arXiv subjects

Mark R. Krumholz

Publications and source records attributed to Mark R. Krumholz.

At least 181 records · Page 10Linked to original sources

arXiv2016

Notes on Star Formation

This book provides an introduction to the field of star formation at a level suitable for graduate students or advanced undergraduates in astronomy or physics. The structure of the book is as follows. The first two chapters begin with a discussion of observational techniques, and the basic phenomenology they reveal. The goal is to familiarize students with the basic techniques that will be used throughout, and to provide a common vocabulary for the rest of the book. The next five chapters provide a similar review of the basic physical processes that are important for star formation. Again, the goal is to provide a basis for what follows. The remaining chapters discuss star formation over a variety of scales, starting with the galactic scale and working down to the scales of individual stars and their disks. The book concludes with a brief discussion of the clearing of disks and the transition to planet formation. The book includes five problem sets, complete with solutions.

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arXiv2016

Enhanced Momentum Feedback from Clustered Supernovae

Young stars typically form in star clusters, so the supernovae (SNe) they produce are clustered in space and time. This clustering of SNe may alter the momentum per SN deposited in the interstellar medium (ISM) by affecting the local ISM density, which in turn affects the cooling rate. We study the effect of multiple SNe using idealized 1D hydrodynamic simulations which explore a large parameter space of the number of SNe, and the background gas density and metallicity. The results are provided as a table and an analytic fitting formula. We find that for clusters with up to ~100 SNe the asymptotic momentum scales super-linearly with the number of SNe, resulting in a momentum per SN that can be an order of magnitude larger than for a single SN, with a maximum efficiency for clusters with 10-100 SNe. We argue that additional physical processes not included in our simulations -- self-gravity, breakout from a galactic disk, and galactic shear -- can slightly reduce the momentum enhancement from clustering, but the average momentum per SN still remains a factor of 4 larger than the isolated SN value when averaged over a realistic cluster mass function for a star-forming galaxy. We conclude with a discussion of the possible role of mixing between hot and cold gas, induced by multi-dimensional instabilities or preexisting density variations, as a limiting factor in the buildup of momentum by clustered SNe, and suggest future numerical experiments to explore these effects.

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arXiv2016

The Bursty Star Formation Histories of Low-mass Galaxies at $0.4<z<1$ Revealed by Star Formation Rates Measured from H$β$ and FUV

We investigate the burstiness of star formation histories (SFHs) of galaxies at $0.4<z<1$ by using the ratio of star formation rates (SFRs) measured from H$β$ and FUV (1500 Å) (H$β$--to--FUV ratio). Our sample contains 164 galaxies down to stellar mass (M*) of $10^{8.5} M_\odot$ in the CANDELS GOODS-N region, where Team Keck Redshift Survey DEIMOS spectroscopy and HST/WFC3 F275W images from CANDELS and Hubble Deep UV Legacy Survey are available. When the {\it ratio} of H$β$- and FUV-derived SFRs is measured, dust extinction correction is negligible (except for very dusty galaxies) with the Calzetti attenuation curve. The H$β$--to--FUV ratio of our sample increases with M* and SFR. The median ratio is $\sim$0.7 at M*$\sim10^{8.5} M_\odot$ (or SFR$\sim 0.5 M_\odot/yr$) and increases to $\sim$1 at M*$\sim10^{10} M_\odot$ (or SFR $\sim 10 M_\odot/yr$). At M*$<10^{9.5} M_\odot$, our median H$β$--to--FUV ratio is lower than that of local galaxies at the same M*, implying a redshift evolution. Bursty SFH on a timescale of a few tens of megayears on galactic scales provides a plausible explanation of our results, and the importance of the burstiness increases as M* decreases. Due to sample selection effects, our H$β$--to--FUV ratio may be an upper limit of the true value of a complete sample, which strengthens our conclusions. Other models, e.g., non-universal initial mass function or stochastic star formation on star cluster scales, are unable to plausibly explain our results.

