Stars in SPHEREx David W Hogg (NYU) (MPIA) (Flatiron) Detailed element and chemical abundances

● There are now 15-30 element abundances measured for many 105 stars. ○ APOGEE, GALAH, Gaia-ESO, and more, including future projects. ● We have shown that wavelength coverage is more important than resolution for making these measurements. ○ Contrary to received wisdom in the stellar-spectroscopy world. ● We already can work at resolutions around 2000. ○ Ting et al, 2017, arXiv:1708.01758 ● We might be able to do a lot at much lower resolutions. ○ Ting et al, 2017, arXiv:1706.00111 Mapping the Milky Way

● Projects like APOGEE and GALAH are making sparse samplings of the Milky Way. ○ But see the SDSS-V MWM proposal! ● A lot of the critical Milky-Way structures (streams, spiral arms, disk warps) are hard to interpret in sparse samplings. ● SPHEREx will create a deeper, more uniform, wider-band, all-sky map than any other spectroscopic survey. ● Gaia will provide 4 to 6 dimensions of phase space for every star. ○ (And a high-resolution baseline map for building models.) Recommendations

● R1. Transfer physical knowledge from outside sources using data-driven models. a. (and from one well understood part of the spectrum to another poorly understood part) ● R2. Employ differential measurements to measure detailed element abundances. ● R3. Analyze the data at higher angular resolution than one SPHEREx pixel. R1. Data-driven models

● You won’t have accurate physical models for stellar spectra across the SPHEREx bandpass. ○ (and, importantly, at SPHEREx resolution) ● You do know some physical properties of some stars. ○ (from, say, Gaia geometry or VLT interferometry) ○ (from, say, high-resolution optical spectra) ● You can build an accurate model of your data from the data themselves. ○ The Cannon; Ness et al, 2015, arXiv:1501.07604 ○ Gaia de-noising; Anderson et al, 2017, arXiv:1706.05055

R2. Differential abundances

● The most precise element abundances ever measured are measured by taking differences in spectra between very similar stars. ○ Eg, Solar Twins; better than percent-level; Bedell & Hogg, forthcoming ● Method: Project spectral differences onto model derivatives. ● Because most elements have sparse spectra, this approach does not require high resolution spectroscopy. R2. Detailed abundances at low spectral resolution

● To obtain 15-element abundances from LAMOST spectra, the procedure is: ● Build a data-driven model of the spectra that controls for basic stellar parameters. ● Project residuals away from baseline model onto theory-based spectral derivative expectations. ○ Also can be used to find stars with recent accretion events; Casey et al, submitted. ○ Or stars with element anomalies in general.

R3. Multi-resolution imaging

● Imagine we have many images of the sky in different bands, and every band is measured at a different angular resolution. ○ Think: HST visible and GALEX UV! ● Can we make an image with the wavelength coverage of all the bands, but at the angular resolution of the highest-resolution band? ● Obviously, I believe the answer to this question is yes. ○ Let’s solve this problem for SPHEREx and it’s natural partners, especially Gaia. ● There is a cost: Some results become necessarily probabilistic. R3. Forced photometry

● Simplest case: Model the (say) WISE data as a linear combination of SDSS sources, convolved with a PSF-matching kernel. ○ Lang, Hogg, Schlegel, 2014, arXiv:1410.7397 ● Delivers WISE photometry for everything in SDSS, even overlapping objects. ○ (and objects that are too faint to be independently detected in WISE) ● Point estimates of these amplitudes have limitations.

R3. Probabilistic catalogs

● In the end, the model will have to be probabilistic and hierarchical. ● It will have to capitalize on the fact that stellar spectra are fundamentally low-dimensional ○ (and learn that low-dimensionality) ● It will have to report responsibly covariant uncertainties. ○ (see, eg, work by Portillo & Finkbeiner) Recommendations

● R1. Transfer physical knowledge from outside sources using data-driven models. a. (and from one well understood part of the spectrum to another poorly understood part) ● R2. Employ differential measurements to measure detailed element abundances. ● R3. Analyze the data at higher angular resolution than one SPHEREx pixel.

(Yes, I realize these recommendations are out of scope for the project!)