Modern Tools and Techniques for Quantitative Spectroscopy

Miguel A. Urbaneja IAPP, U. Innsbruck

Quantitative Spectroscopy

•  Inference of the physical parameters that (uniquely and completely?) characterize an astronomical object based on: – observed spectrum, – theoretical spectra, and – comparison metrics

What should you worry about?

•  Information encoded in the observed data (both quantity and quality) – Spectral range coverage, SNR, …

•  Physics incorporated in the models – Assumptions/simplifications

•  Atomic data •  Comparison metrics •  Uncertainties/Errors

QS as an inversion problem

•  In all instances, QS is approached as an inversion problem

•  The ingredients: – Model atmosphere/line formation code – Observed data – Comparison metrics

x = f

0 (S�)

•  non-LTE •  1D geometry.

•  Plane-parallel •  Spherical

•  Hydrost./mass outflow. •  Blanketing/blocking. •  Micro-clumping.

Model Atmospheres for OB stars DETAIL/SURFACE (Butler & Giddings 1985)

»  ATLAS (Kurucz 1970)

TLUSTY/SYNSPEC (Hubeny 1988)

CMFGEN (Hillier & Miller 1998) FASTWIND (Puls et al. 2005) PoWR (Hamann & Gräfener 2004) WM-basic (Pauldrach el al. 2001)

Parameter space –  No wind: 4d p-space – Teff, logg, He, ξ (bare minimum) –  With wind: 8d p-space – Teff, logg, He, ξ, β, R★, vterm,

Mdot –  + wind clumping, + elemental abundances …

Op#cal   IR   UV  Teff     He,  N,  C,  Si,  O   He   He,  C  logg   H  Balmer  lines   H  Bracke7  lines  micro   He,  metal  lines   He     Metal  lines  He   He  lines   He  lines  Q/Rt  &  beta   Hα,  Hβ,  …    

HeI  5876  H  and  He  lines   P  Cyg  profiles  

vterm   P  Cyg  profiles  Elements  abundances  

Several  lines  from  different  species  

Few  weak  metal  lines  

Several  lines  from  different  species  

Observational information

Clumping  is  included  in  the  wind  invariant:  

EW  invariant  Tau  invariant  

Rt = R⇤

⇣v1/Ms

⌘2/3Q = Ms (R⇤ v1)�2/3

SOME RECENT EXAMPLES Quantitative Spectroscopy of OB stars -

Optical Spectroscopy Martins et al. (2015)

“Surface  abundances  of  GalacWc  ON  stars”  

ObservaWons:  high-­‐resoluWon,  high  SNR  opWcal  spectra.  

Parameters:  Teff,  logg,  He/H,  CNO.  

Comment:  No  wind  analysis  (“reasonable”  values  adopted).    

Models:  CMFGEN  (Hillier  &  Miller  1998).  

Sample  size:  12  stars.  

HD14633 – ON8.5V

Multi-wavelength: OPT + IR

“L-­‐band  spectroscopy  of  GalacWc  OB-­‐stars”  

ObservaWons:  opWcal  spectra,  H-­‐,K-­‐  and  L-­‐band.  

Parameters:  Teff,  logg,  He/H,  β,  Q,  …  (#11)  

Comment:  clumping  law  with  4  parameters.    

Models:  CMFGEN  (Hillier  &  Miller  1998).  

Sample  size:  10  stars.  

Najarro, Hanson & Puls (2011)

HD37128 – B0.5Ia

Multi-wavelength

“StraWficaWon  of  wind  clumping  in  GalacWc  OB-­‐stars”  

ObservaWons:  Hα,  IR,  mm  and  radio.  

Parameters:  Mdot,  β,  clumping  straWficaWon  (#11)  

Comment:  clumping  divided  in  5  zones,  with  4  clumping  factors.      

Models:  approximated  models  calibrated  with  precise  non-­‐LTE  calculaWons.  

Sample  size:  15  stars.  

