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PoS(BASH2015)007 http://pos.sissa.it/ band) are consistent K ar HD 219134 which demonstrates rt) of has implications on var- core rotation rates in red giants and 1 mas for the radii, , and ages) and interior alaxies to understanding . nergy between and o key observational methods for con- e fundamental properties, and present ld stars: the study stellar oscillations & ( ore comment on the reliability of inter- nd give a brief outlook on the expected etry. I will highlight recent breakthrough ity of Sydney, NSW 2006, Australia e Commons al License (CC BY-NC-ND 4.0). ∗ [email protected] Speaker. processes (such as convection and angular momentumious transpo topics in astrophysics, ranging from the evolution of g The study of fundamental properties (such as , In this contribution I will reviewstraining the fundamental basic and principles interior of tw properties(asteroseismology) of and optical single long-baseline fie interferom discoveries in asteroseismology such as the measurement of a new angular diameter measurement forthat the diameters for host stars st which are relatively well resolved the characterization of exoplanet systems. Iferometry will as furtherm a tool to calibrate indirect methods to estimat interferometry to test asteroseismic scalingimpact of relations, space-based a missions such as K2, TESS and Gaia. across different instruments. Finally I will discuss the sy ∗ Copyright owned by the author(s) under the terms of the Creativ c

Sydney Institute for Astronomy, School of Physics, Univers Daniel Huber Precision Stellar Astrophysics in the Kepler Era E-mail: Attribution-NonCommercial-NoDerivatives 4.0 Internation Frank N. Bash Symposium 2015 18-20 October The University of Texas at Austin, USA PoS(BASH2015)007 Scuti δ Daniel Huber treatment of sics for stellar interior physics ravity modes (g ad to differences cross the H-R di- rs such as ave enabled direct pected, the models appeal” of different rstanding of stars in erefore usually only (the number of node nderstanding of stars sics as a whole. | f the . Yet, nearly pherical harmonics of ith buoyancy acting as hlight recent advances dly divided into driving Figure 2). ominated by the uncer- tars. Finally, I will give dels (which themselves, m | trained [7]. n this contribution I will ershooting lead to differ- the characteristics of host arise for cooler and hotter e evolution of re- or red giants, major uncer- vection (so-called solar-like m the Dartmouth [4], t acting as the restoring force. 0 denote non-radial pulsations. Oscillations > l 2 (the number of nodes from the surface to the center). n 0, while = l (the total number of node lines on the surface), azimuthal order l Stellar pulsations are observed across the H-R diagram and can be broa The Cosmic Sexiness Ladder [1], which measures the “relative visceral Despite numerous advances over the last decades, many problems in stellar Over the last decade, space-based has revolutionized our Oscillations can furthermore classified into pressure modes (p modes) and g remain unsolved. Figure 1 compares[5] isochrones and of BASTI [6] different ages databases with fro agree solar well composition for in stars an similar H-R tostars: diagram. the for Sun. As example, However, ex uncertainties significant in differences ent the main-sequence description lifetimes of convective for coreconvection intermediate ov lead to different stars, predictions while oftainties radii uncertainties include for interior in low-mass angular the dwarfs. momentum F transportin and inferred mass ages of loss, up which to can 50% le even if other stellar propertiesthrough are the well application cons of asteroseismologyagram. - At the the study same ofmeasurements time, stellar technical of pulsations advances fundamental - in stellar a long-baseline propertiesreview interferometry the for h basic hundreds principles of of stars. asteroseismologyas and well I as interferometry, and synergies between hig botha techniques brief for outlook the on study the of expected results single from field future s observations. 