Overview

My research interests are broad, and nearly any topic related to stars or planets is fascinating to me. Although I'm a theorist, I tend to work on problems related to observational puzzles. Much of my work focuses on fluid dynamics within stars and planets, and my methods include a variety of analytical and numerical techniques coupled with sophisticated stellar evolution codes. You can learn more about my research at the links provided below.

Pre-Supernova Outbursts

Massive stars explode as supernovae when they die, but historically they were not predicted to give any warning signs that they are about to explode. However, observations of many types supernovae now show evidence for mass loss or eruptions from the star in its final years of life. In a few cases, these outbursts have been observed directly. These eruptions may be linked to evolution in the core of the star, where the nuclear energy generation rate increases by a factor of roughly one million over the last decades of the star's life. However, most of this nuclear energy escapes in neutrinos, and photons in the core of the star cannot diffuse to the surface before the star explodes, so another form of energy transport would be needed to link nuclear energy generation in the core with an outburst at the surface of the star.

I have examined the role of energy transport by hydrodynamic waves that are excited as a byproduct of the core convection associated with energetic nuclear burning. My work shows these waves can carry a small fraction of the nuclear energy toward the surface of the star, and that waves can become the dominant form of energy transport in the last years of a star's life. The waves damp and deposit heat in the envelope of the star, which can cause the star to become much brighter at its surface and generate a pre-supernova outburst. The density structure of the star may also be affected, which will alter the appearance of the subsequent supernova.

Above: Cartoon picture showing how waves excited in the core of a star can travel into the envelope of a star, where they deposit enough energy to power an eruption from the surface of the star.

Below: Movie showing how the structure of a red supergiant might evolve in its final years of life before it goes supernova. The color shows the density of the star: its core contains nearly half its mass but is too small to see at this scale.

Here is my recent article on the subject:

  • Pre-Supernova Outbursts
  • Tides in Giant Planets

    Just as our own moon is slowly moving away from the Earth, the moons of Jupiter and Saturn have slowly migrated outward over the history of the solar system. Recent measurements from Lainey et al. have revealed that the moons are currently migrating much faster than astronomers had guessed. The rapid migration leads to tidal heating of the moons and helps explain why Jupiter's moon Io and Saturn's moon Enceladus are volcanically active. However, the cause of the rapid migration is not clear.

    My research has attempted to explain the rapid migration through a process called resonance locking. In this scenario, moons get trapped in resonances with oscillation modes of their host planets. As the planets evolve, the resonant semi-major axes associated with the oscillation modes can move away from the planet, carrying moons with them. The migration of the moons is therefore determined by the thermal evolution of the planet, which proceeds on a timescale shorter than conventional ("constant Q") tidal migration, and hence the moons migrate faster than expected.

    Above: Animation showing how a moon can "surf" a resonance lock outward.

    Below: The difference in migration histories of the moons according to standard (constant Q) tidal theories and the resonance locking theory. Unlike standard tidal theories, resonance locking is compatible with the contemporaneous formation of Saturn and its moons.

    Click below for a recent article on the subject:

  • Resonance Locking
  • Click below for a cool movie describing some related work:

  • Encelade Team
  • Magneto-asteroseismology

    Magnetic fields are an important but poorly understood aspect of stellar evolution. In the past, our inability to measure magnetic fields within stars has hampered the development of a coherent picture of stellar magnetism. Now, asteroseismology is offering the first glimpses of magnetic fields within stars. In red giant stars, pulsations at the surface of the star are created by waves that travel from the surface of the star, into its core, and back to the surface.

    Above: Animation showing the ray path of a wave propagating in a red giant.

    Below: Cartoon illustrating the trapping of a wave within a red giant with a magnetized core, referred to as the magnetic greenhouse effect.

    If a strong magnetic field lurks within the star's core, the picture changes. When the wave encounters the strong magnetic field, it is redirected by magnetic tension forces. This changes the nature of the wave, such that it can no longer escape from the star's core and propagate back to the surface. The loss of the wave energy at the surface of the star results in a decreased stellar pulsation amplitude, signaling the presence of a strong magnetic field in the star's core. This effect is observed in roughly one out of five red giants, whose cores contain magnetic fields thousands to millions of times stronger than typical refrigerator magnets!

    An open access link to the published article can be found at the

  • Authorea portal
  • See also
  • Red Giant Magnets
  • Saturn Ring Seismology

    Seismology is our most powerful tool for understanding the interiors of stars and planets. Indeed, our knowledge of the interior structures of the Earth and Sun owes its existence primarily to seismic measurements. Unfortunately, remotely detecting seismic disturbances on planets other than the Earth is very difficult, and until recently such a feat had never been achieved. Intriguingly, Saturn offers an unprecedented opportunity to observe seismic oscillations through their gravitational interactions with Saturn's rings. Recent observations of Saturn's ring system have revealed the presence of density waves within the rings excited by global oscillation modes of Saturn. Hedman & Nicholson (2013) used observations of Saturn's rings with the Cassini satellite to measure the frequencies of the waves in the rings, thereby precisely measuring a small set of the planet's mode frequencies. These observations reveal the presence of unexpected planetary oscillation modes, finely split in frequency from those expected, and whose presence may shed new light on Saturn's interior structure.