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arXiv2016

Instability of Supersonic Cold Streams Feeding Galaxies I: Linear Kelvin-Helmholtz Instability with Body Modes

Massive galaxies at high redshift are predicted to be fed from the cosmic web by narrow, dense, cold streams. These streams penetrate supersonically through the hot medium encompassed by a stable shock near the virial radius of the dark-matter halo. Our long-term goal is to explore the heating and dissipation rate of the streams and their fragmentation and possible breakup, in order to understand how galaxies are fed, and how this affects their star-formation rate and morphology. We present here the first step, where we analyze the linear Kelvin-Helmholtz instability (KHI) of a cold, dense slab or cylinder flowing through a hot, dilute medium in the transonic regime. The current analysis is limited to the adiabatic case with no gravity and assuming equal pressure in the stream and the medium. By analytically solving the linear dispersion relation, we find a transition from a dominance of the familiar rapidly growing surface modes in the subsonic regime to more slowly growing body modes in the supersonic regime. The system is parameterized by three parameters: the density contrast between the stream and the medium, the Mach number of stream velocity with respect to the medium, and the stream width with respect to the halo virial radius. We find that a realistic choice for these parameters places the streams near the mode transition, with the KHI exponential-growth time in the range 0.01-10 virial crossing times for a perturbation wavelength comparable to the stream width. We confirm our analytic predictions with idealized hydrodynamical simulations. Our linear-KHI estimates thus indicate that KHI may in principle be effective in the evolution of streams by the time they reach the galaxy. More definite conclusions await the extension of the analysis to the nonlinear regime and the inclusion of cooling, thermal conduction, the halo potential well, self-gravity and magnetic fields.

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arXiv2016

An Unstable Truth: How Massive Stars get their Mass

The pressure exerted by massive stars' radiation fields is an important mechanism regulating their formation. Detailed simulation of massive star formation therefore requires an accurate treatment of radiation. However, all published simulations have either used a diffusion approximation of limited validity; have only been able to simulate a single star fixed in space, thereby suppressing potentially-important instabilities; or did not provide adequate resolution at locations where instabilities may develop. To remedy this we have developed a new, highly accurate radiation algorithm that properly treats the absorption of the direct radiation field from stars and the re-emission and processing by interstellar dust. We use our new tool to perform three-dimensional radiation-hydrodynamic simulations of the collapse of massive pre-stellar cores with laminar and turbulent initial conditions and properly resolve regions where we expect instabilities to grow. We find that mass is channeled to the stellar system via gravitational and Rayleigh-Taylor (RT) instabilities, in agreement with previous results using stars capable of moving, but in disagreement with methods where the star is held fixed or with simulations that do not adequately resolve the development of RT instabilities. For laminar initial conditions, proper treatment of the direct radiation field produces later onset of instability, but does not suppress it entirely provided the edges of radiation-dominated bubbles are adequately resolved. Instabilities arise immediately for turbulent pre-stellar cores because the initial turbulence seeds the instabilities. Our results suggest that RT features are significant and should be present around accreting massive stars throughout their formation.

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arXiv2016

Hybrid Adaptive Ray-Moment Method (HARM$^2$): A Highly Parallel Method for Radiation Hydrodynamics on Adaptive Grids

We present a highly-parallel multi-frequency hybrid radiation hydrodynamics algorithm that combines a spatially-adaptive long characteristics method for the radiation field from point sources with a moment method that handles the diffuse radiation field produced by a volume-filling fluid. Our Hybrid Adaptive Ray-Moment Method (HARM$^2$) operates on patch-based adaptive grids, is compatible with asynchronous time stepping, and works with any moment method. In comparison to previous long characteristics methods, we have greatly improved the parallel performance of the adaptive long-characteristics method by developing a new completely asynchronous and non-blocking communication algorithm. As a result of this improvement, our implementation achieves near-perfect scaling up to $\mathcal{O}(10^3)$ processors on distributed memory machines. We present a series of tests to demonstrate the accuracy and performance of the method.

