arXiv subjects

Julianne J. Dalcanton

Publications and source records attributed to Julianne J. Dalcanton.

At least 73 records · Page 4Linked to original sources

arXiv2021

Old and New Major Mergers in the SOSIMPLE galaxy, NGC 7135

The simultaneous advancement of high resolution integral field unit spectroscopy and robust full-spectral fitting codes now make it possible to examine spatially-resolved kinematic, chemical composition, and star-formation history from nearby galaxies. We take new MUSE data from the Snapshot Optical Spectroscopic Imaging of Mergers and Pairs for Legacy Exploration (SOSIMPLE) survey to examine NGC 7135. With counter-rotation of gas, disrupted kinematics and asymmetric chemical distribution, NGC 7135 is consistent with an ongoing merger. Though well hidden by the current merger, we are able to distinguish stars originating from an older merger, occurring 6-10 Gyr ago. We further find a gradient in ex-situ material with galactocentric radius, with the accreted fraction rising from 0% in the galaxy centre, to ~7% within 0.6 effective radii.

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arXiv2021

The Panchromatic Hubble Andromeda Treasury: Triangulum Extended Region (PHATTER) I. Ultraviolet to Infrared Photometry of 22 Million Stars in M33

We present panchromatic resolved stellar photometry for 22 million stars in the Local Group dwarf spiral Triangulum (M33), derived from Hubble Space Telescope (HST) observations with the Advanced Camera for Surveys (ACS) in the optical (F475W, F814W), and the Wide Field Camera 3 (WFC3) in the near ultraviolet (F275W, F336W) and near-infrared (F110W, F160W) bands. The large, contiguous survey area covers $\sim$14 square kpc and extends to 3.5 kpc (14 arcmin, or 1.5-2 scale lengths) from the center of M33. The PHATTER observing strategy and photometry technique closely mimic those of the Panchromatic Hubble Andromeda Treasury (PHAT), but with updated photometry techniques that take full advantage of all overlapping pointings (aligned to within $<$5-10 milliarcseconds) and improved treatment of spatially-varying point spread functions. The photometry reaches a completeness-limited depth of F475W$\sim$28.5 in the lowest surface density regions observed in M33 and F475W$\sim$26.5 in the most crowded regions found near the center of M33. We find the young populations trace several relatively tight arms, while the old populations show a clear, looser two-armed structure. We present extensive analysis of the data quality including artificial star tests to quantify completeness, photometric uncertainties, and flux biases. This stellar catalog is the largest ever produced for M33, and is publicly available for download by the community.

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arXiv2020

Three-Dimensional Structure and Dust Extinction in the Small Magellanic Cloud

We examine the three-dimensional structure and dust extinction properties in a ~ 200 pc $\times$ 100 pc region in the southwest bar of the Small Magellanic Cloud (SMC). We model a deep Hubble Space Telescope optical color-magnitude diagram (CMD) of red clump and red giant branch stars to infer the dust extinction and galactic structure. We model the distance distribution of the stellar component with a Gaussian and find a centroid distance of 65.2 kpc (distance modulus $μ$ = 19.07 mag) with a FWHM $\approx$ 11.3 kpc. This large extent along the line of sight reproduces results from previous studies using variable stars and red clump stars. Additionally, we find an offset between the stellar and dust distributions, with the dust on the near side relative to the stars by 3.22 $^{+1.69}_{-1.44}$ kpc, resulting in a 73% reddened fraction of stars. Modeling the dust layer with a log-normal $A_V$ distribution indicates a mean extinction $\langle A_V \rangle$ = 0.41 $\pm$ 0.09 mag. We also calculate $A_V/N_H$ = 3.2 - 4.2 $\times10^{-23}$ mag cm$^2$ H$^{-1}$ which is significantly lower than the Milky Way value but is comparable to previous SMC dust-to-gas ratio measurements. Our results yield the first joint dust extinction and 3D geometry properties in a key region in the SMC. This study demonstrates that CMD modeling can be a powerful tool to simultaneously constrain dust extinction and geometry properties in nearby galaxies.

