Stars beat!

By Cristina Rodríguez-López, Instituto de Astrofísica de Andalucía

Excuse me? Stars what? Yes, stars do beat! Even our own Sun! You may think that stars are immobile, comfortably and quietly burning their nuclear fuels up there in the sky, but the reality we have got to know through observations is quite different. Stars ‘breath’ and ‘contort’ and ‘wriggle’ in a variety of ways, altering their radii and surface temperature which produce periodic changes in their luminosity and surface velocity that we detect with our telescopes and instruments. These effects are known by the technical name of pulsations, or oscillations, and the technique that tries to extract all possible information from these pulsating stars is known as Asteroseismology, or, in the specific case of our Sun, Helioseismology.
The naming responds to the techniques used, analogous to the Earth-seismology, that extract information from seismic waves propagating in the interior of our planet to derive the composition and stratification of the Earth. Asteroseismology analyses the frequencies of oscillation of the light coming from the stars, which are a fingerprint of the star’s interior chemical composition and structure, as well as of other fundamental parameters such as its mass, density and age.

So, what are these pulsations? Pulsations are, strictly speaking, pressure and gravity waves (usually referred to as p- and g-modes) that propagate in the interior of the star; you can think about them as sound and maritime waves respectively, this meaning that changes in the pressure and buoyancy are responsible for them. P- and g-modes propagate at different depths inside the star (see Fig. 1), allowing to probe the different regions just by measuring their frequency on the surface, that would be, otherwise, inaccessible.

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Figure 1. Schematic view of two different pulsation modes propagating inside a star. P-mode are shallower and reflected on the surface at higher frequencies than g-modes that travel deeper to the core of the star. Credit: By Tosaka – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=3292274

The fact that some of these oscillations are sound waves, is why, in a more poetic way, we talk about the ‘music of the stars’. Sound waves resonate inside the stars, in much the same way as in a musical instrument, and although their frequencies are too low for us, humans, to hear -and sound does not propagate in vacuum-, some scientists have amplified them, so that we can actually hear how they would sound. The experience is, however, not the pleasantest, as star’s sound waves are not harmonic.

But how do pulsations originate? Pulsations originate from the displacement of the plasma inside the star. The radiation originating from nuclear fusion in the star’s core or layers try to find its way up to the surface, but in doing so, there are some stones in its path: one are the so called partial ionization zones of chemical elements. In these layers, the star’s opacity increases with increasing pressure, holding the radiation coming from the interior and pushing the upper layers, which then become more transparent, releasing the radiation and falling in afterwards, starting the cycle again, as if it was an inhaling-exhaling process, in the same way as an engine works. If the excitation produced in these regions is larger than the damping produced in all other ones, then the star will likely show oscillations in its surface. This is called the kappa-mechanism and it is responsible for the pulsations in several types of variable stars such as RR Lyrae, delta-Scutis, beta Cephei, Hot Subdwarfs or White Dwarfs. In stars that have an inner radiative zone and an outer convective zone, the radiative flux can be blocked and then released at the interphase -or tachocline- of these two layers in a cyclic way, like it is the case for gamma-Doradus variables. Finally, in these partially convective stars, such as our Sun, an stochastic excitation of pulsations, due to the turbulent convective motions in the surface of the star -as it happens when we heat water on a pot- can also be produced.

Do all stars pulsate? And does Proxima pulsate? That’s a good question! To answer it, we may take a look at the Hertzsprung-Russell pulsating diagram (Fig. 2) which locates all types of known pulsating variables, in terms of their temperature and luminosity. The diagonal dashed line that traverses it locates the stars in the main sequence (MS), where they burn hydrogen in the core. Some of the delta Scuti are pre-MS stars, while giants like Cepheids or Mira lie above the MS and subdwarfs and white dwarfs, like GW Vir, sdBV and DAV, that sit below it, are all post-MS more evolved stars. So, it seems that all stars no matter what their mass or temperature, or their evolutionary stage, have the potential to pulsate, although beware that not all stars located there do! that is, these instability strips are not pure, but populated also by ‘normal’ non-pulsating stars.
In the case of Proxima, and more generally for M dwarfs, we do not know it yet. Pulsations have been theoretically predicted, but not yet detected observationally, although we are looking for them! We can only be sure that, if oscillations exist, they will be of very low amplitude, of the order of millionths of a magnitude if we monitor the incoming amount of light, or less than 1m/s if we measure how much the surface of the star rises and falls. If oscillations had larger amplitude than these limits, we would have already detected them.

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Figure 2. Hertzsprung-Russell pulsating diagram. M dwarfs are located at the bottom of the Main Sequence diagonal line in orangish-red colour. Locations of different pulsating star classes are labeled and encompassed by striped ellipses. Credit: http://astro.phys.au.dk/~jcd/HELAS/puls_HR/

So, explain me then how do you detect pulsations? The frequencies of the oscillations, or inversely, their periods, may vary between only a few minutes, to hours or a few days. For M dwarfs, like Proxima, the range is predicted to vary most likely between only 20 minutes and 3 hours. To detect these oscillations, we use two techniques also used in the search for exoplanets: photometry and spectroscopy. Photometry measures the amount of light coming from the star over a period of time: if the star is non-variable, its light-curve, or light received as a function of time, will be constant, whereas it will periodically vary if it is a pulsating star (see Fig. 3). The same technique is used by satellite space missions dedicated to search for planetary transits, such as KEPLER and CoRoT, and future PLATO, that measure the diminishing of the light of a star when an orbiting planet traverses our line-of sight. Spectroscopy, through the radial velocity method, measures the periodic velocity changes in the spectral lines of the star caused by the rising and drop of the stellar surface due to the oscillations, just as velocity changes are caused by the gravitational tug of a planet orbiting the star; this is the same type of observations we are carrying out for Proxima with HARPS spectrograph.

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Figure 3. Light-curves of variable stars in cluster M1. Credit: http://central.oak.go.kr/journallist/journaldetail.do?article_seq=10773&tabname=abst&resource_seq=-1&keywords=null

Then, what role do pulsations play in the discovery of exoplanets? First, we have to be sure that pulsations are not mistaken for a planet, as sometimes, they can mimic them; also if the star is pulsating, the planet search observations have to be designed such as to minimise the influence of the pulsations in the data acquisition, or to a posteriori correct the data from them, before the signature of a planet can be assessed. However, most interestingly, when a pulsating star is a planet host, we can very precisely derive its mass, radius and age, and this is an unique and precious way to pin down the physical parameters of the planet and its evolutionary history.
So, let’s hope that we find lots of planets surrounding pulsating stars!

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About the Author. Cristina Rodríguez López is a post-doctoral researcher at the Instituto de Astrofísica de Andalucía (CSIC, Spain) within the group ‘Low-mass stars and exoplanets and associated instrumentation’. Her research interests include asteroseismology of low-mass stars in different stages of evolution and the search for exoplanets. Previously, she received her PhD from the University of Vigo and was a post-doctoral researcher at the Laboratoire d’Astrophysique de Toulouse-Tarbes (now IRAP, France) and a visiting scientist at the Department of Physics and Astronomy of the University of Delaware (USA). She is responsible for the scientific workpackage ‘Asteroseismology of M dwarf stars’ within the CARMENES Consortium, which brings together 11 Spanish and German Institutions around the scientific exploitation of the CARMENES spectrograph, a new planet hunter focused on discovering Earth-like planets around M dwarf stars, much the same objective pursued by the Pale Red Dot project, of which she is also a co-investigator and editor.

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