<p>You don't say how you are estimating your radial velocities, however there will always be systematic errors if the template does not match the target spectrum.</p>
<p>If you are doing this by cross-correlation, then there is no need to rectify the spectrum to the continuum. You would just fit and then divide target and template by a low-order polynomial before cross-correlation.</p>
<p>If you are doing some sort of chi-squared fitting, with radial velocity shift as a free parameter, then one approach is to make the continuum, represented by a low-order polynomial, just another (set of) free parameter(s). i.e. Do a basic normalisation of the template spectrum and then allow the target spectrum to be normalised with a similar function, but allow the coefficients of that function to be varied in a chi-squared fit along with the radial velocity shift. You then marginalise over the uninteresting coefficients of the normalisation function coefficients to get your best estimate of the radial velocity and its uncertainty.</p>

CC BY-SA 4.0
2024-04-18T18:09:05.357Z
I can see that low order polynomials would work well for the relatively smoothly varying continua of spectral types earlier than M. My reservation about its efficacy for M stars is the presence of the discontinuous level changes at the TiO bandheads: smoothing across these will lower the contrast. I suspect that this again will undermine the usefulness of these strong features in showing up wavelength shifts.
J. Webb
CC BY-SA 4.0
2024-04-18T21:04:52.287Z
@J.Webb that's why I specified a low order polynomial, which does not smooth discontinuities at all.
ProfRob
CC BY-SA 4.0
2024-04-18T16:39:09.030Z
2024-04-18T16:39:09.030Z
ProfRob
<p>I would appreciate references and/or tips on estimating the continuum
in the spectra of M dwarf stars. The ultimate aim is to obtain radial
velocities from sequences of spectra by comparing to a template spectrum.
The continuum shapes of the template spectrum and those of the stars
of interest may differ, hence the necessity to rectify the spectra.
The specific wavelength range available is 5100-6100 Angstrom.</p>

CC BY-SA 4.0
2024-04-18T16:32:45.257Z
If the template is different to the target then you will have systematic errors in the radial velocity. A problem you have in M-dwarfs is that there really isn't any "continuum" - just varying levels of molecular blanketing.
ProfRob
<spectroscopy><radial-velocity>
Rectification of M-type spectra
J. Webb
# Rectification of M-type spectra

(Asked by: username_0 on 2024-04-18)

I would appreciate references and/or tips on estimating the continuum
in the spectra of M dwarf stars. The ultimate aim is to obtain radial
velocities from sequences of spectra by comparing to a template spectrum.
The continuum shapes of the template spectrum and those of the stars
of interest may differ, hence the necessity to rectify the spectra.
The specific wavelength range available is 5100-6100 Angstrom.

**Tags:** spectroscopy, radial-velocity
> **Comments:**
> **username_1**: If the template is different to the target then you will have systematic errors in the radial velocity. A problem you have in M-dwarfs is that there really isn't any "continuum" - just varying levels of molecular blanketing.  

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## 1 answers

### Answer by username_1 on 2024-04-18. Score: 1

You don't say how you are estimating your radial velocities, however there will always be systematic errors if the template does not match the target spectrum.

If you are doing this by cross-correlation, then there is no need to rectify the spectrum to the continuum. You would just fit and then divide target and template by a low-order polynomial before cross-correlation.

If you are doing some sort of chi-squared fitting, with radial velocity shift as a free parameter, then one approach is to make the continuum, represented by a low-order polynomial, just another (set of) free parameter(s). i.e. Do a basic normalisation of the template spectrum and then allow the target spectrum to be normalised with a similar function, but allow the coefficients of that function to be varied in a chi-squared fit along with the radial velocity shift. You then marginalise over the uninteresting coefficients of the normalisation function coefficients to get your best estimate of the radial velocity and its uncertainty.

> **Comments:**
> **username_0**: I can see that low order polynomials would work well for the relatively smoothly varying continua of spectral types earlier than M. My reservation about its efficacy for M stars is the presence of the discontinuous level changes at the TiO bandheads: smoothing across these will lower the contrast. I suspect that this again will undermine the usefulness of these strong features in showing up wavelength shifts.  
> **username_1**: @J.Webb that's why I specified a low order polynomial, which does not smooth discontinuities at all.  

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