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arXiv2020

Mapping the Escape Fraction of Ionizing Photons Using Resolved Stars: A Much Higher Escape Fraction for NGC 4214

We demonstrate a new method for measuring the escape fraction of ionizing photons using Hubble Space Telescope imaging of resolved stars in NGC 4214, a local analog of high-redshift starburst galaxies that are thought to be responsible for cosmic reionization. Specifically, we forward model the UV through near-IR spectral energy distributions of $\sim$83,000 resolved stars to infer their individual ionizing flux outputs. We constrain the local escape fraction by comparing the number of ionizing photons produced by stars to the number that are either absorbed by dust or consumed by ionizing the surrounding neutral hydrogen in individual star-forming regions. We find substantial spatial variation in the escape fraction (0-40%). Integrating over the entire galaxy yields a global escape fraction of 25% (+16%/-15%). This value is much higher than previous escape fractions of zero reported for this galaxy. We discuss sources of this apparent tension, and demonstrate that the viewing angle and the 3D ISM geometric effects are the cause. If we assume the NGC 4214 has no internal dust, like many high-redshift galaxies, we find an escape fraction of 59% (an upper-limit for NGC 4214). This is the first non-zero escape fraction measurement for UV-faint (M$_{\rm FUV}$ = -15.9) galaxies at any redshift, and supports the idea that starburst UV-faint dwarf galaxies can provide a sufficient amount of ionizing photons to the intergalactic medium.

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arXiv2020

Constraining the thermally pulsing asymptotic giant branch phase with resolved stellar populations in the Large Magellanic Cloud

Reliable models of the thermally pulsing asymptotic giant branch (TP-AGB) phase are of critical importance across astrophysics, including our interpretation of the spectral energy distribution of galaxies, cosmic dust production, and enrichment of the interstellar medium. With the aim of improving sets of stellar isochrones that include a detailed description of the TP-AGB phase, we extend our recent calibration of the AGB population in the Small Magellanic Cloud (SMC) to the more metal rich Large Magellanic Cloud (LMC). We model the LMC stellar populations with the TRILEGAL code, using the spatially-resolved star formation history derived from the VISTA survey. We characterize the efficiency of the third dredge-up by matching the star counts and the $K_{\rm s}$-band luminosity functions of the AGB stars identified in the LMC. In line with previous findings, we confirm that, compared to the SMC, the third dredge-up in AGB stars of the LMC is somewhat less efficient, as a consequence of the higher metallicity. The predicted range of initial mass of C-rich stars is between $M_{\rm i} \approx 1.7 - 3~\mathrm{M}_{\odot}$ at $Z_{\rm i} = 0.008$. We show how the inclusion of new opacity data in the carbon star spectra will improve the performance of our models. We discuss the predicted lifetimes, integrated luminosities and mass-loss rate distributions of the calibrated models. The results of our calibration are included in updated stellar isochrones publicly available.

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arXiv2020

PHAT XX. AGB stars and other cool giants in M31 star clusters

The presence of AGB stars in clusters provides key constraints for stellar models, as has been demonstrated with historical data from the Magellanic Clouds. In this work, we look for candidate AGB stars in M31 star clusters from the Panchromatic Hubble Andromeda Treasury (PHAT) survey. Our photometric criteria selects stars brighter than the tip of the red giant branch, which includes the bulk of the thermally-pulsing AGB stars as well as early-AGB stars and other luminous cool giants expected in young stellar populations (e.g. massive red supergiants, and intermediate-mass red helium-burning stars). The AGB stars can be differentiated, a posteriori, using the ages already estimated for our cluster sample. 937 candidates are found within the cluster aperture radii, half (450) of which are very likely cluster members. Cross-matching with additional databases reveals two carbon stars and ten secure variables among them. The field-corrected age distribution reveals the presence of young supergiants peaking at ages smaller than 100 Myr, followed by a long tail of AGB stars extending up to the oldest possible ages. This long tail reveals the general decrease in the numbers of AGB stars from initial values of 50e-6/Msun at 100 Myr down to 5e-6/Msun at 10 Gyr. Theoretical models of near-solar metallicity reproduce this general trend, although with localized discrepancies over some age intervals, whose origin is not yet identified. The entire catalogue is released together with finding charts to facilitate follow-up studies.

