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FORECASTING THE CHEMICAL INFORMATION CONTENT OF STELLAR SPECTRA - PowerPoint PPT Presentation

FORECASTING THE CHEMICAL INFORMATION CONTENT OF STELLAR SPECTRA NATHAN SANDFORD UC BERKELEY With: Dan Weisz Yuan-Sen Ting Hans-Walter Rix N ATHAN S ANDFORD S MALL G ALAXIES , C OSMIC Q UESTIONS 29 JUL 2019 G OLDEN A GE OF S


  1. FORECASTING THE 
 CHEMICAL INFORMATION CONTENT 
 OF STELLAR SPECTRA NATHAN SANDFORD UC BERKELEY With: 
 Dan Weisz 
 Yuan-Sen Ting 
 Hans-Walter Rix

  2. N ATHAN S ANDFORD S MALL G ALAXIES , C OSMIC Q UESTIONS 29 JUL 2019 G OLDEN A GE OF S TELLAR S PECTROSCOPY Observations Techniques ▸ Current Facilities ▸ Improved Spectral Models ▸ Keck, VLT, Magellan ▸ 3D, non-LTE ▸ More complete linelists ▸ >10 5 stars outside the MW ▸ Full Spectrum Fitting ▸ Next Generation Facilities ▸ The Cannon (Ness+ 2015) ▸ Space-based: JWST ▸ The Payne (Ting+ 2018) ▸ Ground-based: 
 ▸ StarNet (Fabbro+ 2017) PFS, E-ELT, MSE ▸ 10+ Elements from 
 R~2000 spectra in MW

  3. N ATHAN S ANDFORD S MALL G ALAXIES , C OSMIC Q UESTIONS 29 JUL 2019 B UT WAIT … What abundances do we need? 
 To what precision? Where is the information located? What observations best provide 
 that information?

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  5. N ATHAN S ANDFORD S MALL G ALAXIES , C OSMIC Q UESTIONS 2 AUG 2019 C HEMICAL I NFORMATION IN S PECTRAL G RADIENTS Strong Gradients Moderate Gradients Weak Gradients

  6. N ATHAN S ANDFORD S MALL G ALAXIES , C OSMIC Q UESTIONS 2 AUG 2019 Q UANTIFYING C HEMICAL I NFORMATION C ONTENT MCMC Sampling of the Posterior ‣ Abundance fitting is many-dimensional σ ‣ Computationally expensive / intractable σ (i.e. [X/Fe])

  7. <latexit sha1_base64="jQ842wHid3WQI3K2/i1/Zw2idcA=">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</latexit> N ATHAN S ANDFORD S MALL G ALAXIES , C OSMIC Q UESTIONS 29 JUL 2019 C RAMÉR -R AO L OWER B OUNDS Fisher Information Matrix ‣ Negative curvature of the log-Posterior σ ⌧ ∂ 2 [ − ln P ( θ )] � F ij = σ ∂θ i ∂θ j (i.e. [X/Fe])

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  ∂ f ( λ , θ )  ∂ f ( λ , θ ) � ( ) Σ − 1 f ( λ , θ ) = F ij = Model ∂θ i ∂θ j { { S/N Spectral Gradient wrt � θ

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