Wed. Nov 30th, 2022

From a supercomputer to your desktop, models of blue variable stars.

The universe is full of things we think we can understand, but we’re not really sure about. What it often comes down to is our computational power: to answer the question of whether models based on the physics we know generate the behavior we see around us. In response to that question, researchers have turned their math gun to a long-standing problem: why do luminous blue variable stars exist?

Luminous blue variables are very large, very bright stars, but their temperature (color) varies quite a bit. Scientists were pretty sure that the variability somehow came down to a combination of radiant pressure, shock waves and convection. But so far no one could confirm that.

Emotional stars lose their balance

In particular, light blue variables range from brightness and temperature ranges that are in equilibrium to brightness values ​​that are far out of balance.

What do we mean by that? At the center of each star, nuclear reactions generate light. The light exerts a pressure on the matter in the star that prevents further collapse of gravity. At equilibrium, the radiant pressure balances the collapse of gravity, and everything should be nice and steady (as it is with our sun). The temperature and brightness of the star reflect this balance.

For stars that are much hotter, such as the blue end of luminescent blue variables, the radiation pressure is greater than the collapse of gravity. During these moments, matter is blown off the star like so many dandelion seeds.

The strange thing about luminescent blue variable stars is that they transition erratically between equilibrium and non-equilibrium states. How and why that happens is a long-standing question.

When in doubt code

It’s not about physics, it’s about solving difficult equations. For example, if you want to understand a star from a mathematical point of view, a few lines of equations solve the problem. But turning those equations into predictive models is difficult.

The usual approach is to simplify: stars are spherical, so maybe we just need to worry about their depth. By reducing the equations from 3D to 1D – a line from the star’s core to the surface – the math becomes simpler and we can generate predictions. Unfortunately, things like turbulence (convection) require a full 3D model. And to calculate results with a 3D model of a star, you need serious computing power.

How much, you ask? Try 60 million CPU hours on an 8.59 petaflop supercomputer. That was enough to generate three data sets for three different brightness and temperature combinations. The values ​​are chosen so that two stars are in balance and one out of balance. Their evolution was followed between 15 and 35 days (at least that’s how much data was shown in the paper).

The helium trap

Left, density variation of the star.  Right, temperature variation of the star.

Left, density variation of the star. Right, temperature variation of the star.

It turns out that convection and shock waves do play an important role. If the star is cooler, the density of helium and iron is high. These materials trap radiation in the star, heat it and cause the outer shell of the star to expand. As the envelope expands, the speed of sound decreases. The density waves driving the expansion find themselves suddenly going supersonic, generating a shock wave. The shock wave expels material at a relatively high speed (the peak is about five percent of the sun’s mass per year).

The expansion, combined with the loss of material, reduces the star’s optical density. Light begins to escape at a faster rate and the radiation pressure decreases again, causing the star to fall back to a cooler state. While this is happening, the heating process has already started again. The enormous distances mean that the density waves that cause these changes take about 10 years to reach the surface.

Strong temperature changes seem to require helium to absorb a lot of light. Iron helps, but without helium the star will be much more stable. The 3D model also emphasized the importance of time scales. The main variations we have already observed (and predicted by the model) seem to be about what we would expect, given the time it takes to change the opacities of helium and iron.

However, the envelope has its own timetable. Convection waves and density waves take about a week to travel from the inner part of the envelope to the outer part of the envelope. The researchers’ model predicts that these waves, which depend mainly on the opacity of iron, will also lead to temperature fluctuations of the order of a week.

There are some observations that seem to confirm this. However, it seems that some telescope time will be needed to properly observe these short-term changes and see how they fit into the model.

It just goes to show what you can achieve with serious computing power.

Nature2018, DOI: 10.1038/s41586-018-0525-0 (About DOIs)

List image by Yan-Fei Jiang

By akfire1

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