What is astroseismology and why is it needed

(ORDO NEWS) — Fred Kavli, having ordered every two years to award a million dollar prize to achievements in the fields of astrophysics, nanotechnology and neuroscience, motivated this decision as follows: one deals with the biggest, the other with the smallest, the third with the most difficult.

This year, the “biggest” science in this triumvirate is represented by textbook objects, stars. And the most common. So astronomers call stars similar in nature, structure and evolution to the Sun. Astrophysicist Anton Biryukov from the SAI of Moscow State University tells about what the laureates learned and, most importantly, how.

The Astrophysics Prize was awarded to Connie Arts (Catholic University Leuven, Belgium), Jørgen Christensen-Dalsgaard (Aarhus University, Denmark) and Roger Ulrich (University of California at Los Angeles, USA) – for “pioneer work and research in the fields of helio- and astroseismology “.

Since the 1970s, these scientists have made a decisive contribution to the then young branch of astrophysics, which took a fresh look at the stars, their properties and internal structure. Although it is even better to say – I heard.

In 1926, the English astrophysicist Arthur Eddington published the now classic monograph on the internal structure of stars. It begins like this: “It seems that the interior of the Sun and other stars is the least accessible for scientific research than any other region of the universe.

Our telescopes can see farther and farther into space, but how can we get reliable knowledge of what is hidden under the thick layer of matter? What instrument can penetrate under the surface of a star and measure the conditions in its interior?

Astrophysics – literally “the science of the nature of stars” – cannot be complete without understanding the inner workings of these objects. And not theoretical, about which Eddington wrote, but also its experimental confirmation.

In 2022, we are still far from launching a measuring probe into the interior of the Sun. However, we are no less far from breaking into the deep bowels of the Earth. However, geophysicists have been studying the structure of the Earth for more than a century by how waves of elastic vibrations propagate inside it.

This is how the science of seismology arose. Astrophysicists borrowed this idea from colleagues and, starting in the 60s of the last century, began to measure how oscillations propagate in the interior of a star. Thus, first helioseismology (studying the Sun) was born, and then astroseismology (exploring other stars as well).

So we had the tool that Eddington needed.

Sounds of the stars

If everyone is more or less familiar with terrestrial seismology, then how and why can this method work for stars at all? After all, we do not install seismic sensors on the surface of the Sun and other stars!

It really is. But the sound that permeates the stars can generally be seen with conventional telescopes. Namely, to see the changes that sound waves generate on the “surface” of the star.

In general, strictly speaking, the assertion that a deafening silence reigns in space is false. In reality, of course, elastic waves exist in any material medium. Including interstellar and interplanetary: they are, of course, sparse, but not empty at all.

And even more so, sound waves propagate in the depths of very dense stars. So, for example, the average density of the Sun is 1.4 times the density of water, in which sound propagates very well – dolphins and whales will not let you lie.

But where does it come from?

To understand this, let’s imagine a star as a teapot on a hot stove. The plate, in this case, is the core of the star, in which thermonuclear reactions take place and energy is generated. This energy is transferred to the higher layers of the star, in the same way that the heat of the stove heats the bottom of the kettle.

The kettle is filled with water, a cold and rarefied substance. It also heats up and then boils. It is very easy to distinguish a boiling kettle from one that has not yet boiled, including by ear – it generates low-frequency noise. The same thing happens with the Sun.

Its outer layers, accessible to the earthly observer, of course, do not completely boil, but they also give off thermal energy. Heat transfer in them occurs due to convection, together with jets of rising matter. And this convection of the outer layers of the Sun also generates sound waves.

The bubbling of water in the kettle is perfectly audible due to the relatively high density of air, which conducts sound well. In space, the environment is much more rarefied, so you literally cannot hear the Sun, not to mention other stars. But peering into its surface, we can see this sound.

Consider the sound of the sun

Research in the field of astroseismology began with helioseismology, that is, with the study of the star closest to us. In the early 60s of the last century, a group of astrophysicists from the California Institute of Technology, led by Robert Leighton, saw the convection of the outer layers on the Sun.

They saw bubbles of plasma about 10,000 kilometers in diameter rise and fall on its surface at a speed of about 500 meters per second and a period of 296 seconds. These were the already famous five-minute fluctuations of the Sun.

It is they who generate waves that propagate into the Sun. And, importantly, they do not propagate in a straight line, but in the same way as seismic waves in the thickness of the Earth – refracting, turning and reaching the surface at a different point. These are the so-called p-waves or pressure waves. They sound.

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Seismic waves inside the Earth. An epicenter is a source of waves, usually an earthquake, that occurs shallowly below the surface. Further, acoustic waves – longitudinal (pressure waves, p-waves) and transverse (seismic, s-waves) – propagate through the bowels of the Earth along curvilinear trajectories. The propagation speed of seismic waves depends on the properties of the Earth’s interior along the propagation path. Therefore, by restoring this path from the delay in the arrival of the wave at different points on the Earth’s surface, one can obtain information about the structure of the planet
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Standing wave modes: short waves – closer to the surface, long waves – go deep, to the core of the star

Elastic vibrations of several types propagate through the solar interior – and they behave differently. So, a pattern of standing sound waves is established near the surface – p-waves, the oscillations of which can be seen. Several p-wave modes arise in the star, which allow testing conditions at different depths. The characteristic frequencies of pressure waves in the Sun are several millihertz.

