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We present a novel statistical algorithm, Stellar Ages, which currently infers the age, metallicity, and extinction posterior distributions of stellar populations from their magnitudes. While this paper focuses on these parameters, the framework is readily adaptable to include additional properties, such as rotation, in future work. Historical age-dating techniques either model individual stars or populations of stars, often sacrificing population context or precision for individual estimates. Stellar Ages does both, combining the strengths of these approaches to provide precise individual ages for stars while leveraging population-level constraints. We verify the algorithm's capabilities by determining the age of synthetic stellar populations and actual stellar populations surrounding a nearby supernova, SN 2004dj. In addition to inferring an age, we infer a progenitor mass consistent with direct observations of the precursor star. The median age inferred from the brightest nearby stars is $\log_{10}$(Age/yr) = $7.19^{+0.10}_{-0.13}$, and its corresponding progenitor mass is $13.95^{+3.33}_{-1.96}$ $\text{M}_{\odot}$., Comment: 15 pages, 12 figures, figures 7 and 12 are most important

Stellar evolution theory restricted to single stars predicts a minimum mass for core-collapse supernovae (CCSNe) of around eight solar masses; this minimum mass corresponds to a maximum age of around 45 million years for the progenitor and the coeval population of stars. Binary evolution complicates this prediction. For example, an older stellar population around 100 million years could contain stellar mergers that reach the minimum mass for core collapse. Despite this clear prediction by binary evolution, there are few, if any CCSNe associated with a distinctly older stellar population...until now. The stellar population within 150 pc of the Vela Pulsar is inconsistent with single-star evolution only; instead, the most likely solution is that the stellar population is $\ge$80 Myr old, and the brightest stars are mass gainers and/or mergers, the result of binary evolution. The evidence is as follows. Even though the main sequence is clearly dominated by a $\ge$80-Myr-old population, a large fraction of the corresponding red giants is missing. The best-fitting single-star model expects 51.5 red giants, yet there are only 22; the Poisson probability of this is $1.7 \times 10^{-6}$. In addition, there is an overabundance of bright, young-looking stars (25-30 Myrs old), yet there is not a corresponding young main sequence (MS). Upon closer inspection, the vast majority of the young-looking stars show either past or current signs of binary evolution. These new results are possible due to exquisite Gaia parallaxes and a new age-dating software called {\it Stellar Ages}., Comment: 13 pages, 7 figures, 1 table. submitted to ApJ

Most massive stars end their lives with core collapse. However, it is not clear which explode as a Core-collapse Supernova (CCSN), leaving behind a neutron star and which collapse to black hole, aborting the explosion. One path to predict explodability without expensive multi-dimensional simulations is to develop analytic explosion conditions. These analytic explosion conditions also provide a deeper understanding of the explosion mechanism and they provide some insight as to why some simulations explode and some do not. The analytic force explosion condition (FEC) reproduces the explosion conditions of spherically symmetric CCSN simulations. In this followup manuscript, we include the dominant multi-dimensional effect that aids explosion, neutrino driven convection, into the FEC. This generalized critical condition (FEC+) is suitable for multi-dimensional simulations and has potential to accurately predict explosion conditions of two- and three-dimensional CCSN simulations. We show that adding neutrino-driven convection reduces the critical condition by $\sim 30\%$, which is consistent with previous multi-dimensional simulations.

Using resolved optical stellar photometry from the Panchromatic Hubble Andromeda Treasury Triangulum Extended Region (PHATTER) survey, we measured the star formation history (SFH) near the position of 85 supernova remnants (SNRs) in M33. We constrained the progenitor masses for 60 of these SNRs, finding the remaining 25 remnants had no local SF in the last 56 Myr consistent with core-collapse SNe (CCSNe), making them potential Type Ia candidates. We then infer a progenitor mass distribution from the age distribution, assuming single star evolution. We find that the progenitor mass distribution is consistent with being drawn from a power-law with an index of $-2.9^{+1.2}_{-1.0}$. Additionally, we infer a minimum progenitor mass of $7.1^{+0.1}_{-0.2}\ M_{\odot}$ from this sample, consistent with several previous studies, providing further evidence that stars with ages older than the lifetimes of single 8 $M_{\odot}$ stars are producing supernovae., Comment: 20 pages, 7 figures, 2 tables, Accepted at ApJ

One of the major challenges in Core-collapse Supernova (CCSN) theory is to predict which stars explode and which collapse to black holes. Gogilashvili and Murphy (2022) derived an analytic force explosion condition (FEC) and showed that the FEC is consistent with CCSN simulations that use the light-bulb approximation for neutrino heating and cooling. In this follow-up manuscript, we show that the FEC is consistent with the explosion condition when using actual neutrino transport in GR1D simulations (O'CONNOR 2015). Since most 1D simulations do not explode, to facilitate this test, we enhance the heating efficiency within the gain region. To compare the analytic FEC and radiation-hydrodynamic simulations, this manuscript also presents a practical translation of the physical parameters. For example: we replace the neutrino power deposited in the gain region, $L_\nu\tau_g$, with the net neutrino heating in the gain region; rather than assuming that $\dot{M}$ is the same everywhere, we calculate $\dot{M}$ within the gain region; and we use the neutrino opacity at the gain radius. With small, yet practical modifications, we show that the FEC predicts the explosion conditions in spherically symmetric CCSN simulations that use neutrino transport., Comment: Figure 5 most clearly highlights the fidelity and the efficacy of the Force Explosion Condition