2. Asteroseismology 2.1 Basic Principles of Asteroseismology stars and Cepheids) and stars whichoscillators). oscillate due In turbulent surface both con cases,degree oscillations (“modes”) can be described with s with larger spherical degrees penetrate to shallower depths within the ( modes). Pressure modes are acoustic waves, withGravity the modes pressure are gradien pulsations due tothe the restoring balance of force. buoyancy and Gravity gravity, w modes are damped in convection zones, and th Precision Stellar Astrophysics in the Kepler Era 1. Introduction and Motivation Radial pulsations are hence denoted as lines crossing the equator), and radial order mechanisms due to opacity changes in the interior (so-called classical pulsato fields in astrophysics, lists starsevery in field in second astrophysics to is last in oneof place way course, just or rely another above dependent heavily studies on on o stellar heliophysics).lies mo on For models example, of understanding simple th isochrones stellar [2]. populations, which On in a turn smallerstars, depend scale, and on properties in the many of input cases exoplanets phy tainties the depend on uncertainties on on the properties radii ofvarious and the stages masses of host are their star evolution d [3]. is important Evidently, to improving advance the our field unde of astrophy PoS(BASH2015)007 ν µ ∆ (2.1) , and can , where n R Daniel Huber / M µ ∝ diameter [12, 8]: T ace. 3]: in radiative zones, and 4000 and ge frequency separation µ / T dotted lines), 1 (solid lines) and 3 p ∝ 6000 c , and consecutive radial order ations in poorly constrained input physics. 1 l − lack) and BASTI (green) databases. Differences  Parsec Dartmouth BASTI c dr R 0 3 Z 8000 2  = ν ∆ can be described by the asymptotic theory of stellar oscillations Effective () l 10000 and low n 0.100 0.010 0.001 1.000 10.000

100.000

1000.000 (Solar) Luminosity Isochrones with solar chemical composition and ages of 0.1 ( is the sound speed. For adiabacity and an ideal gas c Frequencies of high [9, 10, 11], which predicts a series of regularly spaced modes. The lar where is the mean molecular weight. Hence, Equation (2.1) can be expressed as [1 (dashed lines) Gyr taken from the Dartmouthin (red), the Parsec (b models for high and low mass stars are mostly due to vari propagate in the interior forhence cool are more stars. easily Pressure excited with modes amplitudes propagate that mostly are observable at the surf is the separation of modes of the same spherical degree Figure 1: Precision Stellar Astrophysics in the Kepler Era be shown to be equal to the inverse of the sound travel time through the stellar PoS(BASH2015)007 l (2.3) (2.2) Daniel Huber , are sensitive n tar. Small frequency at modes of different y [14, 15], which is the omposition during stellar . The frequency of maxi- uency differences provide . Hence, combined with the max ν ρ 2 and same order l PR GM = modes with different spherical degrees. p 2) mode, respectively. Adapted from [8]. H = . l 2 / . 1 p  c H 3 2 M R 4 =  ac ∝ ν ν ∆ as: 0) and quadrupole ( max = ν l Schematic cross-section of a star illustrating the paths of An additional observable is the frequency of maximum power, For an isothermal atmosphere the pressure scale height is ideal gas equation, we can express The large separation is henceseparations, directly which proportional are to differences the of mean modes with of different degree a s travel to different depths within theinformation about star the (Figure radial 2), structure and of hence the their star. freq to the sound-speed gradient in the stellarevolution interior, and and hence the therefore chemical stellar c age. This can be understood by the fact th mum power has been suggested toupper scale limit for with the the reflection acoustic of cut-off an frequenc acoustic mode [8]: Figure 2: Precision Stellar Astrophysics in the Kepler Era Red and blue lines highlight a radial ( PoS(BASH2015)007 20 (2.4) ∼ cover- are well Daniel Huber ence for most pace photome- rs [35] and sev- s with g modes w enough mode mpaigns [14, 16, sing asteroseismic modes [43], which [45] led to a series iants [41] as well as 24, 25], and further 30] and the Hubble 4], yielding multiple velocities for the de- terior structure of red scending the RGB and as grown by two orders is predominantly due to Infrared Explorer) star- at red giants oscillate in n Rotation and Planetary ally spaced in frequency, btained by the Canadian red giants. Following the yielded detections in ually spaced in period. Kepler which are otherwise difficult an lead to evolutionary stages . eff T M √ 2 R ∝ 5 ac ν ∝ 5, since less evolved stars oscillate above the Nyquist fre- max . ν 3 . 