<p>The axis type ‘FELO’ is regularly gridded in frequency but expressed in velocity units in the <a href="https://science.nrao.edu/facilities/vla/docs/manuals/obsguide/modes/line" rel="noreferrer">optical convention</a>. The unit here is   <span class="math-container">$m/s$</span>. </p>

<p>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
<span class="math-container">$$
v = c \ \frac{\lambda - \lambda_0}{\lambda_0  } ,
$$</span>
where <span class="math-container">$\lambda$</span> is the measured wavelength and <span class="math-container">$\lambda_0$</span> the reference wavelength in a rest frame. </p>

<p>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. </p>

<p>Your distribution, therefore, has a width of about 200 km/s.
And the projected rotational velocity of the galaxy <span class="math-container">$v_\mathrm{rot} \sin(i) \approx 100\,$</span>km/s, where <span class="math-container">$i$</span> is the galaxies <a href="http://star-www.st-and.ac.uk/~kdh1/eg/eg06c.pdf" rel="noreferrer">inclination</a>. </p>

<p>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. </p>

<p>Some more information about frequency and velocity formats can be found in <a href="https://www.atnf.csiro.au/people/mcalabre/WCS/scs.pdf" rel="noreferrer">this paper</a></p>

CC BY-SA 4.0
2019-10-26T11:47:47.380Z
This makes sense. Thank you so much. I really appreciate your help.
AHMED KRS
CC BY-SA 4.0
2019-10-31T16:54:10.820Z
This is NGC925 can you please explain a bit more about the offset. I did not understand that bit? @SpaceBread
AHMED KRS
CC BY-SA 4.0
2019-10-25T13:37:12.747Z
2019-10-25T13:37:12.747Z
SpaceCore
<p>I am using DS9 to calculate the rotational velocity of a galaxy. I have 21cm cube and  I used DS9 to plot this graph <a href="https://i.sstatic.net/5Is7e.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/5Is7e.jpg" alt="This is the plot  for NGC925"></a></p>

<p>I do not understand what is FELO-HEL! and I want to convert the units from FELO-HEL to Km/s?</p>

<galaxy><distances><rotation><units><ds9>
How to convert from FELO-HEL to Km/s?
AHMED KRS
# How to convert from FELO-HEL to Km/s?

(Asked by: username_0 on 2019-10-25)

I am using DS9 to calculate the rotational velocity of a galaxy. I have 21cm cube and I used DS9 to plot this graph [![This is the plot  for NGC925](https://i.sstatic.net/5Is7e.jpg)](https://i.sstatic.net/5Is7e.jpg)

I do not understand what is FELO-HEL! and I want to convert the units from FELO-HEL to Km/s?

**Tags:** galaxy, distances, rotation, units, ds9

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## 1 answers

### Answer by username_1 on 2019-10-25. Score: 5 | Accepted answer

The axis type ‘FELO’ is regularly gridded in frequency but expressed in velocity units in the [optical convention](https://science.nrao.edu/facilities/vla/docs/manuals/obsguide/modes/line). 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](http://star-www.st-and.ac.uk/~kdh1/eg/eg06c.pdf).

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.

Some more information about frequency and velocity formats can be found in [this paper](https://www.atnf.csiro.au/people/mcalabre/WCS/scs.pdf)

> **Comments:**
> **username_0**: This makes sense. Thank you so much. I really appreciate your help.  
> **username_0**: This is NGC925 can you please explain a bit more about the offset. I did not understand that bit? @SpaceBread  

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