# How to convert from FELO-HEL to Km/s?

I am using DS9 to calculate the rotational velocity of a galaxy. I have 21cm cube and I used DS9 to plot this graph I do not understand what is FELO-HEL! and I want to convert the units from FELO-HEL to Km/s?

The axis type ‘FELO’ is regularly gridded in frequency but expressed in velocity units in the optical convention. The unit here is $$m/s$$.

This means that the wavelength/frequency has already been expressed as velocity corresponding to a Doppler shift around a reference wavelength. This velocity is given by $$v = c \ \frac{\lambda - \lambda_0}{\lambda_0 } ,$$ where $$\lambda$$ is the measured wavelength and $$\lambda_0$$ the reference wavelength in a rest frame.

The HEL term on the axis means that velocities have been transferred to the solar systems barycenter (HELiocentric). This means, the velocity of earth around the sun and its rotation has already been removed.

Your distribution, therefore, has a width of about 200 km/s. And the projected rotational velocity of the galaxy $$v_\mathrm{rot} \sin(i) \approx 100\,$$km/s, where $$i$$ is the galaxies inclination.

The offset of 550 km/s probably comes from the relative speed between our sun and the galaxy, but that is hard to tell without knowing which galaxy it is.