1 modes in red giants observed by g = l , or individual frequencies provide a powerful way to determine the ν ∆ , max ν continued the revolution of cool-star asteroseismology by Kepler targets sets a limit of log The A major breakthrough, which is commonly referred to as the beginning of the s While for stars the propagation cavities of p modes and g modes The detection of mixed Early asteroseismic observations were mostly focused on ca try revolution of asteroseismology, was achieved by theTransits) CoRoT (Convectio satellite. CoRoT detected oscillationseral in thousands a red number giant of stars mainnon-radial [36, sequence modes 37], sta [38]. demonstrating for This thegiants opened which first were the time previously door th not for thought to detailed be studies possible. of the in of groundbreaking discoveries in ourdetection understanding of of equal the period interiors spacings of [46], it was demonstrated that giants a stars (see inset of Figure 3). ing the low-mass H-R diagram withover detections, 15,000 including red 500 giants dwarfs [42, and 39]. subg the The fact large oscillation number amplitudes of increase oscillating with reddetections luminosity giants towards (Figure 3), more therefore evolved bia stars.Kepler Additionally, the 30-minute sampling cad separated, the different core and envelopewhere in p evolved modes stars and c g modescontain have contributions similar from frequencies. g This gives modesinertias rise in to to be the mixed observable core at the butg surface. unlike modes While pure high are g order predicted modes p modescauses have to are lo mixed be equ modes equally to spacedfrequencies be in per shifted period. radial order from which their The are original coupling expected to frequency of be spacing p approximately eq [4 mode Measurements of 17, 18, 19, 20,tection 21], of leveraging exoplanets. on the TheMOST improved first telescope measurements space-based led of photometric to Doppler observations detectionsspace-based o in observations a were few performed redtracker giants using [26, [22, the 23] 27, WIRE and 28, (Wide-Field ProcyonSpace 29], [ Telescope [31, the 32, SMEI 33, (Solar 34]. Mass In Ejection total, Imager) observations prior satellite to [ 2009 quency. Overall, the sample of coolof stars magnitude amenable in for the asteroseismology last h 8 . 2.3 Probing the Interior of Red Giants stellar structure and fundamental properties (such asto radius determine and for mass), field stars. 2.2 The Space Photometry Revolution of Asteroseismology Precision Stellar Astrophysics in the Kepler Era PoS(BASH2015)007 n, and that f red giants, Daniel Huber for p-dominated [25, 39, 40]. Color n. stars [49, 50]. The elope. Finally, in the power spectrum of a eriod spacing [47, 37]. by a gradual spin-down Kepler ore rotation rates in models g to a yet unidentified mecha- tions by ed oscillations. Solid lines show solar f CoRoT). ndicated in the plot. The inset shows the same 6 data has since allowed measurements of core rotation rates for hundreds o H-R diagram showing stars with detected solar-like oscilla Kepler Figure 3: Precision Stellar Astrophysics in the Kepler Era coding marks the meanmetallicity amplitude evolutionary per tracks radial with mode different masses of as the i observ diagram with all detections circa 2008 (prior to the launch o He-core burning red giants canShortly be after, separated it based on was theirfrequency discovered mixed-mode splittings that p for mixed g-dominated modes mixedmixed are modes modes split are due into substantially radial higher multiplets differentialred than rotation by giant [48]. exhibiting rotatio mixed Figure modes with 4 the shows signature a of typical radial differential rotatio allowing an unprecedented view into thedata internal show that rotation the evolution cores of spin evolved upas stars as evolve stars towards evolve the towards He-core the burning RGB,are main followed up sequence. to Predicted factors c of 10–100nism larger responsible than for observed transporting [51, angular 52, momentum 53], from pointin the core to the env PoS(BASH2015)007 2) modes are Daniel Huber an important ously used to vances in our = l tions have been r magnetic field 1) modes are high- ial order (highlighted = es observed in some can trap oscillations l d by the fact that high- me. mology, ranging from interior . Dipole ( 1 modes per radial order due to the 0) and quadrupole ( = dle panel: Measured rotational splitting l = Kepler l the envelope (top) and with rigid rotation l ( [57]. The primary application of aster- ltiple arger rotational splitting and hence faster rota- ue circles). Bottom panel: Rotational splittings Kepler 7 1 mode in the top panel. The mixed modes in the wings of each rad = l Top panel: Power spectrum of a observed by In addition to testing stellar models, asteroseismology has recently started to play To date there are approximately 100 exoplanet host stars for which oscilla marked by squares and triangles, respectively. There are mu coupling of p modes withof g each