Astronomy Stack Exchange is a question and answer site for astronomers and astrophysicists. It only takes a minute to sign up.
Sign up to join this community
In the above given picture Vi is the velocity of the i-th galaxy in the cluster while Vm is the mean velocity of a galaxy in the cluster. and V i,r is the radial velocity of the i-th galaxy and V m,r is the mean radial velocity. How does converting mean velocity to mean radial velocity introduce a coefficient of 3.
Image source IOAA 2019 question 13.
The key assumption is that orbital velocity vectors are distributed randomly. Then the dispersion of velocities along each axis must be the same, e.g. $\sigma_x=\sigma_y=\sigma_z$ if $x$, $y$, and $z$ denote perpendicular axes. But then the total squared velocity dispersion is $\sigma^2=\sigma_x^2+\sigma_y^2+\sigma_z^2=3\sigma_x^2$.
