The power of asteroseismology

www.mps.mpg.de/sage

Nearly a century ago Arthur Eddington hadthe foresight to question “Our telescopes mayprobe farther and farther into the depths ofspace; but how can we ever obtain certainknowledge of that which is hidden beneathsubstantial barriers? What appliance canpierce through the outer layers of a star andtest the conditions within?’’ The answer isasteroseismology – the study of the internal structure of stars through theirintrinsic global oscillations. As with musicalinstruments these oscillations resonate in acavity specific to the “instrument”, i.e. a starin this case. In this way the oscillations revealinformation about the properties of this cavityand thus the star.

It has been long known that stars can showperiodic brightness variations that originatefrom an intrinsic mechanism in a star. In sucha mechanism energy flowing from the core tothe surface could be trapped in an opaquelayer before reaching the surface. This causesthe star to expand. Upon expanding theopaque layer becomes more transparent tothe energy flow, which results in the removalof the blockade and making the star contractagain (Eddington 1926, Aerts et al. 2010).These breathing oscillations of a star changeits radius by a few percent in a coherentmanner while at the same time changing itssurface temperature and brightness.

History An early remarkable result from stars withsuch breathing oscillations (Cepheids) is arelation between the period of the oscillationsand the luminosity (absolute brightness) ofthe stars, the so-called period-luminosityrelation (Leavitt and Pickering, 1912). Thisrelation plays an important role in measuringdistances of galaxies and star clusters andultimately the expansion of the universe.

In the 1960s non-coherent oscillations withlow amplitudes (much less than a percent)were first discovered in the Sun. Theseoscillations are stochastically (i.e. in a randomway) excited by the turbulent convection inthe outer layers of the Sun. Effectively someof the convective energy is transferred intoenergy of global oscillations. This type ofoscillations is referred to as solar-likeoscillations.

The oscillations detected in the Sun haveprovided unprecedented detail of the stellarinterior. We now know that the Sun rotates asa solid body in its radiative region up to about0.7 of its total radius. Above this region thereis latitudinal differential rotation in theconvective layer, i.e. the outer layers of theSun rotate faster at the equator than at thepoles. At the boundary between solid bodyrotation and differential rotation there exists a

The power of asteroseismology

shear layer, the so-calledtachocline. This tachocline couldplay an important role in the formationof the large magnetic fields present inthe Sun. Additionally, seismology of the Sunwas pivotal in the discovery that neutrinos arenot massless and that low energy neutrinoschange flavour (Nobel prize for physics 2015).

Asteroseismic revolutionOther stars with an outer convection zonealso excite solar-like oscillations. Amongthese are stars similar to the Sun, with similarmass and hydrogen fusing to helium in thecore, as well as more evolved stars (the futureof our Sun). These evolved stars haveexhausted their core from hydrogen andeither fuse hydrogen in a shell around an inerthelium core, or around a core in which heliumfusion takes place. These stars are red (coldat the surface) and large (up to 100 times theSun) and are referred to as red-giant stars(Hekker and Christensen-Dalsgaard 2017).Over the past decade dedicated spacetelescopes have made it feasible to observesolar-like oscillations in red giants as well assolar-like stars; these observations resulted inan asteroseismic revolution.

It was discovered that red-giant stars are likemusical instruments with two cavities, havingone cavity located in the deep interior of the

star and one in the outer layers. Theoscillations that resonate in both cavities areso-called mixed oscillation modes and providea direct means to pierce into the cores ofred-giant stars and reveal its properties; forinstance whether the helium in the core isinert, or fusing (e.g. Bedding et al. 2011).The mixed modes also allow for studies ofthe rotation of the stellar cores and envelopes.In red giants the cores are rotating about 10 times faster than the envelopes. (e.g. Becket al. 2012).

Through their sensitivity to the internalstructure of the stars, the oscillationscombined with surface properties (temperatureand chemical composition) can also revealthe stellar mass, radius and age withunprecedented accuracy. Although the agesare depending on comparisons with stellarmodels, asteroseismic ages are superior toother age determinations in terms ofprecision and accuracy.

Asteroseismology and computer scienceThe SAGE (Stellar Ages and GalacticEvolution) group at the Max Planck Institutefor Solar System Reseach in Göttingen(Germany) combines asteroseismology withcomputer science techniques to study stellarstructure and evolution and extract the stellarparameters. We have developed a fast andprecise tool to determine stellar parametersthrough the use of machine learning(Bellinger et al. 2016, Angelou et al. 2017).We use random forest regression to measureevolutionary, structural, and chemical stellarattributes from observable features of stars,such as asteroseismic observables. Thisprocedure works by constructing trees thatuse information theory to create decisionrules relating observations to modelproperties. This approach allows us to rapidlyprocess observables and obtain stellarparameters for large catalogues of stars at

different ages and evolutionary states: thusfostering advancement in the theory ofstellar evolution.

Additionally, the random forest providesinformation about so-called featureimportance, i.e. it indicates what observablesare used most often in decisions made bythe trees in the random forest. This isessential feedback to know where to focusobservational efforts on. Finally, the trainingtime of the random forest is virtuallyinsensitive to the number of free parametersin the underlying stellar model grid. We tookadvantage of this by varying severalparameters such as those for diffusion,convection and convective overshoot, whichare most often kept fixed. Hence this allowsus to study the importance and effects ofthese physical mechanisms in stars.Furthermore, the work by Angelou et al.