modes mixed in the core (mixed modes). Mid latest twist in red giant asteroseismology, the puzzling absence of dipole mod (bottom). Adapted from [48]. red giants [54] has beenin explained the by radiative strong core, internal andstrengths magnetic [55]. hence fields These can remarkable which observational be insights usedcomposition, by asteroseis rotation to to place magnetic upper fields,understanding limits promise of on to the the interior enable structure interio important of theoretical red ad giant stars for years2.4 to co Asteroseismology of Exoplanet Host Stars tion than modes in the centeraccording of to each order a (highlighted model as with bl a core spinning 10 times faster than as red circles), which are more sensitive to the core, show a l lighted in red and marked by red and blue circles, while radia Figure 4: Precision Stellar Astrophysics in the Kepler Era detected, most of which have been observed by role the study ofprecision exoplanets time [56]. domain observations This (either indetect synergy exoplanets intensity has and or largely study velocity) stellar been can oscillations. be enable simultane PoS(BASH2015)007 ure l exoplanet Daniel Huber 11 Gyr [62]. ld planet radii ∼ ure the spin-axis ich are split into a long-term trend dynamical history and the axis of the e ages of dozens of 56, a red giant hosting e orbital axis is perpen- n age of modes in rotationally split mul- ) lination of the red giant host star was 1 + l ( l dial-velocity follow-up observations, causes a ing were detected through transits. The ts and the stellar spin axis. Both precessions occur ment. Sizes are not to scale. From [63]. 8 6 degrees and demonstrating the first stellar spin-orbit mis- ± 1–2% in the best cases [58, 59]. Asteroseismology has been used to meas ∼ and CoRoT have enabled asteroseismic inclination measurements for severa Graphical sketch of the Kepler-56 system. The spin-axis inc Kepler Another remarkable application has been the use of asteroseismology to meas tiplets [64]. Stellar inclinations areof important transiting for exoplanets studying by the constrainingplanetary architecture the orbit and angle (the between obliquity). the stellar Sincedicular spin the axis to presence of the transits line shows oforbital that plane th sight, and a the low equatorial plane stellar of inclination the automatically star (a implies high a obliquity). misalignment of the inclination of host stars through the relative heights of the systems [65, 66, 67, 68, 69].two One transiting of the planets. most intriguing Thetriplets, examples Kepler-56 yielding is an Kepler- power inclination spectrum of shows 47 dipole modes wh alignment in a multiplanet system [63]. Radial velocity observations revealed the radius of the smallestexoplanets exoplanet [61], including known the to oldest date known terrestrial-sized [60] planets and with determine a precis to a precision of precession of the orbital axis ofat the different inner rates, transiting causing plane a periodic spin-orbit misalign oseismology is to measure host star radii, which combined with depths yie determined from asteroseismology, while thetorque of inner the transit outer companion, which was detected through ra Figure 5: Precision Stellar Astrophysics in the Kepler Era PoS(BASH2015)007 ep- (3.1) (3.2) nd the ’s double two point r. The total Daniel Huber angle by half ecession of the ignificant mutual ture of the object ction with angular e 5) [70]. This sce- omatic light from a complex visibility is e world. eismology can also be eed to improve stellar object [76]. Therefore, s highlights the impor- screen. nd bright patches of the onstructively and destruc- This fringe contrast is the monstrated for the first time e (“fringe”) pattern is formed. , , min min I I b λ + − 9 = max max I I ∆Θ = V the separation between the slits (the “baseline”). Suppose that b ) (right panel of Figure 6). In this case, the fringes are in anti-phase a b λ 2 is the fringe visibility. A measurement of the visibility at a given wavelength and s is the wavelength and λ V The most basic measurement in stellar interferometry is the angular size of a sta The principle of interferometry is traditionally illustrated by a variation of Young It is evident from this simple discussion that any intermediate separation of the In addition to precise exoplanet radii and orbital architectures, asteros slit experiment performed in thepoint source early passes 19th through century a (FigureEach double slit 6). point (left of panel), As the an monochr wavefronttively interferenc is interfere at a the source screen ofinterference behind spherical