# Converting spectrum into velocity space

1. Oct 7, 2011

### Piano man

Hi,

I've been trying to figure out how to convert a spectrum from wavelength space into velocity space.

I thought it would be a simple relation, but I can't see it - maybe I'm missing something?

I've got Flux v Wavelength at the moment, so I converted into frequency space.
I've played around with $h\nu=1/2 mv^2$, but unsure what to use for mass.

I also looked at a Doppler relation, but I'm sure that's for individual lines rather than for an entire spectrum.

If someone could put me on the right track, I'd appreciate it!

Last edited by a moderator: Oct 8, 2011
2. Oct 8, 2011

### Astronuc

Staff Emeritus
I presume one is referring to particles, because light of different frequencies propagates at the speed of light.

For particles, the wavelength is given by $\lambda = \frac{h}{mv}$, or conversely

$v = \frac{h}{m\lambda}$

Last edited: Oct 8, 2011
3. Oct 8, 2011

### Piano man

Sorry I forgot to say in the original post that I'm looking at spectra that have been redshifted due to mass outflows. I'm trying to get this wind velocity on the x-axis.

What I think I have to do is identify and measure some prominent lines, calculate the redshift by comparing to known values and then come up with some relation that relates the wavelength to the mass velocity. Does that sound plausible?

I'm really not sure about that last part though - I don't think the usual $c=\lambda \nu$ makes sense there..

Any pointers on that?

Thank you.

4. Oct 8, 2011

### Astronuc

Staff Emeritus
One is trying to relate doppler shift in radar (at different frequencies) to wind speed, as in doppler radar or radar anemometry? Similar concept to laser doppler anemometry.

Wind as in air (related to the above, which uses a pitch-catch method), or wind as in solar/stellar/ISM particles (a bit different since it's based on catch (of emissions))?

5. Oct 8, 2011

### matt.o

I think what you are after is $$v={c \Delta \lambda \over \lambda}$$ where $\lambda$ is the wavelength of the line of interest, $\Delta \lambda$ is the difference in the measured wavelength and $\lambda$.

Last edited: Oct 8, 2011
6. Oct 8, 2011

### Piano man

Astronuc - I haven't come across radar anemometry - how would that apply here? And it's the stellar wind velocity I'm looking for.

matt.o - That's exactly the equation I've been using!
Well, a variant of it - I've got $$\Delta v=v-v_{rad}$$ to account for the radial velocity of the star.
So I've been able to calculate velocities in km/s for individual lines, but I'm not sure how to go about getting a plot with Flux on the y-axis and Velocity on the x-axis. So for example, I've calculated the h and k lines for Mg II (measured at 2796.9A and 2804.1A respectively) and corresponding to 146.9km/s and 146.5km/s respectively, using your formula above.
How would this translate onto a flux/velocity plot?