Understanding which stars explode leaving behind neutron stars and which stars collapse forming black holes remains a fundamental astrophysical problem. We derive an analytic explosion condition for spherically symmetric core-collapse supernovae. The derivation starts with the exact governing equations, considers the balance of integral forces, includes the important dimensionless parameters, and includes an explicit set of self-consistent approximations. The force explosion condition is $\tilde{L}_\nu\tau_g - 0.06 \tilde{\kappa} > 0.38$, and only depends upon two dimensionless parameters. The first compares the neutrino power deposited in the gain region with the accretion power, $\tilde{L}_\nu \tau_g = L_{\nu} \tau_g R_{\rm NS}/ ( G \dot{M} M_{\rm NS})$. The second, $\tilde{\kappa} = \kappa \dot{M} / \sqrt{G M_{\rm NS} R_{\rm NS}}$, parameterizes the neutrino optical depth in the accreted matter near the neutron-star surface. Over the years, many have proposed approximate explosion conditions: the critical neutrino-luminosity, ante-sonic, and timescale conditions. We are able to derive these other conditions from the force explosion condition, which unifies them all. Using numerical, steady-state and fully hydrodynamic solutions, we test the explosion condition. The success of these tests is promising in two ways. One, the force explosion condition helps to illuminate the underlying physics of explosions. Two, this condition may be a useful explosion diagnostic for more realistic, three-dimensional radiation hydrodynamic core-collapse simulations., Comment: Figure 10 most clearly highlights the fidelity and the efficacy of the Force Explosion Condition. If you are interested in testing the explosion condition with CCSN simulations, feel free to contact us

We constrained the progenitor masses for 169 supernova remnants, 8 historically observed supernovae, and the black hole formation candidate in NGC 6946, finding that they are consistent with originating from a standard initial mass function. Additionally, there were 16 remnants that showed no sign of nearby star formation consistent with a core-collapse supernova, making them good Type Ia candidates. Using $Hubble$ $Space$ $Telescope$ broadband imaging, we measured stellar photometry of ACS/WFC fields in F435W, F555W, F606W, and F814W filters as well as WFC3/UVIS fields in F438W, F606W, and F814W. We then fitted this photometry with stellar evolutionary models to determine the ages of the young populations present at the positions of the SNRs and SNe. We then infer a progenitor mass probability distribution from the fitted age distribution. For 37 SNRs we tested how different filter combinations affected the inferred masses. We find that filters sensitive to H$\alpha$, [N II], and [S II] gas emission can bias mass estimates for remnants that rely on our technique. Using a KS-test analysis on our most reliable measurements, we find the progenitor mass distribution is well-matched by a power-law index of $-2.6^{+0.5}_{-0.6}$, which is consistent with a standard initial mass function., Comment: 28 pages, 13 figures, 4 tables

We infer the progenitor mass distribution for 22 historic core-collapse supernovae (CCSNe) using a Bayesian hierarchical model. For this inference, we use the local star formation histories to estimate the age for each supernova (SN). These star formation histories often show multiple bursts of star formation; our model assumes that one burst is associated with the SN progenitor and the others are random bursts of star formation. The primary inference is the progenitor age distribution. Due to the limited number of historic SNe and highly uncertain star formation at young ages, we restrict our inference to the slope of the age distribution and the maximum age for CCSNe. Using single-star evolutionary models, we transform the progenitor age distribution into a progenitor mass distribution. Under these assumptions, the minimum mass for CCSNe is ${M_\textrm{min}}~=~8.60^{+0.37}_{-0.41} \ M_\odot$ and the slope of the progenitor mass distribution is $\alpha = -2.61^{+1.05}_{-1.18}$. The power-law slope for the progenitor mass distribution is consistent with the standard Salpeter initial mass function ($\alpha = -2.35$). These values are consistent with previous estimates using precursor imaging and the age-dating technique, further confirming that using stellar populations around SN and supernova remnants is a reliable way to infer the progenitor masses.

Using {\it Gaia} Early Data Release 3 (EDR3) parallaxes and Bayesian inference, we infer a parallax of the Westerlund 1 (Wd1) cluster. We find a parallax of $0.34\pm{0.05}$ mas corresponding to a distance of $2.8^{+0.7}_{-0.6}$ kpc. The new {\it Gaia} EDR3 distance is consistent with our previous result using {\it Gaia} DR2 parallaxes. This confirms that Wd1 is less massive and older than previously assumed. Compared to DR2, the EDR3 individual parallax uncertainties for each star decreased by 30\%. However, the aggregate parallax uncertainty for the cluster remained the same. This suggests that the uncertainty is dominated by systematics, which is possibly due to crowding, motions within the cluster, or motions due to binary orbits., Comment: 3 pages, 1 figure

Recent multi-dimensional simulations of core-collapse supernovae are producing successful explosions and explosion-energy predictions. In general, the explosion-energy evolution is monotonic and relatively smooth, suggesting a possible analytic solution. We derive analytic solutions for the expansion of the gain region under the following assumptions: spherical symmetry, one-zone shell, and powered by neutrinos and $\alpha$ particle recombination. We consider two hypotheses: I) explosion energy is powered by neutrinos and $\alpha$ recombination, II) explosion energy is powered by neutrinos alone. Under these assumptions, we derive the fundamental dimensionless parameters and analytic scalings. For the neutrino-only hypothesis (II), the asymptotic explosion energy scales as $E_{\infty} \approx 1.5 M_g v_0^2 \eta^{2/3}$, where $M_g$ is the gain mass, $v_0$ is the free-fall velocity at the shock, and $\eta$ is a ratio of the heating and dynamical time scales. Including both neutrinos and recombination (hypothesis I), the asymptotic explosion energy is $E_{\infty} \approx M_g v_0^2 (1.5\eta^{2/3} + \beta f(\rho_0))$, where $\beta$ is the dimensionless recombination parameter. We use Bayesian inference to fit these analytic models to simulations. Both hypotheses fit the simulations of the lowest progenitor masses that tend to explode spherically. The fits do not prefer hypothesis I or II; however, prior investigations suggest that $\alpha$ recombination is important. As expected, neither hypothesis fits the higher-mass simulations that exhibit aspherical explosions. In summary, this explosion-energy theory is consistent with the spherical explosions of low progenitor masses; the inconsistency with higher progenitor-mass simulations suggests that a theory for them must include aspherical dynamics., Comment: Figure 10 most clearly illustrates the main conclusions