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arXiv2020

Mass-to-Light Ratios of Spatially Resolved Stellar Populations in M31

A galaxy's stellar mass-to-light ratio ($M_\star/L$) is a useful tool for converting luminosity to stellar mass ($M_\star$). However, the practical utility of $M_\star/L$ inferred from stellar population synthesis (SPS) models is limited by mismatches between the real and assumed models for star formation history (SFH) and dust geometry, both of which vary within galaxies. Here, we measure spatial variations in $M_\star/L$ and their dependence on color, star formation history, and dust across the disk of M31, using a map of $M^\mathrm{CMD}_\star$ derived from color-magnitude diagrams of resolved stars in the Panchromatic Hubble Andromeda Treasury (PHAT) survey. First, we find comparable scatter in $M_\star/L$ for the optical and mid-IR, contrary to the common idea that $M_\star/L$ is less variable in the IR. Second, we confirm that $M_\star/L$ is correlated with color for both the optical and mid-IR and report color vs. $M_\star/L$ relations (CMLRs) in M31 for filters used in the Sloan Digital Sky Survey (SDSS) and Widefield Infrared Survey Explorer (WISE). Third, we show that the CMLR residuals correlate with recent SFH, such that quiescent regions are offset to higher $M_\star/L$ than star-forming regions at a fixed color. The mid-IR CMLR, however, is not linear due to the high scatter of $M_\star/L$ in star-forming regions. Finally, we find a flatter optical CMLR than any SPS-based CMLRs in the literature. We show this is an effect of dust geometry, which is typically neglected but should be accounted for when using optical data to map $M_\star/L$.

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arXiv2020

Stellar Feedback and Resolved Stellar IFU Spectroscopy in the nearby Spiral Galaxy NGC 300

We present MUSE Integral Field Unit (IFU) observations of five individual HII regions in two giant (>100 pc in radius) star-forming complexes in the low-metallicity ($Z$~0.33 $Z_{\odot}$) nearby (D ~ 2 Mpc) dwarf spiral galaxy NGC 300. We combine the IFU data with high spatial resolution HST photometry to demonstrate the extraction of stellar spectra and the classification of individual stars from ground-based data at the distance of 2 Mpc. For the two star-forming complexes, in which no O-type stars had previously been identified, we find a total of 13 newly identified O-type stars in the mass range 15-50 M$_{\odot}$, as well as 4 Wolf-Rayet stars. We use the derived massive stellar content to analyze the impact of stellar feedback on the HII regions. As already found for HII regions in the Magellanic Clouds, the dynamics of the analyzed NGC 300 HII regions are dominated by a combination of the pressure of the ionized gas and stellar winds. By comparing the derived ionized gas mass loading factors to the total gas mass loading factor across the NGC 300 disk, we find that the latter is an order of magnitude higher, either indicating very early evolutionary stages for these HII regions, or being a direct result of the multi-phase nature of feedback-driven bubbles. Moreover, we analyze the relation between the star formation rate and the pressure of the ionized gas as derived from small (<100 pc) scales, as both quantities are systematically overestimated when derived on galactic scales. With the wealth of ongoing and upcoming IFU instruments and programs, this study serves as a pathfinder for the systematic investigation of resolved stellar feedback in nearby galaxies, and it delivers the necessary analysis tools to enable massive stellar content and feedback studies sampling an unprecedented range of HII region properties across entire galaxies in the nearby Universe.

