Static presentation given at the CASCA conference in 2014

1. BAYESIAN STATISTICS AS A NEW
TOOL FOR SPECTRAL ANALYSIS:
Application for Massive Stars Fundamental
Parameters Determination
Jean-Michel Mugnes

2. CLASSICAL SPECTRAL ANALYSIS
 Aim: obtain stellar parameters: Teff, log g, vsin i ,
microturbulence (), macroturbulence,
abundances…
 Many technics used: curve of growth, FFT, model
fitting « by eye » or with χ² calculation…
 Iterative methods with Free & fixed parameters
 a few lines used depending on their sensitivities.
(e.g. : Balmer lines -> log g & Teff, Si lines -> Teff, etc…)

3. THE CLASSICAL APPROACH
 Iterative with Free & fixed parameters:
 Build a Model grid (here TLUSTY Lanz & Hubeny 2007)
 Teff & log g free
 vsin i = 0 km.s-1
  = 0 km.s-1

4. THE CLASSICAL APPROACH
 Chi square analysis on Hbeta (vsin i &  =0 km.s-1)
And it is only for
one line…
 But what happens for different values of vsin i ?
Red diamond = Best
solution for a given vsin i
 And for different values of  ?

5. THE CLASSICAL APPROACH
 And each line has it’s own « opinion »
 The final results depends on the selected lines
 And on the values of the fixed parameters.
 Simultaneity is the key.

6. THE SIMULTANEOUS APPROACH
 From free & fixed parameters to only free parameters.
Most
probable
Less
probable
 « Free & fixed » fit:
χ² calculated for a given
vsin i and  separatly
 Simultaneous fit:
χ² calculated over all
values of Teff, log g, vsin i
and .
« Likelyhood of H »

7. DIFFERENT LINES, DIFFERENT LIKELYHOODS
Likelyhood =
Cexp ( - χ²/2σ²)
(here σ= 10 X σ_real)
a wide variety of
shapes

8. FROM AN ITERATIVE TO A SIMULTANEOUS METHOD
 The Bayes Theorem:
Prior probability (line 1) Likelyhood (line 2)
Posterior probability
= prior probability for
line 3 , etc…
X
=
Likelyhood (line 1)

9. BAYES THEOREM IN PROCESS
Posterior
probability

10. GOING FURTHER
 Final probability
distribution for all the
parameters given by all
the lines in the spectrum
simultaneously
New model grid
Refined final
probability
(Remember that
σ= 10 X σ_real)

11. TESTING THE METHOD
 Applied the method
on a randomly noised
synthetical spectrum
 SNR going from 25 to
350 with steps of 25.
 10 runs where
performed for each
SNR value
SNR=25
SNR=350

12. TESTING THE METHOD
 Overall success rate is over 86 %
 Around 78% for a SNR < 150
 Around 92% for a SNR > 150

13. TESTING THE METHOD ON REAL SPECTRA
 52 spectra of field and cluster B stars collected
at the Mont-Mégantic Observatory.
 « Normal » stars : no binaries, chemicaly peculiar,
pulsating…
 Well studied nearby stars.
 Visible spectra between 3600 Å and 6000 Å, with
moderate resolution (fwhm=2.3 Å)

14. TESTING THE METHOD ON REAL SPECTRA

15. TESTING THE METHOD ON REAL SPECTRA

16. CONCLUSIONS
 We have developed a new spectral analysis
method that :
 simultaneously constraints all the parameters and all the
available lines
 is robust against noise and uncertainties
 is generally more accurate than the classical methods
 is also fast, automated and gives the results with their
associated uncertainties
 Works also with any given model atmosphere
(TLUSTY, ATLAS, PHOENIX,…)

17. THANK YOU FOR YOUR
ATTENTION