Mars lacks a substantial magnetic field; as a result, the solar wind ablates the Martian atmosphere, making the surface uninhabitable. Therefore, any terraforming attempt will require an artificial Martian magnetic shield. The fundamental challenge of building an artificial magnetosphere is to condense planetary-scale currents and magnetic fields down to the smallest mass possible. Superconducting electromagnets offer a way to do this. However, the underlying physics of superconductors and electromagnets limits this concentration. Based upon these fundamental limitations, we show that the amount of superconducting material is proportional to $B_c^{-2}a^{-3}$, where $B_c$ is the critical magnetic field for the superconductor and $a$ is the loop radius of a solenoid. Since $B_c$ is set by fundamental physics, the only truly adjustable parameter for the design is the loop radius; a larger loop radius minimizes the amount of superconducting material required. This non-intuitive result means that the "intuitive" strategy of building a compact electromagnet and placing it between Mars and the Sun at the first Lagrange point is unfeasible. Considering reasonable limits on $B_c$, the smallest possible loop radius is $\sim$10 km, and the magnetic shield would have a mass of $\sim 10^{19}$ g. Most high-temperature superconductors are constructed of rare elements; given solar system abundances, building a superconductor with $\sim 10^{19}$ g would require mining a solar system body with several times $10^{25}$ g; this is approximately 10% of Mars. We find that the most feasible design is to encircle Mars with a superconducting wire with a loop radius of $\sim$ 3400 km. The resulting wire diameter can be as small as $\sim$5 cm. With this design, the magnetic shield would have a mass of $\sim 10^{12}$ g and would require mining $\sim 10^{18}$ g, or only 0.1\% of Olympus Mons.

We determine the ages of the young, resolved stellar populations at the locations of 237 optically-identified supernova remnants in M83. These age distributions put constraints on the progenitor masses of the supernovae that produced 199 of the remnants. The other 38 show no evidence for having a young progenitor and are therefore good Type Ia SNR candidates. Starting from Hubble Space Telescope broadband imaging, we measured resolved stellar photometry of seven archival WFC3/UVIS fields in F336W, F438W, and F814W. We generate color-magnitude diagrams of the stars within 50 pc of each SNR and fit them with stellar evolution models to obtain the population ages. From these ages we infer the progenitor mass that corresponds to the lifetime of the most prominent age that is $<$50 Myr. In this sample, there are 47 SNRs with best-fit progenitor masses $>$15 M$_{\odot}$, and 5 of these are $>$15 M$_{\odot}$ at 84% confidence. This is the largest collection of high-mass progenitors to date, including our highest-mass progenitor inference found so far, with a constraint of $<$8 Myr. Overall, the distribution of progenitor masses has a power-law index of $-3.0^{+0.2}_{-0.7}$, steeper than Salpeter initial mass function ($-2.35$). It remains unclear whether the reason for the low number of high-mass progenitors is due to the difficulty of finding and measuring such objects or because only a fraction of very massive stars produce supernovae., Comment: Accepted for publication in ApJ, 33 pages, 7 figures, 3 tables

There are now $\sim$20 multi-dimensional core-collapse supernova (CCSN) simulations that explode. However, these simulations have explosion energies that are a few times $10^{50}$ erg, not $10^{51}$ erg. In this manuscript, we compare the inferred explosion energies of these simulations and observations of 38 SN~IIP. Assuming a log-normal distribution, the mean explosion energy for the observations is $\mu_{\rm obs} = -0.13\pm 0.05$ ($\log_{10}(E/10^{51}\, {\rm erg})$) and the width is $\sigma_{\rm obs} = 0.21^{+0.05}_{-0.04}$. Only three CCSN codes have sufficient simulations to compare with observations: CHIMERA, CoCoNuT-FMT, and FORNAX. Currently, FORNAX has the largest sample of simulations. The two-dimensional FORNAX simulations show a correlation between explosion energy and progenitor mass, ranging from linear to quadratic, $E_{\rm sim} \propto M^{1-2}$; this correlation is consistent with inferences from observations. In addition, we infer the ratio of the observed-to-simulated explosion energies, $\Delta=\log_{10}(E_{\rm obs}/E_{\rm sim})$. For the CHIMERA set, $\Delta=0.33\pm0.06$; for CoCoNuT-FMT, $\Delta=0.62\pm0.05$; for FORNAX2D, $\Delta=0.73\pm0.05$, and for FORNAX3D, $\Delta=0.95\pm0.06$. On average, the simulations are less energetic than inferred energies from observations ($\Delta \approx 0.7$), but we also note that the variation among the simulations (max($\Delta$)-min($\Delta$) $\approx 0.6$) is as large as this average offset. This suggests that further improvements to the simulations could resolve the discrepancy. Furthermore, both the simulations and the observations are heavily biased. In this preliminary comparison, we model these biases, but to more reliably compare the explosion energies, we recommend strategies to un-bias both the simulations and observations., Comment: 12 pages, 8 figures

Most one-dimensional core-collapse simulations fail to explode, yet multi-dimensional simulations often explode. A dominant multi-dimensional effect aiding explosion is neutrino-driven convection. We incorporate a convection model in approximate one-dimensional core-collapse supernova (CCSN) simulations. This is the 1D+ method. This convection model lowers the neutrino luminosity required for explosion by 30%, similar to the reduction observed in multi-dimensional simulations. The model is based upon the global turbulence model of Mabanta & Murphy (2018) and models the mean-field turbulent flow of neutrino-driven convection. In this preliminary investigation, we use simple neutrino heating and cooling algorithms to compare the critical condition in the 1D+ simulations with the critical condition observed in two-dimensional simulations. Qualitatively, the critical conditions in the 1D+ and the two-dimensional simulations are similar. The assumptions in the convection model affect the radial profiles of density, entropy, and temperature, and comparisons with the profiles of three dimensional simulations will help to calibrate these assumptions. These 1D+ simulations are consistent with the profiles and explosion conditions of equivalent two-dimensional CCSN simulations but are ~100 times faster, and the 1D+ prescription has the potential to be ~100,000 faster than three-dimensional CCSN simulations. The 1D+ technique will be ideally suited to test the explodability of thousands of progenitor models.