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arXiv2016

Chemistry and radiative shielding in star forming galactic disks

To understand the conditions under which dense, molecular gas is able to form within a galaxy, we post-process a series of three-dimensional galactic-disk-scale simulations with ray-tracing based radiative transfer and chemical network integration to compute the equilibrium chemical and thermal state of the gas. In performing these simulations we vary a number of parameters, such as the ISRF strength, vertical scale height of stellar sources, cosmic ray flux, to gauge the sensitivity of our results to these variations. Self-shielding permits significant molecular hydrogen (H2) abundances in dense filaments around the disk midplane, accounting for approximately ~10-15% of the total gas mass. Significant CO fractions only form in the densest, n>~10^3 cm^-3, gas where a combination of dust, H2, and self-shielding attenuate the FUV background. We additionally compare these ray-tracing based solutions to photochemistry with complementary models where photo-shielding is accounted for with locally computed prescriptions. With some exceptions, these local models for the radiative shielding length perform reasonably well at reproducing the distribution and amount of molecular gas as compared with a detailed, global ray tracing calculation. Specifically, an approach based on the Jeans Length with a T=40K temperature cap performs the best in regards to a number of different quantitative measures based on the H2 and CO abundances.

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arXiv2016

What Physics Determines the Peak of the IMF? Insights from the Structure of Cores in Radiation-Magnetohydrodynamic Simulations

As star-forming clouds collapse, the gas within them fragments to ever-smaller masses. Naively one might expect this process to continue down to the smallest mass that is able to radiate away its binding energy on a dynamical timescale, the opacity limit for fragmentation, at $\sim 0.01$ $M_\odot$. However, the observed peak of the initial mass function (IMF) lies a factor of $20-30$ higher in mass, suggesting that some other mechanism halts fragmentation before the opacity limit is reached. In this paper we analyse radiation-magnetohydrodynamic simulations of star cluster formation in typical Milky Way environments in order to determine what physical process limits fragmentation in them. We examine the regions in the vicinity of stars that form in the simulations to determine the amounts of mass that are prevented from fragmenting by thermal and magnetic pressure. We show that, on small scales, thermal pressure enhanced by stellar radiation heating is the dominant mechanism limiting the ability of the gas to further fragment. In the brown dwarf mass regime, $\sim 0.01$ $M_\odot$, the typical object that forms in the simulations is surrounded by gas whose mass is several times its own that is unable to escape or fragment, and instead is likely to accrete. This mechanism explains why $\sim 0.01$ $M_\odot$ objects are rare: unless an outside agent intervenes (e.g., a shock strips away the gas around them), they will grow by accreting the warmed gas around them. In contrast, by the time stars grow to masses of $\sim 0.2$ $M_\odot$, the mass of heated gas is only tens of percent of the central star mass, too small to alter its final mass by a large factor. This naturally explains why the IMF peak is at $\sim 0.2$ $M_\odot$.

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arXiv2016

Mass Transport and Turbulence in Gravitationally Unstable Disk Galaxies II: The Effects of Star Formation Feedback

Self-gravity and stellar feedback are capable of driving turbulence and transporting mass and angular momentum in disk galaxies, but the balance between them is not well understood. In the previous paper in this series, we showed that gravity alone can drive turbulence in galactic disks, regulate their Toomre $Q$ parameters to $\sim$ 1, and transport mass inwards at a rate sufficient to fuel star formation in the centers of present-day galaxies. In this paper we extend our models to include the effects of star formation feedback. We show that feedback suppresses galaxies' star formation rates by a factor of $\sim$ 5 and leads to the formation of a multi-phase atomic and molecular ISM. Both the star formation rate and the phase balance produced in our simulations agree well with observations of nearby spirals. After our galaxies reach steady state, we find that the inclusion of feedback actually lowers the gas velocity dispersion slightly compared to the case of pure self-gravity, and also slightly reduces the rate of inward mass transport. Nevertheless, we find that, even with feedback included, our galactic disks self-regulate to $Q$ $\sim$ 1, and transport mass inwards at a rate sufficient to supply a substantial fraction of the inner disk star formation. We argue that gravitational instability is therefore likely to be the dominant source of turbulence and transport in galactic disks, and that it is responsible for fueling star formation in the inner parts of galactic disks over cosmological times.

