Bayesian spectroscopy Ralph Schnrich (Hubble Fellow, OSU, Oxford) - - PowerPoint PPT Presentation

Ralph Schönrich (Hubble Fellow, OSU, Oxford)

Maria Bergemann

Francesco Fermani, Luca Casagrande, James Binney, Martin Asplund, David Weinberg

Bayesian spectroscopy

What I am not talking about

log(density)

„thin disc“

„thick disc“

Stellar densities in the [Fe/H]-[O/Fe] plane

density contours 0.5 dex

not the consequence of a local ISM trajectory near „endpoints“ of ISM trajectories „upper“ part of ISM trajectories

ISM trajectories

10 7.5 5 2.5 kpc

stellar radial migration forms naturally the two ridges no gap in star formation or merger needed Schoenrich & Binney (2009b)

Mean V velocities

density contours 0.5 dex spacing km/s

Velocity dispersion

km/s

Kinematics in the abundance plane

Gyrs Schoenrich & Binney (2009b)

Mean V velocities

density contours 0.5 dex spacing km/s

Velocity dispersion

km/s

Kinematics in the abundance plane

Gyrs

Lee et al. (2011) Lee et al. (2011)

LSR and other parameters

The Strömberg relation is biased

• in metallicity (radial gradient)

The Strömberg relation is biased

• and ages (inside-out, selection)

Do not use it if you do not have a full model Three simple estimators for Galactic rotation Best values for the LSR: (14, 12, 7) kms-1

Solar position and Galactic rotation: (R = (8.27 +/- 0.29) kpc, Vc ~ 238 km/s)

How can we best avoid biases by Galactic structure?

The issue with big samples

Poisson error drops with N-0.5 Currently systematics are of same order as Poisson noise Future surveys (Gaia, Gaia-ESO, HERMES, etc.) will increase sample sizes by factor 10000 Assessment of errors is the most important

• bservational problem of the next years

Basic problem

Large surveys present huge amounts of stellar data with moderate quality Consistent automated analysis and quality assessment required Need a fair assessment of expectation values and errors in datasets e.g. metallicity scales are not on a consistent analysis level Optimal exploitation of present data requires us to use them at once → need one loop to find and bind all available information (see e.g. Schlesinger et al. 2012)

Bayesian spectroscopy

Vanishing Poisson noise: need to go for quantitative analysis incl. errors

Example: Gravities vs metallicity in SEGUE Subgiants/Giants „Turnoff“ Dwarfs

Basic problem

Large surveys present huge amounts of stellar data with moderate quality Consistent automated analysis and quality assessment required Need a fair assessment of expectation values and errors in datasets e.g. metallicity scales are not on a consistent analysis level Optimal exploitation of present data requires simultaneous analysis → need one loop to find and bind all available information (see e.g. Schlesinger et al. 2012)

Bayesian schemes

• cf. Pont & Eyer (2004), Jörgensen & Lindegren (2005)

Burnett & Binney (2010), Casagrande et al. (2011), Serenelli et al. (2013) Shkedy et al. (2007)

Bayesian schemes

posterior prior Observational constraints X = set of parameters like age, distance, metallicity, temperature, etc. O = set of observations e.g. measurement of a parameter, spectrum taken, even statements like „discovery of phosphorus stars made by person with smoking habit“

Bayesian schemes

Observations are conditionally independent posterior prior Observational constraints

Bayesian schemes

Observations are conditionally independent posterior prior Observational constraints

Bayesian schemes

Observations are conditionally independent posterior prior Observational constraints

Priors and Prejudice

There is no study without priors no prior is a flat prior Beware of violating „Cromwell's Rule“ Beware of wrong confidence Self-fulfilling prophecies Uninterpretable results Steps taken here: leave priors on shown quantities flat Salpeter IMF, standard spatial densities

Stellar models and photometry

Sum in core parameter space over all available stellar model points i Multiply each point with the likelihood of observing the magnitude vector C

error

No prior

age prior

Priors do matter!

Photometric parameters

Top row: Parallaxes + Johnson photometry Bottom row: SDSS photometry

Spectral information

Require accurate information about the full spectroscopic PDF Classical approach of best-fit value + some experienced error estimate is not viable Need to calculate full statistics for synthetic spectra in parameter space Use adaptive, iteratively refined mesh guided by photometry + prior 1

Spectral information

Require accurate information about the full spectroscopic PDF Classical approach of best-fit value + some experienced error estimate is not viable Need to calculate full statistics for synthetic spectra in parameter space Use adaptive, iteratively refined mesh guided by photometry + prior

Understanding Parameter Space

(Teff, log(g), [M/H]) τ Mi d C A P spectra Photometry, models, etc.

Data combination is not trivial

Allende Prieto et al. (2008) SSPP DR9

Specific parameters

spect. phot. comb.

Parallaxes

Specific parameters

spect. phot. comb.

Parameters

HR-diagram

HR diagram revisited

HR-diagram

HR diagram

AMR

distances

Summary

Full probabilistic schemes are mandatory for understanding data Many dimensions, but low dimensionality, demands tailored solutions Need consistent improvements on models: 1D-3D, (N)LTE, rotation, etc. Automatic detection of pathologic (or interesting...) cases Direct ability to quantify systematic shifts/errors, reddening, distances, binary fractions, helium, etc. Need considerable calibration efforts, cf. e.g. IFRM temperatures All parameters within one single, consistent analysis Common pitfalls (e.g. Lutz-Kelker bias) no concern while applying the method