Westerlund 1 (Wd1) is potentially the largest star cluster in the Galaxy. That designation critically depends upon the distance to the cluster, yet the cluster is highly obscured, making luminosity-based distance estimates difficult. Using {\it Gaia} Data Release 2 (DR2) parallaxes and Bayesian inference, we infer a parallax of $0.35^{+0.07}_{-0.06}$ mas corresponding to a distance of $2.6^{+0.6}_{-0.4}$ kpc. To leverage the combined statistics of all stars in the direction of Wd1, we derive the Bayesian model for a cluster of stars hidden among Galactic field stars; this model includes the parallax zero-point. Previous estimates for the distance to Wd1 ranged from 1.0 to 5.5 kpc, although values around 5 kpc have usually been adopted. The {\it Gaia} DR2 parallaxes reduce the uncertainty from a factor of 3 to 18\% and rules out the most often quoted value of 5 kpc with 99\% confidence. This new distance allows for more accurate mass and age determinations for the stars in Wd1. For example, the previously inferred initial mass at the main-sequence turn-off was around 40 M$_{\odot}$; the new {\it Gaia} DR2 distance shifts this down to about 22 M$_{\odot}$. This has important implications for our understanding of the late stages of stellar evolution, including the initial mass of the magnetar and the LBV in Wd1. Similarly, the new distance suggests that the total cluster mass is about four times lower than previously calculated., Comment: 14 pages, 10 figures

We examine parallaxes and distances for Galactic luminous blue variables (LBVs) in Gaia DR2. The sample includes 11 LBVs and 14 LBV candidates. For about half of the sample, DR2 distances are either similar to commonly adopted literature values, or the DR2 values have large uncertainties. For the rest, reliable DR2 distances differ significantly from values in the literature, and in most cases the Gaia DR2 distance is smaller. Two key results are that the S Doradus instability strip may not be as clearly defined as previously thought, and that there exists a population of LBVs at relatively low luminosities. LBVs seem to occupy a wide swath from the end of the main sequence at the blue edge to 8000 K at the red side, with a spread in luminosity reaching as low as log(L/Lsun)=4.5. The lower-luminosity group corresponds to effective single-star initial masses of 10-25 Msun, and includes objects that have been considered as confirmed LBVs. We discuss implications for LBVs including (1) their instability and origin in binary evolution, (2) connections to some supernova (SN) impostors such as the class of SN 2008S-like objects, and (3) LBVs that may be progenitors of SNe with dense circumstellar material across a wide initial mass range. Although some of the Gaia DR2 distances for LBVs have large uncertainty, this represents the most direct and consistent set of Galactic LBV distance estimates available in the literature., Comment: 20 pages, 5 figures, MNRAS accepted. Updated inclusion of excess astrometric noise and discussion of literature distances

Stellar photometric variability offers a novel probe of the interior structure and evolutionary state of stars. Here we present a census of stellar variability on day to decade timescales across the color-magnitude diagram for 73,000 stars brighter than $M_I$=-5 in the Whirlpool Galaxy (M51). Our Cycle 24 HST program acquired V and I-band images over 34 epochs spanning one year with pseudo-random cadences enabling sensitivity to periods from days to months. We supplement these data with archival V and I-band HST data obtained in 1995 and 2005 providing sensitivity to variability on decade timescales. At least 50% of stars brighter than $M_I$=-7 show strong evidence for variability within our Cycle 24 data; among stars with V-I>2 the variability fraction rises to ~100%. Large amplitude variability (>0.3 mag) on decade timescales is restricted to red supergiants and very luminous blue stars. Both populations display fairly smooth variability on month-year timescales. The Cepheid instability strip is clearly visible in our data, although the variability fraction within this region never exceeds ~10%. The location of variable stars across the color magnitude diagram broadly agrees with theoretical sources of variability, including the instability strip, red supergiant pulsational instabilities, long-period fundamental mode pulsations, and radiation-dominated envelopes in massive stars. Our data can be used to place stringent constraints on the precise onset of these various instabilities and their lifetimes and growth rates., Comment: 17 pages, 16 figures (plus an Appendix), accepted to ApJ

We age-date the stellar populations associated with 12 historic nearby core-collapse supernovae (CCSNe) and 2 supernova impostors, and from these ages, we infer their initial masses and associated uncertainties. To do this, we have obtained new HST imaging covering these CCSNe. Using these images, we measure resolved stellar photometry for the stars surrounding the locations of the SNe. We then fit the color-magnitude distributions of this photometry with stellar evolution models to determine the ages of any young existing populations present. From these age distributions, we infer the most likely progenitor mass for all of the SNe in our sample. We find ages between 4 and 50 Myr, corresponding to masses from 7.5 to 59 solar masses. There were no SNe that lacked a young population within 50~pc. Our sample contains 4 type Ib/c SNe; their masses have a wide range of values, suggesting that the progenitors of stripped-envelope SNe are binary systems. Both impostors have masses constrained to be $\lesssim$7.5 solar masses. In cases with precursor imaging measurements, we find that age-dating and precursor imaging give consistent progenitor masses. This consistency implies that, although the uncertainties for each technique are significantly different, the results of both are reliable to the measured uncertainties. We combine these new measurements with those from our previous work and find that the distribution of 25 core-collapse SNe progenitor masses is consistent with a standard Salpeter power-law mass function, no upper mass cutoff, and an assumed minimum mass for core-collapse of 7.5~M$_{\odot}$., Comment: 12 pages, 4 tables, 4 figures, accepted for publication in ApJ

