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BINARY NEUTRON 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 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, , and conducts research in both astrophysics and physics characteristics can help determine 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 Binary Neutron Star Mergers 53 . The nuclear equation The nuclear equation . 3 g/cm 15 INTRODUCTION Neutron are stars at supranuclear density, density, are stars at supranuclear Neutron stars of to two times that have masses one tending to we 10 km. From this a radius of about the sun with density of a neutron that the maximum determine star is roughly 10 of state of matter at this extreme density is not of state of matter at mechanisms, two neutron known. Due to various form a gravitationally bound stars can sometimes neutron star (BNS) system. pair called a binary stars will lose orbital Over time these two toward one another until and gradually inspiral This event is called a BNS they eventually merge. and see Baiotti For a summary review, merger. are especially violent mergers Rezzola (2017). BNS waves producing gravitational and highly energetic, ray burst (Abbot et al., 2017b) and a short gamma process (Abbot et al., 2017a). During the merger neutron star material can become gravitationally it to unbound by several mechanisms, allowing One such method escape out into the host . and shock for ejection relies on tidal interactions high velocity; heating to throw material outward at (hereafter this material is called dynamical ejecta role in galactic simply ejecta). Ejecta play a critical of heavy chemical including the formation can be elements, which due to their high velocity Numerical dispersed over interstellar distances. of the ejecta simulations typically include estimates and characteristics, such as the mass, velocity, Based on results geometric distribution of the ejecta. Dietrich and of simulations from many researchers, developed Ujevic (2017) and Radice et al. (2018) tted models of ejecta properties. fi Currently the total number and spatiotemporal known, but distribution of neutron stars is not fully by using population synthesis models a multitude of estimates can be made regarding the number These population of neutron star binary systems. models predict that a detectable fraction of BNS will have mass ratios as high as q = 2.00 mergers community (Dietrich et al., 2015). However, research has focused mostly on simulations of BNS Although this with mass ratios q < 1.5. mergers are is understandable, since most BNS mergers expected to have mass ratios near 1, there may be that distinctive traits for high mass ratio mergers could provide stronger insights regarding neutron Thus, our star structure and remnant properties. research seeks to explore these possibilities by 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 , 52–61. , 52–61. Keywords neutron stars, gravitational holes, black kilonova, astrophysics, numericalwaves, relativity Abstract Neutron stars are extremely dense stellar corpses sometimes which existin orbiting pairs known as binary neutron star (BNS) systemsystems. The a BNS mass of ratio (q) ned as of the heaviermassneutron the is defi star divided the by the mass lighter of neutron Overstar. time the neutron stars will inspiral anothertoward one and produce a merger Althoughevent. rare, these can events be rich sources observational of data due to their many electromagnetic emissions as as well the gravitational they produce. The waves ability to extract information physical from observationssuch heavily numerical on relies In mergersimulations events. this of project, reportwe results six simulations BNS of for mergers having total system masses of and with mass ratios of 2.75Msun or 2.50 highest mass and (the 2.00, 2.25 ratio 1.75, Oursimulated are goals in to the (a) world). test community-developed the of models examine mergers,ejecta produced (b) BNS by the gravitational distinctive for waveforms spectral estimate characteristics, the and (c) electromagnetic the emissions merger of remnants. Simulations are run using the a semirealistic and employ Einstein Toolkit piecewise-polytropeseven-segment model the neutronfor stars based the on Skyrme- nd that the fi equation state. We of Lyon community ejecta are of models robust, with systematicsome overestimation the amount of ejecta producedof extremely at high mass ratios. Also, several gravitational and wave ed, electromagnetic characteristics are identifi assuch reduced gravitational spectral peaks and extended emissions kilonova in the near weeks after for the merger. Binary neutron star A. (2020). Murray, high ejecta mass- for models Testing mergers: ratios. Undergraduate Purdue of Journal Research, 10 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 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 , 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). This shows that the ejecta is far from uniform provide our best estimates. The deviations between within the spherical sector that it occupies, with these results and the results of identical simulations greatest density occurring in a thin clump moving run at a lower resolution of 554 m are used to near the +y-axis. calculate the uncertainties attached to our best estimates. All simulations are conducted on the Rice Estimations of the total mass, average velocity, cluster housed at Purdue University using 160 cores. and total kinetic energy of the ejecta are made by creating Python scripts within VisIt. These Once completed, the data produced from each results are then compared to predictions based on simulation are downloaded to a local workstation the community models from Dietrich and Ujevic for study. Visualizations of the data are produced (2017), producing the residuals shown in Figure 4. using a publicly available software package called The uncertainties on each residual are obtained VisIt (Childs et al., 2016). These visualizations are by similar calculations for the ejecta produced in used to ensure that the simulations are well behaved the corresponding lower-resolution versions of the

54 Journal of Purdue Undergraduate Research: Volume 10, Fall 2020 Binary Neutron Star Mergers 55 = 11 milliseconds, showing diffuse ejecta material in green, with dense bound diffuse ejectagreen, showing in material time t = 11 milliseconds, at , q = 1.75 simulation sun material in orange orbiting the recently formed black hole produce from the merger. from black hole produce formed orbiting the recently in orange material Note: M = 2.75M Note: Figure 1. 3-D ejecta density model. Figure = 14 milliseconds. The perspective has been zoomed out to include the to out perspective has been zoomed The time t = 14 milliseconds. later 1 at Figure from same simulation The Note: green. in sectorexpanding of diffuse ejectacolored material Figure 2. 3-D ejecta density out). model (zomed Figure Figure 3. 2-D ejecta density model.

Note: The same simulation as Figures 1 and 2 at time t = 14 milliseconds, plotting the density of ejecta material only in both equatorial (top) and meridional (bottom) planes. The colors here do not correspond to the colors in Figures 1 or 2.

