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

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

Nov 27, 2023 358 likes •547 views

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

slide-1
SLIDE 1

FORECASTING THE 
 CHEMICAL INFORMATION CONTENT
 OF STELLAR SPECTRA

NATHAN SANDFORD

UC BERKELEY

With:
 Dan Weisz
 Yuan-Sen Ting
 Hans-Walter Rix

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SLIDE 2

NATHAN SANDFORD 29 JUL 2019 SMALL GALAXIES, COSMIC QUESTIONS

GOLDEN AGE OF STELLAR SPECTROSCOPY

Observations

▸ Current Facilities ▸ Keck, VLT, Magellan ▸ >105 stars outside the MW ▸ Next Generation Facilities ▸ Space-based: JWST ▸ Ground-based:


PFS, E-ELT, MSE

Techniques

▸ Improved Spectral Models ▸ 3D, non-LTE ▸ More complete linelists ▸ Full Spectrum Fitting ▸ The Cannon (Ness+ 2015) ▸ The Payne (Ting+ 2018) ▸ StarNet (Fabbro+ 2017) ▸ 10+ Elements from 


R~2000 spectra in MW

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SLIDE 3

NATHAN SANDFORD 29 JUL 2019 SMALL GALAXIES, COSMIC QUESTIONS

BUT WAIT…

What abundances do we need?
 To what precision? Where is the information located? What observations best provide
 that information?

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SLIDE 4

2 AUG 2019 NATHAN SANDFORD SMALL GALAXIES, COSMIC QUESTIONS

SYNTHETIC DEIMOS RGB SPECTRUM

6500˚ A < λ < 9000˚ A R = 6500

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Teff = 4750 K log(g) = 1.8 vturb = 1.9 km/s [Fe/H] = −1.5

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Normalized Flux

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SLIDE 5

NATHAN SANDFORD 2 AUG 2019 SMALL GALAXIES, COSMIC QUESTIONS

CHEMICAL INFORMATION IN SPECTRAL GRADIENTS

Strong Gradients Moderate Gradients Weak Gradients

slide-6
SLIDE 6

2 AUG 2019 NATHAN SANDFORD SMALL GALAXIES, COSMIC QUESTIONS

MCMC Sampling of the Posterior

  • Abundance fitting is many-dimensional
  • Computationally expensive / intractable

QUANTIFYING CHEMICAL INFORMATION CONTENT

σ σ

(i.e. [X/Fe])

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SLIDE 7

29 JUL 2019 NATHAN SANDFORD SMALL GALAXIES, COSMIC QUESTIONS

Fisher Information Matrix

  • Negative curvature of the log-Posterior

Fij = ⌧∂2[− ln P(θ)] ∂θi∂θj

  • <latexit sha1_base64="jQ842wHid3WQI3K2/i1/Zw2idcA=">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</latexit>

CRAMÉR-RAO LOWER BOUNDS

σ σ

(i.e. [X/Fe])

slide-8
SLIDE 8

29 JUL 2019 NATHAN SANDFORD SMALL GALAXIES, COSMIC QUESTIONS

Fij = ∂f(λ, θ) ∂θi T Σ−1 ∂f(λ, θ) ∂θj

  • <latexit sha1_base64="1Xn+KDGYjDoPCB4KloQR6zw6ywM=">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</latexit>

CRAMÉR-RAO LOWER BOUNDS

Fisher Information Matrix

  • Negative curvature of the log-Posterior
  • Can be written in terms spectral gradients (Ting+ 2017)

f(λ, θ) =

<latexit sha1_base64="o0DNb4dnQnuw2ngLZRjPR3dyZE=">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</latexit>

Spectral
 Model

(

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)

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{ {

Spectral Gradient wrt

θ

S/N

slide-9
SLIDE 9

29 JUL 2019 NATHAN SANDFORD SMALL GALAXIES, COSMIC QUESTIONS

Fij = ∂f(λ, θ) ∂θi T Σ−1 ∂f(λ, θ) ∂θj

  • <latexit sha1_base64="1Xn+KDGYjDoPCB4KloQR6zw6ywM=">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</latexit>