The so-called g-waves propagate in the central region of the star. These are gravity waves and should not be confused with gravitational waves. It is not a sound, but waves, similar to the vibration of the surface of water into which a stone is thrown.

They have a lower frequency (tens of microhertz) and are “locked” in the inner part of the star – the zone of radiative transfer. These are layers that are hot enough to transfer energy by radiation rather than convection. In the interiors of stars, g-waves also have an additional effect on the propagation of sound p-waves.

Exactly how p-waves penetrate into the interior of a star, where exactly they turn, where they emerge to the surface, what pattern of standing waves they form – all this depends on the specific physical properties of the thickness of the star.

First of all, it depends on the temperature, density and state of aggregation of the substance. Roger Ulrich developed a rigorous theory that relates the properties of the observed oscillations of the Sun to its internal structure. He linked observations and physics.

Actually, similar physics is used in seismology. With the difference that the sources of seismic waves in the Earth are natural earthquakes or artificial shocks. The bowels of the Moon and Mars have already been investigated by the same method.

Comparing the vibrations of the earth’s surface at different points, the delay in the arrival of a sound wave from one earthquake to different measuring points, geologists can draw conclusions about the internal structure of the Earth. At least about the density of its matter at different depths.

Helioseismology follows the same method. A picture of standing sound waves of different lengths is established on the Sun. This length is a multiple of the path length traveled by the sound wave. Which, in turn, is determined by the size of the Sun and the depth to which these waves reach.

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One of the harmonics of standing sound waves in the Sun. Different colors indicate “dips” and “hills” on the surface of the Sun at a given point in time. They change places with a period of several minutes. The heights of these hills (as well as the depths of the dips) are very small – only a few meters. But the effect of these fluctuations is quite measurable

In reality, the picture of standing waves is a little more complicated than in the figure, which shows only one harmonic of the oscillations. The sun looks even more dappled. But all oscillations can be disassembled into components and their spectrum can be constructed – the dependence of the intensity of each harmonic on its frequency.

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The spectrum of a sun-like star. The horizontal axis shows the oscillation frequency in millihertz, while the vertical axis shows the amplitude of changes in the brightness of the star at this frequency, in millionths of the average brightness. The frequencies at which individual peaks are observed in this spectrum, and the distances between these peaks are the main information that astroseismologists process

It is the type of this spectrum – the positions of individual peaks and the distance between them – that ultimately tells researchers how the interior of a star is arranged, in which sound waves propagate.

Sound waves reaching the surface of the Sun cause it to slowly wiggle up and down – something like the membrane of a large sounding speaker trembles. These surface movements are captured using the Doppler effect.

Using the spectrum of different parts of the Sun, observers can measure the position of the lines of known chemical elements, and their shift relative to the laboratory wavelength will indicate the speed of the movement of matter.

Ad astri

But what about other stars? We cannot see their surface in detail, unlike the solar one. Due to the gigantic distances, the rest of the stars appear simply as luminous dots. But we can measure the brightness of these points with high accuracy – and do it regularly.

We can say that all stars are variable (and the Sun is no exception) – their brightness changes over time. Some to a greater extent, others to a lesser extent. And in some cases, this variability is determined precisely by the fluctuations of the surface of the star.

We have long known stars whose surface fluctuates very strongly – these are the so-called pulsating variable stars. One of the brightest of these stars is the Cepheids. These are supergiant stars, owing their name to Delta in the constellation Cepheus.

They expand and contract over a period of several days. As they expand, they cool down, much like the air coming out of a pressurized can cools down. And when cooled, they dim greatly, since the luminosity of a heated body in a good approximation is proportional to the fourth power of its temperature.

The colder the star, the less its luminosity. But the opposite is also true: as the star shrinks, it heats up and becomes brighter. This is what we observe in Cepheids. Moreover, Doppler measurements of surface motion confirm that the change in their brightness is associated precisely with physical pulsations.

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Dependence of the observed parameters of the Cepheid on time. The upper figure shows the apparent brightness of the star, which periodically rises and falls with a period of several days. This is the light curve of a star. The second figure shows the temperature of the outer layers of the star, measured from the shape of the spectrum. The higher the temperature, the higher the brightness. And vice versa. In the third figure, the calculated radius of the star (in relative units). The star alternately contracts and expands with an amplitude of about 10 percent. The smaller the star, the brighter it is. Finally, the lower figure shows the synchronously measured speed of the star relative to the observer. It is these velocity fluctuations that correspond to the pulsating surface

However, imagine that different parts of the star pulsate differently. Some go down, some go up. Some become brighter, and some, on the contrary, dim. Moreover, the sizes of such heterogeneity cells can be very different. Then the dependence of the star’s brightness on time will change.

