Neutrinos play an important role in the plethora astrophysical phenomena associated with neutron stars and their mergers: from helping newly born neutron stars cool down after their explosive births, to changing the composition of the material that undergoes nucleosynthesis and eventually produces gold, to potentially mitigating the impact of bulk viscosity after the merger. In this work we use an approximate, yet still-accurate, neutrino transport scheme to understand how neutrinos impact some of the aforementioned phenomena. We consider several key phenomena that inform us about the state of matter during binary neutron star mergers including the impact of neutrinos on the fluid dynamics and luminosity during the late inspiral and post-merger phases, the properties of ejecta and outflow, and the post-merger nucleosynthesis. To the left we show the nucleosynthetic patterns (i.e., the relative amount of heavy elements produced, where A is the atomic number of the element) during and after binary neutron star mergers for several descriptions of neutron star matter. We compare the patterns to that of the Sun, and find general agreement between what is predicted from our simulations and what is found in our Solar system.

• Pedro Luis Espino, David Radice, Francesco Zappa, Rossella Gamba, Sebastiano Bernuzzi, Impact of moment-based, energy integrated neutrino transport on microphysics and ejecta in binary neutron star mergers 

The environment following a merger of two neutron stars is highly dynamical with physics operating on many different length, energy, and time scales. An important area of research is understanding the oscillations and dynamics of the post-merger environment when two neutron stars merge to create a single remnant neutron star. As that remnant neutron star evolves, it is possible its oscillations are damped by emergent bulk viscosity in the star (which can force the star to relax its oscillations in just milliseconds after it was formed). Neutrinos are copiously produced throughout the environment during the merger, and if they can remained sufficiently trapped within the remnant star, they can help lessen the impact of bulk viscosity by keeping the star close to equilibrium as established by the weak nuclear force. In this work we simulated binary neutron star mergers with enhanced neutrino transport using the WhiskyTHC code to show that neutrinos can remain sufficiently trapped in the remnant neutron star and may potentially mitigate the impact of bulk viscosity.

To the (bottom) left we show an image from one of our simulations depicting the ratio of relevant timescales that let's us understand how significantly neutrinos can be trapped in the remnant neutron star. Regions where neutrinos interact much faster than the star is locally oscillating show up in red, and regions where neutrinos take much longer to interact than the star is oscillating show up in blue. For most of the star neutrinos interact much faster than the star oscillates (red), which suggests a significant amount of neutrino trapping. The neutrinos trapped there keep the matter close to weak equilibrium which could mean that the bulk viscosity is not very strong there.

• Pedro Luis Espino, Peter Hammond, David Radice, Sebastiano Bernuzzi, Rossella Gamba, Francesco Zappa, Luis Felipe Longo Micchi, Albino Perego, Neutrino trapping and out-of-equilibrium effects in binary neutron star merger remnants

In this work, we found that if this kind of phase transition occurs at the densities relevant to binary neutron star mergers, then the fluid patterns that develop after the merger may be altered. This in turn may affect the gravitational waves emanating from the system. This can have interesting implications for the design of future-generation gravitational wave detectors.

• Pedro L. Espino, Aviral Prakash, David Radice, Domenico Logoteta, Revealing Phase Transition in Dense Matter with Gravitational Wave Spectroscopy of Binary Neutron Star Mergers

The field of Numerical Relativity fosters a culture of collaboration and open-source code development which allows for wonderful scientific exploration. One of the best-maintained efforts in this regard is the EinsteinToolkit, which is a collection of open-source codes that allow for the simulation of general relativistic systems including black holes and neutron stars, among other things. The EinsteinToolkit is built upon the Cactus framework, named as such for the base (Cactus flesh) set of codes and additional (Cactus thorns) supporting codes that allow one to run numerical relativity simulations. There are even open-source post-processing tools with which one can extract the `fruit' of Cactus simulations, such as kuibit (named after the tool used by the Tohono O'odham people of the Sonora Desert to extract the fruit of the towering Sahuaro Cactus). 

Over the past few decades, many numerical relativists have continued the traditions within open-source culture and made their codes free and open to the public. As a result, there are now many different numerical relativity codes which model many different phenomena. Relevant to the simulation of binary neutron star mergers are the IllinoisGRMHD, GRHydro, WhiskyTHC, and Spritz codes. Although all of the aforementioned codes are free and open to the public, no detailed comparison of the Physics they predict has been carried out. In this work we extend the IllinoisGRMHD code such that it has feature parity with the other mentioned codes, and carry a detailed comparison of the results of simulations. We consider many systems relevant for neutron star astrophysics, including isolated and binary stars, both with and without magnetic fields.

It turns out that, despite the similarity between all of these codes, some striking differences do occur among them. The predictions of these codes are often used to inform us about what gravitational waves from binary neutron stars are expected to look like. As more precise gravitational wave detectors come online, the differences in Physical phenomena predicted by each of these codes must be resolved. For a link to our codes which extend IllinoisGRMHD, please visit the "Codes" section of this page.

• Pedro L. Espino, Gabriele Bozzola, Vasileios Paschalidis, Quantifying uncertainties in general relativistic magnetohydrodynamic codes

The environment following a binary neutron star merger is extreme. The combination of extreme temperatures, densities, angular momentum, and magnetic fields make the sites of BNS mergers unique in the universe. Under these extreme conditions some of the hadronic matter that composed the original system can cross into an exotic phase of matter called a quark-gluon plasma. Matter in these environments under less extreme conditions will remain in the hadronic phase. This is the perfect scenario for the formation of hadron-quark hybrid stars: a stellar configuration consisting of asymptotically free quarks surrounded by hadronic matter. Other astrophysical systems that could produce hadron-quark hybrid stars include core collapse supernova or white dwarf-neutron star mergers. It is possible that in their lifetime these stars step into an unstable regime, where small perturbations can grow to be large. We investigated the dynamics of hadron-quark hybrid stars in this regime of instability. We found that they naturally tend to lose their quark cores and become pure hadron stars, but they can also be driven into strong oscillations between being hybrid and neutron stars. These oscillations could lead to unique gravitational wave signals that indicate the evolution of hybrid stars close by.