σi ≤ p (F −1)ii

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CRAMÉR-RAO LOWER BOUNDS

Fisher Information Matrix

  • Negative curvature of the log-Posterior
  • Can be written in terms spectral gradients (Ting+ 2017)

CRLB: Highest precision achievable
 from a set of observations

f(λ, θ) =

<latexit sha1_base64="o0DNb4dnQnuw2ngLZRjPR3dyZE=">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</latexit>

Spectral
 Model

(

<latexit sha1_base64="QcEhQ2DA9HLM2xyBPK0qSDJ2QYI=">AEyXicnVNb9MwFM7WAqNc1sEjLxbrpE7bKidNl1Zi0gTShMTLgN2kOqsc10m9OZfZzsSI8sQ/5I0n/gpOmo5dJdiRIn05n893vnMSewlnUkH4a26+Vn/0+MnC08az5y9eLjaXh3IOBWE7pOYx+LIw5JyFtF9xRSnR4mgOPQ4PfROPxT84TkVksXRnrpIqBviIGI+I1jp1Ghp/neGSpWhCDw3g52BY3YHg3UNel27BwvQN2HPyVvtVt5Y+efTfhtxbWOM15GaUIVXt+4ot204rbJ7PWfTmQLYN3Pk0YBFGaGRokLXtWwIXgHKk2NnWmhZCmvoAtUNCtxgqi0XhW9B9md0YZO8m1DOLUV7pHFHCKfIFJhIsFMP82BpuIB6B3XY1jptfctPMiN14P8mRYMFEIVHqPdjP8LoTcGuzf52AmZWqtXu8B9BXFoT4ONsw8wfrzUZxbw9hOt2ubWvPacPB6YGfQvalpUjWfQdsaLpGZJnQmXtYjCWr1VUxtYTwWKRa3NWvlpavOz3dthrRynXW25HMrU3i/FtaSVj5rLZgeWAfSCdTh2BQYmFHL2y2jN1R8ycaxyQN9V9EOJZyaMJEuVmxEFJ8RZRKmByigM61DCIZVuVjrOwYrOjIEfC/1ECpTZqxUZDqW8CD19MsRqIm9yRfIubpgqv+9mLEpSRSMybeSnHKgYFNcajJmgRPELDTARTHsFZIL1SvRVkI2rS7gfHFgds9uxPlvL2+n2zAWjDfGW6NtmIZjbBsfjV1j3yC1nRqvpbXz+qf6Wf1b/fv06PxcVfPauBb1H38AG9V9ng=</latexit>

)

<latexit sha1_base64="3UyOKx0EKrx3j8qbgnrLoYeFPk=">AEyXicnVNb9MwFM7WAqNc1sEjLxbrpE7bKidNl1Zi0gTShMTLgN2kOqsc10m9OZfZzsSI8sQ/5I0n/gpOmo5dJdiRIn05n893vnMSewlnUkH4a26+Vn/0+MnC08az5y9eLjaXh3IOBWE7pOYx+LIw5JyFtF9xRSnR4mgOPQ4PfROPxT84TkVksXRnrpIqBviIGI+I1jp1Ghp/neGSpWhCDw3g52BY3YHg3UNel27BwvQN2HPyVurbyx8s+n/Tbi2sYryM1oQqvbt1RbtwWmX3es6mMwWwb+bIowGLMkIjRYWua9kQvAOVJoabepMCyFNfQFboKBbjRVEo/Gs6D/M7owydpJrGcSpr3SPKOAU+QKTDCVYKIb5sTXcQDwCu+1qHDe/5KaZEbvxfpIjwYKJQqLUe7Cf4XUn4NZm/zoBMytVa/d4D6CvLAjxcbZh5g/Wm43i3h7CdLpd29be04fDkwN+ha0LStHsug7YkXTMyTPhMraxWAsX6uojK0ngsUi1+asfLW0eMdnu7fDWjlOu9pyOZSpvV+Ka0krHzWXzQ4sA+gF63DsCgxMKOWt1tGbuj5k80jka6r+IcCzl0ISJcrNiIaT4iVNMHkFAd0qGEQyrdrHScgxWdGQM/FvqJFCizVysyHEp5EXr6ZIjVRN7kiuRd3DBVft/NWJSkikZk2shPOVAxK41GDNBieIXGmAimPYKyATrleirIBtXl3A/OLA6ZrdjfbaWt9Pt2EsG+Mt0bMA3H2DY+GrvGvkFqOzVeS2vn9U/1s/q3+vfp0fm5qua1cS3qP/4AIA59nw=</latexit>

