Example Barnard's Star

Credit: Michael Richmond at spiff.rit.edu

When we discussed proper motion in the Parallax chapter, we saw Barnard’s star had a large proper motion (perpendicular to our line of sight.
Let us now find out what the radial velocity is of Barnard's star.

The graph gives a small part of a high resolution spectrogram from the star compared with that of the Sun. The wavelength range covers part of the orange section of the visible spectrum.

Any distinct peaks (absorption lines) in the Barnard's spectrum can be used to measure the wavelength shift, when we find corresponding peaks in the Sun's spectrum. Knowing that the Sun does not have a significant radial velocity with respect to Earth, any shift we see must be due to the radial velocity of Barnard's star.

We can use the red peak just to the right of the 610 nm that has a corresponding green line to the right of it or the red peak at 612 nm that has a corresponding green peak to the right of it.

The first thing we note is that the Barnard spectrum (red line) is shifted to the left, meaning towards the smaller wavelength. This is a "blue shift" and it means that Barnard's star is moving towards us.

One of the green peaks is at about 612.218 nm. The red peak is at 612.000 nm. The measured shift gives thus a change in wavelength of -0.218 nm. When we now apply the Doppler formula we get: change in wavelength / original wavelength = -0.218 / 612.218 = -3.561x10-4 With the speed of light being 3x105 km/s we get: radial velocity = -3.561x10-4 x 3x105 = -106.8 km/s. The negative sign indicates that it is moving towards us (blue shift). Hence Barnard's star is moving towards us with a radial velocity of -106.8 km/s.

With modern spectrographs an amazing radial velocity accuracy of about 3 m/s is possible, provided we have very sharp spectral lines that can be carefully calibrated with the stationary equivalent.

Locally, meaning within our own galaxy and towards the nearest neighbour galaxies, redshift is a very important technique to measure relative velocity. Chief applications are in studying rotation of binary systems, finding exoplanets, and measuring galaxy rotation, including that of the Milky Way.

In this EBook we are concerned with measuring distance and as such the redshift discussed isn't very relevant. But we needed to explain the basics of redshift as a Doppler effect, to pave the way for the discussion how redshift does play an important role to measure distance at much larger scale. In that situation redshift is not caused by radial velocity, but by the expansion of space, which is called Cosmological Redshift. So, now we must introduce the expansion of the Universe and relate that to measuring distances at the largest of scales.