The Life and Death of Stars

The night sky is the silent backdrop of human experience.

It is populated by an incredibly large number of stars, separated by vast distances and mostly empty space. We now know that there is a profound connection between these objects and our own existence: Not only stars lighten up an otherwise dark Universe, but through their lifecycle also produce and shed the fundamental elements required by biological life. All the elements we are made of, except for hydrogen, have been forged inside the hot and dense cores of stars. The calcium in our bones, the iron in our blood, the nitrogen and oxygen in the air and in our DNA. Basically every important ingredient of life came from the stars. We are literally made of stardust.

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Massive Stars

Studying stars humans discovered that, aside from hydrogen, all of the elements we are made of have been synthesized inside stars. A star is a self-regulating system, with the amount of energy released by nuclear burning is exactly the amount needed to counteract the gravitational force.

Binary Stars

If the equilibrium is perturbed, the star readjust its structure, such that the nuclear reactions provide again the right amount of energy. In this way stars can be stable for long timescales during hydrogen burning (the so-called main sequence). This phase cannot last forever, since the amount of fuel inside of stars is ﬁnite, and energy is released only from the fusion of isotopes lighter than iron.

Magnetic Fields

When a sufficient amount of energy can no longer be extracted from the rest mass of the star, the battle against gravity is lost. Then the final fate of the star depends on the mass of the object: low mass stars end their lives as white dwarfs, while massive stars (more massive than about 8 solar masses) die in spectacular explosions or disappear quietly forming a black hole.

Computational Tools

Since 3D stellar evolution is not feasible in the foreseeable future, progress in our understanding of the physics and evolution of stars relies on the synergy between local 3D (radiation) MHD calculations and 1D stellar evolution modeling.

DEDALUS

DEDALUS is a flexible framework for solving differential equations using spectral methods. It is open source, written in Python and MPI-parallelized. Key features are symbolic equation entry, spectral domain discretization and implicit-explicit timestepping.

ATHENA++

Athena++ is a complete re-write of the Athena astrophysical magnetohydrodynamics (MHD) code in C++. Features include flexible coordinate and grid options including adaptive mesh refinement (AMR), radiation transport and general relativity, significantly improved performance and scalability, and improved source code clarity and modularity.

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MESA

MESA, Modules for Experiment in Stellar Astrophysics, is an open source software instrument widely adopted in the astrophysics community. The star module allows to calculate the 1D stellar structure and evolution of single and binary stars. The full capabilities of MESA are documented in the instrument papers. I have been a member of the MESA council since 2013.

ATHENA++ simulation of radiation dominated convection in a massive star — **ATHENA++** simulation of radiation dominated convection in a massive star

Normalized radial extension of core, surface, and subsurface convection zones for stars in the mass range 0.9–25 Msun (Cantiello & Braithwaite 2019)

Kippenhahn diagram for an AGN star evolving in a disk with a density of ~10e-16 g/cm^3 (MESA) — Kippenhahn diagram for an AGN star evolving in a disk with a density of ~10e-16 g/cm^3 (**MESA**)

Evolution of a 16 Msun + 14 Msun binary system with a 3 day initial orbital period. MESA calculations are compared with models performed using the STERN code (Paxton et al. 2015).

Close binarity across the color–magnitude diagram: color-magnitude diagram (CMD) for all APOGEE sources, colored by the fraction of sources identified as binary-star systems (From Price-Whelan+ 2020) — Close binarity across the color–magnitude diagram: color-magnitude diagram (CMD) for all **APOGEE** sources, colored by the fraction of sources identified as binary-star systems (From Price-Whelan+ 2020)

Artistic illustration of a Hot Jupiter engulfed by its host stellar companion. Stellar transients are likely associated with this process (e.g. MacLeod, Cantiello, Soares-Furtado 2018)

The density structure 400 s after jet launch in a FLASH simulation. The jet is breaking out of a rotating blue supergiant envelope structure evolved with MESA (Perna, Lazzati & Cantiello 2018).

Available Projects at CCA

This would be in collaborations with me (Matteo Cantiello) and Jared Goldberg (co-mentor).

The Center for Computational Astrophysics (CCA) at the Flatiron Institute is a vibrant research center in the heart of New York City with the mission of creating new computational frameworks that allow scientists to analyze big astronomical datasets and to understand complex, multi-scale physics in a cosmological context.

