Ryan Golant
@rgolant.bsky.social
PhD candidate in Astronomy at Columbia University || cancer survivor || science communicator || cat enthusiast || professional waster of time
Inside you there are two wolves: one's a toilet and the other's a hydraulic press.
May 10, 2025 at 7:52 PM
Inside you there are two wolves: one's a toilet and the other's a hydraulic press.
A phenomenon that we do fully understand is the propagation of Alfvie waves across the surface of my cat. By perturbing his fur perpendicular to his stripes, we excite oscillations that propagate along his stripes. The energy in these waves is then usually converted into bites and scratches.
May 5, 2025 at 12:38 AM
A phenomenon that we do fully understand is the propagation of Alfvie waves across the surface of my cat. By perturbing his fur perpendicular to his stripes, we excite oscillations that propagate along his stripes. The energy in these waves is then usually converted into bites and scratches.
Alfvén waves are thought to be especially important in our Sun. By carrying energy from the solar surface to the corona, Alfvén waves may be responsible for heating the corona to its anomalously high temperature and for launching the solar wind – two processes that we still don’t fully understand.
May 5, 2025 at 12:38 AM
Alfvén waves are thought to be especially important in our Sun. By carrying energy from the solar surface to the corona, Alfvén waves may be responsible for heating the corona to its anomalously high temperature and for launching the solar wind – two processes that we still don’t fully understand.
Therefore, if we perturb a straight magnetic field line in the perpendicular direction, the line will want to snap back to its stable equilibrium; the field line will oscillate, launching a wave – an Alfvén wave – along the field line, much like a wave propagating along a plucked guitar string.
May 5, 2025 at 12:38 AM
Therefore, if we perturb a straight magnetic field line in the perpendicular direction, the line will want to snap back to its stable equilibrium; the field line will oscillate, launching a wave – an Alfvén wave – along the field line, much like a wave propagating along a plucked guitar string.
One phenomenon unique to MHD and incredibly important in astrophysical plasmas is known as the Alfvén wave. In my previous thread (bsky.app/profile/rgol...), I noted that magnetic field lines in MHD carry an effective tension, like taut strings.
As such, it’s not too far-fetched to picture magnetic field lines in MHD as tensile rubber ropes threading fluid-like plasmas; as a plasma flows, it tugs on the field lines and the field lines tug back.
May 5, 2025 at 12:38 AM
One phenomenon unique to MHD and incredibly important in astrophysical plasmas is known as the Alfvén wave. In my previous thread (bsky.app/profile/rgol...), I noted that magnetic field lines in MHD carry an effective tension, like taut strings.
Some of these MHD phenomena resemble waves or instabilities that one might find in a neutral fluid – like the magnetic Kelvin-Helmholtz instability (depicted below in a simulation of the solar wind interacting with Earth's atmosphere) – while others are wholly unique to plasmas.
May 5, 2025 at 12:38 AM
Some of these MHD phenomena resemble waves or instabilities that one might find in a neutral fluid – like the magnetic Kelvin-Helmholtz instability (depicted below in a simulation of the solar wind interacting with Earth's atmosphere) – while others are wholly unique to plasmas.
If we add magnetic fields into a fluid – that is, if we consider magnetohydrodynamics (MHD) – we’re faced with a whole new spectrum of possible waves and instabilities. (see my earlier thread for a primer on MHD: bsky.app/profile/rgol...)
This is my cat, Alfvie. He’s very cute. But why did I name him Alfvie?
A thread on magnetohydrodynamics:
#astronomy #astroedu #cats
A thread on magnetohydrodynamics:
#astronomy #astroedu #cats
May 5, 2025 at 12:38 AM
If we add magnetic fields into a fluid – that is, if we consider magnetohydrodynamics (MHD) – we’re faced with a whole new spectrum of possible waves and instabilities. (see my earlier thread for a primer on MHD: bsky.app/profile/rgol...)