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arXiv2016

Suppression of star formation in dwarf galaxies by grain photoelectric feedback

Photoelectric heating has long been recognized as the primary source of heating for the neutral interstellar medium. Simulations of spiral galaxies found some indication that photoelectric heating could suppress star formation. However, simulations that include photoelectric heating have typically found that it has little effect on the rate of star formation in either spiral galaxies or dwarfs suggesting that supernovae and not photoelectric heating are responsible for setting the star formation law in galaxies. This result is in tension with recent work indicating that a star formation law that depends on galaxy metallicity, as expected for photoelectric heating but not for supernovae, reproduces the present-day galaxy population better than a metallicity-independent one. Here we report a series of simulations of dwarf galaxies, where the effects of both photoelectric heating and supernovae are expected to be strongest. We simultaneously include space- and time-dependent photoelectric heating, and we resolve the Sedov phase of every supernova blast wave, allowing us to make a direct measurement of the relative importance of momentum injection by supernovae and dust heating by far ultraviolet (FUV) photons in suppressing star formation. We find that supernovae are unable to account for the long observed gas depletion times in dwarf galaxies. Instead, ordinary photoelectric heating is the dominant means by which dwarf galaxies regulate their star formation rate at any given time, suppressing the star formation rate by more than an order of magnitude relative to simulations with only supernovae.

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arXiv2016

Is Turbulence in the Interstellar Medium Driven by Feedback or Gravity? An Observational Test

Galaxies' interstellar media (ISM) are observed to be supersonically-turbulent, but the ultimate power source that drives turbulent motion remains uncertain. The two dominant models are that the turbulence is driven by star formation feedback and/or that it is produced by gravitational instability in the gas. Here we show that, while both models predict that the galaxies' ISM velocity dispersions will be positively correlated with their star formation rates, the forms of the correlation predicted by these two models are subtly but measurably different. A feedback-driven origin for the turbulence predicts a velocity dispersion that rises more sharply with star formation rate, and that does not depend on the gas fraction (i.e. $\dot{M}_* \propto σ^2$), while a gravity-driven model yields a shallower rise and a strong dependence on gas fraction (i.e. $\dot{M}_* \propto f_g^2 σ$). We compare the models to a collection of data on local and high-redshift galaxies culled from the literature, and show that the correlation expected for gravity-driven turbulence is a better match to the observations than a feedback-driven model. This suggests that gravity is the ultimate source of ISM turbulence, at least in the rapidly-star-forming, high velocity dispersion galaxies for which our test is most effective. We conclude by discussing the limitations of the present data set, and the prospects for future measurements to enable a more definitive test of the two models.

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arXiv2016

The Necessity of Feedback Physics in Setting the Peak of the Initial Mass Function

A popular theory of star formation is gravito-turbulent fragmentation, in which self-gravitating structures are created by turbulence-driven density fluctuations. Simple theories of isothermal fragmentation successfully reproduce the core mass function (CMF) which has a very similar shape to the initial mass function (IMF) of stars. However, numerical simulations of isothermal turbulent fragmentation thus far have not succeeded in identifying a fragment mass scale that is independent of the simulation resolution. Moreover, the fluid equations for magnetized, self-gravitating, isothermal turbulence are scale-free, and do not predict any characteristic mass. In this paper we show that, although an isothermal self-gravitating flow does produce a CMF with a mass scale imposed by the initial conditions, this scale changes as the parent cloud evolves. In addition, the cores that form undergo further fragmentation and after sufficient time forget about their initial conditions, yielding a scale-free pure power-law distribution $\mathrm{d} N/\mathrm{d} M\propto M^{-2}$ for the stellar IMF. We show that this problem can be alleviated by introducing additional physics that provides a termination scale for the cascade. Our candidate for such physics is a simple model for stellar radiation feedback. Radiative heating, powered by accretion onto forming stars, arrests the fragmentation cascade and imposes a characteristic mass scale that is nearly independent of the time-evolution or initial conditions in the star-forming cloud, and that agrees well with the peak of the observed IMF. In contrast, models that introduce a stiff equation of state for denser clouds but that do not explicitly include the effects of feedback do not yield an invariant IMF.