56 Journal of Purdue Undergraduate Research: Volume 10, Fall 2020 Binary Neutron Star Mergers 57 show delayed sun shows the waveforms shows the waveforms sun result in a short-lived hypermassive a short-lived hypermassive result in sun Gravitational waveforms for each of the 6 for waveforms 5. Gravitational Figure simulations. mode of the dominant amplitudes for Wave Note: emission--called the (2,2)-mode--are wave gravitational as functionsshown of time. disappear almost immediately after a black hole disappear almost immediately after a This is because the forms in each simulation. gravitational centrifugal effect is too weak to delay collapse. is observed These results are different from what the same total having for low mass ratio mergers systems mass as in De Pietri et al. (2016), where with total masses as high as 3.0M neutron star (HMNS) with a smaller-amplitude with a smaller-amplitude neutron star (HMNS) for many milliseconds until “rumbling” that persists The term “hypermassive” the end of our simulations. neutron stars are so means that these remnant collapse directly to form black massive they would their rapid However, stationary. holes if they were a temporary centrifugal effect rotation rates provide attraction of the that counters the gravitational some for formation hole black off staves and remnant events other pattern for merger The amount of time. 2.75M with a total mass of same nuclear black hole formation despite using the This is likely equation of state as our simulations. achieved by low due to the greater rotational velocity systems show mass ratio systems. High mass ratio due to the extended size of the a prompter merger tidal effect lightweight neutron star and the greater neutron across it that is produced from the heavier to occur more rapidly, the merger By causing star. and the stars do the inspiral is unable to last as long, weakening the not reach as high an orbital velocity, respective velocities increase. The amplitude reaches The amplitude velocities increase. respective then of coalescence, and at the moment a maximum total depending on the different patterns we see two a total events for BNS system. Merger mass of the mass of 2.50M Note: Deviations between our results and the fitted models and the fitted our results between Deviations Note: ejecta mass, for plotted of Dietrich and Ujevic (2017) are Our results and ejecta velocity. ejecta kinetic energy, with some with these models, consistent generally are ratio. mass the ejectadiscrepancy increasing mass at for Comparison of our results to community models. to of our results 4. Comparison Figure The gravitational waveforms are plotted in Figure 5. The gravitational waveforms are plotted increase in Inspecting this figure, we can see an two stars’ gravitational wave amplitude as the Overall, the results reinforce the community models Overall, the results and average velocity of energy for the total kinetic a systematic overestimation the ejecta and suggest that worsens at the highest mass of the ejecta mass indicates that at extremely high This ratio of 2.25. attraction of the heavier mass ratios the gravitational the amount of ejecta by a neutron star decreases for ratios small amount, but this effect is insignificant are broadly below roughly 2.25. Overall, the models ratios. Results confirmed even at these extreme mass from Radice for the residuals relative to the models et al. (2018) are qualitatively similar. simulations, as described in the “Methods” section. It the “Methods” section. as described in simulations, the tidal shearing beforehand whether was not clear each system might neutron star in of the lighter producing more ejecta pronounced, become more the or whether mass ratio mergers, than for low of the heavier neutron star in gravitational attraction dominate, producing less ejecta each system might ratio mergers. than for low mass centrifugal effect that helps to prop up the neutron likely due to the tidal effects that drive our high star remnant against gravitational collapse. mass ratio systems to quick mergers. The origins of the secondary peaks are not well understood, Figure 6 displays spectrograms that illustrate how although the lower-frequency peak may be due to the energy of the gravitational waves was distributed the one-armed spiral pattern of material orbiting the over frequencies up to 5500 Hz, while Figure 7 shows hypermassive neutron star remnant that was formed the associated power spectral densities. Using the from shearing of the low-mass neutron star during

M = 2.50Msun, q = 1.75 simulation as an example, inspiral. The higher-frequency peak near 2600 Hz is after the merger the distinct “rumbling” can be seen less understood and may be produced by pulsating as a continuing high-frequency signal near 1800 Hz in oscillations in the shape of the remnant itself. Figure 6. Examination of the power spectral density for this simulation in Figure 7 shows a well-defined peak Finally, the estimated light curves for the kilonova near this frequency, with associated secondary peaks produced by ejecta are calculated and several on either side of it at roughly 1000 Hz and 2600 Hz. illustrative results are shown in Figure 8. For each

of the two total system masses (M = 2.50, 2.75Msun), The primary frequency is produced by the bar- light curves for the lowest mass ratio (1.75) are deformed remnant spinning after the merger, plotted as solid lines, and those for the highest mass consistent with results from lower mass ratio ratio (2.25) are plotted as dashed lines. The light simulations such as De Pietri et al. (2016). However, curves for the intermediate mass ratio (2.00) lie the primary frequencies are far lower, and the between these two and are not plotted for the sake of amplitudes for each peak are also smaller, again visual clarity.

Figure 6. Gravitational wave spectrograms for each of the 6 simulations.

Note: Powers are color-coded for frequencies up to 5500 Hz as functions of time, with yellow indicating high-intensity emission at a particular frequency during a particular instant of time and purple indicating low intensity.

58 Journal of Purdue Undergraduate Research: Volume 10, Fall 2020 Binary Neutron Star Mergers 59

sun and M = 2.75M sun simulations near 1800 Hz due to postmerger emissions. near 1800 Hz simulations postmerger due to sun Note the dominant peak for M = 2.50M peak for the dominant Note merger events. merger M = 2.50M in Difference spectral each of the 6 simulations: density plots for power 7. Gravitational Figure Figure 8. Kilonova light curves for mass ratios.

Note: q = 1.75 (solid lines), and q = 2.25 (dashed lines).

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