pattern the wavelets, is: slits. which The c spacing between dark a aration of the twobeing slits observed. (or telescopes) Stating is theequal above therefore to more directly the generally, spatial related Fourier it transform to canmeasuring of the be the visibilities intensity struc shown at distribution that different of baselines the aresolutions given in that principle far allows exceed image the diffraction reconstru limit of the largest telescopes3.2 in th Stellar Angular Diameters and the CHARA Array where where interference patterns form an incoherent sum to give an evenly illuminated used to constrain orbital eccentricitiestance [74, of 75]. stellar The astrophysics varietymodels of for in application order the to field advance our of understanding exoplanet of exoplanets. science, and the n 3. Optical Long-Baseline Interferometry 3.1 Basic Principles of Interferometry the light hitting the doublethe slit fringe is spacing emitted ( by two point sources that are separated in Precision Stellar Astrophysics in the Kepler Era due to a massive companioninclination on to a the wide inner transiting orbit planets, which,orbital can under axis explain the the of misalignment the assumption through inner of a planetsnario a pr due has s to previously the been torque of proposedthat the theoretically spin-orbit wide [71, misalignments companion 72, are (Figur 73], not confined and to de hot systems. energy radiated by a star per unit surface area and per unit time is: sources or a singleratio extended of source the will fringe amplitude result to in the different fringe intensity: contrasts. PoS(BASH2015)007 (3.4) (3.5) (3.3) , Equation θ Daniel Huber received by an ) or with bol f is the limb darkening y) therefore enables a both measurements (in le of stellar interferometry. From [76]. . 4 / . 1 , 2  2 for the apparent angular diameter 4 d eff R 2 is the effective temperature. Given a star with a 2 θ T bol f F d σ eff σθ 10 4 T = = =  R bol F = f eff T , the total (bolometric) flux emitted over all wavelengths d Young’s two slit experiment illustrating the basic princip is the Stefan-Boltzmann constant and at a distance σ R Figure 6: (3.3) can be rearranged as: Combined with the straightforward relation Precision Stellar Astrophysics in the Kepler Era The angular diameter of a star combineda with a measurement distance of (e.g. the from a received trigonometric measurement bolometric of flux the (e.g. radius from and spectrophotometr particular effective the temperature radius) of are almost star. model Importantly, independent. An important exception where radius observer on is: PoS(BASH2015)007 . H Daniel Huber ometers, most , who visually t to realize that s. For example, ks to test stellar dwarfs by up to irect methods. A m. The CHARA cience operations e often somewhat eclipsing binaries) of uncertainty if the to encompass differ- 80] located at Mount f late-type dwarfs for ndred stars across the 94]. Such calibrations rometry? range of spectral types . ever, such error sources nresolved point sources Additional uncertainties elationships [79]. pagate into uncertainties e diameters of 32 bright d by Hanbury Brown and ] and TESS [96], which y in terms of fundamental ed visibilities are reduced anged in a non-redundant nd is currently the largest st image of a single main- ed flux method (IRFM) with 5, 86, 87], yielding empirical -band diameters to predict higher K 11 1 mas [98], while smaller diameters measured in . Ori using a 20-foot interferometer mounted on the 100-inch Hooker tele- α [83], in agreement with constraints from eclipsing binary systems [88, 89] eff T The first stellar angular diameter measurement dates back to Michelson [77] The following decades saw the development of a number of modern interfer Interferometric angular diameters have traditionally been used as benchmar While interferometry is often considered as the “ground-truth”, it is importan Such differences can have a significant impact on the calibration of more ind determined the size of collaborators [78] using thestars, Narrabri which Intensity subsequently Interferometer led to to the measur first calibration of color-temperature r notably the CHARA (Center for High AngularWilson Resolution Observatory. Astronomy) Array [ The array consistsY-shaped configuration of with six baselines 1-m ranging class fromarray telescopes 34 uses m arr instruments to in a both maximumoperating optical optical of long-baseline and 331 interferometer near-infrared in wavelengths, thein a world. 