1. Karine ROUSSELET-PERRAUT
Determination of fundamental parameters of (Chemically Peculiar) A stars through optical interferometry
Karine ROUSSELET-PERRAUT
Institut de Planétologie et d’Astrophysique de Grenoble
(with contributions of Denis Mourard, Margarida Cunha, Nicolas Nardetto)
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd

2. Science drivers
The stellar atmospheric parameters of effective temperature and surface gravity are of fundamental astrophysical importance. As well as defining the physical conditions in the stellar atmosphere, these parameters are directly related to the physical properties of the star; mass, radius and luminosity. They are the prerequisites to any detailed abundance analysis. Model atmospheres are our analytical link between the physical properties and the observables - flux distributions and spectral line profiles. We can obtain effective temperature and surface gravity from suitable observations, assuming of course that the models we use are adequate and appropriate.
A-F stars are an ideal laboratory for studying physical processes
radiative diffusion, differential gravitational settling, grain accretion, convection, rotation, magnetic fields, non-radial pulsations
that show their most extreme manifestations in these stars.
These processes are based on fundamental parameters
Mass M, radius R, luminosity L, abundances
Effective temperature Teff, surface gravity log g, mean density r
From the measurement of these fundamental parameters and theoretical evolutionary tracks, one can put into test models
Stellar interiors, evolutionary stages
Magnetic field topology, pulsation excitation
(when coupled with complementary observational data)
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd

3. Outline
How can optical interferometry help to better understand the A stars ?
Principle
Instruments
Results
Prospects
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd

4. Interest of High Angular Resolution
High Angular Resolution (HAR) is fundamental for understanding star formation and evolution as well as physical process at play within stellar objects.
Sun is the best known star since we manage to "resolve" its surface, i.e. to see details on its surface like:
photosphere convection cells
dark spots
active areas
chromosphere jets
Clues for better understanding:
internal structure
pulsation modes
activity
magnetism
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
0.5º = 1 800"
Extreme Ultraviolet Imaging Telescope (EIT), Sept. 1999

5. Telescope angular resolution
Telescope size D
(m)
Resolution l/D (millisecond of arc)
Smallest detail « seen » on the stellar surface
8 m
(VLT + perfect AO)
18 (l = 0.6 µm)
42 m
(E-ELT + perfect AO)
~ 3 (l = 0.6 µm)
200 m
(with perfect AO)
~ 0.6 (l = 0.6 µm)
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
Main-sequence A stars
Need for optical interferometry

6. Interferometry principle
Interferometry is a imaging technique with (small) diluted apertures, which allows a giant mirror to be synthetized.
The longer the distance b between the
apertures, the higher the angular
resolution (given by l/b).
This technique is fully mature in radioastronomy and produces high angular resolution images.
VLTI
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
ALMA
R Scu (imaged by ALMA)

7. Optical interferometric arrays
Apertures
Number / diameter
Maximal baseline b (m) l
(µm)
Resolution
(mas)
KECK
2 / 10 m 85 IR
~ 20
VLTI
4 / 8 m
4 / 1.8 m
130
200
Near-
Mid-IR
2 – 15
1.5 – 2.5
CHARA
6 / 1 m
330
Visible
Near-IR
0.3 – 0.5
0.9 – 1.5
NPOI
6 / 0.12
430
0.25 – 0.4
CHARA
VLTI
NPOI
KECK
Generally we have not enough apertures to obtain images

8. Interferometric observables
In optical range we generally observe interference fringe patterns between the different apertures.
The visibility V and the phase  of these fringe
patterns are related to the Fourier transform
of the object brightness (Van-Cittert theorem) V
V eij = TF{Object} (b/l)
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
p p
Photocenter p
We can deduce angular diameter, binary orbit, environment extent, etc.

9. How to measure angular diameters?
The VLTI b
The VLTI b
The VLTI b V
combination b
We record fringes for different telescope separations b.
We compute the visibility V and the phase j for each fringe pattern
We fit the curve V = f(b) with an angular diameter model.
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd V

10. Fundamental parameters’ determination
Angular diameter LD
Distance d
Radius R
Interferometry
Hipparcos
Bolometric flux fbol
Distance d
Luminosity L
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
Spectro-photometry
Mass M
Age
Gravity log g
Effective temperature Teff

11. Application to A stars
In addition to their many other peculiarities, the ages of A stars are poorly known. As main sequence stars, they evolve in Teff and in L/R, which affords an opportunity to establish their ages through interferometric means.
Observational data can be compared to models on an H-R diagram, which will then indicate their ages and masses.
Significant improvement of measurement accuracy
First statistical studies
Application to A-star sub-classes
Exoplanet host stars
provide R for planetary system modeling
Chemically Peculiar (CP) stars
provide Teff that is not affected by the abnormal surfaces
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd

