It’s time to get serious with my spectroscopy. 🙂
Introduction
With the moon full but very low in the sky, this is the perfect time to challenge myself by capturing and analysing a quasar. A quasar, short for quasi-stellar, is basically an extremely bright galaxy that is powered by the friction of matter quickly orbiting a supermassive black hole[1]https://en.wikipedia.org/wiki/Quasar. The luminosity of a quasar can be thousands of times brighter than an average galaxy, making them very bright for the far distances that they exist at. This also makes them ripe for amateur analysis. There are quite a few relatively bright quasars that are well within reach of amateur visual, photographic, and spectrographic means[2]http://spider.seds.org/spider/Misc/qso.html. In the northern hemisphere, there are several in the 14-16 magnitude range, making them approachable for the long exposure manual techniques I must employ with my Shelyak ALPY 600 spectrograph. Our goal is to capture a spectrum of this quasar of sufficient quality to allow us to unmistakably recognize elemental emission lines, and from these emission lines, determine the redshift, velocity, and distance of the galaxy.
I decided to start with QSO B1634+7037, also known as PG 1634+706[3]http://simbad.cds.unistra.fr/simbad/sim-id?mescat.velocities=on&Ident=%40364443&Name=QSO+B1634%2B7037. This quasar lives between Draco and Ursa Minor, just about 30° from the north celestial pole. This is the perfect time of year to observe this object.
You can view the quasar in the following image. Its coordinates are RA 16 34 29 DEC +70 31 32 (J2000).
Data Acquisition
I have the ALPY 600 spectrograph along with the guiding module[4]https://www.shelyak.com/produits/?lang=en. This allows me to use a science camera, in this case the monochrome ASI183MM, to capture the spectrum, and another camera, the color ASI183MC, to view the field. The guiding camera can accurately guide the telescope while the science camera takes exposures.
The first step is to mount the cameras to the spectrograph and focus them. Focusing them both is very easy and can be done on the bench. After that, the assembly can simply be installed in the telescope focuser. The science camera has active cooling, while the guide camera does not.
PHD2 is used for autoguiding. Before beginning acquisition, I slewed near the equator to calibrate with the guiding camera. After that was complete, I slewed to the star Thuban, placed it in the slit, and began guiding.
Thuban is a binary star system that has a primary spectral type of A0IV, making it a good candidate for creating an instrument response later in the data reduction process[5]Thuban was actually once the pole star, back around 2,000BC. It will become the pole star again around 20,000AD. https://en.wikipedia.org/wiki/Thuban#Pole_star. I took 200 short exposures of it.
Now, it was time to slew to the target. With a V-band magnitude around 14.66, it was readily apparent in my guide camera with exposures of just a few seconds. You can see the quasar and the spectroscope slit in the following image. I manually manipulated the mount until the quasar disappeared in the slit.
Once the target was within the slit, I started the autoguider to keep it there. Sharpcap was used to capture the data frames, which were 10 minute exposures at a gain of 300, 2x binning, and 0°C cooling. Before I knew it, the first exposure was ready,
The thin horizontal line near the center of the image is the quasar! The vertical lines are the spectrum of the atmosphere and light pollution. The starburst to the right is amp glow, an unfortunate flaw of the camera I am using[6]https://astronomy-imaging-camera.com/tutorials/what-is-amp-glow.html. The amp glow can be corrected later in the calibration phase. Twenty-four dark frames for the science camera were taken on the bench at the same set temperature of 0°C. The median of the dark frames shows the hot pixels and amp glow,
Over two nights, I was able to collect 44 frames, or a little over 7 hours of data.
Data Reduction
With all of the data collected, the first thing to do is to calibrate it. I began by using Siril to take a median of the dark frames. I then subtracted this master dark from each of the data frames to remove most of the hot pixels and amp glow. The manual registration in Siril was used to align the frames as well as I could by eye. Then, I did a simple sum stack of the frames. Here is a stretched view of the calibrated master data,
Since the exposures for Thuban were so short, at 478ms, I did not dark calibrate the data files. The master data files were then imported into BASS. I created an instrument response by dividing the Thuban profile by an A0-IV reference spectrum. I then manually created an instrument response from the resulting curve. My data on Thuban then matched the reference spectrum pretty well,
Now that I had calibration completed and a instrument response, I imported the quasar spectrum. At first, it did not look like much more than noise. Applying a low pass filter revealed a few humps in the chart, and gave me something to work with.
Spectral Analysis
But what are these humps? I cheated a bit by already knowing the redshift of this quasar from SIMBAD. So I started looking around at a chart of common element lines found in galaxies[7]http://astronomy.nmsu.edu/drewski/tableofemissionlines.html. The range of my spectroscope is around 350-800nm, a little more than the visual band. The Lyman series is still too short to be detected by my camera, and the Balmer series is way off the chart into the infrared[8]https://en.wikipedia.org/wiki/Hydrogen_spectral_series. So I needed to find something in the ultraviolet that would be redshifted enough to lie within the visible range, something between 170 to 350nm. There are quite a number of emission lines that have been observed in this range, many of them semi-forbidden[9]https://en.wikipedia.org/wiki/Forbidden_mechanism. These will be elements outside of the accretion disk of the supermassive black hole, elsewhere in the galaxy.