2004 Since commencing it s hassequence produced star [81]. several One breakthrough of the results, moststellar influential properties such results have of been as the angular CHARA the diameter Arra measurementsH-R fir of more diagram than [82, a 83, hu 84],radii and including temperatures several to exoplanet test stellar host atmosphereand stars and evolutionary interior [8 states models (Figure across a 7). 3.3 Calibrating Models and Indirect Methods: How Accurate is Interfe scope on Mt. Wilson observatory. The first systematic study was performe Precision Stellar Astrophysics in the Kepler Era correction for the angular diameter,visibility which curve is can well become constrained the (see dominant next section). source CHARA diameters have since been used towhich calibrate methods direct to measurements predict radii are o notexplore possible new [90, physical 91] mechanisms and to (in improveare models combination for particularly with cool important stars [92, for 93, predominantly exoplanet target late-type transit dwarfs. surveys such as K2 [95 models and calibrate indirect methodsCHARA to diameters estimate have fundamental confirmed properties10% that of for interior star a models fixed overpredict radii of M interferometric data can be affected byby strong atmospheric turbulence systematic and errors. hence Observ needas to closely be in calibrated time by and observingresolved, position u and on hence the systematic sky errors asof in the possible. the angular assumed diameter, In in calibrator practice particular sizes calibrators ifinclude pro the ar errors target in is the not wavelength well scale resolvedare and [97]. not limb-darkening always correction. taken How into account,ences leading between to diameter uncertainties measurements that sometimes by fail different groups and instruments recent comparison of effective temperatures determined frominterferometry the infrar revealed a systematic differencetemperatures for for CHARA stars with angular sizes PoS(BASH2015)007 ity, 008 mas . 0 Daniel Huber ± d by measure- . 109 . tly started cross- dominated by the 1 tainties. The Classic September 2015 us- rved with the Classic = 304 mas), HD 225289 . 0 nsiting exoplanet known ith limb-darkened diame- PAVO = , evere for smaller diameters θ LD nd wavelength), this indicates θ band) beam combiner [100]. Fig- ngular diameters measurements with ar, and the color coding denotes the R 05) and . 0 ± 29 . 0 = 12 K µ 177 mas). The data PAVO resolve HD 219134 nearly down . 0 = θ 012 mas (using . 5 model, and a 5% and 3 nm uncertainty was assumed for the calibrator 0 . 4 ± = g 093 05). Limb darkening coefficients were taken from [103] for a solar metallic . . 1 0 ± = 67 . 0 Classic , Stellar radius versus effective temperature derived from a = R LD 206 mas) and HD 223386 ( θ µ . band) beam combiner with the higher-resolution ( PAVO 4750 K and log 0 To test the accuracy of interferometric angular diameters, we have recen K = = / eff θ H ( (using Figure 7: Precision Stellar Astrophysics in the Kepler Era uncertainty in the limb-darkening correction, while the Classic diameter is dominate diameters and wavelength scale, respectively. Note that the PAVO diameter is (red squares) and (black PAVO diamonds) dataters show of good agreement, w to the first null, making them largely independent of calibrator diameter uncer T band showed better agreement [99]. Since calibration errors are more s the CHARA Array.spectroscopically The determined . symbol From size [84]. scales with the size of the st (corresponding to more unresolved sources, giventhat a some diameters fixed measured baseline with a CHARA may be affected by systematic errors calibration efforts with the CHARA Array by( revisiting stars which were obse ure 8 shows preliminary results for theto K date dwarf HD [101, 219134, the 102]. closesting tra two PAVO data baselines (E2W2, were W1W2), taken and over calibrated four using HD nights 218376 ( in August and PoS(BASH2015)007 R 8 band are band. 011 mas and . K R 0 Daniel Huber ± sts of interior the ly understood. 2.5·10 066 . 1 ear-model indepen- ystematic errors ex- ous dual beam com- = er of beam combiners as 0.6 mas (16 Cyg A) de for single stars, and lusion of uncertainties in cali- Classic sponding to near-identical , UD θ ) 8 -1 et host star HD 219134 measured in the eters are reliminary new data obtained with the ne shows the fitted diameter model to the Cyg) have shown stark discrepancies sic data. 2.0·10 θ 1 mas diameters measured in & Classic (K Band) Classic (K PAVO (R Band) 13 8 HD219134 . Future observations will focus on measuring fringes in the 1 1.5·10 Spatial Frequency (rad 8 005 mas, respectively. . 0 ± 1.0·10 0.0 0.4 0.2 0.6 033

.