• Pedro L. Espino, Vasileios Paschalidis Fate of twin stars on the unstable branch: Implications for the formation of twin stars Phys.Rev.D 105 (2022) 4, 043014

The only gravitational wave event that coincided with a significant detection of electromagnetic radiation to date was that of a compact binary star merger. The radiation detected from the system suggests that the components of the binary were neutron stars. However, it is also possible that at least one of the components is a more exotic object: a so-called hybrid star. Hybrid stars are cousins of neutron star in the scenario where the densities inside compact stars reach the conditions for the QCD deconfinement phase transition. The denser regions of these stars are composed of asymptotically free quarks, while regions of lower density are composed of hadrons. In this project we explored the solution space of relativistic stars described by equations of state which model this high-density phase transition. We focused on stars of maximum mass, both non-rotating and rotating. Some of the most extreme models we consider have a high amount of differential rotation and can be very exotic objects that take on a quasi-toroidal topology with a 'ring' of quarks surrounded by hadronic matter (a cross-section of which is pictured on the left). 

• Gabriele Bozzola, Pedro L. Espino, Collin Lewin, Vasileios Paschalidis  Maximum mass and universal relations of rotating relativistic hybrid hadron-quark stars, Eur.Phys.J.A 55 (2019) 9, 149

Binary neutron star mergers received much attention following the detection of a BNS merger in the form of both gravitational and electromagnetic waves. The merger of two neutron stars leads to a spectacular environment, consisting of extreme temperatures, angular momentum, and magnetic fields. In these extreme environments the remnant of the merger can take on extreme properties. One of the remnant properties observed in numerical simulations of BNS mergers is a quasi-toroidal morphology (that's right, BNS merger remnants can look like almost-donuts!). These very strange remnants are associated with specific evolution properties. In work guided by Dr. Vasileios Paschalidis, we investigated whether such extreme shapes could arise in neutron stars modeled using realistic equations of state (all of which include microphysical descriptions of the matter). We found that the solution space originally mapped out for simplified equations of state has many of the same features when realistic equations of state are considered. The results were published in PRD (see link below).

In a follow-up project we also investigated the stability of these extreme quasi-toroidal solutions. Using fully general relativistic hydrodynamic simulations, we considered quasi-toroidal stars built using a simplified equation of state. We found evidence that quasi-toroidal neutron stars are dynamically unstable and produce unique features in the gravitational wave signature. These stars are prone to the growth of the one-arm spiral instability. The results of this project were also published in PRD (see link below)

• Pedro L. Espino, Vasileios Paschalidis, Thomas Baumgarte, Stuart L. Shapiro, Dynamical stability of quasitoroidal differentially rotating neutron stars, Phys.Rev.D 100 (2019) 4, 043014

• Pedro L. Espino, Vasileios Paschalidis, Revisiting the maximum mass of differentially rotating neutron stars in general relativity with realistic equations of state, Phys.Rev.D 99 (2019) 8, 083017

In the first half of my PhD I became fascinated with particle dark matter (PDM) and ways to constrain its properties. 

The nature of dark matter (DM) is one of the big open questions in Physics today. A viable candidate for what the dark matter could be is a species of weakly interacting massive particle (WIMP). Many astrophysical observations allow the WIMP scenario (and some actually favor it). Most DM direct detection experiments (for example, consisting of a shielded vat of dense matter (the hope being that an incident DM flux leaves a detectable signature)) have not found evidence for PDM on Earth. Therefore, indirect ways of detecting DM could be the way forward.

Models for the galactic distribution of DM often predict a sharp increase in the DM density toward the galactic center. At the same time, the distribution of neutron stars increases toward the galactic center.  The extreme density inside of neutron stars makes them ideal DM detectors. The problem is that we cannot get anywhere near a neutron star. We could, however, observe properties of different stars (such as their masses, radii, and (inferred) surface temperature). Using these properties and knowledge of the DM distribution across the galaxy, we could infer the properties of PDM. 

In research guided by Dr. Ina Sarcevic I considered the effect of PDM on neutron star observables (specifically, the mass and radius of cold neutron stars). I wrote a code that calculates the number of DM particles that can accumulate in a neutron star, given its location in the Milky Way, composition (i.e, equation of state), approximate age, mass, and radius. 

The distribution of DM inside of a particular neutron star, assuming a model and set of properties such as interaction strength and mass for the DM, can in turn affect its mass and radius outside of the observed bounds, indicating that PDM should not be described by such properties. A second set of codes calculates the acceptable ranges for simple bosonic and fermionic DM particles.

These codes can be found here and are free to use. Here you can find the slides for a talk I gave detailing a few of my findings.

This project began my obsession with neutron stars (some of the most extreme astrophysical objects in existence). 

This was a set of tutorials/pedagogical research carried out in my first year of grad school with Dr. Doug Toussaint. I was still interested in lattice QCD and was exploring the history, methods, and relevant problems of the field. With Dr. Toussaint's guidance I wrote a basic lattice code which calculated relevant physical observables in a lattice gauge theory using Monte Carlo methods. Below you can find a report of what I learned in this tutorial. A bonus report can be found below that, with details on solving the Ising model using similar methods. 

A study of lattice QED

Solving the Ising model using the Metropolis algorithm