12. Improvement of accuracy
The recent improvement of the accuracy on interferometric observables has led to an angular diameter precision of typically 1-2% and consequently to an improved determination of stellar fundamental parameters, which in turn allows to test stellar models in an independent way.
The constraint put on the mass allows the authors to conclude that Procyon is currently ending its life on the main sequence, as its luminosity calss indicates.
Procyon
« classical » error box
« interferometric »
error box
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
[Kervella et al. A&A, 413, 251(2004)]

13. Statistical studies
Several surveys of main-sequence stars have been led with optical interferometry but they mainly consists of G and K targets.
Survey of 44 stars by T.
Boyajian with CHARA
The result of this selection is that the radii of ≃ 450 stars can be derived with a relative uncertainty smaller than 3%. Their positions in the
Hertzsprung-Russell (MV , V −K) diagram are presented
Average accuracy of 1.5 %
d < 22 pc
Accuracy on R< 3%
[Boyajian et al. ApJ, 746, 101 (2012)]
[Cunha et al. A&AR, 14, 217 (2007)]

14. Statistical studies
[Boyajian et al. ApJ, 746, 101 (2012)]
[Boyajian et al. ApJ, in prep (2013)]
Comparison of interferometric diameters with SED ones
Effective temperature law
A stars
Relationships useful in extending our knowledge to a larger number of stars, at distances too far to accurately resolve their sizes.

15. Surface-Brightness relationship
In the recent distance determination to the Large Magellanic Cloud (the best anchor point of the cosmic distance scale) with an accuracy of 2%, the main uncertainty comes from Surface-Brightness relationships [Pietrzynski et al. 2013, Nature]
+ Di Benedetto (2005)
+ Boyajian (2012)
+ Brown (1974)
+ Challouf (in prep)
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
Bright early-type stars (O-A-B)
for distances in Local Group
Late-type stars (F-G)
for LMC distance

16. Interest of multi-technique studies
Interferometry + Spectroscopy:
R, L, Teff accurate determination requires interferometric angular diameters, accurate parallaxes and accurate bolometric flux.
Interferometry + Asteroseismology:
[Creevey et al., ApJ, 659, 616 (2007)]
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
Accurate R allows accurate masses M to be derived

17. Small rotational speed
Case of the roAp stars
Small rotational speed
(< 100 km/s)
Abundance inhomogeneities
(with a contrast up to 1000)
< 1 mas
Strong magnetic field (up to ~30 kG) large-scale organized
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
roAp: intersection of Main-Sequence and instability strip
Pulsations (period of a few minutes)
Optical interferometric allows to have a direct (and unbiased) measurement of the linear radius of these tiny stars.

18. Example of 10Aql qLD = 0.275 0.006 mas + Bolometric flux and parallax
[CHARA/VEGA]
R =  R V²
+ Bolometric flux and parallax
+ Large frequency separation Dn
+ Evolutionary track (CESAM2K) 
B/l
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
M =  0.05 M
[Perraut et al. A&A, submitted]

19. Test of roAp excitation models
[Cunha et al. A&A, in prep]
g Equ
« Interferometric » fundamental parameters
for 4 roAp (aCir, bCrB, gEqu, 10 Aql)
Stellar interior models
Prediction of excitation modes
Comparison with observed modes
Excited
Considering the four roAp stars for which angular diameters determined based on interferometric data are currently available, we were able to verify that for three of them the frequency region in which modes are predicted to be unstable, according to the models described in Balmforth et al. (2001) and Cunha (2002), agrees well with the region where frequencies are observed. Based on the comparison of model results and observations we were also able to put constraints on the minimum extent of the angular region in which envelope convection must be suppressed, according to the proposed models. Oscillations with frequency above the acoustic cutoff are particularly sensitive to the real
dynamics of the atmospheric layers of the star, where the magnetic field plays an important role. Because they neglect that effect,
our models become particularly inadequate to study these high frequency oscillations.
Not excited
Observed modes
10 Aql
 Cir
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
Predicted modes derived for interferometric parameters ( ) are in agreement with observed ones but for Cir.

