Asteroseismology 'Institut fur Astronomie, Vienna, Austria; 2Universitdtsstemwarte Gottingen, Germany Introduction These 'normal' stars are best suited diagram. The most prominent new tools Probably the most convincing definl- for significant tests for various asp&$ are: tion for what astwoseismology actually of fundamental stellar physics. Con- preclse distances, measured by the is, was given by Dappen, Dziembowskl fronting realistic stellar models with Hpparcos satelthe, and Sienklewlcz (IAU Symp. No. 123, p. high-quality observations will tell us pulsation periods, observed wlth 233,1988) as a method of testing stellar much about the underlaying physics. ground-based telescope networks structure and evolution theory, uslng J In addition, stars constitute essential and with space experiments, avallable pulsation data (including also laboratories for studying important as- rotational velocities and magnetic growth rates, phases, the fact that mode pects of basic physics (convection, fields, derived from surface imaging exists, and sometimes are transient, MHD, nuclear reactions, equation of techniques, etc.), and not just observed frequencles. states, transport processes, etc.. ..) new powerful deters which help Asteroseismology probably opens the under conditions which cannot be re- to increase the S/N of obsenrations accessible parameter space well be- produced in terrestrial laboratories. For significantly, yond the classical lnstabllii strips, if extremely high and low temperatures dramatic advances in computer solar-type oscillations can be obsewed and densities, this stellar laboratory is technology. for a large variety of stars. It has become indispensable for Wing physical an increasingly accepted opinion that theories. are just a few examples These Scientific pulsation (probably mody In the form of for the significance of stellar physics Goals non-radial pulsation) is the rule, rather to what may be called laboratory phy- The key Issue of asteroseismology is than the exception. Unfortunately, the sics. the theory of stellar structure and evolu- obsewable quantities tend to be ex- Not surprisingly, many international don. In the present status of the theory, tremely small and new instrumentation conferences have been devoted In re- a stellar model is typically characterized is needed, for ground-based observa- cent years to heliu- and asteroseismolo- by flve parameters (mass, age, initial tlons as well as for observations from gy. IAU Colloquium No. 137 (Vienna, compositions In helium and metals, and space. The prospects, however, are Aprtt 13 to 17, 1992) will be dwd, mixing length - a parameter describing magnificent since it appears to be pos- among others, to aspects raised in the the convective transport of energy) for sible to test stellar Interior and evolution present artlcle and is entitled "Inside the whlch we usually have only two obser- over most of the parameter space of the Stars". vable~(luminosity and surface gravity). HR dlagram. Stars where relativistic A short ovewlew over the last 30 Consequently, stelIar models cannot be effects are not important and whlch years of stellar astrophysics illustrates adequately tested. Moreover, we have might therefore be classified as 'nor- the immense increase of knowledge some reasons not to trust our descrlp- mal', will probably serve as most com- about how stars are working, but also tion of stellar Interiors. Let us take two mon targets for asteroseismology. about the serious shortcomings in our examples. 'Normal' stars are very Interesting as- physical concepts and accuracy of our When ensembles of stars (like open tronomical objwts In themselves and data. clusters or binary systems) are ob- certainly are not 'boring'. They play a In the slxties, a very important step In sewed for which independent con- crucial rote In the chemkal evolution of stellar moddljng was achieved by qual- straints on some astrophysical para- the Universe. Stars on me Maln Se- itative!~explaining the structure of the meters are available (same age and quence and close to it are by far the HR diagram at the level of accuracy of same initial composition for each star most frequent and easily observable in- the observational data. h the late In the ensemble), it Is usualty imposs- gredients of the Universe. All our under- seventies and in the elghties the de- ible to reproduce the observed prop- standing of the Cosmos is based on velopment of solar neutrino astronomy erties of the stars with the same val- cal tbratlons (age, distance, mass, etc.) as well as helioseisrnology showed that ue of the mixing length. This may obtained from our closest neighbours. there is not yet a satisfactory model indicate that the representation of We will nat be able to appreclate our which can predict the observed quan- convective transport by the mixing Cosmos untll we fully understand its tities at the very high level of accuracy length theory Is not adequate. constituent