1 Squared Visibility Squared Squared visibility verus spatial frequency for the exoplan = The combination of asteroseismology and interferometry allows a powerful te Note that the Classic uncertainty is larger than the published value due to the inc While the results for HD 219134 demonstrate that PAVO 1 , band using the Classic beam combiner (red squares) [82] and p UD models. Using asteroseismic densities and interferometricdent angular measurements diameters, of n the radius, mass and effective temperature can be ma [105, 104]. In addition to revisitingbiner diameters, observations of we the are same also target pursuing andspatial simultane calibrators frequencies with for baselines each corre instrument.cept This for the will absolute eliminate visibility most calibration sources between of instruments, s which is still poor 3.4 Combining Interferometry and Asteroseismology K θ Figure 8: Precision Stellar Astrophysics in the Kepler Era brator sizes, limb darkening and wavelength scale. The uniform disc diam second visibility lobe, which will allow direct constraints on the limb-darkening in band PAVO beam combiner (black diamonds). data,PAVO while The the green dashed solid green li line shows the fit to the Clas ment/calibrator diameter uncertainties likely reliable, cross-calibrations for smaller diametersare and for needed. a larger Some numb results[104], have while shown other good agreement measurements for (such stars as as 18 small Sco and PoS(BASH2015)007 Daniel Huber r astrophysics requencies for e asteroseismic particular, astero- pular to determine mic detections and alibration of astero- 4%, while giants are vations will alleviate dels for the metal-rich e 9 shows comparions recise which . een used to confirm that uire careful calibration, in xcellent agreement between ved from scaling relations as a function e the source of the measurements as given in the 14 , ground-based surveys such as APOGEE [113], GALAH [114] and Kepler Interferometric radii divided by asteroseismic radii deri star HD 173701 [106], and constrain the modeling of individual oscillation f Asteroseismology and interferometry will continue to flourish as tools for stella Alternatively, interferometry can also be used to test asteroseismology. In over the coming decades.seismic scaling A relations particularly for important giants.revolution initiated synergy While by concerns space-based the missions c will continue th seismic scaling relations (Equations 2.2stellar and properties. 2.4) However, these have relations become areparticular increasingly only for approximate po and stars req which are significantlybetween more radii evolved from than the both Sun. methodswell Figur based resolved diameters on [106, a 104, collection 111,interferometric 112]. of The high radii comparison S/N and shows asteroseis e asteroseismic radiidominated for by dwarfs large with uncertainties a inthis problem scatter the by of Hipparcos focusing on parallaxes. brighter redwill giants, Future soon as be obser well available as from the the use Gaia of satellite. more p 4. Future Prospects solar-type stars [107, 108, 109]. hence directly compared to evolutionary models. Such approaches have b of asteroseismic radii. Different colorslegend. and From symbols [110]. denot 18 Sco is a true solar twinKepler [105], detect a potential discrepancy in interior mo Figure 9: Precision Stellar Astrophysics in the Kepler Era PoS(BASH2015)007 ur hosts Daniel Huber CHARA Array rvations of stars w unprecedented 16, 117], therefore ence asteroseismic ovided by the Aus- parallaxes by Gaia, stellar populations in p between stellar sam- rometry. the . Recognizing underway to combine as- crucially on our ability to number DE140101364). , Kepler’s follow-up mission scillating red giants targeted in the and CoRoT (see Figure 10). However, ismology combined with spectroscopy will Sydney). targets, and hence amenable to interfero- an unprecedented manner. Image Credit: Kristin Kepler Kepler 15 I thank Frank Bash, Rachael Livermore, Stefano Meschiari and all o Illustration of the Milky Way with predicted detections of o Importantly, future space-based missions will also obtain asteroseismic obse with an upcoming adaptive-optics upgradeples will that further can increase be observed the withthe overla sample both of techniques. single Combined stars with withtests the directly of measured release stellar fundamental of models properties over will the allo coming decade. Acknowledgements: at UT Austin for a fantastictralian Research and Council’s memorable Discovery meeting. Projects funding Financial scheme support (project was pr metric follow-up observations. At the same time, the increased sensitivity of the first 10 campaigns of the K2 Mission (colored dots). Asterose allow to map the metallicity and age distribution of stars in Figure 10: Riebe (Potsdam), Sanjib Sharma (Sydney) and Dennis Stello ( LAMOST [115] are obtaining spectrathe powerful of synergy thousands between of both stars methods,teroseismic major throughout and efforts spectroscopic are data currently to probeour the Galaxy chemo-dynamical (often history referred of toK2 as [95] “galactic is archeology”). measuring In oscillationsdramatically particular of expanding red the giants galactic throughout field the ofthe ecliptic view determination plane of [1 of stellarscaling ages relations. depends sensitively Therefore, on theaccurately stellar success calibrate masses, asteroseismology of using and galactic direct h archeology methods such relies as interfe which will be significantly brighter than typical Precision Stellar Astrophysics in the Kepler Era PoS(BASH2015)007 109 AJ , (June, Daniel Huber (Feb., 1968) 530 , p. 53, 2001. ology: Let the ieste Stellar 11 (1980) 469. 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