# Majadahonda Astronomical Observatory

## Spectrometry projects

## Calculation of the speed and distance of quasar 3C273

The quasar 3C273, in the constellation of Virgo, is one of the first quasars discovered and quite affordable for the study of amateur astronomy for its apparent luminosity of 12.7 in V despite being a very distant object, in fact it is the quasar more luminous known. The study of its spectrum allows us to measure the displacement to red, estimate its speed and from the Hubble Law, calculate its distance.

To measure the displacement to red, a C11 tube with focal reducer f6.3 was used on EQ8 mount, with ST8XME camera and SA200 filter. We have made 16 shots of 300s with tracking OFF AXIS with Lodestar X2 camera.

RSpec software has represented the spectrum obtained and indicated the hydrogen emission lines H alpha, beta and gamna:

For the calibration (correspondence of pixels with wavelength in Angstroms), a capture of the Vega spectrum was made by 15 shots of 0.05s. Since Vega is an excellent reference and the hydrogen absorption lines are clearly identified, we can perform the calibration with the corresponding RSpec utility.

Superimposing both spectra, we clearly see the redshift as shown in the following figure:

We calculate the redshift for each hydrogen line indicated as:

z = (measured wavelength - emitted wavelength) / emitted wavelength

For H alfa:

z = (7531 - 6563) / 6563 = 0.147

For H beta:

z = (5551 - 4861) / 4861 = 0.142

For H gamma:

z= (5008 - 4340) / 4340 = 0.153

The correct value is z = 0.158 so the data obtained are reasonably good, especially considering a dispersion in the measurements of 21.1 angstroms per pixel.

###### Interpretation of the data

The redshift measured, around 0.15, implies that the quasar moves away from us at a speed of approximately 15% of the speed of light. This apparent speed is not really a kinematic speed, but corresponds to the expansion of the universe. For this reason, and applying the Hubble law, we can deduce the distance of the quasar.

If instead of the data obtained from z equal approximately to 0.15, we use the accepted of 0.1583, we obtain an approximate speed of:

v=z*c aprox 47400 km/s

Applying the Hubble Law v = H * D, we obtain:

D = c * z / H and considering H = 73 km / s * Mpc we obtain a data of approximately 650 Mpc or 2.12 trillion light years

A surprising data of 3C273 is the apparent magnitude of 12.7 at a distance of 650 Mpc. Let's calculate the absolute magnitude (magnitude with which it would look at 10 pc) by the formula: M = m-5 * log (D / 10) where m is the apparent magnitude and D is the distance in pc:

M=12.7-5*log(650000000/10)=-26.3

This value of absolute magnitude is similar to the apparent magnitude of the Sun (-26.7) which means that at 10pc (about 32 light years) we would see 3C273 with a brightness like the one we see the Sun from Earth.

## Spectra with homemade slit spectrometer

The spectra shown below are examples captured with a homemade slit spectrometer based on a reflection diffraction grating with 600 lines / mm.

The spectrometer was coupled to the primary focus of an 8" LX200. The camera used was the QHY Img2 Pro, the control software of the MaximDL camera and the spectrum processing with the RSpec application, including the stacking of images.

The dispersion is of the order of 2.2 Angstroms / Pixel, which gives a resolution power in the best case of 4.4 Angstroms (2 pixels). Comparing the captured spectrum with another captured with a higher resolution spectrometer, it can be seen that reasonably well solves lines with separation of about 10 or 15 Angstroms. Of course it is a low-resolution spectrograph as might be expected from the diffraction grating used, but with reasonably good results.

###### Vega

Vega:

In red the captured spectrum and in blue a spectrum obtained in the Chritian Bill page and captured with the MERIS spectrometer (MEdium Resolution Imager Spectrograph).

Both the captured and the used reference spectrum are displayed without instrument response calibration.

The spectrum covers from 3900 and 7000 angstroms, with a dispersion of 2.2 angstroms per pixel.

The similarity of both spectra is evident, especially in the most pronounced absorption lines.

In red the same spectrum of the Vega star and in blue the star reference of spectral type AV0. The coincidence of the absorption lines is clear.

In this comparison, the profiles of the spectra are more different given that the reference spectrum is calibrated and the captured one is not, although the main absorption lines continue to coincide.

The spectrum of the star Vega is shown in which the main lines have been indicated.

The hydrogen lines are clearly visible.

The telluric O2 absorption line has also been pointed out, which is the main difference between the captured spectrum and the spectral reference type AV0 in the range of 3900 to 7000.

###### Procyon

Spectrum captured of Procyon

Spectrum of Procyon compared to reference spectrum.

In red the captured spectrum and in blue the reference spectrum of the spectral type F5iv

###### Betelgeuse

Spectrum of Betelgeuse

Betelgeuse spectrum compared to reference spectrum.

In red the captured spectrum, in blue the reference spectrum of the spectral type M2i

###### Sirius

Spectrum of Sirius

Sirius spectrum compared to reference spectrum.

In red the captured spectrum and in blue the reference of spectral type av2.