I am an Assistant Professor of Physics at DigiPen Institute of Technology and my research focuses on the end stage of stellar evolution. I study the mass-loss process that occurs during the final stages of a star's life, simulating stellar winds in red supergiants (RSGs) and asymptotic giant branch (AGB) stars.
Computational Atomic and Molecular Structure |
Hybrid Magnetohydrodynamic Stellar Winds |
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When an atom is subjected to strong magnetic fields, it undergoes a dramatic change in structure. In a terrestrial setting the strongest achievable magnetic fields (B ≈ 10-100 T) merely perturb the motion of the electron in their bound states, and the atom maintains overall spherical symmetry. Whereas, a strong magnetic field (B > 100,000 T) introduces a fundamental anisotropy in the atom. It severely restricts the motion of the electron in any diretion transverse to the field, thus the electron cloud is restricted to lie close to the magnetic axis. However, as a result of this restriction the electrons sample the potential well of the positively charged nucleus a lot more, and they are dragged deeper into the well. This results in the electron cloud shinking even along the direction of the magnetic axis. Thus, the stronger the magnetic field, the greater the shrinking of the atom in all directions. This can be seen here for the hydrogen atom. As the magnetic field strength parameter (β) is increased, the electron cloud shrinks and the binding energy increases. Spherical symmetry is lost and the atom assumes a cigar-shaped geometry. Hydrogen atoms in neutron star and magnetised white dwarf star atmospheres are subjected to such strong fields. This results in a drastic change in energy levels of the atom from the field-free prescription and has a profound effect on transition rates, oscillator strengths, ion populations at different levels and ionization cross-sections. Thus, the emergent spectra of magnetised compact objects are vastly different from those of main sequence stars, even ones with appreciable magnetic fields.
A. Thirumalai and J.S. Heyl, Phys. Rev. A. 79, 012514 (2009)
The effect of the magnetic field is profound. This movie shows the nature of the drastic anisotropy introduced by the magnetic field. The electron density shrinks and the geometry becomes increasingly extreme. In intense fields the orbitals become first cigar shaped, then pencil shaped. The binding energies become vastly greater than their zero-field counterparts. From a computing perspective, the difficulty is one of scales: how can you maintain resolution of the electron wave function close to the singularity at the magnetic axis in the vicinity of the singular Coulomb potential of the nucleus? And how do you simulataneously describe accurately the decaying wave functions far away from the nucleus as well?
A. Thirumalai and J.S. Heyl, Phys. Rev. A. 89, 052522 (2014)
The usual wind picture for AGB stars is one in which dust forms at a distance of a few stellar radii from the photosphere. This dust is accelerated through the atmosphere due to impinging stellar radiation. The dust particles act as exiguous solar sails dragging the gas along with them as they move. This results in a prodigious and combined mass efflux from the star - the so-called dust-driven wind. This sort of picture seems to work fine for carbon-rich AGB stars, but fails for the oxygen-rich variety of AGB stars. With the discovery of magnetic fields, other mechanisms were suggested such as Alfven waves coupled with pulsation, but such models also have problems with wind velocities in the inner regions. As a result the question of how matter is transported from close to the photosphere out to distances of a few stellar radii where dust can then form, is an open question - the missing mass-loss mechanism problem.
My research adresses this question with a different approach. I incorporated the dust-driving picture with the presence of a magnetic field alongside rotation of the star - a dusty-magento-centrifugal wind, with two fluids: dust and gas. This was the first time that such a hybrid picture was proposed for these stars. In this scenario, a slow mangeto-centrifugal mechanism transports material from the photosphere out to a few stellar radii (see vertical dashed line at around 8 stellar radii), and thereafter, dust condenses where the temperatures are favourable. From this point on, the wind consists of the gas carrying the magnetic field and radiation pressure on dust grains. Traits of both types of mechanisms are preserved, and the emergence of the Alfvenic points makes the topology of solutions very rich. This hybrid wind model provides a way for solving the missing mass-loss mechanism problem and explains the mass loss in oxygen-rich AGB stars. It also brings together disparate areas of physics into a single scenario, opening the doors for multi-physics computations.