    Above: Animation of an oscillation mode of Saturn creating waves in the rings.

    Below: Cartoon of the interior structure of Saturn inferred from my seismic analysis.

    My work has focused on the origin of the unexpected oscillation modes of Saturn, and to understand their implications for its structure. I construct interior structure models of Saturn, compute the corresponding mode frequencies, and compare them with the observed mode frequencies. The frequencies of the fundamental modes of my models (which are expected in standard Saturn models) match the observed frequencies to an accuracy of roughly 1%. The additional unexpected modes only exist in models containing a stably stratified (non-convective) region of the planet. The stable stratification allows for the presence of gravity modes which can mix with the fundamental modes to obtain a detectable influence on the rings. I find stable stratification must exist deep within the planet near the large density gradients between the core and fluid/gaseous envelope. The presence of stable stratification is somewhat surprising, and may provide evidence for processes such as helium condensation or core dissolution within the fluid metallic hydrogen of Saturn's interior. My simple models cannot easily reproduce the exact differences between observed mode frequencies, suggesting that unincluded processes (such as differential rotation) may occur within Saturn.

    Here are a couple of my articles on the subject:

  • Saturn II
  • Saturn I
  • Neutron Star Spin

    Pulsars are rotating neutron stars whose spin periods can be very accurately measured via radio pulses emitted when the star's magnetic field points toward the Earth. Most pulsars rotate with periods of roughly one second, but we have a poor understanding of what determines the rotation rate of a pulsar as it is first born during a supernova explosion. My work has focused on the final days and hours of a stars life, during which nuclear burning proceeds so rapidly that the star's core is irradiated by waves launched by extremely vigorous convection. These waves are powerful enough to change the spin direction and spin rate of the core, such that its spin undergoes a random walk. The spin period of the core at the end of the random walk (when the supernova occurs) is tantalizingly similar to that needed to match the observed spin periods of young pulsars!

    Above: Animation of the spin-up of a massive stellar core (here made to look like the Earth). The direction of the rotation axis varies randomly, although on average the spin frequency slowly increases in time.

    Below: The distribution of expected spin periods of a massive stellar core just before core-collapse (bottom axis) and soon after neutron star formation (top axis).

    My article on the subject:

  • NSspin
  • Heartbeat Stars

    Click Here for Interactive Model of KIC 8164262!!!

    Heartbeat stars are an emerging class of eccentric short-period binary stars. The characteristic "heartbeat'' signal evident in their light curves is produced by a combination of tidal distortion, reflection, and Doppler boosting near orbital periastron. Many heartbeat stars continue to oscillate after periastron, indicative of the tidal excitation of oscillation modes within one or both stars. These systems are among the most eccentric short period binaries known, and they constitute an exciting opportunity to observe and understand tidal effects in action.

    The video above shows an animation of the orbit of the heartbeat star KOI-54. The bottom panel shows the light curve, which contains a spike near periastron (due to the effects listed above) and oscillations away from periastron due to tidally excited stellar oscillations modes. The stellar oscillations cuase the stars to dissipate orbital energy, causing their orbit to slowly circularize. My research seeks to understand the tidally excited oscillations and their effect on the orbital evolution of eccentric binary stars.

    What would a heartbeat star sound like? Click below to find out! To generate this "sound curve", I have converted the light curve (measured by Kepler) into a sound byte, and sped it up by a factor of 5 million. The "heartbeat" sound you'll hear is produced by the tidal distortion, reflection, and Doppler boosting at periastron. The steady tone is produced by the tidally excited oscillations.

    Hear the Heartbeat!

    Here is an article on the subject:

  • KOI-54
  • Stay tuned, more work on heartbeat stars is underway!

    Collapsing Neutron Stars

    Two observational enigmas have arisen in recent years. First, we have not detected any radio pulsars near the supermassive black hole at the center of the galaxy. Second, we have seen extremely bright and brief flashes of radio waves known as fast radio bursts, whose sources are currently unkown. It is possible that these mysteries are both explained via the collapse of neutron stars near galactic centers. In this scenario, neutron stars near the center of a galaxy accumulate enough dark matter in their cores to form a small black hole which then devours the neutron star. As the neutron star collapses into the black hole, its magnetic field is expelled and generates a burst of electromagnetic energy, which may be sufficient to generate a fast radio burst. This scenario is unconventional (and perhaps unlikely) but would have profound implications if it occurs!

    Here is my article proposing this idea:

  • FRBs
  • Tides in Triples

    In addition to finding planets, the Kepler satellite uncovered a bunch of very interesting stellar systems. One such system is HD 181068, aka, "Trinity", which is composed of a red giant primary star orbited by a pair of K dwarf stars. The dwarf stars orbit each other every 0.9 days, and their center of mass orbits the red giant every 45 days. The animation below depicts the system, with all sizes and orbital periods shown to scale.

