BINARY NEUTRON STAR MERGERS: Testing Ejecta Models for High Mass-Ratios Student Author Mentor Allen Murray is currently a Aaron Warren is an associate junior at Purdue University professor of physics and director Northwest and is majoring in of the Science Interdisciplinary both physics and mathematics, Research Center at Purdue with minors in astrophysics and University Northwest. Dr. Warren French. He currently conducts completed his AB degree at research with Dr. Aaron Warren Vassar College, with majors that focuses on binary neutron in physics, mathematics, and star mergers of particularly astronomy, in 2000 and his PhD high mass ratio. Their research seeks to see how from Rutgers University in physics in 2006. He mass ejecta, kilonova, and gravitational wave conducts research in both astrophysics and physics characteristics can help determine neutron star education research. His early work in computational structure and the nuclear equation of state. Murray astrophysics studied simulations of stellar intends to pursue a graduate degree in physics after collisions and the production of blue stragglers in completion of his BS in the spring of 2021. He also globular clusters. Currently, Warren focuses on enjoys casual astronomical observation and French simulations of binary neutron star mergers having cooking. exceptional characteristics such as high mass ratios and magnetizations, with a particular interest in determining whether and how the electromagnetic and gravitational signals from such mergers may provide insights regarding the nuclear equation of state, neutron star structure, and merger remnant properties. 52 Journal of Purdue Undergraduate Research: Volume 10, Fall 2020 http://dx.doi.org/10.7771/2158-4052.1442 INTRODUCTION Abstract Neutron stars are stars at supranuclear density, tending to have masses one to two times that of Neutron stars are extremely dense stellar the sun with a radius of about 10 km. From this we corpses which sometimes exist in orbiting determine that the maximum density of a neutron pairs known as binary neutron star (BNS) star is roughly 1015 g/cm3. The nuclear equation systems. The mass ratio (q) of a BNS system of state of matter at this extreme density is not is defi ned as the mass of the heavier neutron known. Due to various mechanisms, two neutron star divided by the mass of the lighter neutron stars can sometimes form a gravitationally bound star. Over time the neutron stars will inspiral pair called a binary neutron star (BNS) system. toward one another and produce a merger Over time these two stars will lose orbital energy event. Although rare, these events can be rich and gradually inspiral toward one another until sources of observational data due to their they eventually merge. This event is called a BNS many electromagnetic emissions as well as merger. For a summary review, see Baiotti and the gravitational waves they produce. The Rezzola (2017). BNS mergers are especially violent ability to extract physical information from and highly energetic, producing gravitational waves such observations relies heavily on numerical (Abbot et al., 2017b) and a short gamma ray burst simulations of merger events. In this project, (Abbot et al., 2017a). During the merger process we report results of six simulations for BNS neutron star material can become gravitationally mergers having total system masses of unbound by several mechanisms, allowing it to 2.50 or 2.75Msun and with mass ratios of escape out into the host galaxy. One such method 1.75, 2.00, and 2.25 (the highest mass ratio for ejection relies on tidal interactions and shock simulated in the world). Our goals are to (a) heating to throw material outward at high velocity; test community-developed models of the this material is called dynamical ejecta (hereafter ejecta produced by BNS mergers, (b) examine simply ejecta). Ejecta play a critical role in galactic the gravitational waveforms for distinctive chemical evolution including the formation of heavy spectral characteristics, and (c) estimate the elements, which due to their high velocity can be electromagnetic emissions of the merger dispersed over interstellar distances. Numerical remnants. Simulations are run using the simulations typically include estimates of the ejecta Einstein Toolkit and employ a semirealistic characteristics, such as the mass, velocity, and seven-segment piecewise-polytrope model geometric distribution of the ejecta. Based on results for the neutron stars based on the Skyrme- of simulations from many researchers, Dietrich and Lyon equation of state. We fi nd that the Ujevic (2017) and Radice et al. (2018) developed community models of ejecta are robust, with fi tted models of ejecta properties. some systematic overestimation of the amount of ejecta produced at extremely high mass Currently the total number and spatiotemporal ratios. Also, several gravitational wave and distribution of neutron stars is not fully known, but electromagnetic characteristics are identifi ed, by using population synthesis models a multitude such as reduced