The red supergiant Betelgeuse, that can be spied with the naked eye in the constellation Orion, is an oxygen-rich star. It is about 15 times more massive than our sun and has a large, cool, distended atmosphere. Observations indicate that there is dust surrounding the star, but it is only seen at around 30 stellar radii away. One of the mysteries surrounding Betelgeuse's mass-loss, is that mechanism is responsible for the wind remains unknown. I applied my dust-driven magneto-centrifugal wind model to explain this question and found that the model works remarkably well. I investigated several dust formation scenarios, with multiple kinds of dust, alumina and silica forming at different distances from the wispy photosphere with a gentle magneto-centrifugal wind buffetting material upwards from the gravitational potential well of the star. One possible scenario is that alumina dust can form close to the star, and is transparent to infra-red observations, and gets transported in a hybrid wind out to about 30 stellar radii, where the temperatures are cool enough that silica can condense upon already existing alumina grains (scenario 2). I also considered a scenario where alumina forms close to the star, but then spalls when it encounters a chromospheric component, and later silica condenses at large distances (scenario 3). Overall, my modelling of Betelgeuse reveals that the magnetic field may play a significant role in its stellar wind.
A. Thirumalai and J.S. Heyl, MNRAS, Volume 422, pp. 1272−1282, (2012)
The great advantage of using pseudospectral methods for smooth PDE's, particularly for the solution elliptic eigenvalue problems, is the considerably reduced computational overhead coupled with spectral accuracy. The domain of computation is compactified and then grid points are collocated on the zeros of Chebyshev polynomials. The solution is defined only in a cardinal fashion on the zeros, and the polynomials interpolate the solutions between the points. The method exhibits spectral convergence, meaning that errors diminish exponentially rather than say quadratically with mesh refinement, as is common in finite-difference methods. The implementation of boundary conditions is however tricky as they are implemented only along certain rows and columns of the resulting psuedospectral operators. Overall, with as few as 40-50 grid points in each direction (a fully coupled 2D problem), the structure of a helium-like atom/ion can be determined to fourth-decimal place accuracy in less than 10 seconds. Such speeds coupled with accuracy are crucial for incorporating atomic structure codes into atmosphere modelling codes.
A. Thirumalai and J.S. Heyl, Phys. Rev. A. 89, 052522 (2014) J.S. Heyl and A. Thirumalai, MNRAS, Volume 407, pp. 590-598 (2010)
Utilising the pseudospectral atomic structure software that I have developed, I have been able to compute the energy landscape of carbon in intense magnetic fields, including 10 states that have never been calculated before. This work is of immediate consequence to not only filling a large void in our understanding of strong-field quantum mechanics, but also of considerable practical concern for understanding the spectra of magnetised compact objects. Such data are the first step towards calculating transition wavelengths for facilitating spectral analysis of DQ white dwarfs. But there is a long way to go still. In white dwarfs, apart from carbon, there are also other species such as phosphorus, silicon and sulphur which are present in appreciable quantities, even in cooler and therefore older white dwarfs. This has been a great surprise to the astrophysical community as stellar evolution models predict nearly a completely H or He atmosphere with very short timescales for the heavier atoms to submerge in the atmospheres of white dwarfs. Thus, the older the white dwarf, the less the contaminants, and the chemistry is usually expected to be either purely H or He. In neutron stars on the other the hand, the story is the reverse, only the younger neutron stars are expected to have H and He, which are the remnants from supernova fallback material during collapse. The older neutron stars are expected to have purely heavier elements such as Fe and Ni etc; the products of nuclear burning of lighter elements. Therefore it is now understood that the presence of low- and mid-Z elements such as carbon (and for that matter Si, P, S etc) in older varieties of both white dwarfs and neutron stars is probably only possible from accretion of ambient material - namely the detritus left over from the progentior's planetary system. The study of white dwarfs and neutron star atmospheres therefore gives us hints regarding the composition of erstwhile exoplanetary systems that are perhaps being accreted onto the surfaces of these compact objects. In addition to accretion, in younger white dwarfs however, the presence of heavier elements may also provide clues regarding the progenitor and the envelope's chemistry during Assymptotic Giant Branch evolution.
A. Thirumalai, S.J. Desch and P. Young, Phys. Rev. A 90, 052501
Mira, o-Ceti, is an oxygen-rich star with a problematic mass-loss mechanism. Further, in recent years there has been much speculation about magnetic activity in the star. There has been debate regarding whether it is the AGB star itself or its white dwarf companion that is responsible for the magnetic activity. I chose to investigate the possibility that Mira does harbour a dynamically important magnetic field and asked the question whether it could then be responsible for a hybrid wind. I found that with a weak magnetic field of about 4G, a slow wind could be generated which also matches the temperatures observed and the observations of dust. This dust can form in a small region between about 3 and 6 stellar radii and can result in a slow dust-driven magneto-centrifugal wind. It then remains to be seen whether magnetic activity is observed in Mira, and if so, whether any average longitudinal field which may be observed is consistent with my model prediction of about 4G. Although, recent observations of a different Mira-type star χ-Cyg reveal the presence of a weak magnetic field around 2-3G in the vicinity of its wispy photospheric region, so it appears to be a reasonable prediction.