Puls et all. (2006)

zet Pup – O4I(n)f

OB stars - analysis

•  Multi-dimensional parameter space. •  Teff, logg, He, ξ, abundances, wind …

•  Parameter degeneracy. – Well known cases with significant covariance •  Teff—logg •  Abundance—microturbulence •  Mdot—beta •  (micro)clumping—Mdot

– Unknown degeneracies (high likelihood).

OB stars – analysis: Uncertainties

•  In most cases, only internal errors are reported. – These are almost always connected to the SNR.

•  Uncertainties related to the models are completely disregarded. – Hard to estimate. –  Fine if working in relative terms, but, – What happens when a comparison in absolute

terms is required?

•  99% of the cases “symmetric” uncertainties.

QS of large spectroscopic samples

•  Inversion problem

•  A standard procedure is no longer viable. – Move beyond the individual analysis.

•  Endless Math possibilities … – Minimum distance (MD) methods – Projection methods – Pattern recognition methods

x = f

0 (S�)

Scouting the OB literature

•  Only MD methods have been considered for OB stars so far

•  Gaussian likelihood

L =

Y

j

(1p

2⇡ �j

exp

"� (Oj � Mj)

2

2�2j

#)

d (O,M) ,X

j

(Oj � Mj)2

Peeking into other fields •  A lot of work has been done for the analysis of

cool(er) stars and stellar population of galaxies . •  Projection methods

–  Recio-Blanco+2006 – MATISSE –  Urbaneja+2008 – (PCA)

•  MD methods –  Valenti+1996 – SME –  Koleva+2009 – ULySS –  Bijoui+2012 – GAUGIN –  Garcia Perez+ 2014 - ASPCAP

•  Pattern recognition –  Bailer-Jones+1997 –  Re Fiorentin+2007 –  Kordopatis+2011 – DEGAS

QS tools in the OB literature Mokien+2005   Lefever+2006   Simón-­‐Díaz

+2011  Irrgang+2014  

Targets   O  Stars   B  Stars   O  Stars   B  stars  Metrics     MD   MD   MD   MD  Models   FASTWIND   FASTWIND   FASTWIND   ADS  Parameters   6   7     6   13  Method   GA   Grid     Grid   Grid  #  of  models   7000/star   3x105   2x105   ~2x106  

Comment   on  the  fly   Grid   Grid   Grid  MD  –  Minimum  distance.  GA  –  GeneWc  algorithm.  

ADS  –  Atlas  +  Detail  +  Surface  

A word of caution

•  Gaussian likelihood is often used. •  In particular for defining (internal)

uncertainties

•  HOWEVER … – this explicitly claims that the model is being

used is the correct model underlying the observed data,

– errors are normally distributed.

L =

Y

j

(1p

2⇡ �j

exp

"� (Oj � Mj)

2

2�2j

#)

�2 = �2min + 1

An example

Gazak (2014)

Simulated residuals

Real residuals

�2 = �2min + 1

Some numbers

•  Mokiem+2005: 7x103 models per star •  Lefever+2006: ~3x105 models •  Simón-Díaz+2011: ~2x105 models

•  This is possible because … – All used a very fast model atmosphere/line

formation code (FASTWIND – Puls+ 2005).

•  Clearly, theses methods are not suitable for all codes/applications.

And when we move to a higher p-space

•  New physics to come. – Meaning more parameters •  i.e. macro-clumping, magnetic fields, 2D/3D …

– Higher computational cost per model.

•  Complex parameter space -> potential degeneracies.

•  Explore the multi-d parameter space using Markov Chains, relying on the construction of a statistical emulator that is based on an optimized, fix, model grid.

My take on this

– Optimal model grid design. – Lower dimensional representation using PCA.

–  “A spectrum is worth a thousand images.” (RPK)

– Gaussian Process regression. •  Outcome: can emulate a spectrum for any given set

of parameters within the limits of your grid.

– Parameter space explored with Markov Chains. •  Monte Carlo (Metropolis-Hastings) •  Differential Evolution (beautifully elegant, but

slower than MC)

My take on this (cont.)

