Ask Ethan No. 16: What are Variable Stars?

In this Hubble photo you can see RS Puppis, a Cepheid-like variable star. The period of Cepheid changes is quite large - for example, the brightness of this star changes five times every 40 days. It is surrounded by dense dark clouds of dust, which allows you to observe in detail the effect of the light echo.

To be means to be the value of a variable.
- Willard Van Orman Quine

The reader asks:

After watching a video about the variable star RS Puppis, shot by him. Hubble, I would really like to know about what variable stars are.

Indeed, there was such a video in which the RS Puppis star was presented, the brightness of which changes with time, and there it was shown how this leads to the appearance of a light echo :



It looks amazing, and I really want to tell you about it, but three different ways that you can do it come to mind, depending on the point of view you would like to adhere to: historical, scientific or physical. There are a lot of nuances in this phenomenon, so let's look at all three approaches!



1) Historical.Once upon a time, stars were believed to be fixed points in the sky. Sometimes a catastrophic event like the appearance of a supernova occurred, which created a temporary bright object in the sky. But such events were quite rare, and very few such phenomena could be observed with the naked eye throughout the history of mankind. Although most stars do not really change their position and brightness, but this is not true for all of them. In 1596, David Fabrizius saw something in the sky, and decided that it was a supernova because he saw a point in the sky that shone brightly in August and then completely disappeared at the end of October. But to his surprise, the dot reappeared in the sky in 1609. No supernova has appeared before this twice. What Fabricius saw was not a supernova, but Mira - in fact,



At first it was believed that variable stars are quite rare, because it took as many as two centuries before they were counted 10 pieces. But the number of detected variable stars has increased dramatically with the advent of astrophotography. It became possible to accurately measure and directly compare the apparent brightness of the star over the course of days, weeks, months, and even years - both the strength of the brightness change and the period of its change.



In the early 1890s, a young woman named Henrietta Lewit attended the Collegiate Institution for Women, now known as Radcliffe College. In 1893, she was hired at the Harvard Observatory to measure and catalog the brightness of stars captured in the collection of photographic plates of the observatory. In particular, she cataloged the stars found in the Small Magellanic Cloud, and over the next twenty years found more than a thousand variable stars of different classes, which she cataloged.



But one of the classes of stars, Cepheids, was especially interesting, which Lewit noticed. When she observed the 25 brightest Cepheids, she saw that their period of change in brightness was longer than that of the other stars — the period during which they reached maximum brightness, then became dimmer and returned to maximum brightness again. All the stars changed in brightness by about the same amount (in terms of visual magnitude), but the brightest stars took several months to go from bright to dim, and back to bright. When the average brightness of the observed stars decreased, the period of brightness variation also decreased. The dimmer the star, the faster its brightness changed, up to a period of one day. In fact, she found a well-observed correlation between



This connection is known today as the ratio of period and brightness, and this discovery led to amazing consequences, which lead us to the second way of answering the question of variable stars.



2) Scientific.Regarding the Cepheids discovered by Lewit, we can say that they were stars located at rather large distances from us - approximately 199,000 light years. And the physical size of the object in which these stars were located was approximately 7,000 light years. Because of this, all the stars in the Small Magellanic Cloud are approximately at the same distance from the Earth. Changes in the brightness of stars correspond to their actual luminosity. If there is a connection between the period of the pulsation of a star and its brightness, this means that if you measure the period of a variable Cepheid star, you will know what its actual luminosity is. And if you measured the luminosity, then knowing how the brightness and the distance are related, you can calculate the distance to it.



We call these objects “candlestick standards” because if you know the actual brightness with which the object glows, and then you measure the apparent brightness, then you can understand how far the object is from you. Thanks to the Cepheid work of Henrietta Lewit, we have standard candles for measuring vast distances in space. And thanks to Edwin Hubble and the discovery of variable stars located in spiral nebulae, which he observed in the 1920s, we were able to understand how far these objects (turned out to be galaxies) are actually located.



There are many types of variable stars that differ in color and brightness. In addition to the Cepheids discovered by Lewit (of which there are 2 types) there are stars with a smaller mass and a shorter RR Lyrae period, variable red giants (such as Mira), pulsating white dwarfs and a whole crowd of others, some of which are shown in the picture below.



For the most part, there is a well-defined correlation between the periods of change of these objects and their nominal luminosity, which means that if we find and identify them somewhere, then we can immediately accurately determine how far the object is. And, according to science, this is one of the most important discoveries related to the staircase of cosmic distances. The best way to measure distances to stars is parallax, or changing their positions in the sky during the year (when the Earth rotates around the Sun). But this method only works for stars located 1600 light-years from us. Although, the Gaia mission, launched recently, will try to increase this distance by ten times.



But at a distance of 1600 light-years from Earth, there are quite a few variable stars, for which we measured using parallax. And there are also many variable stars, the distance to which, judging by the calculations, is at least 100 million light years.



Observing how these stars change over time, how their brightness changes, what their period of brightness changes, we assigned these stars to the corresponding class of variables, and in this way we have already determined the distances to thousands of space objects outside our galaxy. So, now we know how we discovered them, we know what they are used for, but why does their brightness change? And this leads us to the third answer.



3) Physical. It can be decided (and this will be wrong) that the core of the star, where nuclear fusion takes place, undergoes some changes that are transmitted to the surface, which leads to pulsations. This is unlikely because the time spent by the photon created in the nucleus to reach the surface of the star is approximately 100,000 years. During this time he is experiencing trillions of collisions! Generally speaking, the fusion rate in the nucleus is almost the same for all known types of stars. And yet, the brightness of stars varies.

For most variable stars, changes in brightness are explained by what happens in the outer layers.



The photosphere of a star, the layer from which photons fly away from a star forever, is a special place from the point of view of physics. For a very stable star, the photosphere will remain constant over time. The radiation pressure that pushes particles outward on the surface will be completely compensated by the force of gravity, which pulls the particles to the center of the star. The sun is a close approximation of this model, but even a boring star like the sun is not perfect in this sense.



Even the sun's outer layers experience convection - the rise and descent of matter. In such systems, equilibrium is never achieved, and the outer layers are subject to a cyclic process in which:

• too much pressure forces the star to expand
• when it expands and the top layer moves away from the center of the star, gravity drops, but the radiation pressure drops faster
• as a result, the acceleration of the outer layer slows down, passes the equilibrium point and reaches a state where gravity is stronger than the radiation pressure
• then it begins to accelerate inward, causing the star to contract
• it again passes through the equilibrium point to the other side, when the radiation pressure rises to the point where it begins to push the layers out again with force and the cycle repeats.

The intensity of our sun fluctuates at the level of 0.1%.



But for stars, which we call variables, brightness and radius can change by a huge value - by 90% or even more! For stars like Mira, the actual luminosity changes during one cycle a thousand times, while for ordinary Cepheids, the radius changes by millions of kilometers, and the temperature by thousands of degrees.



This topic is a storehouse of interesting information, because amateurs and professionals spend their whole lives studying such objects. I gave you an introduction on the topic of variable stars, and now we know how they were discovered, why they are used, and why they are variables. For further study, I recommend that you AAVSO(American Association for Variable Star Observers). There you will find interesting information for both researchers and ordinary amateurs.