A. Thirumalai and J.S. Heyl, MNRAS, Volume 430, pp. 1359-1368 (2013)
Several recent observations of Betelgeuse have pointed towards temperature inhomogeneities on the surface of Betelgeuse, and the existence of perhaps two or three large spots. This raises the question of whether these spots can have an effect on the stellar wind, in particular if the spots are also magnetic. This is of course complicated by the fact that as yet it is unknown what mechanism is responsible for levitating material from the stellar photosphere out to about 30 stellar radii away, where subseqently siliacate dust grains can form and a regular dust-driven wind by stellar radiation pressure ensues. Using a hybrid dusty-magnetohydrodynamic wind model for Betelgeuse, I was able to investigate, in a qualitative sense, whether a hybrid Weber-Davis like magneto-centrifugal mechanism coupled with dust-driven by radiation pressure on alumina dust grains, in the vicinity of a magnetic cool spot, could result in material being levitated in the atmosphere and resulting in a stellar wind. The dual-fluid model is however constrained by observational evidence for silicate dust which forms in the extended atmosphere of Betelgeuse at around 30 stellar radii away. The horizontal dashed lines in the above figure are model atmosphere models that predict upper and lower bounds for the temperature at which alumina dust condenstation can occur. The vertical green band on the other hand is a model called MOLsphere which places a bound on where in the atmosphere alumina dust can condense. My modelling indicates that if the photospheric spot temperature is around 2600 K then there is a small overlap between the three sets of models; the green solid line has an intersection with the green vertical band and simultaneously lies within the upper and lower temperature bounds of the model atmosphere calculations for alumina dust condensation. Thus, a hybrid MHD-dust-driven wind can levitate materials to great distances in the atmosphere of red supergiants, and also provide a route for rationalising large temperature inhomogeneities on the surface to be interpreted as spots.
A. Thirumalai and J.S. Heyl, MNRAS, Volume 422, pp. 1272−1282, (2012)
The envelope of a neutron star consists of a very thin atmosphere less than a centimeter thick sitting atop a very dense ocean layer of condensed matter. The envelope is generally thought to be dynamic with mixing. Not only is the density (ρ) of the envelope high, but also the pressure too is very high, even in the uppermost layers of the ocean; comparable to the pressures inside the gas giant planets, in the tens or hundreds of GBar range. Such high pressures are not easily attained in the laboratory environment. This environment also hosts the most intense magnetic fields in the observable Universe. During mixing materials from the atmosphere may get embebbed or trapped inside denser surrounding material of the ocean layer underneath. This would subject the trapped material to incredibly high pressure and confinement. This study examines the effect of an atom simultaneously subjected to an intense magnetic field and a high pressure enviroment. The finding reveal that when astrophysically relevant atoms (hydrogen and helium) are subjected to such an extreme environment, the negative parity states of these atoms do no survive high pressures. The positive parity states do however survive. Thus, under high pressures and intense magnetic fields, not only are the structures of atoms radically changed, but also several states themselves are not bound. As a result, this will impact the relative abundance of atoms in various states, thereby drastically altering oscilaltor strength, transitions, and ultimately neutron star envelope models as well as modelling of neutron star atmospheres.
A. Thirumalai, J. Phys. Chem. A (Special Issue: Trygve Helgaker Festschrift, 2025)Theoretical, Computational and Observational • Suitable for graduate students
A large focus of my research deals with determining what happens to atoms and molecules in the extremely dense, hot and highly magnetised atmospheres of compact objects; these are magnetised white dwarfs and neutron stars. These are collectively the most highly magnetised objects in the known Universe - with magnetic fields that are billions of times greater than what we can ever achieve in the lab. Almost all the photons that we get from these unique astrophysical laboratories originate in their atmospheres, and in order to gain a good understanding of the nature of these objects, we need to be able to model their atmospheres with accuracy. A large part of this puzzle is interpreting their spectra properly. This requires a wealth of data for atomic and molecular electronic structure.
I have over half a dozen projects available for interested graduate students to work on in this area. There are projects available in both atomic as well as the more complicated molecular structure domains. A large portion of the work will also involve astronomical data from telescopes such as The Hubble Space Telescope. The aim is to explore this wholly uncharted area of computational astrophysics. I collaborate with researchers at the University of British Columbia, in Vancouver, Canada, and at the University of Oslo in Norway, as well as with researchers at the University of Mainz, in Germany, so there is the possibility for spawning further research directions with these international collaborators. If you are interested in working with me in this exciting area of physics, then get in touch with me.