stars. Understanding stellar meanwhile achieved. The immense pro- The obsew6d solar neutrino flux Is evolution Is fundamental for a coherent gress in this field, accelerated by suc- much lower than expected, which in- picture of the Universe, because the life cessfut space experiments, suffers from dicates that modelling of the solar of galaxies largely depends on the life of a tack of generality, as was demon- interior is incomplete. their basic, luminous constituents: the strated, e.g., at IAU Cdloquium No. 121, Already these two examples demon- stars. "Inside the Sun". New steps forward are strate that an improvement of stdlar For many years, astronomers have needed to constrain theories by study- modelting is absolutely necessary. How- struggled with the problem posed by ing stars wlth different physical parame- ever, such an Improvement is possible these 'simple' objects, but find them- ters (effective temperature, luminosity, only if adequate tests for current models selves still far from the goal anticipated chemical composition, rotation rate, can be provided, Asteroseismology is a by Eddlngton who, In 1926, finished his magnetic flelds, etc.). new tool for this purpose. book on The Internal Constltutlon of the In the nineties, still more accurate ob- Stars with the sentence: ". but It is servational techniques are being de- Pulsation reasonable to hope that in a not too veloped which are sulted to challenge distant future we shall be competent to theories in a parameter space more Classical pulsating stars have already understand so simple a thlng as a star." complex than the two-dimensional HR been known since 1784, when 6 Cephei Agure 1: Sok pmodes, equatwial cmss Rgure 2: Solar p-modes, qua-/ Cmss ngure 3: Sdar p-modes, equatorla1 cm section 1-80, m -40. 1-3.175 mHz. section 1-40, m-0, vc3.175 mM. section 1-2, rn-2, v-3.147 mu, was discovered as a variable star. It star, and c is the travel sped of sound. be measured to a very htgh accuracy In took nearly 200 mow years to under- For a rotating star, the unpertutBed such a power spectrum: the "larg# and stand the masons for this type of stellar frequency v,, as obsewed fmthe the "smallu separations. The large ssp- variability. earth, is fuher spllt in a symmetric fre- sratton Av, Is the frequency dierence Eigenmodes of pulsations cany a quency multiplet according to: between two modes of same degree I, Wealth of information on the state of the but of quantum numbers n diffel-lng by tot Interior of stars. A mode of a glven de- u,,,, = m (1 ot,nl Q, one. The small sepmtion 6,, Is the fm QrmI is confined to a glven cavlty wWn quency difference between mode n, I he star. High-dgree modes, llke the with -I<m< I, m being an integer, Sa and mode n - 1, I+ 2. It turns out that Av, one represented In ngures 1 and 2, are the stellar rotatation frequency, and C a depends on the 'average" sound speed restrictd to sub-surface layers, while constant whlch strongly depends on the In the steIlar interior, and therefore low-degm modes, as shown in Flg stellar structure. carries information on the "average" ure3, propagate a!I the way to the In addfllon, the global magnetb fleld structure, while a,,, Is sensitive to the centre of the star. The Ftgures 1 to 3 are structure of a star also Influences the detalb of the stellar structure close to quatorial cross &Ions through vi- elgenfrequendes and pulsation am- the core. brating solar models and have been plitudes. Hence, arnptitude ratios of fre- On# the large and the small separa- kindly provided by S. Frandsen (Astro- quency multiplets allow to derive Infor- tions have been measured to a high nomlsk Instltut, mus). Amplitudes of mathon this magnetfc field structure. acwracy for a given star, one can, for the displacement mrsof the solar As is evident, a full mode identlflca- example, locate them In the w-calted p-modes are colour wdd. Another tlon (n, I and m)-la necessary in order to astemismologlcal HR diagram, where Illustration of non-radial pulsation oompare any ~~ pulsation ff& the structure constant Do,proporttonal modes is given in Weiss and Schnsider quency wlth predictions. For most of the to the small separation, is plotted verws (hMessenger, No. 33). For dlstant ctasdcal pulsating stars only one pula- the large separation Avo. This diagram stars, ony tow-degree mode can be tlon frequency has been observed, was Introduced into asteroselsmology detected because of the lack of spatial sometimes two, ve~yrarely three fie by J. Chrlstensen-Dalsgaard (Aarhus). In resolution, Fortunately, these modes are quencles. Frequently, the observed f#- such a diagram (Fig. 5), llnes of constant precisely those that probe the structure quench do only poorly mr~pondto mass (full llnes) and llnes of constant from surface to centre. those predicted hy models. The solutbn central hydrogen content (dashed lines) The roots of astermisrnology are, of to #Is dlscmpancy fs oflen pmnted can be drawn.