Determination of fundamental parameters of Determination of fundamental parameters of (Chemically Peculiar) A stars (Chemically Peculiar) A stars

through optical interferometrythrough optical interferometry

Karine ROUSSELET-PERRAUT

Institut de Planétologie et d’Astrophysique de Grenoble

(with contributions of Denis Mourard, Margarida Cunha, Nicolas Nardetto)

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Science driversScience drivers

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

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)

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OutlineOutlineHow can optical interferometry help to better

understand the A stars ?

Principle Instruments Results Prospects

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InterestInterest of High Angular Resolution 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

Extreme Ultraviolet Imaging Telescope (EIT), Sept. 1999

0.5º = 1 800"

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Telescope angular resolutionTelescope angular resolution

Main-sequence A stars

Telescope size D (m)

Resolution /D (millisecond of arc)

Smallest detail « seen » on the stellar surface

8 m (VLT + perfect AO)

18 ( = 0.6 µm)

42 m(E-ELT + perfect AO)

~ 3 ( = 0.6 µm)

200 m(with perfect AO)

~ 0.6 ( = 0.6 µm)

Need for optical interferometry5IA

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Interferometry principleInterferometry 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 /b).

This technique is fully mature in radioastronomy and produces high angular resolution images.

R Scu (imaged by ALMA)

ALMA

VLTI

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Optical interferometric arraysOptical interferometric arraysArray Apertures

Number / diameter

Maximal baseline b (m)

(µm)

Resolution (mas)

KECK 2 / 10 m 85 IR ~ 20

VLTI 4 / 8 m4 / 1.8 m

130200

Near-Mid-IR

2 – 151.5 – 2.5

CHARA 6 / 1 m 330 VisibleNear-IR

0.3 – 0.50.9 – 1.5

NPOI 6 / 0.12 430 Visible 0.25 – 0.4

CHARA VLTI KECKNPOI

Generally we have not enough apertures to obtain images7

Interferometric observablesInterferometric 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 ei = TF{Object} (b/)

pp

Photocenter p

We can deduce angular diameter, binary orbit, environment extent, etc.

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How to measure angular diameters?How to measure angular diameters?The VLTI

b

The VLTI

b

The VLTI

b

We record fringes for different telescope separations b.

We compute the visibility V and the phase for each fringe pattern

We fit the curve V = f(b) with an angular diameter model.

combination

V

b

V

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Fundamental parameters’ Fundamental parameters’ determinationdetermination

Angular diameter LD

Bolometric flux fbol

Distance d Radius R

Effective temperature Teff

Distance d Luminosity L

Hip

parc

os

Inte

rfer

omet

rySp

ectr

o-ph

otom

etry

Mass MAgeGravity log g

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Application to A starsApplication to A starsIn 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 accuracyFirst 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

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Improvement of accuracyImprovement of accuracyThe 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.

[Kervella et al. A&A, 413, 251(2004)]

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« classical » error box

« interferometric » error box

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Statistical studiesStatistical studiesSeveral 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

d < 22 pc Accuracy on R< 3%

[Cunha et al. A&AR, 14, 217 (2007)][Boyajian et al. ApJ, 746, 101 (2012)]

Average accuracy of 1.5 %

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Statistical studiesStatistical studiesComparison of interferometric diameters with SED ones

A stars

Effective temperature law

Relationships useful in extending our knowledge to a larger number of stars, at distances too far to accurately resolve their sizes.

[Boyajian et al. ApJ, 746, 101 (2012)][Boyajian et al. ApJ, in prep (2013)]

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Surface-Brightness relationshipSurface-Brightness relationship

+ Di Benedetto (2005)+ Boyajian (2012)+ Brown (1974)+ Challouf (in prep)

Late-type stars (F-G) for LMC distance

Bright early-type stars (O-A-B) for distances in Local Group

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]

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Interest of multi-technique studiesInterest of multi-technique studies

[Creevey et al., ApJ, 659, 616 (2007)]

Interferometry + Spectroscopy:

R, L, Teff accurate determination requires interferometric angular diameters, accurate parallaxes and accurate bolometric flux.

Interferometry + Asteroseismology:

Accurate R allows accurate masses M to be derived16IA

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Case of the roAp starsCase of the roAp stars

roAp: intersection of Main-Sequence and instability strip

< 1 mas

Abundance inhomogeneities(with a contrast up to 1000)

Strong magnetic field (up to ~30 kG) large-scale organized

Pulsations (period of a few minutes)

Optical interferometric allows to have a direct (and unbiased) measurement of the linear radius of these tiny stars.

Small rotational speed(< 100 km/s)

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Example of 10AqlExample of 10Aql

V² LD = 0.275 0.006 mas [CHARA/VEGA]

R = 2.317 0.070 R

+ Bolometric flux and parallax+ Large frequency separation + Evolutionary track (CESAM2K)

M = 1.95 0.05 M

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[Perraut et al. A&A, submitted]

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B/

Test of roAp excitation modelsTest of roAp excitation models « Interferometric » fundamental parameters for 4 roAp (Cir, CrB, Equ, 10 Aql) Stellar interior models

Prediction of excitation modes Comparison with observed modes

0

Excited

Not excited

Equ

Observed modes

Predicted modes derived for interferometric parameters ( ) are in agreement with observed ones but for Cir.

10 Aql Cir

[Cunha et al. A&A, in prep]

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Go beyond diameter measurementGo beyond diameter measurementOptical 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-likeSearch 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)

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Fomalhaut

Deneb

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Debris disksDebris disks

[Akeson et al. ApJ, 691, 1896 (2009)]

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.

Leo

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V²

b (m)

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Supergiant windSupergiant windThe 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)]

Visibility Phase

Deneb

H line

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RotationRotation 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.

[Monnier et al. Science, 317, 342 (2008)]Altair

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ConclusionConclusion 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.

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ProspectsProspects

Position of 109 stars with an accuracy of ~20 µas Go towards an Angular Diameter Anthology

Needs togo to higher sensitivity and to smaller targets

Increase accuracy for putting into test stellar models

Go towards surface imaging across spectral lines

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[Boyajian et al. ApJ, in prep (2013)]

Breakthrough for CP starsBreakthrough for CP stars

[See poster of D. Shulyak et al. in this conference] 26IAU

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[Lüftiger et al., A&A, 509, A71 (2010)]HD24712

Thanks for your attentionThanks for your attention

The CHARA Array

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An example of simulation : An example of simulation : 22CVnCVn

Predicted interferometric phases

0.5-0.5

Interferometric phases provide 2D geometrical constraints

• Spectra of 2CVn (CrII4824 line)

• Doppler maps (Kochukhov,2002)

0.5-0.5

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Abundance study with CHARA/VEGAAbundance study with CHARA/VEGA

Resolved target Large visibility effects Observations in the visibility

lobes

CHARA/VEGA + 2CVn models

CHARA

Line for various stellar phases

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

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Limb-darkening effectLimb-darkening effectLimb 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.

[ten Brummelaar et al. MROI meeting (2011)]

Sirius

H line

Uniform-disk diameter (mas)

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Determination of fundamental parameters of (Chemically Peculiar) A stars Determination of fundamental parameters of (Chemically Peculiar) A stars through optical interferometrythrough 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.

[Kervella et al. A&A, 413, 251(2004)]

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« classical » error box

« interferometric » error box

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