Theoretical and Computational • Suitable for graduate students
I am interested in simulations of the prodigious mass-loss which occurs at the very last phase of evolution of the majority of the stars in the Universe, namely, as they end their lives on the Asymptotic Giant Branch (AGB). It has been observed that in the cool outer atmospheres of these dying stars, micron-sized dust grains can condense and grow. These form exiguous solar sails, and they absorb the momentum from the impinging stellar radiation from the interior. As a result of this, these dust grains move through the surrounding gas, and as they do so, they drag they gas along with them, and this results in a prodigious stellar wind. There are however several mysteries still. Approximately half the AGB stars in the Universe are oxygen-rich stars, and in these stars there is a huge mystery regarding how stellar material is transported from the stellar photosphere out to large distances where dust grains can form. I had proposed one such mechanism - a hybrid wind scenario, in which a magneto-centrifugal wind levitates material out to distances where dustr grains (silicates) can condense, and thereafter, the wind is a dual fluid wind, with the gas carrying the magnetic field, and the dust grains acting as solar sails and absorbing stellar radiation, and causing a large efflux. I am interested in developing 2D (or 3D) magnetohydrodynamic wind models for AGB stars, with dust grains in the flow, forming in-situ. This has never been done and would provide a great amount of insight regarding the question of whether magnetic fields in these stars (for which evidence is now starting to emerge) play a role in the mass-loss process, and if so, how does that ties in with observations of dust formation and a wind.
If you are interested in developing a dual-fluid hydrodynamics code and using it to look at the mysteries of how nearly half the stars in the Universe end their lives, then get in touch with me. I have several projects available for interested graduate students to work on in this area.
Theoretical and Computational • Suitable for graduate and senior undergrad students>p
I have recently become interested in exploring the question of how rocky planets form. This is of course tied to the question of how indeed planetisimals form in the first place - the precursors of planets. If we break this down even further, then it brings us to the mind-boggling question of how indeed do we take dust grains that can condense in protoplanetary disks, and convert them into planetesimals on timescales of about a hundred thousand years - a blink of an eye as far as a solar system is concerned. The mystery deepens when we think about the physics of dust coagulation and growth, and ask how do we go from millimetre-scale grains to kilometre-scale chunks relying only upon the physics of coagulation and sticking - which is an entire field of study unto itself. This is a complete mystery and an open question in astronomy. I am interested in a few related questions. First, carrying out simulations of in-situ dust grain formation and growth in protoplanetary disks. These can start out as semi-analytical models, and can get more advanced. I am also interested in asking the question - what size of objects can be made from simple particle-particle collisions and relying upon coagulation and sticking of dust grains, and third, what role does turbulence play in the protoplanetary disks, and do we need other mechanisms such as gravitational instabilities to aid in making the process rapid.
These exploratory questions are ideal for a graduate student or a senior undergraduate student to work on for their thesis projects. If this area of research and the big question of how rocky planets form excites you, then get in touch with me.
This is a 2D code in cylindrical coordinates for calculating the structure of atoms in strong and intense magnetic fields. It is based on a parallel pseudospectral implementation. The magnetic fields of strength that can be explored with this code are high B (> 100,000 T). It would be necessary to adaptively change the domain and mesh sizes for large fields as well as for mid-Z atoms.
The software is developed for 64-bit machines and utilises hyperthreading. It utilises the Armadillo C++ library and can also be compiled to utilise Intel MKL. It is highly recommended that you install the latest version of Armadillo C++ and include those libraries for compiling PSEUDASP. Minimum requirements for memory are about 8GB of RAM.
Please get in touch with me (see contact details below) for obtaining a suitable version of this code for your needs. It is requested that the author (Anand Thirumalai) be added as a co-author in any scientific articles that are the outcome of your research carried out with PSEUDASP.
This is the GPU version of my 2D code in cylindrical coordinates for calculating the structure of atoms in strong and intense magnetic fields. It is written using CUDA to run on Nvidia GPUs. The purpose of the code is to explore atomic structure of mid- and high-Z atoms (e.g. S, P, Fe etc) in high fields without sacrificing accuracy and gaining a speed boost on the GPU.
The software is currently in active development and testing.
Please get in touch with me (see contact details below) if you would like to get involved in developing the software.
I recently had the privilege to read through an outstanding biography of the renowned scientist Vera Rubin, written by Ashley Jean Yeager.
I was invited by Seattle Town Hall to do a podcast to interview Ashley and talk about her debut book and about the astonishing and inspiring life of Vera Rubin.
See the following link for details: Podcast.