20. Go beyond diameter measurement
Optical interferometry is clearly a powerful means to derive accurate fundamental parameters through angular diameter measurement but this technique can also be used to study the environments of A stars:
Study debris disks around VEGA-like
Search for companion(s)
and coupled with spectrometry for kinematic studies
Study of wind and mass loss
A supergiants, (magnetic) Herbig AeBe
Study of limb-darkening
Imaging of stellar surfaces (rotation)
[i.e. fringes are dispersed with a spectral resolution of a few thousands
visibilities and phases are computed vs. wavelength]
Fomalhaut
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
Deneb

21. Debris disks
The short-baseline visibilities are lower than expected for the stellar photosphere alone. The visibility offset of a few percent is interpreted as a near-infrared excess arising from dust grains which must be located within several AU of the central star. V²
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
Leo
b (m)
[Akeson et al. ApJ, 691, 1896 (2009)]

22. Supergiant wind
The line-formation region is extended (∼1.5–1.75 R*) since the visibility decreases in the H line. There is a significant asymmetry in the line forming region since the phase is not null in the line.
[Chesneau et al. A&A, 521, A5 (2010)]
Ha line
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
Visibility
Phase
Deneb l l

23. Rotation
Optical interferometry can image the surface of fast rotators.
The image clearly reveals the strong effect of gravity darkening on the highly-distorted stellar photosphere.
Standard models for a uniformly rotating star cannot explain the results, requiring differential rotation, alternative gravity darkening laws, or both.
Beta = gravity darkening
[Monnier et al. Science, 317, 342 (2008)]
Altair
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd

24. Conclusion
Optical interferometry is a powerful means for deriving accurate fundamental parameters of A stars through accurate angular diameter determinations.
With long-baseline arrays an angular resolution of about 0.3 mas is now reachable.
There is a huge potential of combining interferometric (radius and derived effective temperature) and asteroseismic (large frequency separation) data to improve the determination of the mass of pulsating stars.
Coupled with spectroscopy, optical interferometry can allow kinematics studies of A stars’ environments.
Going beyong angular diameter measurements allows limb- darkening to be derived and besides surfaces of fast rotators to be imaged.
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd

25. Prospects Position of 109 stars with an accuracy of ~20 µas Needs to
 Go towards an Angular Diameter Anthology
Needs to
go to higher sensitivity and to smaller targets
Increase accuracy for putting into test stellar models
Go towards surface imaging across spectral lines
[Boyajian et al. ApJ, in prep (2013)]
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd

26. Breakthrough for CP stars
HD24712
[Lüftiger et al., A&A, 509, A71 (2010)]
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
[See poster of D. Shulyak et al. in this conference]

27. Thanks for your attention
The CHARA Array
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd

28. An example of simulation : 2CVn
0.5
-0.5
Spectra of 2CVn (CrII4824 line)
Doppler maps (Kochukhov,2002)
Observations d’Oleg
Reconstruction Doppler
information spatiale = série des spectres
Outil de simulation
1) reproduit les spectres observés = validation de la modélisation
2) prédit les observables interférométriques
phase des franges en fonction de pour deux orientation de base
Intérêt :
localisation géométrique 2D des structures
chaque phase stellaire contiens une information spatiale indépendante 
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd 
0.5
-0.5
Predicted interferometric phases
Interferometric phases provide 2D geometrical constraints
Rousselet-Perraut et al., A&A, 422, 193

29. Abundance study with CHARA/VEGA
Courbe de visibilité pour étoile magnétique bCrB :
noir = continu
vert / bleu = polar. circulaires
Le passage GI2T -> CHARA :
second lobe
augmentation des importantes des signatures en visibilité
Chp Magnétique dipolaire = tache égales à une fraction du diamètre = second lobe
Analyse géométrique paramétrique
Resolved target
Large visibility effects
Observations in the visibility lobes
Line for various
stellar phases
CHARA
Abundance spots of a fraction of stellar diameter can be detected in the 2nd and 3rd visibility lobes
BUT
Imaging may be difficult due to the small number of telescopes
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
CHARA/VEGA + 2CVn models

30. Limb-darkening effect
Limb darkening in an absorption line is expected to be less than it would be for the continuum at the wavelength of the line because the line is formed all the way out to the stellar surface.
Sirius
Uniform-disk diameter
(mas)
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
Ha line l
[ten Brummelaar et al. MROI meeting (2011)]

31. Determination of fundamental parameters of (Chemically Peculiar) A stars through optical interferometry
Karine ROUSSELET-PERRAUT (IPAG, France)
The recent improvement of the accuracy on interferometric observables has led to an angular diameter precision of typically 1-2% and consequently to an improved determination of stellar fundamental parameters, which in turn allows to test stellar models in an independent way.
Procyon
« classical » error box
« interferometric »
error box
IAU Conference « Putting A Stars into Context”
Moscow, 2013 June 3rd
[Kervella et al. A&A, 413, 251(2004)]