S� (x0) =

X

ı

✓

ı (x0) eı (�)

•  (1) Optical spectroscopy of BSgs: •  FASTWIND, 300 models, 11 parameters, optimal grid

design. –  Teff, logg, ξ, β, Q, He, C, N, O, Mg, Si

•  (2) IR spectroscopy of Wolf-Rayets: •  CMFGEN, 350 models, 11 parameters, non optimal

grid design. –  T20, Rt20, vterm, β, cl1, cl2, cl3, cl4, He, N, C

A couple of examples

3900 4000 4100 4200 4300Wavelength (Å)

2

4

6

Flux

+ c

onst

ant (

a.u.

)

Sk−68−40

Sk−66−166

Sk−67−36

Sk−67−228

Sk−66−1

Sk−68−92

Sk−69−43

Sk−67−14

Sk−68−171

4300 4400 4500 4600 4700Wavelength (Å)

2

4

6

Flux

+ c

onst

ant (

a.u.

)

Sk−68−40

Sk−66−166

Sk−67−36

Sk−67−228

Sk−66−1

Sk−68−92

Sk−69−43

Sk−67−14

Sk−68−171

Spectroscopy  of  LMC  B-­‐type  supergiants.  

ObservaWons:  opWcal  spectra.  

Sample:  40  stars    

Parameters:  11  

Models:  FASTWIND  –  Puls  et  al.  (2005)    

Grid:  300  models    (opWmal  grid).  

Urbaneja et al. (2015)

3.81 4.07 4.32T20 (104 K)

0.0

0.2

0.4

0.6

0.8

1.0

3.81 4.07 4.32 1.18 1.31 1.45logRT20

0.0

0.2

0.4

0.6

0.8

1.0

1.18 1.31 1.45 0.85 1.17 1.49bet1

0.0

0.2

0.4

0.6

0.8

1.0

0.85 1.17 1.49 1.3 1.6 1.9vinfty

0.0

0.2

0.4

0.6

0.8

1.0

1.3 1.6 1.9

−1.670 −1.078 −0.485lcl1

0.0

0.2

0.4

0.6

0.8

1.0

−1.670 −1.078 −0.485 66 240 413fcl2

0.0

0.2

0.4

0.6

0.8

1.0

66 240 413 0.42 0.59 0.77He

0.0

0.2

0.4

0.6

0.8

1.0

0.42 0.59 0.77 0.0128 0.0277 0.042N

0.0

0.2

0.4

0.6

0.8

1.0

0.0128 0.0277 0.042

3.9 4.0 4.1 4.2 4.3T20 (104 K)

1.20

1.25

1.30

1.35

1.40

logR

T20

95%

68%

3.9 4.0 4.1 4.2 4.3T20 (104 K)

0.5

0.6

0.7

He

95%

68%

−1.6−1.4−1.2−1.0−0.8−0.6lcl1

0.5

0.6

0.7

He

95% 95

%

68%

0.5 0.6 0.7He

0.015

0.020

0.025

0.030

0.035

0.040

N

95%

68%

De la Fuente et al. (in prep.)

NIR  studies  of  obscured  GalacWc  massive  stellar  populaWon.  

ObservaWons:  IR  spectra  (H-­‐,  K-­‐band).  

Parameters:  11  

Models:  CMFGEN  

Grid:  350  models    

Comment:  4-­‐param  clumping  law  

Closing remarks •  Spectroscopic surveys -> wealth of data. •  There is already a tool for your needs.

•  Extremely easy “optimization”/ “data mining”/“machine learning”/“pattern recognition” task, compared to what is required in other fields.

•  Values without realistic uncertainties are meaningless.

•  In an era in which our Cosmology colleagues claim parameter determinations with unprecedented accuracy, Stellar spectroscopy should strive at least for properly measured uncertainties.

Many thanks to …

A.J. Nebro, R.-P. Kudritzki, J. Puls, C.E.A. Rasmussen, D.J.C. Mackay, A. Asensio, S. Simón-Díaz, A. Herrero, F. Najarro, N. Przybilla

SOME EXTRA SLIDES Need more details?