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arXiv2019

Combined Effects of Rotation and Age Spreads on Extended Main Sequence Turn Offs

The extended main sequence turn offs (eMSTOs) of several young to intermediate age clusters are examined in the Magellanic Clouds and the Milky Way. We explore the effects of extended star formation (eSF) and a range of stellar rotation rates on the behavior of the color-magnitude diagram (CMD), paying particular attention to the MSTO. We create synthetic stellar populations based on MESA stellar models to simulate observed Hubble Space Telescope and Gaia star cluster data. We model the effect of rotation as a non-parametric distribution, allowing for maximum flexibility. In our models the slow rotators comprise the blueward, and fast rotators the redward portion of the eMSTO. We simulate data under three scenarios: non-rotating eSF, a range of rotation rates with a single age, and a combination of age and rotation effects. We find that two of the five clusters (the youngest and oldest) favor an age spread, but these also achieve the overall worst fits of all clusters. The other three clusters show comparable statistical evidence between rotation and an age spread. In all five cases, a rotation rate distribution alone is capable of qualitatively matching the observed eMSTO structure. In future work, we aim to compare our predicted Vsin(i) with observations in order to better constrain the physics related to stellar rotation.

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arXiv2019

Star formation at the edge of the Local Group: a rising star formation history in the isolated galaxy WLM

We present the star formation history (SFH) of the isolated (D~970 kpc) Local Group dwarf galaxy WLM measured from color-magnitude diagrams constructed from deep Hubble Space Telescope imaging. Our observations include a central (0.5 $r_h$) and outer field (0.7 $ r_h$) that reach below the oldest main sequence turnoff. WLM has no early dominant episode of star formation: 20% of its stellar mass formed by ~12.5 Gyr ago (z~5). It also has an SFR that rises to the present with 50% of the stellar mass within the most recent 5 Gyr (z<0.7). There is evidence of a strong age gradient: the mean age of the outer field is 5 Gyr older than the inner field despite being only 0.4 kpc apart. Some models suggest such steep gradients are associated with strong stellar feedback and dark matter core creation. The SFHs of real isolated dwarf galaxies and those from the the Feedback In Realistic Environment suite are in good agreement for $M_{\star}(z=0) \sim 10^7-10^9 M_{\odot}$, but in worse agreement at lower masses ($M_{\star}(z=0) \sim 10^5-10^7 M_{\odot}$). These differences may be explainable by systematics in the models (e.g., reionization model) and/or observations (HST field placement). We suggest that a coordinated effort to get deep CMDs between HST/JWST (crowded central fields) and WFIRST (wide-area halo coverage) is the optimal path for measuring global SFHs of isolated dwarf galaxies.

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arXiv2019

Fast and inefficient star formation due to short-lived molecular clouds and rapid feedback

The physics of star formation and the deposition of mass, momentum, and energy into the interstellar medium by massive stars (`feedback') are the main uncertainties in modern cosmological simulations of galaxy formation and evolution. These processes determine the properties of galaxies, but are poorly understood on the $\lesssim$100 pc scale of individual giant molecular clouds (GMCs) resolved in modern galaxy formation simulations. The key question is why the timescale for depleting molecular gas through star formation in galaxies ($t_{\rm dep}\approx 2$ Gyr) exceeds the dynamical timescale of GMCs by two orders of magnitude. Either most of a GMC's mass is converted into stars over many dynamical times, or only a small fraction turns into stars before the GMC is dispersed on a dynamical timescale. Here we report our observation that molecular gas and star formation are spatially de-correlated on GMC scales in the nearby flocculent spiral galaxy NGC300, contrary to their tight correlation on galactic scales. We demonstrate that this de-correlation implies rapid evolutionary cycling between GMCs, star formation, and feedback. We apply a novel statistical method to quantify the evolutionary timeline and find that star formation is regulated by efficient stellar feedback, driving GMC dispersal on short timescales (~1.5 Myr) due to radiation and stellar winds, prior to supernova explosions. This feedback limits GMC lifetimes to about one dynamical timescale (~10 Myr), with integrated star formation efficiencies of only 2-3%. Our findings reveal that galaxies consist of building blocks undergoing vigorous, feedback-driven lifecycles, that vary with the galactic environment and collectively define how galaxies form stars. Systematic applications of this multi-scale analysis to large galaxy samples will provide key input for a predictive, bottom-up theory of galaxy formation and evolution.