The failed supernova N6946-BH1 likely formed a black hole (BH); we age-date the surrounding population and infer an age and initial mass for the progenitor of this BH formation candidate. First, we use archival Hubble Space Telescope imaging to extract broadband photometry of the resolved stellar populations surrounding this event. Using this photometry, we fit stellar evolution models to the color-magnitude diagrams to measure the recent star formation history (SFH). Modeling the photometry requires an accurate distance; therefore, we measure the tip of the red giant branch (TRGB) and infer a distance modulus of $29.47 \pm 0.079$ to NGC~6946, or a metric distance of $7.83 \pm 0.29$ Mpc. To estimate the stellar population's age, we convert the SFH and uncertainties into a probabilistic distribution for the progenitor's age. The region in the immediate vicinity of N6946-BH1 exhibits the youngest and most vigorous star formation for several hundred pc. This suggests that the progenitor is not a runaway star. From these measurements, we infer an age for the BH progenitor of $10.6^{+14.5}_{-5.9}$ Myr. Assuming that the progenitor evolved effectively as a single star, this corresponds to an initial mass of $17.9^{+29.9}_{-7.6}$ $M_{\odot}$. Previous spectral energy distribution (SED) modeling of the progenitor suggests a mass of $\sim$27 $M_{\odot}$. Formally, the SED-derived mass falls within our narrowest 68\% confidence interval; however, $91\%$ of the probability distribtuion function we measure lies below that mass, putting some tension between the age and the direct-imaging results., Comment: 12 pages, 8 Figures, accepted to ApJ. Figure 3 presents the main result

Using the star formation histories (SFHs) near 94 supernova remnants (SNRs), we infer the progenitor mass distribution for core-collapse supernovae. We use Bayesian inference and model each SFH with multiple bursts of star formation (SF), one of which is assumed to be associated with the SNR. Assuming single-star evolution, the minimum mass of CCSNe is $7.33^{+0.02}_{-0.16}$ $\text{M}_\odot$, the slope of the progenitor mass distribution is $\alpha = -2.96^{+0.45}_{-0.25}$, and the maximum mass is greater than $\text{M}_\textrm{max} > 59$ $\text{M}_\odot$ with a 68% confidence. While these results are consistent with previous inferences, they also provide tighter constraints. The progenitor distribution is somewhat steeper than a Salpeter initial mass function ($\alpha$ = -2.35). This suggests that either SNR catalogs are biased against the youngest SF regions, or the most massive stars do not explode as easily as lower mass stars. If SNR catalogs are biased, it will most likely affect the slope but not the minimum mass. The uncertainties are dominated by three primary sources of uncertainty, the SFH resolution, the number of SF bursts, and the uncertainty on SF rate in each age bin. We address the first two of these uncertainties, with an emphasis on multiple bursts. The third will be addressed in future work., Comment: 15 pages, 8 figures

An important result in core-collapse supernova (CCSN) theory is that spherically-symmetric, one-dimensional simulations routinely fail to explode, yet multi-dimensional simulations often explode. Numerical investigations suggest that turbulence eases the condition for explosion, but how is not fully understood. We develop a turbulence model for neutrino-driven convection, and show that this turbulence model reduces the condition for explosions by about 30%, in concordance with multi-dimensional simulations. In addition, we identify which turbulent terms enable explosions. Contrary to prior suggestions, turbulent ram pressure is not the dominant factor in reducing the condition for explosion. Instead, there are many contributing factors, ram pressure being only one of them, but the dominant factor is turbulent dissipation (TD). Primarily, TD provides extra heating, adding significant thermal pressure, and reducing the condition for explosion. The source of this TD power is turbulent kinetic energy, which ultimately derives its energy from the higher potential of an unstable convective profile. Investigating a turbulence model in conjunction with an explosion condition enables insight that is difficult to glean from merely analyzing complex multi-dimensional simulations. An explosion condition presents a clear diagnostic to explain why stars explode, and the turbulence model allows us to explore how turbulence enables explosion. Though we find that turbulent dissipation is a significant contributor to successful supernova explosions, it is important to note that this work is to some extent qualitative. Therefore, we suggest ways to further verify and validate our predictions with multi-dimensional simulations., Comment: 17 pages, 7 figures, submitted to ApJ, most important results are in figures 5 and 6

We model the size distribution of supernova remnants to infer the surrounding ISM density. Using simple, yet standard SNR evolution models, we find that the distribution of ambient densities is remarkably narrow; either the standard assumptions about SNR evolution are wrong, or observable SNRs are biased to a narrow range of ambient densities. We show that the size distributions are consistent with log-normal, which severely limits the number of model parameters in any SNR population synthesis model. Simple Monte Carlo simulations demonstrate that the size distribution is indistinguishable from log-normal when the SNR sample size is less than 600. This implies that these SNR distributions provide only information on the mean and variance, yielding additional information only when the sample size grows larger than $\sim{600}$ SNRs. To infer the parameters of the ambient density, we use Bayesian statistical inference under the assumption that SNR evolution is dominated by the Sedov phase. In particular, we use the SNR sizes and explosion energies to estimate the mean and variance of the ambient medium surrounding SNR progenitors. We find that the mean ISM particle density around our sample of SNRs is $\mu_{\log{n}} = -1.33$, in $\log_{10}$ of particles per cubic centimeter, with variance $\sigma^2_{\log{n}} = 0.49$. If interpreted at face value, this implies that most SNRs result from supernovae propagating in the warm, ionized medium. However, it is also likely that either SNR evolution is not dominated by the simple Sedov evolution or SNR samples are biased to the warm, ionized medium (WIM).

Observations show that luminous blue variables (LBVs) are far more dispersed than massive O-type stars, and Smith & Tombleson suggested that these large separations are inconsistent with a single-star evolution model of LBVs. Instead, they suggested that the large distances are most consistent with binary evolution scenarios. To test these suggestions, we modelled young stellar clusters and their passive dissolution, and we find that, indeed, the standard single-star evolution model is mostly inconsistent with the observed LBV environments. If LBVs are single stars, then the lifetimes inferred from their luminosity and mass are far too short to be consistent with their extreme isolation. This implies that there is either an inconsistency in the luminosity- to-mass mapping or the mass-to-age mapping. In this paper, we explore binary solutions that modify the mass-to-age mapping and are consistent with the isolation of LBVs. For the binary scenarios, our crude models suggest that LBVs are rejuvenated stars. They are either the result of mergers or they are mass gainers and received a kick when the primary star exploded. In the merger scenario, if the primary is about 19 solar masses, then the binary has enough time to wander far afield, merge and form a rejuvenated star. In the mass-gainer and kick scenario, we find that LBV isolation is consistent with a wide range of kick velocities, anywhere from 0 to ~ 105 km/s. In either scenario, binarity seems to play a major role in the isolation of LBVs., Comment: 15 pages, 10 figures, 2 tables