For example, if we gently tap the surface of a body of water at rest, wave-like ripples will radiate outwards along the surface. However, if we blow air parallel to the surface of the water, the surface will quickly wrinkle and contort due to the so-called Kelvin-Helmholtz instability.
May 5, 2025 at 12:38 AM
For example, if we gently tap the surface of a body of water at rest, wave-like ripples will radiate outwards along the surface. However, if we blow air parallel to the surface of the water, the surface will quickly wrinkle and contort due to the so-called Kelvin-Helmholtz instability.
Fluids are incredibly complex dynamical systems that are subject to myriad types of perturbations, some of which produce waves – which can propagate throughout the fluid – and others of which trigger instabilities – which cause the fluid to exponentially depart from equilibrium.
May 5, 2025 at 12:38 AM
Fluids are incredibly complex dynamical systems that are subject to myriad types of perturbations, some of which produce waves – which can propagate throughout the fluid – and others of which trigger instabilities – which cause the fluid to exponentially depart from equilibrium.
It’s important to note that not all equilibria are stable – consider a ball at rest on top of a sharp peak. Perturbations to these equilibria don’t induce waves, but instead trigger runaway processes called “instabilities” (to be explored further in future threads).
May 5, 2025 at 12:38 AM
It’s important to note that not all equilibria are stable – consider a ball at rest on top of a sharp peak. Perturbations to these equilibria don’t induce waves, but instead trigger runaway processes called “instabilities” (to be explored further in future threads).
This is the basic principle of a wave: if we perturb a dynamical system in stable equilibrium, the system will oscillate around its initial state in an attempt to return to stable equilibrium.
a black and white photo of a violin with the letter g on the headstock
Alt: A slow-motion video clip of a violin string oscillating around its stable equilibrium position after being perturbed by a violin bow.
media.tenor.com
May 5, 2025 at 12:38 AM
This is the basic principle of a wave: if we perturb a dynamical system in stable equilibrium, the system will oscillate around its initial state in an attempt to return to stable equilibrium.
However, the ball likely won’t come to rest immediately after rolling back – it’ll probably overshoot the dip, roll back from the other side, overshoot again, and continue to oscillate back and forth before finally settling back into its stable equilibrium.
a blue and orange drawing of a pendulum with a ball on it
Alt: An animation of a pendulum oscillating around its equilibrium position. This is similar to a ball -- having been perturbed -- oscillating around its stable equilibrium position at the bottom of a valley.
media.tenor.com
May 5, 2025 at 12:38 AM
However, the ball likely won’t come to rest immediately after rolling back – it’ll probably overshoot the dip, roll back from the other side, overshoot again, and continue to oscillate back and forth before finally settling back into its stable equilibrium.
Picture a ball at rest at the bottom of a valley. This ball is said to be in stable equilibrium: if we push this ball a little bit up the hill and then let it roll back (or, in physics speak, if we perturb this ball from its equilibrium), it’ll eventually return to rest at the bottom of the valley.
May 5, 2025 at 12:38 AM
Picture a ball at rest at the bottom of a valley. This ball is said to be in stable equilibrium: if we push this ball a little bit up the hill and then let it roll back (or, in physics speak, if we perturb this ball from its equilibrium), it’ll eventually return to rest at the bottom of the valley.
To conclude: how does Alfvén’s theorem apply to my cat? Just as magnetic field lines are frozen into perfectly conducting plasmas, my cat’s stripes are frozen into his perfectly fluffy fur. This phenomenon – Alfvie's theorem – has been readily reproduced in laboratory experiments (see photos below).
April 28, 2025 at 12:18 AM
To conclude: how does Alfvén’s theorem apply to my cat? Just as magnetic field lines are frozen into perfectly conducting plasmas, my cat’s stripes are frozen into his perfectly fluffy fur. This phenomenon – Alfvie's theorem – has been readily reproduced in laboratory experiments (see photos below).