Statistical emulator: Predict the outcome of an experiment for an unsampled point in the parameter space just by using the information already contained in previously sampled points. A statistical emulator acts as a surrogate of a simulator, providing predictions (and corresponding uncertainties) at unsampled input values (Sacks et al. 1989). How this works in practice. (1)  Information compression: from k-wavelenghts to i-

coefficients, with i<<k (Karhunen—Loèwe transform/PCA). (2) Gaussian Process regression: PC coefficients depend on

model parameters. (3) Outcome: for unsampled x’

S� (x0) =

X

ı

✓

ı (x0) eı (�)

Note that the emulator requires a pre-computed grid of models. This is a grid-based method; on-the-fly simulations are not used.

S� (x0) =

X

ı

✓

ı (x0) eı (�)

Emulated spectrum

Model parameters

Coefficients (PCA + GP)

Eigenvectors resulting from the PC analysis

Minimum Distance: Minimization of the distance between the observed spectra and each of the spectra in the reference grid.

d (O,M) /X

�

(O� �M�)2

Projection methods: Using the reference grid, a set of basis vectors are calculated, one for each parameter to be determined. For an object in the observed sample, each parameter is derived by projecting the observed spectrum onto the corresponding basis vector.

✓ =X

�

B✓� O�

Projection

4300 4400 4500 4600 47000.60.70.80.91.01.1

Nor

m. f

lux

4300 4400 4500 4600 47000.000.010.020.030.040.050.06

4300 4400 4500 4600 4700−0.06−0.04−0.02

0.000.020.040.06

2.5 2.6 2.7 2.8 2.9 3.0 3.1Teff (kK)

−1.0−0.5

0.00.51.0

Proj

. (PC

1)

Wavelength (Å)

Variance

EigenVec (PC1)

This is the basis vector These are the

projections.

2 models with different Teff, but the rest is the same

4300 4400 4500 4600 4700Wavelength (Å)

−0.06−0.04−0.02

0.000.020.040.060.08

Flux

(a.u

.)

4300 4400 4500 4600 4700Wavelength (Å)

−0.06−0.04−0.02

0.000.020.040.06

Flux

(a.u

.)

B(logg)

B(Teff) PCA basis vector for Teff

PCA basis vector for logg

Pattern recognition: Given an unknown function g:X->Y (the truth) that maps input instances x to output labels y, along with training data D={(x1,y1), (x2,y2), …, (xn,yn)} assumed to represent accurate examples of the mapping, produce a function h:X->Y that approximates as closely as possible the correct mapping g. Identification of regularities in the reference data. Typical examples for constructing the h function are decision trees and neural networks.

G : S� ! {Te↵ , log g, ...}In

put:

Spe

ctru

m

Out

put:

par

amet

ers

QS tools in the OB literature

•  PIKAIIA (GA) – Mokiem+ 2005 – 6d p-space •  Teff, logg, micro, He/H, wind invariant, beta

– Tramper+ 2014 – 5d p-space •  Teff, logg, micro, He/H, wind invariant

•  As used in Mokiem+ 2005 – 7000 models per star (100 iterations, 70

models per iteration). – Model fitness defined as F =

0

@nX

j

!j �2j

1

A�1

Mokiem et al. (2005) ObservaWons:  opWcal  spectra.  

Parameters:  Teff,  logg,  ξ,  He/H,  β,  Q  

Models:  FASTWIND  –  Puls  et  al.  (2005)    

Sample  size:  12  stars.  

Comments:  MD,  GA,  7000  models/star  

HD15629 – O5V((f))

QS tools in the OB literature (II)

•  Grid-based search – Lefever+ 2006 (AnalyseBstar) •  Teff, logg, ξ, He/H, Si/H, Q, β

– Simon-Diaz+ 2011 (IACOB-GBAT) •  Teff, logg, ξ, H/He, Q, β

– Castro+ 2012 •  Teff, logg, ξ, He/H, Si/H, Q

–  Irrgang+ 2014 •  Teff, logg, ξ, He/H, C, N, O, Ne, Mg, Al, Si, Ar, Fe

Simón-Díaz et al. (2011)