    HD 181068 also shows a type of stellar pulsation never observed before. The motion of the K dwarfs around each other causes the red giant to feel a changing gravitational field. The force from this gravitational field excites oscillations within the red giant, which can be detected by the Kepler satellite. Because the K dwarfs orbit each other very fast, their motion excites sound waves, or p-modes, within the red giant. This is the first star system in which p-modes have been observed to be excited by companion stars.

    Here is my article on the system:

  • HD 181068
  • Supernova Seismology

    If the core of a massive star is rapidly rotating just before the star dies, its collapse into a neutron star will occur faster along the poles than it will along the equator. This asymmetry causes the neutron star to be born rapidly oscillating. These oscillations create gravitational waves whose frequencies depend on the properties of the neutron star. The detection of these gravitational waves is possible for a supernova within the local group of galaxies, and could be used to learn about the extreme conditions within newborn neutron stars. My work presents semi-anlaytic calcultions to explain the amplitudes and frequencies of the gravitational waves generated during the supernova, in addition to their lifetime. I find that the amplitude of the gravitational waves decays on timescales of about 10 ms as fluid motions generated by the oscillating neutron star carry energy outwards into the surrounding supernova material.

    Above: Rapidly rotating core-collapse simulation (created by collaborators Hannah Klion, Ernazar Abdikamalov, and Christian Ott) showing the oscillating proto-neutron star. The associated gravitational wave signal is shown by the lower curve.

    Below: The timescale on which the energy contained in the proto-neutron star oscillations leaks into the surrounding supernova. The peak at 770 Hz is created by the fundamental oscillation mode of the neutron star, which is responsible for the bulk of the gravitational wave emission.

    My article on the subject:

  • Supernova
  • Angular Momentum Redistribution by Internal Gravity Waves

    Internal gravity waves are low frequency waves which propagate through stably stratified regions of stellar interiors. In many types of stars, they are excited by fluid motions in convective regions of the star. The video below shows a simulation of internal gravity waves (top) being excited by convection (bottom) in ta tank of water. The physics of wave excitation in a star is very similar!

    Movie provided courtesy of Daniel Lecoanet.

    The waves extract energy and angular momentum from excitation regions, and deposit it wherever they damp. This entails that gravity waves can change the rotation profile of stars. My work has sought to determine whether gravity waves can affect the interior rotation of red giant stars, which are observed to have cores that rotate much faster than the surface. Gravity waves can substantially impact rotation rates of these stars, but they are likely aided by some other (still unknown!) angular momentum transport mechanism.

    The figure above is an HR diagram, with stellar evolution tracks shown by colored lines. The symbols show stars with measurements of rotation for both the core and the surface. My work predicts that stars to the left of the vertical lines should be nearly rigidly rotating, while stars to the right are able to exhibit substantial differential rotation. So far, this is indeed the case! A link to my article:

  • Waves
  • Tides in White Dwarfs

    White dwarfs with short orbital periods emit gravitational waves, which causes the orbit to decay until the white dwarfs merge or begin mass transfer. Much of my graduate work focused on the tidal interactions in the white dwarfs before they merge, which effect the outcome of the merger or mass transfer process. The image below shows my inner artist's conception of the J0651 binary white dwarf system, which has an orbital period of just 12.75 minutes. The sizes/separations of all objects below are shown to scale! My main results are summarized below.

    1. Tidal heating makes white dwarfs much hotter before they merge.

    As inspiraling white dwarfs tidally synchronize with each other, the friction associated with this process generates enormous amounts of heat. Our calculations indicate the heat is deposited in the outer layers of the white dwarf, where it diffuses outward to make the white dwarf appear much hotter and brighter. In some cases, the heat may be deposited deep enough that it can't quickly diffuse outwards, causing the interior of the white dwarf to heat up. The heating may be sufficient to reignite thermonuclear fusion in the hydrogen shell of the white dwarf, creating a nova-like outburst.

    The above figure shows my calculations of the surface temperature of an inspiraling white dwarf as a function of its orbital period, using different parameters t_coup to describe angular momentum redistribution within the white dwarf. These calculations are for a 0.6 solar mass white dwarf with a 0.3 solar mass companion. Tracks that end in stars indicate the occurrence of tidal novae. The asterisk marks the position of the observed white dwarf binary J0651+2844 as measured by Hermes et al. (2012).

    2. White dwarfs tidally synchronize with each other before they merge.

    My research on tides in inspiraling white dwarf binaries suggest that white dwarfs are able to nearly synchronize with one another before they merge. They begin to synchronize at orbital periods of approximately one hour, well before they merge or begin mass transfer at orbital periods of a few minutes.

    The plot above shows our prediction for the spin frequency of a white dwarf (in units of the orbital frequency) as a function of its orbital period. In this scenario, a 0.6 solar mass white dwarf orbits an equal mass companion, and the orbit decays due to the emission of gravitational waves. The three different curves are for white dwarfs of different temperatures (black is hottest, blue is coolest). The solid lines are numerical results, the dashed lines are analytical approximations. The vertical dotted line is the critical orbital period (for our hottest white dwarf model) at which tidal effects begin to synchronize the white dwarf.

    Below are links to the full 5-part series on tides in white dwarfs!

  • Paper V
  • Paper IV
  • Paper III
  • Paper II
  • Paper I