Within BASS, I took measurements of several obvious humps in the chart. I used Gaussian fitting to find the peak and the FWHM. Here are the results of the measurements,
Gauss fit : StdDv 4.63707 FWHM 10.87773 Mean 445.333nm R 40.9399
Gauss fit : StdDv 3.7283 FWHM 8.745927 Mean 654.016nm R 74.7794
Gauss fit : StdDv 7.01866 FWHM 16.46452 Mean 730.71nm R 44.3809So, I have peaks at 445.3, 654.0, and 730.7nm. I can take the ratios of these,
654.016 / 445.333 = 1.468599901646633
730.71 / 445.333 = 1.6408170964199824
730.71 / 654.016 = 1.1172662442509054As wavelengths change due to redshift, the ratios between them remain the same. This means we need to find elements whose ratios match the ones observed. Simple elements should be more common, such as carbon and oxygen. I found that C III] at 190.8nm and O III at 313.2nm matched my observed ratios. This led to finding Mg II] at 280.2nm. Finally, I could label the emission humps on my chart,
Here are the results of my measurements,
| Element | Rest (nm) | Observed (nm) | FWHM |
| C III] | 190.8 | 445.333 | 10.87773 |
| Mg II] | 280.2 | 654.016 | 8.745927 |
| O III | 313.2 | 730.71 | 16.46452 |
Now, let’s find the ratios of the elements at rest,
| Rest Ratios | |||
| C III] | Mg II] | O III | |
| C III] | 1 | ||
| Mg II] | 1.4685534591195 | 1 | |
| O III | 1.64150943396226 | 1.11777301927195 | 1 |
And let’s calculate the ratios of the observed means,
| Observed Ratios | |||
| C III] | Mg II] | O III | |
| C III] | 1 | ||
| Mg II] | 1.46859990164663 | 1 | |
| O III | 1.64081709641998 | 1.11726624425091 | 1 |
Looking pretty good, right? Let’s find the errors of the observations,
| Ratio Errors | |||
| C III] | Mg II] | O III | |
| C III] | 0.000E+00 | ||
| Mg II] | -4.644E-05 | 0.000E+00 | |
| O III | 6.923E-04 | 5.068E-04 | 0.000E+00 |
And the percentage errors,
| Ratio Error Percentages | |||
| C III] | Mg II] | O III | |
| C III] | 0.0000 | ||
| Mg II] | 0.0032 | 0.0000 | |
| O III | 0.0422 | 0.0453 | 0.0000 |
Wow, this spectrograph is impressively accurate! We have error percentages of less than half a tenth of a percent. And this likely could be attributed to the bounds I used to estimate the peaks.
So now that I am pretty confident in my measurements, let’s induce the information we really want. Since we now know the rest wavelengths of the emissions as well as the highly redshifted observed wavelengths, we can calculate the redshift,
z = \frac{\lambda_o - \lambda_e}{\lambda_e}where λe is the rest wavelength, and λo is the observed wavelength. We can also calculate the velocity that the object is moving away from us using the relativistic Doppler effect,
v = -c \frac{1-(\frac{\lambda_o}{\lambda_e})^2)}{1+(\frac{\lambda_o}{\lambda_e})^2)}where c is the speed of light. The rotational velocity of the galaxy is related to the FWHM of the emission lines,
v_{\textrm{rot}} = c \frac{\Delta_{\textrm{FWHM}}}{\lambda}where ΔFWHM is the FWHM of the emission lines[10]https://www.shelyak.com/how-to-measure-the-redshift-of-a-galaxy/?lang=en. Light age, travel time, and comoving radial distance were calculated using an online calculator assuming a flat model[11]https://astro.ucla.edu/~wright/CosmoCalc.html. The following table shows the results, along with averages,
| z | v | Age | Travel | Comoving Radial Distance | Rotational Velocity | |
| km/s | Gy | Gy | Gly | km/s | ||
| C III] | 1.33403039832285 | 206800 | 4.759 | 8.962 | 13.397 | 17092 |
| Mg II] | 1.33410421127766 | 206805 | 4.758 | 8.962 | 13.398 | 9357 |
| O III | 1.33304597701149 | 206734 | 4.762 | 8.959 | 13.391 | 15760 |
| Average: | 1.333726862204 | 206780 | 4.760 | 8.961 | 13.395 | 14070 |
Our observed redshift z = 1.334 exactly matches the results on SIMBAD! v is the velocity that the galaxy is receding away from us, roughly 207,000 km/s, or about 128,000 miles per second. This velocity is 69% that of the speed of light! The universe was 4.76 billion years old when the light I captured was emitted from this galaxy, and the light took 8.961 billion years to reach my telescope! The distance that the galaxy would be away from us right now is about 13.4 billion light years. Finally, the galaxy is spinning at about 14,000 km/s.
Conclusion
I find it remarkable that with relatively affordable equipment, I am able to, from the comfort of my home, observe, measure, and induce about cosmological objects. I’m not sure what the limiting magnitude may be for my setup, but I will certainly be hunting for more extremely deep space objects.
I think on the next project I may try to do some continuum removal to try to get more accurate measurements of emission lines, and I have an idea for a computer program to determine what elements are in the spectrum based on the ratios of the observed peaks.
Files
Below are links to the files used in this project.
References