We derive an integral condition for core-collapse supernova (CCSN) explosions and use it to construct a new diagnostic of explodability. The fundamental challenge in CCSN theory is to explain how a stalled accretion shock revives to explode a star. In this manuscript, we assume that the shock revival is initiated by the delayed-neutrino mechanism and derive an integral condition for spherically symmetric shock expansion, $v_s > 0$. One of the most useful one-dimensional explosion conditions is the neutrino luminosity and mass-accretion rate ($L_{\nu}-\dot{\mathcal{M}}$) critical curve. Below this curve, steady-state stalled solutions exist, but above this curve, there are no stalled solutions. Burrows & Goshy suggested that the solutions above this curve are dynamic and explosive. In this manuscript, we take one step closer to proving this supposition; we show that all steady solutions above this curve have $v_s > 0$. Assuming that these steady $v_s > 0$ solutions correspond to explosion, we present a new dimensionless integral condition for explosion, $\Psi > 0$. $\Psi$ roughly describes the balance between pressure and gravity, and we show that this parameter is equivalent to the $\tau$ condition used to infer the $L_{\nu}-\dot{\mathcal{M}}$ critical curve. The illuminating difference is that there is a direct relationship between $\Psi$ and $v_s$. Below the critical curve, $\Psi$ may be negative, positive, and zero, which corresponds to receding, expanding, and stalled-shock solutions. At the critical curve, the minimum $\Psi$ solution is zero; above the critical curve, $\Psi_{\rm min} > 0$, and all steady solutions have $v_s > 0$. Using one-dimensional simulations, we confirm our primary assumptions and verify that $\Psi_{\rm min} > 0$ is a reliable and accurate explosion diagnostic., Comment: 18 pages and 12 figures; published in ApJ. Figures 8 & 9 and equation 21 show the main results

Using Hubble Space Telescope (HST) photometry to measure star formation histories, we age-date the stellar populations surrounding supernova remnants (SNRs) in M31 and M33. We then apply stellar evolution models to the ages to infer the corresponding masses for their supernova progenitor stars. We analyze 33 M33 SNR progenitors and 29 M31 SNR progenitors in this work. We then combine these measurements with 53 previously published M31 SNR progenitor measurements to bring our total number of progenitor mass estimates to 115. To quantify the mass distributions, we fit power laws of the form $dN/dM \propto M^{-\alpha}$. Our new, larger sample of M31 progenitors follows a distribution with $\alpha = 4.4\pm 0.4$, and the M33 sample follows a distribution with $\alpha = 3.8^{+0.4}_{-0.5}$. Thus both samples are consistent within the uncertainties, and the full sample across both galaxies gives $\alpha = 4.2\pm 0.3$. Both the individual and full distributions display a paucity of massive stars when compared to a Salpeter initial mass function (IMF), which we would expect to observe if all massive stars exploded as SN that leave behind observable SNR. If we instead fix $\alpha = 2.35$ and treat the maximum mass as a free parameter, we find $M_{max} \sim 35-45M_{sun}$, indicative of a potential maximum cutoff mass for SN production. Our results suggest that either SNR surveys are biased against finding objects in the youngest (<10 Myr old) regions, or the highest mass stars do not produce SNe., Comment: 12 pages, 4 figures, 3 tables, accepted to ApJ

Using HST photometry, we age-date 59 supernova remnants (SNRs) in the spiral galaxy M31 and use these ages to estimate zero-age main sequence masses (MZAMS) for their progenitors. To accomplish this, we create color-magnitude diagrams (CMDs) and use CMD fitting to measure the recent star formation history (SFH) of the regions surrounding cataloged SNR sites. We identify any young coeval population that likely produced the progenitor star and assign an age and uncertainty to that population. Application of stellar evolution models allows us to infer the MZAMS from this age. Because our technique is not contingent on precise location of the progenitor star, it can be applied to the location of any known SNR. We identify significant young SF around 53 of the 59 SNRs and assign progenitor masses to these, representing a factor of 2 increase over currently measured progenitor masses. We consider the remaining 6 SNRs as either probable Type Ia candidates or the result of core-collapse progenitors that have escaped their birth sites. The distribution of recovered progenitor masses is bottom heavy, showing a paucity of the most massive stars. If we assume a single power law distribution, dN/dM proportional to M^alpha, we find a distribution that is steeper than a Salpeter IMF (alpha=-2.35). In particular, we find values of alpha outside the range -2.7 to -4.4 inconsistent with our measured distribution at 95% confidence. If instead we assume a distribution that follows a Salpeter IMF up to some maximum mass, we find that values of M_max greater than 26 Msun are inconsistent with the measured distribution at 95% confidence. In either scenario, the data suggest that some fraction of massive stars may not explode. The result is preliminary and requires more SNRs and further analysis. In addition, we use our distribution to estimate a minimum mass for core collapse between 7.0 and 7.8 Msun., Comment: 24 pages, 14 figures, 2 tables. Accepted to ApJ

The multidimensional character of the hydrodynamics in core-collapse supernova (CCSN) cores is a key facilitator of explosions. Unfortunately, much of this work has necessarily been performed assuming axisymmetry and it remains unclear whether or not this compromises those results. In this work, we present analyses of simplified two- and three-dimensional CCSN models with the goal of comparing the multidimensional hydrodynamics in setups that differ only in dimension. Not surprisingly, we find many differences between 2D and 3D models. While some differences are subtle and perhaps not crucial to understanding the explosion mechanism, others are quite dramatic and make interpreting 2D CCSN models problematic. In particular, we find that imposing axisymmetry artificially produces excess power at the largest spatial scales, power that has been deemed critical in the success of previous explosion models and has been attributed solely to the standing accretion shock instability. Nevertheless, our 3D models, which have an order of magnitude less power on large scales compared to 2D models, explode earlier. Since we see explosions earlier in 3D than in 2D, the vigorous sloshing associated with the large scale power in 2D models is either not critical in any dimension or the explosion mechanism operates differently in 2D and 3D. Possibly related to the earlier explosions in 3D, we find that about 25% of the accreted material spends more time in the gain region in 3D than in 2D, being exposed to more integrated heating and reaching higher peak entropies, an effect we associate with the differing characters of turbulence in 2D and 3D. Finally, we discuss a simple model for the runaway growth of buoyant bubbles that is able to quantitatively account for the growth of the shock radius and predicts a critical luminosity relation., Comment: Submitted to the Astrophysical Journal

