigned to the local maximum pixel in the region of the assumed emission line. The observational error is therefore equal to the wavelength difference between 2 pixels, 10.714 .

linespectral valuelaboratory valueredshift
7606.9 10.7 6564.61 0.1588 0.0016
5614 10.7 4862.68 0.1545 0.0022
7607 10.7 4341.68 0.1549 0.0025

These results match the very well.

The following figure shows a comparison between the stronger normalized NTT/EMMI data and our recorded spectrum:

The NTT/EMMI recording was reported in A historic jet-emission minimum reveals hidden spectral features in 3C 273 by Türler M., Chernyakova M., Courvoisier T. J.-L., et al., 2006, A&A 451, L1-L4

For non-relativistic redshifts
z ≈ —
applies, where v is the velocity of the emitter and c is the speed of light. According to this formula the 3C273 moves away from us with a velocity of ≈ 4.73×107 ms-1. By dividing this by the Hubble constant (3.2×10-8 s-1) we calculate a distance of 1.48×1025 m = 1.56×109 ly.

However, when velocities in the range of 107 are concerned, relativistic effects must be regarded. The relativistic redshift is calculated by the formula:
 v + c 
z + 1 = ————————
        √ v - c 
The resulting velocity is 4.37×107 ms-1, the distance is 1.36×1025 m = 1.44×109 ly, which also complies with the literature value.