Cramér-Rao Inequality

slide-10
SLIDE 10

2 AUG 2019 NATHAN SANDFORD SMALL GALAXIES, COSMIC QUESTIONS

DEIMOS 1200G THEORETICAL PRECISION

More Precise

6500˚ A < λ < 9000˚ A R = 6500

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slide-11
SLIDE 11

29 JUL 2019 NATHAN SANDFORD SMALL GALAXIES, COSMIC QUESTIONS

BLUE SPECTRA ARE INFORMATION RICH

DEIMOS 1200G DEIMOS 1200B LRIS 600/4000

10 Elements 21 Elements 21 Elements

r-process s-process

3900˚ A < λ < 5500˚ A R = 1800

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6500˚ A < λ < 9000˚ A R = 6500

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4000˚ A < λ < 6400˚ A R = 4000

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slide-12
SLIDE 12

NATHAN SANDFORD 2 AUG 2019 SMALL GALAXIES, COSMIC QUESTIONS

JWST SPECTRA: FAINT STARS, CROWDED FIELDS

0.7µm < λ < 1.27µm R = 2700

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0.97µm < λ < 1.8µm R = 2700

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17 Elements 15 Elements

slide-13
SLIDE 13

2 AUG 2019 NATHAN SANDFORD SMALL GALAXIES, COSMIC QUESTIONS

In Practice:

▸ Information lost

▸ Detector gaps, Sky lines, Masked non-LTE lines

▸ Imperfect Calibrations

▸ Continuum normalization, Sky subtraction, Wavelength solution

▸ Imperfect Models

▸ Non-LTE lines, Incomplete linelists

▸ Model Interpolation

▸ Many-dimensional fitting

These are all being actively improved upon!

ARE THE CRLBS REALISTIC?

slide-14
SLIDE 14

2 AUG 2019 NATHAN SANDFORD SMALL GALAXIES, COSMIC QUESTIONS

EXPLORE ON YOUR OWN!

slide-15
SLIDE 15

29 JUL 2019 NATHAN SANDFORD SMALL GALAXIES, COSMIC QUESTIONS

Take-Aways:

  • CRLBs provide a quantitive measure of the 


information content of spectra

  • Benchmark for achievable precision
  • Useful tool for designing observations / instruments
  • CRLBs are applicable to all spectral analysis (e.g. galaxies, HII regions)

Explore on your own!

▸ Github: https://github.com/NathanSandford/Chem-I-Calc ▸ PyPi: pip install Chem-I-Calc ▸ Web Applet: Coming soon…

CONCLUSION

slide-16
SLIDE 16

29 JUL 2019 NATHAN SANDFORD SMALL GALAXIES, COSMIC QUESTIONS

DEIMOS 1200G CRLB METALLICITY DEPENDENCE

slide-17
SLIDE 17

2 AUG 2019 NATHAN SANDFORD SMALL GALAXIES, COSMIC QUESTIONS

DEIMOS 1200G CRLBS V. OBSERVATIONS

slide-18
SLIDE 18

29 JUL 2019 NATHAN SANDFORD SMALL GALAXIES, COSMIC QUESTIONS

Fij = ∂f(λ, θ) ∂θi T Σ−1 ∂f(λ, θ) ∂θj

  • <latexit sha1_base64="1Xn+KDGYjDoPCB4KloQR6zw6ywM=">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</latexit>

BAYESIAN CRLBS

For Gaussian Priors:

+Fij,prior

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Fii,prior = ⇣

1 σi,prior

⌘2

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σi ≤ q (F + σ−2

prior)−1 ii

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+ σ−2

prior)

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