The CCA Pre-Doctoral Program will enable graduate student researchers from institutions around the world to participate in the CCA mission by collaborating with CCA scientists for a period of 5 months on site. With this opportunity, the selected group of researchers will be able to participate in the many events at the CCA and interact with CCA scientists working on a variety of topics in computational astrophysics (including both numerical simulations and sophisticated analyses of observational data), thereby deepening and broadening their skill sets.

Apply here. Description of some available projects below.

Modeling Stellar Convection

Stellar modeling is limited by our understanding of turbulence. We are looking for a student interested in studying stellar convection, either near the star’s surface where it can cause measurable brightness fluctuations or in deeper regions where it plays a crucial role in distributing angular momentum and setting stellar rotation rates. These projects likely involve a combination of hydrodynamic simulations with the Athena or Dedalus software instruments, as well as semi-analytic work developing prescriptions for 1D stellar evolution instruments like MESA.

Stars in AGN Disks

Stars are likely formed in, or captured by, the disks of active galactic nuclei (AGN). The disk conditions profoundly change the star’s evolution, with AGN stars accreting large amounts of mass and becoming massive / very massive. This project could involve either modeling the accretion stream with radiation hydrodynamics software instruments like Athena++, modeling the long-term stellar evolution in the MESA software instrument, or studying the interplay of stellar dynamics, AGN disk models, and evolution, tying together output from a variety of tools with semi-analytic models. Another possible porject could involve calculating the rate of visible explosive transients in AGN disks from a population of massive AGN stars. This predictions could be useful for e.g. VRO/LSST, LIGO/VIRGO

Ref: Cantiello, Jermyn & Lin 2020, Dittmann et al. 2021, Jermyn et al. 2021, Perna et al. 2021

Binary Stars

The majority of massive stars live their life with companions and will exchange matter through their Roche lobes or possibly merge before exploding. These binary interactions have a strong impact on the appearance and structure of both stars, and observational advancements (e.g., Gaia, VRO/LSST, LIGO/VIRGO) require detailed understanding of common and rare evolutionary paths.

Many stellar phenomena have been linked with accretion in a binary system (e.g., Be stars, LBVs, etc.), and detailed modeling of the internal structure of both stars and their reactions to binary interactions is possible with the MESA software instrument, while rapid population synthesis simulations (e.g., COSMIC) can be used to explore the parameter space and make predictions for event rates, and (magneto-)hydrodynamical codes (e.g., Athena++) might allow to run direct numerical simulations of rapid binary interactions in the very high mass regime.

Project ideas:

Mass transfer with MESA: Study stellar structure reaction to varying mass and angular momentum accretion rates. Compare to full binary run, possibly find analytic fits.
Model grid of accretors to be used for unpublished galactic eclipsing binaries, Be stars in LB1 and HR6819 right after RLOF, Be-XRB, Be vs. B[e] stars
Modeling of late CCSNe from RSG+CO WD, to check if it leads to lifting the WD degeneracy or to a type 1.5 SN.
ATHENA++ modeling of RLOF accretion on a 50+Msun star: relevant to GW formation scenarios and might be possible if thermal and dynamical timescale are similar.

APOGEE Binaries

Binary stars represent a powerful probe of stellar evolution. Data from the APOGEE radial velocity survey have been used to identify a large population of binary main-sequence and red giant stars. This project would involve studying the chemical abundances, eccentricities, periods, and rotation periods of the APOGEE binaries, and leveraging semi-analytic models as well as 1D stellar evolutionary models to gain insight into how both single and binary stars evolve.

Modeling Stellar Ingestions with MESA

Planets and stars can be engulfed when, e.g., their host or companion star ascends the giant branch. Using a 1D code (MESA) it is possible to account for the energy deposited during the spiral in and determine the evolution of the primary star. This project aims at creating a grid of light-curves to be used as templates for observations with VRO/LSST.

Late Phases of Massive Stars Evolution

The spin rate of black holes and neutron stars, and its relation to the pre-explosion core structure and the physics of stellar explosion is an as-yet insufficiently explored topic. Present measurements in X-ray binaries and GW sources show very different black hole spin-distributions, and many theoretical processes might influence the final core spin and the explosion of massive stars. These include stochastic spin up/down of the inner core by late shell burning and accretion of high angular momentum material from convective shells in red supergiants. These mechanisms can introduce a stochastic component in the spin evolution of stars, and their importance for the sample of observed compact object spins is as of yet poorly explored.

