
This guest post was written by Tom Wagg, a 4th year PhD student at the University of Washington. Tom loves understanding and modelling binary stars from all sorts of angles – from pulsations and asteroseismology to gravitational waves and galactic positions. Outside of astronomy, you’ll find him playing field hockey and pickleball or wandering around on top of a mountain.
Paper 1
Title: Über die Wirkung der Windschwankungen auf die Pilotbeobachtungen
Authors: Vilho Väisälä
First Author’s Institution: Finnish Meteorological Institute
Status: Published in Societus Scientiarum Fennica Commentationes Physico-Mathematicae [open access]
Paper 2
Title: The period of simple vertical oscillations in the atmosphere
Author: David Brunt
First Author’s Institution: Imperial College
Status: Published in Quarterly Journal of the Royal Meteorological Society [closed access]
Paper 3
Title: Correlated 1-1000 Hz magnetic field fluctuations from lightning over Earth-scale distances and their impact on gravitational wave searches
Authors: Kamiel Janssens, Matthew Ball, Robert Schofield, Nelson Christensen, Raymond Frey, Nick van Remortel, Sharan Banagiri, Michael W. Coughlin, Anamaria Effler, Mark Golkowski, Jerzy Kubisz and Michal Ostrowski
First Author’s Institution: Universiteit Antwerpen
Status: Published in Physical Review D [open access]
Asteroseismology probes stellar interiors
Most observations of stars are used to infer their external properties, such as their luminosity or effective temperature. In the past, it was often thought that it would not be possible to observationally probe the internal structure of a star – indeed, in 1926 Arthur Eddington famously lamented: “What appliance can pierce through the outer layers of a star and test the conditions within?”. However, we now have an answer: asteroseismology! We can measure stellar interiors by modelling the pulsations which travel through a star and in the process are imprinted with information about the internal structure. This information has been extremely useful for understanding many aspects of stellar structure and evolution. Additionally, based on the measured pulsations, one can determine a star’s mass and age.
In this post, we’ll focus on gravity wave (g-mode) pulsations, for which the restoring force (the force driving the oscillations) is buoyancy. Each of these modes oscillates at a different period, which we observe as pulsations in many stars, such as Gamma Doradus and Slowly Pulsating B stars. These observed periods are determined by the Brunt-Väisälä frequency profile, which changes shape for stars of different masses and ages. So if we can understand and model this frequency for a star, then we can fit the observed pulsation periods to models and infer a star’s age through its internal structure.
Buoyancy and the Brunt-Väisälä frequency
Physically, you can define the Brunt-Väisälä frequency with a quick thought experiment. Imagine a small parcel of material in a radiative region of a star is displaced vertically downwards slightly, fast enough so that its density doesn’t change (i.e. it all happens adiabatically). Now it is surrounded by denser material and so, like a rubber duck in a bathtub, it will be driven back upwards as a result of buoyancy. This parcel will then do the opposite in the other direction – it moves past its original position, is denser than its surroundings and sinks back down. This simple harmonic oscillation will occur with a characteristic frequency – that’s the Brunt-Väisälä frequency!
Inferring stellar properties
The frequency depends on the surrounding environment and so it changes throughout a star. This is why we discuss a Brunt-Väisälä frequency profile, the value of the frequency as a function of position within the star. As we mentioned above, this profile determines the pulsation periods of g-mode oscillations – such that the details of the internal structure of a star are imprinted upon its pulsations as they pass through it.
So, if we observe a star undergoing g-mode pulsations and measure their period of oscillation, we can estimate the star’s Brunt-Väisälä frequency profile and from this place constraints on its internal structure and infer its mass and age.
Atmospheres of a more Earthly nature
But what does all of this have to do with meteorology? Well, the same argument for parcels of material in stars applies directly to parcels of gas in our atmosphere. In fact, the frequency was originally derived with this in mind and only later applied to astrophysics!
The frequency plays a large role in our understanding of atmospheric stability. If a region is unstable, then a parcel of material that is displaced will not oscillate around its original position, but will instead continue moving (resulting in convection!). In this case, the Brunt-Väisälä frequency is not physically defined. This means a frequency of 0 is the boundary for stability.
Cloud formation on Earth is strongly linked to stability, both in terms of whether clouds will form, as well as what type of clouds will form. An unstable atmosphere is much more conducive to cloud formation, as unstable parcels of air can rise quickly and reduce their capacity to hold moisture. So, the measurement of the stability in a particular region of the atmosphere through its Brunt-Väisälä frequency can provide a useful indicator of the expected rate of cloud formation.
Origins of the frequency
Instabilities in the Earth’s atmosphere were indeed the first motivator for the derivation of the frequency. Despite his name appearing second in “Brunt-Väisälä”, the derivation was actually first published by Vihlo Väisälä in 1925 in his paper “Über die Wirkung der Windschwankungen auf die Pilotbeobachtungen” (you’ll note that’s a year before Eddington was worrying about how to probe stellar interiors!). This Finnish meteorologist explained how wind fluctuations (oscillating with a frequency that he derived) affected pilot observations using weather balloons.
Two years later in 1927, Sir David Brunt, a Welsh meteorologist, published “The Period of Simple Vertical Oscillations in the Atmosphere”. This paper performed a similar derivation to arrive at the same frequency. It includes a note acknowledging that he had been made aware of the Väisälä paper but that “[Brunt’s derivation] formed a portion of one of a series of lectures on Dynamical Meteorology delivered at the School of Meteorology during the years 1921-1924”, seemingly implying that his work was completed prior to Väisälä’s publication. I encourage you to read the last page of this paper in full – it includes both this note and a public referee report and response!
Nowadays, the typical ordering of the names is “Brunt-Väisälä”, but given the publication order one might consider whether this is perhaps more related to David Brunt publishing his work in English and being more well known, than from completing the derivation first.
From gravity waves to gravitational waves
Finally, I’ll leave you with a fun fact. Unperturbed by history’s naming conventions, Vihlo Väisälä went on to found a highly successful company, Väisälä, which to this day manufactures a variety of weather monitoring equipment.
Decades later, the LIGO collaboration is working tirelessly to reduce the noise in their detectors and further enable the detection of gravitational waves. A recent paper investigated the impact of lightning on Earth and demonstrated it may cause problems for future generation gravitational wave detectors.
How did they make these predictions? Through the comparison of LIGO measurements to those available from the Global Lightning Detection network (GLD360), measured by none other than the Väisälä company!
In summary, nearly a century after his paper deriving the Väisälä-Brunt frequency was published, we can once again thank Vihlo Väisälä for inadvertently helping us understand astrophysical phenomena, all the way from gravity waves to gravitational waves.
Astrobite edited by Sonja Panjkov
Featured image credit: ESA
Interesting to have the history too !