Warrick Ball highlights some recent discoveries in the context of the past present and future of asteroseismology
['Astrophysics - Solar and Stellar Astrophysics', 'Astrophysics - Earth and Planetary Astrophysics']
Finger on the pulse of asteroseismology
{'Finger on the pulse of asteroseismology ∗': 'Warrick H. Ball  \nWarrick Ball highlights some recent discoveries in the context of the past, present and future of asteroseismology.', 'Introduction': "Many stars pulsate or oscillate : their surfaces expand and contract periodically, and their brightnesses and apparent line-of-sight velocities vary correspondingly. The stars that vary the most have been known for centuries at least. Mira ( 𝑜 Cet), exemplar of the Mira variables, was recorded as a variable star at least as early as 1596 (Hoffleit, 1997). The first Cepheid variables, 𝜂 Aql and 𝛿 Cep, were reported in the mid-1780s. As astronomical instruments have become more sensitive, astronomers have steadily identified many more classes including, to name just a few, the 𝛿 Scuti variables and 𝛽 Cephei variables during the early 20th century and the 𝛾 Doradus variables and slowly-pulsating B-type stars (SPBs) stars toward its end. There is now a zoo of classes of pulsating variable stars usually named after the exemplar of that class.  \nIt the late 1950s and early 1960s, the Sun, too, was discovered to be pulsating (Leighton et al., 1962; Evans & Michard, 1962), though with much, much lower amplitude than observed in other pulsating stars. Over the subsequent decades, the nature of these pulsations, known as solar oscillations , was understood and they became a tool with which we could infer the deep structure of the Sun. This is now the field we know as helioseismology . Some helioseismologists soon speculated on whether oscillations like the Sun'ssolar-like oscillations -might be detected in distant Sun-like stars, which would be identified as solar-like oscillators . Dedicated campaigns to detect solar-like oscillations first bore fruit when they were detected in Procyon by Brown et al. (1991).  \nThe properties of stellar pulsations-in particular the pulsation periods-give us important information about a star that largely complements the other things we can observe, like its (average) brightness or temperature. At the simplest extreme, a single mode tells us about how long it takes for pressure perturbations to be restored to equilibrium, which is closely related to a star's average density. Even such a simple connection leads to tight relationships between the pulsation periods and intrinsic luminosities of certain kinds  \nof pulsating star. Henrietta Leavitt famously determined such a period-luminosity relation for the classical Cepheids, with which Edwin Hubble showed that some nebulae, like what we now know is the Andromeda Galaxy, could not be part of the Milky Way.  \nAt the other extreme, when multiple pulsations are present, each distinct period offers slightly different information about a star's interior, so the observation of many modes allows us to 'see' inside the star. We have measured many hundreds of pulsation periods in the Sun and combined them to map the density, speed of sound and rotation rate in most of its interior. These constraints demonstrated that the apparent lack of neutrinos emanating from the Sun was a problem for particle physics, not stellar physics. The tension was resolved by the discovery of neutrino oscillations, for which the Nobel Prize in Physics was awarded in 2015.  \nBy the end of the 20th century, we had clearly already learned a great deal from stellar pulsations. The study of stellar pulsations, now known as asteroseismology , was about to undergo its first space-based revolution.", 'The long journey to space-based photometry': "When observing periodic variations of any sort, there are three qualities to aim for. First, one should observe with enough sensitivity to detect the periodic variations, either by using a sensitive detector or observing for a long time. Secondly, one should observe for at least as long as the periodic variation being studied, and preferably longer, to be able to distinguish between variations with similar periods. Longer observations also increase the overall sensitivity, in essence because most noise (any variability we aren't interested in) is spread more evenly across all periods. Finally, it helps to observe as close to continuously as possible. Interruptions lead to ambiguity about the precise period of variation.  \nFor astronomical observations, these considerations raise a few issues. The first is the duration of observations. To distinguish between the closely-spaced periods in some pulsating stars, one needs observations that last many months. That is in principle possible except that Telescope Allocation Committees aren't always happy to commit so much time to a single star when other astronomers are yearning to look briefly at many other things. Second, one (typically) cannot observe continuously from a single site for more than about 12 hours. It is possible to combine observations from  \nmultiple telescopes or observe certain stars from near the North or South Pole (though only the South Pole is at all practical) but is difficult to co-ordinate and still requires a lot of telescope time. Finally, some classes of pulsating star only pulsate at very low amplitudes, which limits observations either to very bright targets or very large telescopes.  \nThis is not to say asteroseismology is impossible from the ground. Far from it! Clearly, every discovery I've mentioned so far was made using ground-based observations and even now many ground-based projects are produced outstanding data. In 1986, astronomers from the University of Texas set up a project that became the Whole Earth Telescope (WET), in which various telescopes around the world coordinated their observations to monitor pulsations in white dwarfs (Nather et al., 1990). A similar principle is being pursued by the Stellar Observations Network Group, which aims to continuously monitor solar-like oscillations in bright stars (Fredslund Andersen et al., 2019). Asteroseismology has also been possible using long-term projects that have been monitoring for other transient events. The Optical Gravitational Lensing Experiment ( OGLE ), for example, was largely intended to monitor many stars for gravitational microlensing, where a distant star briefly appears brighter because an object between focusses its light towards us. OGLE's data was used in the discovery of what we now call the blue large-amplitude pulsators ( BLAP s, Pietrukowicz et al., 2017), which are intrinsically rare and probably the precursors of other small pulsating stars. The All Sky Automated Survey for SuperNovae ( ASAS-SN ) and Wide-Angle Search for Planets ( WASP ) have also published extensive catalogues of variable stars. These ground-based observations will always have their place because they can keep operating for longer than space-based missions at much lower cost.  \nNotwithstanding these successes, the community knew that observations from space would overcome many of the obstacles of ground-based observations, particularly for solar-like oscillations. By the early 1990s, teams in the United States and Europe were proposing roughly 1-m class space telescopes that would record brightness variations in a large number of stars simultaneously. The larger European proposal became known as Eddington and was abandoned in 2003, though in many ways laid the foundation of what is now the European Space Agency's (ESA's) Planetary Transits and Oscillations (PLATO) mission. The American proposal, which was really a planet-finding mission to be used for asteroseismology on the side, eventually became Kepler and launched in 2009.  \nEven before Kepler launched, however, other smaller missions played an important role. In particular, the Frenchled COROT satellite detected solar-like oscillations in a about a dozen main-sequence stars and thousands of red giants. Among other things, its data showed without a doubt that not only did red giants show solar-like oscillations, but their pulsations were rich with detail (De Ridder et al., 2009). What's more, this detail can be used to relatively  \neasily infer the red giants' masses, and thus their ages, which is critical for understanding how the Milky Way formed. Many of the principal techniques with which we now study solar-like oscillations were refined on the basis of COROT 's observations.", 'The first space-based revolution': "Then came Kepler . There is absolutely no doubt in the asteroseismology community that Kepler revolutionised the field. The data that it produced during its original mission, as well as its second life as K2, remains unparalleled in duration and quality and is still being explored. I shall only highlight a few results from its nominal mission. Naturally, most are for pulsations whose analysis benefits most from Kepler 's strengths.  \nOne group of pulsating stars whose study has benefitted from the long time series are the red giants (see Hekker & Christensen-Dalsgaard, 2017, for a review). Early results from Kepler demonstrated that it was possible to distinguish the speed with which a red giant's core and envelope rotated (e.g. Beck et al., 2012). Surprisingly, the cores turned out to rotate much more slowly than cutting-edge models predicted (Eggenberger et al., 2012; Marques et al., 2013). This is still not fully explained and scientists are still proposing and testing different physical processes by which the cores might transfer some of their rotation to the envelopes.  \nAstronomers also noticed that in some red giants, some of the pulsations are much weaker than in other red giants, even if they are otherwise very similar (Mosser et al., 2012). Fuller et al. (2015) proposed that strong magnetic fields in the cores of the red giants could dampen selected pulsations in a certain range of periods. Mosser et al. (2017) contested this interpretation, on the grounds that the pulsations are present, though weak, and the proposed mechanism would suppress them completely. Recently, Li et al. (2022) reported direct evidence of strong core magnetic fields, again from asteroseismology, but there is still no consensus on what causes the selective dampening.  \nAnother group of stars that benefit from Kepler 's long observations are the 𝛾 Doradus variables. These stars pulsate in a large number of modes that fall into groups with very similar periods. What's more, these pulsation periods are often frustratingly close to one cycle per day, so ground-based observations, even if taken for long enough, are easily confounded by only being able to observe with the same frequency as the pulsations themselves. Kepler 's long, almost uninterrupted observations have thus led to an enormous leap in our understanding of these stars. Among other things, Ouazzani et al. (2017) demonstrated how one can measure the rotation rate inside these stars using the patterns among the many observed modes. Ouazzani et al. (2020) further showed that there are also cases where the visible pulsations in the outer layers couple to a different class of pulsations near the centre.  \nKepler also demonstrated the synergy between asteroseismology and the search for (and study of) exoplanets. Consider for a moment what it takes to detect and study the small drop in brightness as an exoplanet passes between us and its host star, known as a transit . First, one wants to watch the star for as long and as continuously as possible, to avoid missing a transit. Second, one wants to use very sensitive detectors, since an Earth-like planet would only occlude about one ten-thousandth of a Sun-like star's light. These requirements should sound familiar: they're precisely what we seek in asteroseismic observations. Thus, pulsations were often detected in the same Kepler data used to detect planets. This allows a better characterisation of the star, which sets the absolute scales for the exoplanets. It also led to some intriguing results, like the misalignment of Kepler -56 and its exoplanets (Huber et al., 2013). The synergy between asteroseismology and exoplanetology is at the core of the upcoming PLATO mission.  \nAfter the second of Kepler 's four reaction wheels failed, the spacecraft could no longer point accurately enough for the primary mission, which thus ended. The satellite's detectors were still operating, however, and by ingeniously balancing the satellite (unstably) against the solar wind, Kepler continued to observe under a new mission: K2 . All the stars to be observed were now selected by proposal and a remarkable variety of objects were observed, including Neptune, in whose reflected light Gaulme et al. (2016) detected the Sun's oscillations. One asteroseismic highlight was the study of variability among the seven brightest stars of the Pleiades cluster-all B-type giants or supergiants-by White et al. (2017), which includes Maia . Struve (1955) claimed to detect variability in Maia and proposed a new class of Maia variables whose existence quickly became contentious and is still debated. Whatever the Maia variables are, and whether or not the class even exists, White et al. (2017) argued convincingly that 'Maia is variable, but Maia is not a Maia variable'.  \nThough Kepler 's observations were of unparalleled quality, it only observed stars in a relatively small region of the sky-about 115 square degrees-, prioritised cool stars around which planets were more likely to be found and only observed a few hundred main-sequence stars often enough to potentially analyse solar-like oscillations. K2 's community-driven target selection led to a greater range of science than the primary mission but its observations were still limited to relatively small fields, all along the ecliptic. Kepler 's observations were also limited to relatively faint stars for which complementary observations were difficult. With the new insight that exoplanets are common, the next step would be to survey brighter stars over a wider area, which was precisely the idea behind NASA's Transiting Exoplanet Survey Satellite ( TESS ), led by George Ricker.", 'A second revolution': "TESS is a distinctly different mission from Kepler . It is has a smaller collecting area-just four cameras with 10 cm apertures-that covers a 96 by 24 degree segment of sky for about 27 days at a time. These fields of view overlap to various extents, depending on the satellite's planned observations, with a maximum continuous overlap of about a year achieved for stars near the ecliptic poles.  \nThe time series are neither as long nor as precise as Kepler 's. What TESS lacks in quality, however, is more than made up for by the quantity of data. The entire field of view is recorded at intervals that have shortened as the mission has continued. During the original two-year mission, these full-frame images (FFIs) were taken every 30 minutes and covered about 85 per cent of the sky. In the first mission extension, the imaging interval decreased to 10 minutes. In the second extension, it will decrease to just 3 minutes and 20 seconds! In addition, some stars are selected by open proposal to be observed every two minutes and an additional observing mode to take data every twenty seconds was added in the first extended mission. This has provided a truly staggering amount of data, especially to those fields of asteroseismology-particularly of hot stars-that were neglected by Kepler 's planet-hunting mission. I think it's safe to say that we have not kept up with the data: there's just too much! But we've found plenty of interesting things where we have had time to look.  \nLet's begin with the solar-like oscillators. TESS 's observations are, expectedly, not as sensitive as Kepler 's, so our analyses of main-sequence and subgiant stars have been limited to very bright stars ( 𝑉 ≲ 6, naked eye in ideal conditions). Instead of being limited to the hundred or so stars that happened to be selected for observations, however, we can now choose stars that are otherwise interesting and search their TESS data for solar-like oscillations.  \nSo far, this has mostly been limited to individual systems, including stars that were already known to host planets, e.g. 𝜆 2 Fornacis (Nielsen et al., 2020), HD 38529 (Ball et al., 2020), HD 212771 and HD 203949 (Campante et al., 2019). These complement the measurement of solar-like oscillations in two systems-HD 221416 (Huber et al., 2019) and HD 19916 (Addison et al., 2021)-whose planets were themselves detected in TESS data. Hatt et al. (2023) very recently searched for solar-like oscillations in the TESS data of over 250 000 stars, finding solar-like oscillations in 4 177 of them. The catalogue includes 28 known planet hosts, so more individual studies like this are possible.  \nExoplanets aside, there are also new analyses of systems that are interesting for stellar physicists, of which I shall mention three examples. The binary system 12 Boo comprises two stars of which the more massive component is only a few percent heavier but about 60 per cent brighter than its companion. This can only mean that the stars are in a very particular phase of evolution, in which the pulsations would tell us a great deal about how the stars' cores have  \nFigure 1: Brightness variations over a few days in the singlesided pulsator CO Cam. The long-period variation is three orbital cycles in which the brightness changes because the brighter star is distorted into a slight teardrop shape by its companion. The short-period variations are its pulsations, which, unexpectedly, have higher amplitudes in the troughs of the orbital variation.  \n<!-- image -->  \nevolved. Though Ball et al. (2022) were unable to measure the individual pulsation periods, the broader characteristics of the observations have led to more precise parameters for the system.  \nChontos et al. (2021) studied the solar-like oscillations of the solar analogue 𝛼 Men, which is orbited by a lowmass red dwarf. Low-mass stars evolve very slowly, which makes it notoriously difficult to determine how old they are: they look much the same after one billion years as they do after ten. By measuring the brighter star's age through its oscillations, Chontos et al. also precisely constrained the age of the low-mass companion.  \nFinally, Chaplin et al. (2020) studied the solar-like oscillations of the metal-poor subgiant 𝜈 Indi, which was observed by TESS near the beginning of the mission. This star formed early in the Milky Way's life and its motion through the galaxy has been affected by the Milky Way's interactions with other galaxies as it has grown over many billions of years. In particular, 𝜈 Indi's orbit was affected by the Milky Way's last major merger with another dwarf galaxy, known as Gaia Enceladus . Because the merger must have happened after 𝜈 Indi formed, the star's age of about 11 billion years-inferred using asteroseismology-places an upper limit on how long ago the merger could have happened.  \nThese results are interesting examples of how TESS has allowed us to take the lessons learned from Kepler and apply them to other solar-like oscillators. But TESS 's revolutionary results in asteroseismology have been in other types of pulsating stars. As a first example, consider what we now call tidally trapped pulsations. Handler et al. (2020) discovered pulsations in the A-type binary star HD 74423. The apparent brightness of the primary varies  \nFigure 2: A periodogram of the young planet host 𝛽 Pictoris, showing multiple pulsations at frequencies higher than usually found in 𝛿 Scuti variables. The inset shows a composite infrared image of the system, which includes two planets and a debris disk.  \n<!-- image -->  \nbecause it's distorted into a teardrop shape by the gravity of its companion. In addition, the pulsations are modulated during the orbit such that they must be somehow confined to the side of the primary pointing either toward or away from the companion. More of these tidally trapped pulsators have been detected in TESS's data (e.g. in CO Cam, Kurtz et al., 2020, Fig. 1) and they offer an opportunity to study the interaction between pulsations and tidal forces, the latter of which influence how binary stars evolve.  \nA further revolutionary discovery among the 𝛿 Scuti variables has been a group of stars that pulsate at a large number of relatively short periods. To understand the value of these results, let me first digress on the importance of mode identification . To compare observed pulsation periods to predictions from stellar models, we need to know which mode we're actually seeing. In certain regimes, this is quite easy. Solar-like oscillations in main-sequence stars, for example, follow certain formulae called asymptotic relations that allow us to tell which mode is which. For other kinds of pulsating star, including many 𝛿 Scuti variables, this is much more difficult. The asymptotic relations aren't valid and there's no guarantee that some modes simply aren't excited to measurable levels.  \nBedding et al. (2020) serendipitously discovered a group of 𝛿 Scuti variables in which a large number of modes are excited at shorter periods than the typical fundamental pulsation. These pulsations do satisfy a sort of asymptotic relation, which has opened up the opportunity to precisely characterise the pulsating stars, because now we can tell which modes are which. It's also a happy coincidence that these are young stars and some (e.g. 𝛽 Pic, Fig. 2) have features that suggest that planets are forming or recently formed. Murphy et al. (2021) analysed one of these shortperiod 𝛿 Scuti variables to very precisely constrain the age of  \nthe stellar association (a kind of loose star cluster) of which it is part. With hindsight, astronomers are also revisiting Kepler 's observations (Murphy et al., 2022).  \nAs a final example, Dorn-Wallenstein et al. (2019) searched for rapid variability in the yellow supergiants in the Large Magellanic Cloud (LMC). The LMC is near the Southern Ecliptic Pole and TESS observed it almost continuously for the first year of its observations. The team quickly found a handful of yellow supergiants that appear to be pulsating with periods shorter than a day. Though they initially dubbed these stars the fast yellow pulsating supergiants , we still don't know quite what these stars are. They might be cooler versions of the 𝛼 Cygni variables or something else entirely. Whatever the nature of their pulsations, they may well be red supergiants that lost a significant fraction of their envelope and are about to (in astronomical terms) become supernovae.", 'The revolutions yet to come?': "TESS has already been observing the sky for over four years and has funding to do so until late 2024. Its novel orbit, which resonates with the Moon, should be stable for decades and require little fuel to maintain. Its exciting to consider the potential for over a decade of TESS observations but the satellite still has some limitations.  \nOne of TESS's limitations is that, particularly for the study of solar-like oscillations, which we hope to find in cool, main-sequence planet hosts, TESS is not particularly sensitive. Kepler was better but had a limited field of view and ultimately only observed a few hundred solar-like oscillators very precisely. Two upcoming missions plan to fill this gap. The first is Earth 2.0 (ET; Ye, 2022), which is being developed in China. ET is in many ways a successor to Kepler and intends to monitor a region of sky about four times larger than (and selected to include) Kepler 's field-of-view with the aim of detecting 'Earth twins': Earthlike planets in Earth-like orbits around Sun-like stars. By designing the mission to mitigate Kepler 's noise sources, the aim is detect perhaps ten times as many planets but the data will again be valuable for the study of pulsating stars.  \nThe second mission is the European Space Agency's (ESA's) Planetary Transits and Oscillations mission (PLATO;Raueretal., 2014). The synergy between solar-like oscillations and exoplanet transits is at the core of PLATO's mission, so it has been designed to detect solar-like oscillations in thousands (and perhaps tens of thousands) of solar-like oscillators. PLATO will have a larger overall field of view than ET (about twenty times larger than Kepler ) but its sensitivity varies across that field of view and it will concentrate on brighter stars. Both ET and PLATO are currently expected to launch by the end of 2026.  \nAnother limitation of TESS (and one shared by PLATO and ET, to different extents) is the large size of its pixels. Many modern astronomical detectors have pixels, much like  \nordinary digital cameras. Each pixel in TESS's detectors spans quite a large patch of sky-about 21 arcseconds across-which makes it difficult to work out which star's light is varying when there are many stars in a small region of the sky. This 'blending' often happens in star clusters, particularly the old globular clusters that surround the Milky Way. Understanding the stars in these environments would offer many insights and a suitably small pixel scale is the basis of a proposed mission dubbed High-precision AsteroseismologY in DeNse stellar fields (HAYDN; Miglio et al., 2021). HAYDN was very recently selected as one of five candidates from which ESA will select its next mediumclass mission, which would launch some time in the late 2030s.  \nTESS should operate for many more years, two new missions are being prepared for launch in a few years' time and another mission might launch before 2040. It's clear that space-based photometry has already revolutionised the study of stellar pulsations. It is difficult to believe that there are not more revolutions waiting in the data.", 'What is the nature of stellar pulsations?': "Many stars, including the Sun, rotate slowly enough that they can be treated as perfectly spherical. It's worth keeping in mind that some stars (e.g. Altair) rotate so fast they are measurably oblate. If we also assume the stars are alone, stable over short timescales (which for stars might mean millenia) and not magnetised, we can compute useful models of how stars change over long timescales. Given one of these models, we can then ask what happens over short timescales if the star is somehow perturbed. As long as any subsequent pulsations are fast, we can further assume that the pulsation is an entirely mechanical thing: the different layers move back and forth without affecting how much heat is exchanged between them.  \nAll these assumptions lead to a set of equations that we can solve to determine how a star will vibrate if it is perturbed. We'll leave to another box the question of how a star is perturbed in the first place. If we presume the pulsations happen, we find that their dependence on the depth inside the star separates them into two families, distinguished by which force pushes the perturbed star back towards equilibrium. In both cases, there are certain depths within the star where there is not motion during the pulsation: these are the nodes and their number is the radial order 𝑛 of a mode.  \nFirst, there are pressure modes or acoustic modes . Here, as the name implies, the perturbation is restored by the pressure, just like the perturbations in the air around you that you perceive as sound. These are the modes that we observe in the Sun, main-sequence solar-like oscillators, 𝛿 Scuti variables, 𝛽 Cephei variables, RR Lyrae variables and Cepheid variables, among others.  \nSecond, there are gravity modes . Here, the perturbations are instead restored by buoyancy of denser layers trying to rise into more rarefied layers. These are observed, for example, in the 𝛾 Doradus variables and slowly-pulsating B-type stars.  \nThere are also stars, particularly red giants, in which some pulsations are simultaneously like pressure modes near the surface and gravity modes nearer the centre. We call these mixed modes . The coupling between the two varieties of modes changes the frequencies from those of pure pressure modes, revealing properties of the core. The mixed modes are much of the reason that Kepler 's observations of red giants have been so powerful.  \nAll the observed modes can be further classified by how they vary across the surface of the star. In this case, there are lines across the star's surface (really, planes through the whole star) that don't move during the pulsation. Their total number is the angular degree ℓ and the number that pass through the star's poles is the azimuthal order 𝑚 . Radial modes have ℓ = 0, so every layer of the star expands or contracts in unison. In the case that all the layers move together as a function of depth, too, we have the radial  \nFigure 3: The eigenfunction of a pressure mode in a standard model of the Sun, with angular degree ℓ = 6, azimuthal order 𝑚 = 4 and a frequency of about 3 mHz. Alternating red and blue regions would be moving in opposite directions at a given phase of the pulsation.  \n<!-- image -->  \nfundamental mode, which is the most common pulsation mode among the classical pulsators. Modes in which the star pulsates differently at different latitudes and longitudes are non-radial modes.  \nThe spherical harmonics turn up whenever we solve an equation for waves in spherically symmetric system. In quantum mechanics, this situation arises in the atomic orbitals too so the wavefunctions of electrons are also described by spherical harmonics.  \nI'll finish by returning to the original assumption: stars don't rotate. In truth they do and when the rotation is slow, this gently causes the modes of the same angular degree ℓ but different azimuthal order 𝑚 to pulsate at slightly different frequencies. If we can measure these slight differences, we can learn about how a star rotates beneath the surface, and, for the Sun, we have even done so as a function of both depth and latitude!  \nFor fast rotating stars, the equations become dramatically more complicated. But in the last decade, we have discerned pulsations in many stars, including the Sun itself, that exist because of rotation. These are the inertial modes, restored by the Coriolis force, and their rich insights are on offer to all those who can afford to toil through their (relative) theoretical complexity.", 'What drives stellar pulsations?': "For a star to pulsate, something must drive the pulsations. Two reasonably well-understood mechanisms cover most  \npulsating stars. First, there is the 𝜅 -mechanism , so called because it is related to how a star's opacity -denoted by 𝜅 -varies with temperature. Imagine a layer beneath the surface of a star where the opacity happens to increase as the temperature decreases. If that layer absorbs a bit more heat than the long-term average, it will expand slightly and cool. But by cooling, it becomes more opaque and absorbs more heat. This process runs away until the opacity starts to decrease with decreasing temperature again, at which point the excess heat is able to escape. The layer contracts, the temperature rises again, and the cycle repeats. Eddington (1917) observed that the relevant layer of a star acts like a heat engine and the mechanism is still occasionally referred to as the Eddington valve .  \nThe cause of the opacity bumps that destabilise stars turns out the be the changing ionisation states of some of its atoms. The Cepheid, RR Lyrae and 𝛿 Scuti variables are destabilised by helium going back and forth between its first and second ionisation states. The 𝛽 Cephei variables and slowly-pulsating B-type stars are destabilised by a feature associated with a number of metals, including iron, around a few hundred thousand kelvin. The same mechanism is thought to destabilise the variable subdwarf B stars.  \nThe other broad driving mechanism is near-surface convection, which is responsible for all solar-like oscillations, be they in main sequence stars, subgiants or red giants. In stars with surfaces cooler than about 7 000 kelvin, radiation alone is unable to transport all of the heat from nuclear fusion into space. The plasma becomes unstable to convection and large, turbulent flows develop. These flows become very strong-they can travel at a good part of the speed of sound near the surface-and their turbulent motions perturb the whole star, like a continuously rolling drum. The convective motions also dampen the oscillations but the star nevertheless resonates measurably at certain frequencies. It's fair to say that this mechanism is not fully understood though the principles are well-established.  \nThese two mechanism are not the whole story. There are several classes of pulsator for which there is no consensus on what drives their pulsations. One class is the 𝛾 Doradus variables, whose luminosities and temperatures are very similar to the 𝛿 Scuti variables. Another class are the Mira variables, whose pulsations might be driven by the changing ionisation state of hydrogen and helium, by near-surface convection or by some combination of the two.", 'Why are there so many classes of pulsating stars?': "Each class of pulsating star can be thought of as an intersection of four properties. First, there are only certain conditions under which stellar pulsations can be driven, usually by the 𝜅 -mechanism or near-surface convection. Second, there is the variety of pulsation mode that is driven, where we usually distinguish pressure modes, gravity modes and mixed modes. Third, stars are born with a distinct  \ndistribution of properties, which is related to how the Milky Way evolved and how stars form from collapsing clouds of gas. Finally, as they evolve, stars only ever obtain certain combinations of properties and those properties change at varying rates.  \nTake, as an example, the classical instability strip . This is a region of temperature-luminosity space in which stars are unstable to the 𝜅 -mechanismbecauseofthesecondionisation of helium. The instability strip itself spans luminosities from 10 to 100 000 times the Sun's luminosity and surface temperatures from about 8 000 kelvin at low luminosity down to about 5 000 kelvin at high luminosity. The strip is not completely full of stars because they evolve at different rates across the instability strip at different times in their lives. When a star about twice as massive as the Sun is on the main sequence, it might spend much of its life in the instability strip as a 𝛿 Scuti pulsator. When a star five times as massive as the Sun has begun fusing helium into carbon and oxygen in its core, it might evolve across the instability strip as a classical Cepheid variable. If the 𝛿 Scuti variable is relatively lacking in heavy elements, we might identify it as an SX Phoenicis variable instead, even though much of the underlying physics is the same as the 𝛿 Scuti variable. All three classes just mentioned are likely to pulsate in the radial fundamental mode, though many 𝛿 Scuti variables also pulsate in higher order modes.  \nAs another example, consider the 𝛽 Cephei variables and slowly-pulsating B-type stars. Both classes are generally B-type stars near the main-sequence, in which oscillations are driven by an opacity feature related to heavy elements, including iron. The two classes are distinct mainly because the 𝛽 Cephei variables pulsate in low-order pressure modes (like the 𝛿 Scuti variables) whereas the slowly-pulsating Btype stars' pulsations are gravity modes (like the 𝛾 Doradus variables). That the B-type variables are rarer than the lower-mass variables is largely unrelated to pulsation. More massive stars simply form less often than less massive stars.  \nThis framework, though useful to understand the classification, does not offer a complete understanding of stellar pulsations. A critical point is that we find stars in instability strips that are not pulsating and it is unclear why. The waters are also muddied somewhat by stars that have probably interacted with companion stars. As our observations grow ever more numerous, so too we discover new, intrinsically rare classes of pulsators that we must somehow fit into our schemes above. Like much of astronomy, now as in the past, new classes of pulsating stars tend to be invented before we fully understand what we are actually looking at.  \nFigure 4: A Hertzsprung-Russell diagram showing typical surface temperatures and luminosities of many (but not all!) types of pulsating star. The different colours are only to help distinguish the different classes. Thin solid lines show theoretical evolutionary sequences for stars of the indicated masses. The thick solid lines show the zero-age main sequence (ZAMS, where hydrogen fusion begins) and the approximate evolution of a 0 . 6 𝑀 ⊙ white dwarf.  \n<!-- image -->  \neffective temperature (kelvin)", 'Author': 'Warrick H. Ball is a Senior Research Software Engineer in the Advanced Research Computing team at the University of Birmingham. Until recently, he was a Postdoctoral Fellow in the School of Physics & Astronomy, where he tried to make model stars pulsate at the same frequencies as real ones.'}