New ways to measure Velocity of a Star

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New ways to measure Velocity of a Star

 Introduction:

Measuring the velocity of a star with respect to the motion of Earth and the solar system is a very important task for astronomers. For decades astronomers are always trying to measure the velocity of stars with maximum accuracy. Astronomers use a very famous concept called Doppler shift to measure velocity. You might have heard of the Doppler effect (change in sound intensity of any object as it approaches or moves away from the observer). Similarly, the Doppler shift tells whether the object is approaching or is moving away from the observer. Redshift if it is moving away and blue shift if it is approaching the observer.

But the standard Doppler method has few drawbacks. Several white dwarfs showed excess gravitational redshifts. This makes it difficult for astronomers to calculate the velocity. Astronomers faced the same problem in the case of Sirius A and Sirius B.

To solve this problem, astronomers developed a new method to measure a star's speed along the line of sight without finding their Doppler shifts. This new method overcomes the drawbacks of Doppler Shifts and is especially useful for studying white dwarfs. This new method can also be used to find life-supporting exoplanets orbiting other Sun-like stars. 

Three Fields :

To determine the total velocity of a star, traditionally three fields are required. These are,
  1. Proper motion
  2. Distance
  3. Doppler Shift
Proper motion is how much a star moves across our line of sight rather than along our line of sight. In other words, it is changes in apparent positions of a star with respect to the centre of mass of the solar system. Stars nearer to the solar system tend to show larger proper motions. Distant stars show very less proper motion. Edmund Halley in 1718 provided the proof of proper motion. He noticed that stars like Aldebaran, Sirius and Arcturus were half a degree away from the positions mentioned by Greek astronomer Hipparchus about 1900 years ago.

New ways to measure Velocity of a Star
Change in position in Barnard's star in two decades.

The second quantity is distance. About one century after the discovery of proper motion, Friedrich Wilhelm Bessel in Prussia first measured the distance of a star beyond the solar system. He successfully applied the trigonometric parallax method on 61 Cygni. 

When any nearby star is observed from two ends of the Eath's orbit, i.e. after six months, a small angular displacement is observed relative to the fixed background (any other star). With the radius of the earth's orbit as the baseline, the distance of a star can be measured from the parallactic angle. Distance helps astronomers to convert proper motion into tangential velocity, i.e. how fast the star is moving across our line of sight (unit - km/s).

The third field is Doppler Shift, as stated above it is used to measure how fast a star is moving towards or away from us. The faster the star, the greater the shift. But today, astronomers measure the positions of stars so precisely that any changes in proper motion reveal the accurate radial velocity, without using the Doppler shift.

Drawbacks of Doppler Shift :

Generally, the outer layer of most stars has similar conditions. Hot gas rises, radiates the heat, gets cooled and again sinks back. Now, the hot rising gases actually move towards us, hence showing blueshift. While the cooled sinking gases move away from us and show redshift. But this opposite red and blue shift does not cancel outs. In fact, the hot, blueshifted gas is brighter. This induces overall blueshift while measuring the radial velocity through Doppler Shift. By using proper motions, the problem of "extra blueshift" is automatically solved. 

Successful Examples : 

The recently developed new technique is very accurate for white dwarfs because they are highly dense and have gravities about 100,000 greater than that of the Earth. Recently, Lennart Lindegren and Dainis Dravins obtained radial velocities of a small number of stars, with an accuracy of up to 1 km/s. This proved that the new method is very accurate for stars relatively closer to the Sun. However, this recent success is the work of astronomers for more than 3 decades. It's just the proper application of basic geometry that led to the development of this new technique.  

This new technique is not just applicable for nearby stars, but it also works for stars that are fast. The best example is Barnard's star. Among the stars in the night sky, Barnard's star has the largest proper motion. In fact, the Barnard star is approaching us! In 1916 its distance was about 6 light-years and now it is about 5.96 light-years. It is also the second-closest star to the Sun. The radial velocity by Lindegren and Dravins was 0.4 km/s and that obtained from Doppler shift observations was 0.6 km/s.

New ways to measure Velocity of a Star
Image Credit: Lucy Reading-Ikkanda.

Another star that proved the success of this new technique is Proxima Centauri, located about 4.25 light-years away from the Sun. This red dwarf star is the nearest star to the solar system. Lindegren and Dravins used changing proper motion of the star to determine radial velocity of 23 km/s, differing from the Doppler value by only 0.8 km/s. However, the new technique does not work for Alpha Centauri A and B.

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