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arXiv2019

Spatially Resolved Metal Loss from M31

As galaxies evolve, they must enrich and exchange gas with the surrounding medium, but the timing of these processes and how much gas is involved remain poorly understood. In this work, we leverage metals as tracers of past gas flows to constrain the history of metal ejection and redistribution in M31. This roughly $L*$ galaxy is a unique case where spatially resolved measurements of the gas-phase and stellar metallicity, dust extinction, and neutral ISM gas content are all available, enabling a census of the present metal mass. We combine spatially resolved star formation histories from the Panchromatic Hubble Andromeda Treasury survey with a metal production model to calculate the history of metal production in M31. We find that $1.8\times10^9 \, M_\odot$ of metals, or 62\% of the metal mass formed within $r < 19 \,\mathrm{kpc}$, is missing from the disk in our fiducial model, implying that the M31 disk has experienced significant gaseous outflows over its lifetime. Under a conservative range of model assumptions, we find that between 3\% and 88\% of metals have been lost ($1.9\times10^7 - 6.4\times10^9 \, M_\odot$), so metals are missing even when all model parameters are chosen to favor metal retention. We show that the missing metal mass could be harbored in M31's CGM if the majority of the metals reside in a hot gas phase. Finally, we find that some metal mass produced in the past 1.5 Gyr in the central $\sim5 \,\mathrm{kpc}$ has likely been redistributed to larger radii within the disk.

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arXiv2019

Self-consistent predictions for LIER-like emission lines from post-AGB stars

Early type galaxies (ETGs) frequently show emission from warm ionized gas. These Low Ionization Emission Regions (LIERs) were originally attributed to a central, low-luminosity active galactic nuclei. However, the recent discovery of spatially-extended LIER emission suggests ionization by both a central source and an extended component that follows a stellar-like radial distribution. For passively-evolving galaxies with old stellar populations, hot post-Asymptotic Giant Branch (AGB) stars are the only viable extended source of ionizing photons. In this work, we present the first prediction of LIER-like emission from post-AGB stars that is based on fully self-consistent stellar evolution and photoionization models. We show that models where post-AGB stars are the dominant source of ionizing photons reproduce the nebular emission signatures observed in ETGs, including LIER-like emission line ratios in standard optical diagnostic diagrams and H$α$ equivalent widths of order 0.1-3 angstroms. We test the sensitivity of LIER-like emission to the details of post-AGB models, including the mass loss efficiency and convective mixing efficiency, and show that line strengths are relatively insensitive to post-AGB timescale variations. Finally, we examine the UV-optical colors of the models and the stellar populations responsible for the UV-excess observed in some ETGs. We find that allowing as little as 3% of the HB population to be uniformly distributed to very hot temperatures (30,000 K) produces realistic UV colors for old, quiescent ETGs.

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arXiv2019

The Masses of Supernova Remnant Progenitors in M83

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.