(2017) also shows the intrinsic accuracy withwhich stellar parameters can be determinedfollowing the information captured in theobservables.

Asteroseismology of binary starsTo obtain a handle on the precision andaccuracy with which stellar parameters can bedetermined using asteroseismology, it isessential to compare the same stellarparameters obtained with differentindependent methods. An excellent test-bed for such a comparison is aneclipsing binary system with at least oneoscillating component.

In a binary system two stars aregravitationally bound and therefore the Keplerlaws of motion can be applied to infer theorbital parameters (orbital period, distance ofthe stars from the gravitational center of the

binary system expressed as semi-major axis,and eccentricity) and stellar parameters(mass and radius) of the two stars. In casethe system is aligned such that from our pointof view the stars pass in front of each other,the system is a so-called eclipsing binarysystem. During an eclipse one of the starspasses in front of, i.e. occults, the other star,and consequently blocks part of the lightemitted by the occulted star. This results in atemporary reduction in the intensity of thelight that we can measure from the system.From an eclipse it is possible to get a measureof the stellar radius with respect to the semi-major axis of the orbit of the occulting star.From the measurements of a series ofeclipses one can infer the radius as a functionof semi-major axis of both binary componentsand the time it takes the stars to complete afull orbit, i.e. the orbital period. In case alsoDoppler velocities, i.e. the relative velocities of

the stars in our direction, are obtained it ispossible to obtain the masses of the stars andsemi-major axes of the system by combiningour knowledge of the system orientation withthe obtained relative velocities. Hence, thestars can be fully characterized in terms oftheir mass and radius through themeasurements of binary signatures.

The SAGE group compared the stellarparameters obtained through asteroseismologyand from the binary orbital (Themeßl, Hekker etal. submitted). Interestingly the derivedmasses, radii and mean densities are notconsistent within their uncertainties.

The reason for this inconsistency can be sought in several directions. It could just be astatistical error as we have looked at only a fewsystems. However, it could also be that theprecision of the derived parameters is now sohigh that we get sensitive to the slightlydifferent intrinsic definitions of masses andradii that are measured using asteroseismologyand that can be derived from the binarysolution. The impact of the stars in the systemon each other could also play a role in this(Themeßl, Hekker, Elsworth 2017).

Asteroseismology and beyondThe power of asteroseismology reachesfarther than the structure and properties ofstars. It also impacts significant on our

knowledge of extra-solar planets, the MilkyWay and as mentioned before the expansionof the universe. The determination of theplanetary properties (mass, radius and age)critically relies on the knowledge of the sameproperties of the host star. Indeed, it wasthanks to asteroseismology that it waspossible to detect earth-mass planets in thehabitable zone (e.g. Borucki et al. 2012).Furthermore, stars are a main observableingredient of the Milky Way and galaxies ingeneral. To understand the formation andevolution of the Milky Way (galacticarchaeology) knowledge of stellar properties,and particularly stellar ages, is indispensable.With asteroseismology it now becomespossible to derive stellar masses and ages toan accuracy level that is needed for galacticarchaeology.

To utilise the full extent of the power ofasteroseismology it is essential to fullyunderstand all the oscillation features that arepresent in the data and understand theirphysical origin. This work is still in its infancyand will require many in-depth asteroseismicstudies as the field matures.

“To understand theformation and evolution

of the Milky Way(galactic archaeology)

knowledge of stellarproperties, and

particularly stellar ages,is indispensable.”

“To understand theformation and evolution

of the Milky Way(galactic archaeology)

knowledge of stellarproperties, and

particularly stellar ages,is indispensable.”

www.mps.mpg.de/sage

References:Aerts, C., Christensen-Dalsgaard J. and Kurtz D.W.(2010) Asteroseismology, Springer Science Media

Angelou, Bellinger, Hekker, Basu (2017) On thestatistical properties of the lower main-sequence,Astrophysical Journal 839: 116

Beck P.G. et al. (2012) Fast core rotation in red-giant stars as revealed by gravity-dominated mixedmodes, Nature 481:55-57

Bedding T. et al. (2011) Gravity modes as a way todistinguish between hydrogen- and helium-burningred giant stars, Nature 471:608-611

Bellinger, Angelou, Hekker et al. (2016)Fundamental parameters of main-sequence starsin an instant with machine learning, AstrophysicalJournal, 830:31

Borucki et al. (2012) Kepler-22b: A 2.4 Earth-radius Planet in the Habitable Zone of a Sun-likeStar, The Astrophysical Journal 745: 120

Eddington A.S. (1926) Then internal constitution ofthe stars. Cambridge University Press.

Hekker S. and Christensen-Dalsgaard J. (2017)Red giant seismology, Astronomy and Astrophysicsreview, 25:1

Leavitt H.S. and Pickering E.C. (1912) Periods of25 variable stars in the small magellanic cloud.Harvard college observatory circular 173:1-3

Themeßl, Hekker et al. (2017) Red giants ineclipsing binary systems:asteroseismology versusorbital solution, MNRAS, submitted

Themeßl, Hekker, Elsworth (2017) Presence ofmixed modes in red giants in binary sytems, toappear in the proceedings of the jointTASC2/KASC9/SPACEINN/HELAS8 conference“Seismology of the Sun and the Distant Stars2016”