Multi-dimensional instabilities have become an important ingredient in core-collapse supernova (CCSN) theory. Therefore, it is necessary to understand the driving mechanism of the dominant instability. We compare our parameterized three-dimensional CCSN simulations with other buoyancy-driven simulations and propose scaling relations for neutrino-driven convection. Through these comparisons, we infer that buoyancy-driven convection dominates post-shock turbulence in our simulations. In support of this inference, we present four major results. First, the convective fluxes and kinetic energies in the neutrino-heated region are consistent with expectations of buoyancy-driven convection. Second, the convective flux is positive where buoyancy actively drives convection, and the radial and tangential components of the kinetic energy are in rough equipartition (i.e. K_r ~ K_{\theta} + K_{\phi}). Both results are natural consequences of buoyancy-driven convection, and are commonly observed in simulations of convection. Third, buoyant driving is balanced by turbulent dissipation. Fourth, the convective luminosity and turbulent dissipation scale with the driving neutrino power. In all, these four results suggest that in neutrino-driven explosions, the multi-dimensional motions are consistent with neutrino-driven convection., Comment: Accepted by the Astrophysical Journal

We investigate the structure of the stalled supernova shock in both 2D and 3D and explore the differences in the effects of neutrino heating and the standing accretion shock instability (SASI). We find that early on the amplitude of the dipolar mode of the shock is factors of 2 to 3 smaller in 3D than in 2D. However, later in both 3D and 2D the monopole and dipole modes start to grow until explosion. Whereas in 2D the (l,m) = (1,0) mode changes sign quasi-periodically, producing the "up-and-down" motion always seen in modern 2D simulations, in 3D this almost never happens. Rather, in 3D when the dipolar mode starts to grow, it grows in magnitude and wanders stochastically in direction until settling before explosion to a particular patch of solid angle. In 2D we find that the amplitude of the dipolar shock deformation separates into two classes. For the first, identified with the SASI and for a wide range of "low" neutrino luminosities, this amplitude remains small and roughly constant. For the other, identified with higher luminosities and neutrino-driven convection, the dipolar amplitude grows sharply. Importantly, it is only for this higher luminosity class that we see neutrino-driven explosions within ~1 second of bounce. Moreover, for the "low" luminosity runs, the power spectra of these dipolar oscillations peak in the 30-50 Hz range associated with advection timescales, while for the high-luminosity runs the power spectra at lower frequencies are significantly more prominent. We associate this enhanced power at lower frequencies with slower convective effects and the secular growth of the dipolar shock amplitude. On the basis of our study, we hypothesize that neutrino-driven buoyant convection should almost always dominate the SASI when the supernova explosion is neutrino-driven., Comment: Accepted to the Astrophysical Journal; updated with additional figures and analysis

Using Hubble Space Telescope (HST) photometry, we characterize the age of the stellar association in the vicinity of supernova (SN) 2011dh and use it to infer the zero-age main sequence mass (M_{ZAMS}) of the progenitor star. We find two distinct and significant star formation events with ages of <6 and 17^{+3}_{-4} Myrs, and the corresponding M_{ZAMS} are >29 and 13^{+2}_{-1} M_{Sun}, respectively. These two bursts represent 18^{+4}_{-9}% (young) and 64^{+10}_{-14}% (old) of the total star formation in the last 50 Myrs. Adopting these fractions as probabilities suggests that the most probable M_{ZAMS} is 13^{+2}_{-1} M_{Sun}. These results are most sensitive to the luminosity function along the well-understood main sequence and are less sensitive to uncertain late-stage stellar evolution. Therefore, they stand even if the progenitor suffered disruptive post-main-sequence evolution (e.g. eruptive mass loss or binary Roche-lobe overflow). Progenitor identification will help to further constrain the appropriate population. Even though pre-explosion images show a yellow supergiant (YSG) at the site of the SN, panchromatic SN light curves suggest a more compact star as the progenitor. In spite of this, our results suggest an association between the YSG and the SN. Not only was the star located at the SN site, but reinforcing an association, the star's bolometric luminosity is consistent with the final evolutionary stage of the 17 Myr old star burst. If the YSG disappears, then M_{ZAMS}=13^{+2}_{-1} M_{Sun}, but if it persists, then our results allow the possibility that the progenitor was an unseen star of >29 M_{Sun}., Comment: 5 pages in emulateapj, 2 figures, accepted by ApJL. Comments are welcome

Simulations of core-collapse supernovae (CCSNe) result in successful explosions once the neutrino luminosity exceeds a critical curve, and recent simulations indicate that turbulence further enables explosion by reducing this critical neutrino luminosity. We propose a theoretical framework to derive this result and take the first steps by deriving the governing mean-field equations. Using Reynolds decomposition, we decompose flow variables into background and turbulent flows and derive self-consistent averaged equations for their evolution. As basic requirements for the CCSN problem, these equations naturally incorporate steady-state accretion, neutrino heating and cooling, non-zero entropy gradients, and turbulence terms associated with buoyant driving, redistribution, and dissipation. Furthermore, analysis of two-dimensional (2D) CCSN simulations validate these Reynolds-averaged equations, and we show that the physics of turbulence entirely accounts for the differences between 1D and 2D CCSN simulations. As a prelude to deriving the reduction in the critical luminosity, we identify the turbulent terms that most influence the conditions for explosion. Generically, turbulence equations require closure models, but these closure models depend upon the macroscopic properties of the flow. To derive a closure model that is appropriate for CCSNe, we cull the literature for relevant closure models and compare each with 2D simulations. These models employ local closure approximations and fail to reproduce the global properties of neutrino-driven turbulence. Motivated by the generic failure of these local models, we propose an original model for turbulence which incorporates global properties of the flow. This global model accurately reproduces the turbulence profiles and evolution of 2D CCSN simulations., Comment: 20 pages in emulateapj, 14 figures, accepted by ApJ