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Light curves of giant stars of different sizes. Smaller stars “noise” at a higher frequency. Here lies the same physics that sets the range of sound of musical instruments of different sizes. So, the piccolo flute is several times smaller than the alto flute, but it also sounds, on average, one and a half octaves higher

Glitter will change in complex, unpredictable ways. However, if we catch separate periods in these changes (by decomposing all this noise into components), then we can find out which fluctuations on the surface of the star are larger and which are smaller. Which ones are stronger and which ones are weaker. This is the same observational problem that is solved in helioseismology.

The brightness fluctuations caused precisely by acoustic waves are very small. To notice them, you need telescopes that can measure the brightness of a star with very high accuracy – up to hundredths and even thousandths of a percent.

Such telescopes appeared not so long ago. These are, first of all, space telescopes: European CoRoT, American TESS and Kepler. Especially the last one. All these telescopes were created primarily for the search and study of exoplanets by the transit method.

This task also required high accuracy of brightness measurements. Unlike aperiodic elastic oscillations of the surface of a star, transit is a strictly periodic phenomenon. It results in a slight drop in the brightness of the star at the moment when the planet eclipses part of the disk of the star, once during its orbital period.

Why is all this necessary?

Helioseismology has made it possible to reconstruct the picture of the rotation of the interior of the Sun.

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The sun “in the cut.” The axis of rotation of the Sun is directed along the vertical, and different colors in the figure show the speed of rotation of various layers of the star. The outer layers rotate at different speeds, depending on the latitude: the equator makes a revolution in about 25 days, and the poles in 30. At the same time, at a depth of about 0.7 of the radius of the Sun, the rotation speed levels off and does not depend on the distance to the center of the star , nor from latitude. The so-called rigid-body rotation is realized there

Now we know that inside the Sun rotates as a solid body until the beginning of the convective zone. It occupies only the outer 30 percent, and it exhibits what is known as differential rotation: the outer layers of the Sun rotate faster at the equator than at the poles.

The boundary between the inner and outer zones plays an important role in the formation of the large-scale magnetic field of our star. A great contribution to this result was made by the second laureate of this year, Jørgen Christensen-Dalsgaard.

Helioseismology played a key role in confirming the model of the internal structure of the Sun, which predicted that the solar neutrino flux should be three times greater than the observed one. This problem has plagued astrophysicists for decades.

She had two solutions: either admit that the existing model of the Sun is wrong, or say that something inexplicable is happening to the neutrino.

And thanks to helioseismology, it was possible to find out that the matter is in neutrinos. The neutrino flux depends on the density distribution, temperature, and chemical composition of the solar core. Which can be checked by helioseismology methods.

Therefore, it was the researchers of elementary particles who had to make adjustments to the theory, and not their fellow astrophysicists (read more about the problem of solar neutrinos in the materials “H means neutrino” and “Pure anomaly”).

Connie Arts is known for her astroseismic studies of giant stars – which have already passed the solar stage and used up hydrogen fuel. These stars have a slightly different internal structure. Astroseismology made it possible to distinguish between stars at different stages of their evolution and to answer the question of which of them burns helium in a thermonuclear manner.

After all, if helium is burning in the core of a star right now, then its temperature and density will differ from the temperature and density of a quiet core. Therefore, elastic waves propagate in it differently. Helium burning is a fairly fast process compared to the lifetime of a star, so it can be used to determine the age of a star quite accurately.

In addition, the measurement of the oscillation spectrum made it possible to better understand the rotation of the inner layers of evolved stars and compare it with that

Astroseismology turned out to be one of the most accurate methods for measuring the masses, sizes, and, as a result, the ages of single stars. The masses of stars are related to their density – and the speed of sound in the interior of a star depends on it.

Together with the size of the star, this speed determines the characteristic time it takes for a sound wave to travel through the entire star. And time is a quantity associated with the frequency of surface oscillations.

Starting with the works of Ulrich in the 80s and other theorists, astroseismologists have in their arsenal the so-called similarity relations, which, by the maximum frequency with which the star’s brightness changes, as well as by the difference in frequencies between the main harmonics, make it possible to restore the mass, radius, and density of the star in solar units. On the other hand, models of stellar evolution predict quite specific values ​​for the mass, radius,

All these relationships and models make it possible to test the theories of stellar evolution, one of the fundamental theories in astrophysics, using astroseismological methods. This means that it is correct to understand what future awaits our Sun.

But the possibilities of asteroseismology do not end there. For example, determining the parameters of an exoplanet, in general, depends on how well we know the parameters of the star around which the exoplanet orbits. It is thanks to asteroseismology that it has become possible to detect terrestrial-mass planets located in the so-called habitable zone of their stars.

Helio- and astroseismology make it possible to answer many questions about the life of stars not from a speculative, but from a practical point of view. They turned out to be exactly the tool that Eddington thought of, and which allowed him to pierce the surface of a star and look into its center. And if today he decided to write the same book about the stars, it would almost certainly begin with the word “astroseismology.”


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