M-dwarf Abundances from LAMOST spectra

Overall science goal:

Get systematic "stellar parameters" and abundances for M-dwarf, who have risen to prominence through the TESS focus/fixation as planet hosts.

My loose definition of M-dwarf is all stars cool enough to show serious molecular features in the red optical.

The thoughts below have in part emerged from discussions with Yuan-Sen Ting, Maosheng Xiang and Doug Finkbeiner.

Devise a way to get such labels for all/most TESS targets by 2023; but this note is only about technique

Stellar Parameters: Ideally we'd like mass, age, ... ; that is conventionally rephrased in spectroscopy as Teff and logg, whose relation for (late) M-dwarfs is not trivial because the Hyashi track takes so long. But in data-driven approaches th eproblem is that we'd need trustworthy training labels Teff and logg which we do not have in the first place.

Proposal: introduce M_K and J-K (or some other absolute magnitude and color) as basic stellar labels; for a sub-set of M-dwarfs these are known exquisitely.

Abundances: there are many ideas about which abundances matter (encased in the photospheric abundances)  for planet formation; let's start with [Fe/H] and then add other [X/Fe]; the target precision of [Fe/H] should be < 0.1dex; else it is not very interesting.

A new data-driven angle at the problem:

Gaia DR2 has given us vast sets of wide binaries (>10"), including a significant number of G-dwarf -- M-dwarf binaries where there are LAMOST spectra for both components. The idea is that we get extremely precise distances to the G-dwarfs, and well understood abundances ([Fe/H] and ~10 more).

As atomic diffusion is a minor issue in cool stars with convective envelopes, we can assume that in a binary [Fe/H](G-dwarf) = [Fe/H](M-dwarf). With photometry for the M-dwarfs that gives us training labels labels= (M_K, J-K, [Fe/H]).

We'll train a Cannon type model f(lam) = f(labels), and then infer in a test step labels for all M-dwarfs with spectra.

Implementation

Many of the LAMOST spectra of M-dwarf in wide binaries are of modest S/N, seemingly unsuited to training a model. So, let'd take denoising measures first.

1. take high S/N M-dwarfs (selected in the CMD from M_K and J-K) and construct a clean PCA; determine how many components are needed to get an excellent representation; let's presume 50 components.    The projection of f(lambda) onto the first 50 PCA components become the new "spectral pixels".
2. Take the M-dwarf spectra in binaries (low-ish S/N) and project onto the 50 PCA.
3. Train a 3-label Cannon on this, and do test step (as the first "dumbest" step)

How to do better? Acknowledge that there may be more latent labels (whose existence for the moment we acknowledge, but whose phys. interpretation we don't care about for now).

1. take the residuals from the steps above, and perform a PCA on them.
2. declare the first few components (K) of this residual-PCA as the Cannon vectors to go with latent labels.
3. Project each training stars' residuum spectrum onto these PCA components, and declare the coefficients to be the (initial) latent labels of the training set.
4. Fit a Cannon for those K+3 labels,... iterate?

Diagnostic plots

The following plots compare the LDR5 sample and its ddPayne analysis to Padvova solar-abundance isochrones, in order to 

a) see how many M-dwarfs have observations

and

b) what the ddPayne does in this interpolation regime?

Note that M-dwarfs start at <3800k div="">

This just shows that low-mass stars take >100Mio years to settle on the main sequence

The current implementation of the ddPayne does not give robust Teff values below 4000K. This shows that there is a vast number of M-stars in the sample (100.000) that TESS folks care about, and about which the current ddPayne says nothing. The file with presumed LDR5 M-dwarfs (selected by their (G-H nd M_H) is here: https://www.dropbox.com/s/fy5je8bdkllczao/LAMOST_DR5_Gaia_WISE_Mdwarfs.fits?dl=0

 This shows (ddPayne Teffs small dots; large dots isochrones) that the ddPayne Teff 'stalls' at 4000K; actually a sensible behaviour.

Same as above, just different color as X-axis.

Here the isochrones are color-coded by stellar Mass.