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arXiv2019

Constraining the thermally-pulsing asymptotic giant branch phase with resolved stellar populations in the Small Magellanic Cloud

The thermally-pulsing asymptotic giant branch (TP-AGB) experienced by low- and intermediate-mass stars is one of the most uncertain phases of stellar evolution and the models need to be calibrated with the aid of observations. To this purpose, we couple high-quality observations of resolved stars in the Small Magellanic Cloud (SMC) with detailed stellar population synthesis simulations computed with the TRILEGAL code. The strength of our approach relies on the detailed spatially-resolved star formation history of the SMC, derived from the deep near-infrared photometry of the VISTA survey of the Magellanic Clouds, as well as on the capability to quickly and accurately explore a wide variety of parameters and effects with the COLIBRI code for the TP-AGB evolution. Adopting a well-characterized set of observations -- star counts and luminosity functions -- we set up a calibration cycle along which we iteratively change a few key parameters of the TP-AGB models until we eventually reach a good fit to the observations. Our work leads to identify two best-fitting models that mainly differ in the efficiencies of the third dredge-up and mass loss in TP-AGB stars with initial masses larger than about 3 M$_{\odot}$. On the basis of these calibrated models we provide a full characterization of the TP-AGB stellar population in the SMC in terms of stellar parameters (initial masses, C/O ratios, carbon excess, mass-loss rates). Extensive tables of isochrones including these improved models are publicly available.

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arXiv2018

Asymmetric Drift in the Andromeda Galaxy (M31) as a Function of Stellar Age

We analyze the kinematics of Andromeda's disk as a function of stellar age by using photometry from the Panchromatic Hubble Andromeda Treasury (PHAT) survey and spectroscopy from the Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo (SPLASH) survey. We use HI 21-cm and CO ($\rm J=1 \rightarrow 0$) data to examine the difference between the deprojected rotation velocity of the gas and that of the stars. We divide the stars into four stellar age bins, from shortest lived to longest lived: massive main sequence stars (0.03 Gyr), more luminous intermediate mass asymptotic giant branch (AGB) stars (0.4 Gyr), less luminous intermediate mass AGB stars (2 Gyr), and low mass red giant branch stars (4 Gyr). There is a clear correlation between the offset of the stellar and the gas rotation velocity, or the asymmetric drift: the longer lived populations lag farther behind the gas than short lived populations. We also examine possible causes of the substructure in the rotation curves and find that the most significant cause of scatter in the rotation curves comes from the tilted ring model being an imperfect way to account for the multiple warps in Andromeda's disk.

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arXiv2018

Comparing Chandra and Hubble in the Northern Disk of M31

The X-ray source populations within galaxies are typically difficult to identify and classify from X-ray data alone. We are able to break through this barrier by combining deep new Chandra ACIS-I observations with extensive Hubble Space Telescope imaging from the PHAT survey of the M31 disk. We detect 373 X-ray sources down to 0.35-8.0 keV flux of 10$^{-15}$ erg cm$^{-2}$ s$^{-1}$ over 0.4 square degrees, 170 of which are reported for the first time. We identify optical counterpart candidates for 188 of the 373 sources, after using the HST data to correct the absolute astrometry of our Chandra imaging to 0.1$"$. While 58 of these 188 are associated with point sources potentially in M31, over half (107) of the counterpart candidates are extended background galaxies, 5 are star clusters, 12 are foreground stars, and 6 are supernova remnants. Sources with no clear counterpart candidate are most likely to be undetected background galaxies and low-mass X-ray binaries in M31. The 58 point sources that are not consistent with foreground stars are bright enough that they could be high mass stars in M31; however, all but 8 have optical colors inconsistent with single stars, suggesting that many could be background galaxies or binary counterparts. For point-like counterparts, we examine the star formation history of the surrounding stellar populations to look for a young component that could be associated with a high mass X-ray binary. For the 40 point-like counterpart candidates associated with young populations, we find that their age distribution has two peaks at 15-20 Myr and 40-50 Myr. If we only consider the 8 counterpart candidates with typical high-mass main sequence optical star colors, their age distribution peaks mimic those of the sample of 40. Finally, we find that intrinsic faintness, and not extinction, is the main limitation for finding further counterpart candidates.

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arXiv2018

Progenitor Mass Distribution for Core-Collapse Supernova Remnants in M31 and M33

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 $α= -2.96^{+0.45}_{-0.25}$, 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 ($α$ = -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.

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