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)