The tension from the field lines slows the rotation of the cloud, allowing a star to form.
April 28, 2025 at 12:18 AM
The tension from the field lines slows the rotation of the cloud, allowing a star to form.
However, these clouds are threaded by magnetic field lines that are (nearly) frozen into the plasma. As the cloud spins and collapses, Alfvén’s theorem tells us that the plasma will try to twist up the field lines, but the tension in the field lines will resist this twisting.
April 28, 2025 at 12:18 AM
However, these clouds are threaded by magnetic field lines that are (nearly) frozen into the plasma. As the cloud spins and collapses, Alfvén’s theorem tells us that the plasma will try to twist up the field lines, but the tension in the field lines will resist this twisting.
For example, stars form when massive, spinning clouds of plasma collapse in on themselves. In the absence of a magnetic field, a cloud would spin faster and faster as it collapses, eventually yielding a centrifugal force that would tear the forming star apart.
April 28, 2025 at 12:18 AM
For example, stars form when massive, spinning clouds of plasma collapse in on themselves. In the absence of a magnetic field, a cloud would spin faster and faster as it collapses, eventually yielding a centrifugal force that would tear the forming star apart.
Alfvén’s theorem allows us to intuit the behavior of a plasma (often quite accurately) without needing to consider any mathematical equations – we just need to consider the interplay between the plasma’s motions and the feedback from the plasma’s embedded field lines.
April 28, 2025 at 12:18 AM
Alfvén’s theorem allows us to intuit the behavior of a plasma (often quite accurately) without needing to consider any mathematical equations – we just need to consider the interplay between the plasma’s motions and the feedback from the plasma’s embedded field lines.
Alfvén’s theorem states that, if a plasma conducts electricity perfectly (often a good approximation in astrophysical systems), then magnetic field lines are “frozen into” the plasma. If the plasma moves, the field lines move with it; if the field lines move, the plasma is dragged along, too.
April 28, 2025 at 12:18 AM
Alfvén’s theorem states that, if a plasma conducts electricity perfectly (often a good approximation in astrophysical systems), then magnetic field lines are “frozen into” the plasma. If the plasma moves, the field lines move with it; if the field lines move, the plasma is dragged along, too.
Enter Alfvén’s theorem, one of the most important theorems in plasma (astro)physics.
April 28, 2025 at 12:18 AM
Enter Alfvén’s theorem, one of the most important theorems in plasma (astro)physics.
As such, it’s not too far-fetched to picture magnetic field lines in MHD as tensile rubber ropes threading fluid-like plasmas; as a plasma flows, it tugs on the field lines and the field lines tug back.
April 28, 2025 at 12:18 AM
As such, it’s not too far-fetched to picture magnetic field lines in MHD as tensile rubber ropes threading fluid-like plasmas; as a plasma flows, it tugs on the field lines and the field lines tug back.
When we add magnetic fields to the equations of hydrodynamics, we find (mathematically) that magnetic field lines embedded in a fluid/plasma exert a pressure on their surroundings and carry an effective tension.
April 28, 2025 at 12:18 AM
When we add magnetic fields to the equations of hydrodynamics, we find (mathematically) that magnetic field lines embedded in a fluid/plasma exert a pressure on their surroundings and carry an effective tension.
However, in magnetohydrodynamics (MHD), magnetic field lines act like physical structures. (see last week's thread for an intro to MHD: bsky.app/profile/rgol...)
This is my cat, Alfvie. He’s very cute. But why did I name him Alfvie?
A thread on magnetohydrodynamics:
#astronomy #astroedu #cats
A thread on magnetohydrodynamics:
#astronomy #astroedu #cats
April 28, 2025 at 12:18 AM
However, in magnetohydrodynamics (MHD), magnetic field lines act like physical structures. (see last week's thread for an intro to MHD: bsky.app/profile/rgol...)