Bayesian spectroscopy Ralph Schönrich (Hubble Fellow, OSU, Oxford) Maria Bergemann Francesco Fermani, Luca Casagrande, James Binney, Martin Asplund, David Weinberg
What I am not talking about
Stellar densities in the [Fe/H]-[O/Fe] plane stellar radial migration forms naturally the two ridges no gap in star formation or merger needed „thick disc“ log(density) „upper“ part of ISM trajectories ISM trajectories 10 7.5 5 2.5 kpc „thin disc“ not the consequence of a local ISM trajectory near „endpoints“ of ISM trajectories density contours 0.5 dex Schoenrich & Binney (2009b)
Kinematics in the abundance plane Gyrs km/s km/s Mean V velocities Velocity dispersion density contours 0.5 dex spacing Schoenrich & Binney (2009b)
Kinematics in the abundance plane Gyrs Lee et al. (2011) km/s km/s Mean V velocities Velocity dispersion density contours 0.5 dex spacing Lee et al. (2011)
LSR and other parameters The Strömberg relation is biased The Strömberg relation is biased - in metallicity (radial gradient) - and ages (inside-out, selection) Do not use it if you do not have a full model How can we best avoid biases by Galactic structure? 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)
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 observational problem of the next years
Bayesian spectroscopy Basic problem Large surveys present huge amounts of stellar data with moderate quality Vanishing Poisson noise: need to go for quantitative analysis incl. errors Consistent automated analysis and quality assessment required e.g. metallicity scales are not on a consistent analysis level (see e.g. Schlesinger et al. 2012) Optimal exploitation of present data requires us to use them at once Need a fair assessment of expectation values and errors in datasets → need one loop to find and bind all available information
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 e.g. metallicity scales are not on a consistent analysis level (see e.g. Schlesinger et al. 2012) Optimal exploitation of present data requires simultaneous analysis Need a fair assessment of expectation values and errors in datasets → need one loop to find and bind all available information
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 prior Observational constraints posterior 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 prior Observational constraints posterior Observations are conditionally independent
Bayesian schemes prior Observational constraints posterior Observations are conditionally independent
Bayesian schemes prior Observational constraints posterior Observations are conditionally independent
Priors and Prejudice Beware of There is no study without priors wrong confidence no prior is a flat prior Self-fulfilling prophecies Beware of violating „Cromwell's Rule“ 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
No prior error
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 spectra A P τ d (T eff , log(g), [M/H]) M i C Photometry, models, etc.
Data combination is not trivial SSPP DR9 Allende Prieto et al. (2008)
Specific parameters phot. spect. comb.
Parallaxes
Specific parameters phot. spect. 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 All parameters within one single, consistent analysis Common pitfalls (e.g. Lutz-Kelker bias) no concern while applying the method Automatic detection of pathologic (or interesting...) cases Direct ability to quantify systematic shifts/errors, reddening, distances, binary fractions, helium, etc. Need consistent improvements on models: 1D-3D, (N)LTE, rotation, etc. Need considerable calibration efforts, cf. e.g. IFRM temperatures
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