gravitational spectral peaks of estimates can be made regarding the number and extended kilonova emissions in the near of neutron star binary systems. These population infrared for weeks after the merger. models predict that a detectable fraction of BNS Binary Mergers Star Neutron mergers will have mass ratios as high as q = 2.00 Murray, A. (2020). Binary neutron star (Dietrich et al., 2015). However, community mergers: Testing ejecta models for high mass- research has focused mostly on simulations of BNS ratios. Journal of Purdue Undergraduate mergers with mass ratios q < 1.5. Although this Research, 10, 52–61. is understandable, since most BNS mergers are expected to have mass ratios near 1, there may be Keywords distinctive traits for high mass ratio mergers that could provide stronger insights regarding neutron neutron stars, black holes, gravitational star structure and remnant properties. Thus, our waves, kilonova, astrophysics, numerical research seeks to explore these possibilities by relativity focusing on extreme mass ratios q > 1.5, with three goals in mind. First, we aim to test the accuracy of the community-developed ejecta models. Second, we study the distinct gravitational wave characteristics 53 in order to test spectral features found in low and to aid interpretation of numerical analyses. mass ratio BNS mergers. Third, estimation of the Also using VisIt, ejecta are identified following the electromagnetic emissions produced by high mass method of Dietrich and Ujevic (2017), and their ratio mergers may show distinctive features relative total mass and energy are calculated. We created to low mass ratio mergers. Python scripts to extract gravitational waveforms from the simulations, based on the method METHODS described in De Pietri, Feo, Maione, and Loffler We conduct simulations at two different resolutions (2016). Spectrograms and power spectral densities for each of six different BNS systems. The six of the waveforms are then calculated to identify systems have total neutron star masses of either 2.50 distinguishing features of high mass ratio systems. or 2.75 Msun and mass ratios of either 1.75, 2.00, or Finally, calculations of the light emitted from the 2.25. While the last of these mass ratios is perhaps ejecta (called a kilonova) are performed using unrealistically large, it is hoped that its inclusion light curve model estimates by Dietrich and Ujevic may exaggerate and make clearer any distinguishing (2017). trends or signals that may be present but less pronounced at the lower mass ratios. RESULTS Examples of the identified ejecta from the Initial models of the neutron stars for each system simulations are shown in the first three figures below. are constructed using the LORENE pseudospectral Figure 1 shows a snapshot from the M = 2.75Msun, code (Gourgoulhon, Grandclement, Taniguchi, q = 1.75 simulation, with surfaces representing Marck, & Bonazzola, 2001). The neutron stars are various densities of bound matter (in shades of initially placed 45 km apart, allowing several orbits orange) orbiting the black hole that has formed before merger. We assume a Skyrme-Lyon equation (the small dark sphere corresponds to the apparent of state for the neutron stars, modeled as seven- horizon) and other surfaces representing various segment piecewise-polytropes. This is a standard and densities of ejected matter (in shades of green and semirealistic assumption that is generally consistent blue). Note that the densities of the ejected material with observations of neutron stars to date, such as are far lower than the densities of the bound material, seen in Abbot et al. (2017b). Our model has several and there is quite a bit of diffuse bound material flaws, including an absence of neutrinos as well as not shown here for the sake of visual clarity. The neutrino-driven winds and cooling, no modeling background stars and nebula in the image are purely of neutron capture or electron fraction, and an aesthetic and not part of the simulation. assumption of no initial magnetization of the neutron stars. It is left to future work to alleviate these flaws. The ejecta are again plotted with green surfaces in Figure 2, which is zoomed out. In general, portions Once constructed, each BNS system is evolved of the ejecta travel as fast as 30% the speed of light, using the Einstein Toolkit (Loffler et al., 2012), covering hundreds of kilometers in milliseconds on an open-source community-developed numerical their way out of the system. As seen in Figure 2, relativity package. All simulations reported here the physical time for this snapshot is nearly 14 use the “Tesla” release of the Einstein Toolkit. To milliseconds after the start of the simulation. estimate uncertainties due to numerical rounding and Figure 3 plots the density of the ejecta in both the resolution limitations, we evolved each system at equatorial and meridional planes at this time. The two different resolutions. Results from the highest- distance scales are plotted in code units (100M = 147 resolution simulations, accurate down to 369 m, km).