Project ideas:

Study the spin rate of compact remnants due to:

Stochastic spin up from IGWs (extending the work of Fuller et al. 2015)
Stochastic angular momentum accretion from convective shells fallback (extending the work of Quataert et al. 2019)

In particular the goal will be to characterize amplitude and relative orientation of the spin vector, consider different types of objects (e.g. He stars) for applications to GW progenitors from isolated binaries.

Stellar Evolution Videos

Evolution of a Massive Star

This video shows the evolution of a non-rotating massive star with initial mass 15 times the mass of the Sun and a metallicity of Z=0.02. The model is evolved from the beginning of Hydrogen core burning till Silicon Burning. This was calculated using the software instrument MESA (Modules for Experiments in Stellar Astrophysics). The red super giant star Betelgeuse (Alpha Orionis) is believed to have a mass of approximately 15 solar masses and to be currently burning He in its core.

Evolution of a Low-Mass Star

Stellar Evolution calculation of a 1 Solar Mass star from the beginning of core H-burning to the White Dwarf cooling sequence. The model is non-rotating and has an initial metallicity of Z=0.02. This model shows the evolution of a star like our own Sun past its current stage (about half-way during hydrogen core burning). This was calculated using the software instrument MESA (Modules for Experiments in Stellar Astrophysics).

Evolution during the He-Flash

Evolution of a red giant star during off-center ignition of Helium in a degenerate core (Helium Flash). The model is evolved from the onset of neutrino losses that create a temperature inversion in the core eventually leading to the Helium off-center ignition, to Helium core burning and exhaustion. The model is non-rotating and was initiated with a mass of 1 solar masses and a metallicity of Z=0.02. It was calculated using the software instrument MESA (Modules for Experiments in Stellar Astrophysics).

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Thermohaline Mixing

Thermohaline mixing is a hydrodynamic instability that arises when an unstable gradient in composition is stabilized by a gradient in temperature. Its name derives from the greek words for 'heat' and 'salt'. Because it involves the diffusion of two different components (particles and heat) it belongs to the more general class of double-diffusive instabilities. In the ocean this instability can occur, for example, in regions where the evaporation leaves a warm layer of saltier water on top of less salty, cooler water. In this situation the saltier water can sink only after exchanging its heat excess. The optimal configuration for an efficient heat exchange requires a large contact surface; long fingers satisfy this requirement, reason for which in oceanography this instability is called "Salt fingers".

This instability has a major role in the Earth climate system, since
it regulates the ocean conveyor belt, a large scale circulation also
known as Thermohaline circulation. This circulation helps
redistributing heat across latitudes in the Earth ocean-atmosphere
system.

Thermohaline mixing can also occur in stars in case of inverse mean molecular weight gradients in a thermally stabilized medium. This can take place during the accretion of material in a binary system or in the case of off-center burning. Thermohaline mixing can be important also in red giant stars, where the mixing process can help explaining some anomalous surface abundances. In these stars a reaction of the pp-chain is able to create an inversion in the mean molecular weight gradient, as the H-shell burning operates in an homogenous region (due to the first dredge-up). The resulting thermohaline mixing could be responsible for the destruction of 3He in low mass stars. In fact these stars are net producers of 3He in standard stellar evolution calculations, but the amount of 3He observed in the interstellar medium matches the predictions of Big-Bang nulceosynthesis. Therefore, thermohaline mixing could help to reconcile predictions of stellar evolution calculations with the observations and theoretical models of Big-Bang nulceosynthesis.

If you want to know more about the possibility of salt fingers occurring in the future Sun, take a look at my paper on "Thermohaline Mixing in Evolved Low Mass Stars" (Cantiello & Langer 2010).

It is possible to see the development of the hydrodynamical instability in a simple kitchen-experiment. All you need is water, salt, ink, a transparency and two glasses. Below you can find a few pictures of the experimental setup and of the beautiful fingers that can develop if you do things right. A tip: you just need a very small amount of salt to prepare the warm salty water that goes in the top glass. If you put too much you will see another instability: Rayleigh-Taylor. Pictures below are from this very experiment performed by myself and Evert Glebbeek at Utrecht University in 2007.