Abridged: Using a suite of progenitor models, neutrino luminosities, and two- dimensional (2D) simulations, we investigate the matter gravitational-wave (GW) emission from postbounce phases of neutrino-driven core-collapse supernovae (CCSNe). The relevant phases are prompt and steady-state convection, the standing accretion shock instability (SASI), and asymmetric explosions. For the stages before explosion, we propose a model for the source of GW emission. Downdrafts of the postshock-convection/SASI region strike the protoneutron star "surface" with large speeds and are decelerated by buoyancy forces. We find that the GW amplitude is set by the magnitude of deceleration and, by extension, the downdraft's speed and the vigor of postshock-convective/SASI motions. However, the characteristic frequencies, which evolve from ~100 Hz after bounce to ~300-400 Hz, are primarily independent of these speeds, but are set by the deceleration timescale, which is in turn set by the buoyancy frequency at the lower boundary of postshock convection. Consequently, the GW characteristic frequencies are dependent upon a combination of core structure attributes, specifically the dense-matter equation of state (EOS) and details that determine the gradients at the boundary, including the accretion-rate history, the EOS at subnuclear densities, and neutrino transport. During explosion, the high frequency signal wanes and is replaced by a strong low frequency, ~10s of Hz, signal that reveals the general morphology of the explosion (i.e. prolate, oblate, or spherical). However, current and near-future GW detectors are sensitive to GW power at frequencies >50 Hz. Therefore, the signature of explosion will be the abrupt reduction of detectable GW emission., Comment: 30 pages in emulateapj, including 15 figures, accepted for print in ApJ. Added figures and text further describing the GW signal during the explosion phase

We present an alternative technique for measuring the precursor masses of transient events in stars undergoing late stage stellar evolution. We use the well-established techniques of stellar population modeling to age-date the stars surrounding the site of the recent transient event in NGC 300 (NGC 300 OT2008-1). The surrounding stars must share a common turnoff mass with the transient, since almost all stars form in stellar clusters that remain physically associated for periods longer than the lifetime of the most massive stars. We find that the precursor of NGC 300 OT2008-1 is surrounded by stars that formed in a single burst between 8-13 Myr ago, with 70% confidence. The transient was therefore likely to be due to a progenitor whose mass falls between the main sequence turnoff mass (12 Msun) and the maximum stellar mass (25 Msun) found for isochrones bounding this age range. We characterize the general applicability of this technique in identifying precursor masses of historic and future transients and supernovae (SNe), noting that it requires neither precursor imaging nor sub-arcsecond accuracy in the position of the transient. It is also based on the well-understood physics of the main sequence, and thus may be a more reliable source of precursor masses than fitting evolutionary tracks to precursor magnitudes. We speculate that if the progenitor mass is close to 17 Msun, there may be a connection between optical transients such as NGC 300 OT2008-1 and the missing type II-P SNe, known as the "red supergiant problem.", Comment: 11 pages, 6 figures, accepted for publication in ApJ; revised to indicate a larger range for mass estimate

In this paper, we describe a new hydrodynamics code for 1D and 2D astrophysical simulations, BETHE-hydro, that uses time-dependent, arbitrary, unstructured grids. The core of the hydrodynamics algorithm is an arbitrary Lagrangian-Eulerian (ALE) approach, in which the gradient and divergence operators are made compatible using the support-operator method. We present 1D and 2D gravity solvers that are finite differenced using the support-operator technique, and the resulting system of linear equations are solved using the tridiagonal method for 1D simulations and an iterative multigrid-preconditioned conjugate-gradient method for 2D simulations. Rotational terms are included for 2D calculations using cylindrical coordinates. We document an incompatibility between a subcell pressure algorithm to suppress hourglass motions and the subcell remapping algorithm and present a modified subcell pressure scheme that avoids this problem. Strengths of this code include a straightforward structure, enabling simple inclusion of additional physics packages, the ability to use a general equation of state, and most importantly, the ability to solve self-gravitating hydrodynamic flows on time-dependent, arbitrary grids. In what follows, we describe in detail the numerical techniques employed and, with a large suite of tests, demonstrate that BETHE-hydro finds accurate solutions with 2$^{nd}$-order convergence., Comment: 51 pages in emulateapj, including 25 figures, replace with version accepted to ApJS, corrected typos and included minor referee's comments

We investigate the criteria for successful core-collapse supernova explosions by the neutrino mechanism. We find that a critical-luminosity/mass-accretion-rate condition distinguishes non-exploding from exploding models in hydrodynamic one-dimensional (1D) and two-dimensional (2D) simulations. We present 95 such simulations that parametrically explore the dependence on neutrino luminosity, mass accretion rate, resolution, and dimensionality. While radial oscillations mediate the transition between 1D accretion (non-exploding) and exploding simulations, the non-radial standing accretion shock instability characterizes 2D simulations. We find that it is useful to compare the average dwell time of matter in the gain region with the corresponding heating timescale, but that tracking the residence time distribution function of tracer particles better describes the complex flows in multi-dimensional simulations. Integral quantities such as the net heating rate, heating efficiency, and mass in the gain region decrease with time in non-exploding models, but for 2D exploding models, increase before, during, and after explosion. At the onset of explosion in 2D, the heating efficiency is $\sim$2% to $\sim$5% and the mass in the gain region is $\sim$0.005 M$_{\sun}$ to $\sim$0.01 M$_{\sun}$. Importantly, we find that the critical luminosity for explosions in 2D is $\sim$70% of the critical luminosity required in 1D. This result is not sensitive to resolution or whether the 2D computational domain is a quadrant or the full 180$^{\circ}$. We suggest that the relaxation of the explosion condition in going from 1D to 2D (and to, perhaps, 3D) is of a general character and is not limited by the parametric nature of this study., Comment: 32 pages in emulateapj, including 17 figures, accepted for publication in ApJ, included changes suggested by the referee