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arXiv2015

Sub-Eddington Star-Forming Regions are Super-Eddington: Momentum Driven Outflows from Supersonic Turbulence

We show that the turbulent gas in the star-forming regions of galaxies is unstable to wind formation via momentum deposition by radiation pressure or other momentum sources like supernova explosions, even if the system is below the average Eddington limit. This conclusion follows from the fact that the critical momentum injection rate per unit mass for unbinding gas from a self-gravitating system is proportional to the gas surface density and that a turbulent medium presents a broad distribution of column densities to the sources. For an average Eddington ratio of ~0.1 and for turbulent Mach numbers >30, we find that ~1% of the gas is ejected per dynamical timescale at velocities larger than the local escape velocity. Because of the lognormal shape of the surface density distribution, the mass loss rate is highly sensitive to the average Eddington ratio, reaching 20-40% of the gas mass per dynamical time for =1. Using this model we find a large scatter in the mass-loading factor for star-forming galaxies, ranging from 0.001-10, but with significant uncertainties. Implications for the efficiency of star formation in giant molecular clouds are highlighted. For radiation pressure feedback alone, we find an increasing star formation efficiency as a function of initial gas surface density. Uncertainties are discussed.

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arXiv2015

Mass Transport and Turbulence in Gravitationally Unstable Disk Galaxies. I: The Case of Pure Self-Gravity

The role of gravitational instability-driven turbulence in determining the structure and evolution of disk galaxies, and the extent to which gravity rather than feedback can explain galaxy properties, remains an open question. To address it, we present high resolution adaptive mesh refinement simulations of Milky Way-like isolated disk galaxies, including realistic heating and cooling rates and a physically motivated prescription for star formation, but no form of star formation feedback. After an initial transient, our galaxies reach a state of fully-nonlinear gravitational instability. In this state, gravity drives turbulence and radial inflow. Despite the lack of feedback, the gas in our galaxy models shows substantial turbulent velocity dispersions, indicating that gravitational instability alone may be able to power the velocity dispersions observed in nearby disk galaxies on 100 pc scales. Moreover, the rate of mass transport produced by this turbulence approaches $\sim 1$ $M_\odot$ yr$^{-1}$ for Milky Way-like conditions, sufficient to fully fuel star formation in the inner disks of galaxies. In a companion paper we add feedback to our models, and use the comparison between the two cases to understand what galaxy properties depend sensitively on feedback, and which can be understood as the product of gravity alone. All of the code, initial conditions, and simulation data for our model are publicly available.

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arXiv2015

Star Cluster Properties in Two LEGUS Galaxies Computed with Stochastic Stellar Population Synthesis Models

We investigate a novel Bayesian analysis method, based on the Stochastically Lighting Up Galaxies (slug) code, to derive the masses, ages, and extinctions of star clusters from integrated light photometry. Unlike many analysis methods, slug correctly accounts for incomplete IMF sampling, and returns full posterior probability distributions rather than simply probability maxima. We apply our technique to 621 visually-confirmed clusters in two nearby galaxies, NGC 628 and NGC 7793, that are part of the Legacy Extragalactic UV Survey (LEGUS). LEGUS provides Hubble Space Telescope photometry in the NUV, U, B, V, and I bands. We analyze the sensitivity of the derived cluster properties to choices of prior probability distribution, evolutionary tracks, IMF, metallicity, treatment of nebular emission, and extinction curve. We find that slug's results for individual clusters are insensitive to most of these choices, but that the posterior probability distributions we derive are often quite broad, and sometimes multi-peaked and quite sensitive to the choice of priors. In contrast, the properties of the cluster population as a whole are relatively robust against all of these choices. We also compare our results from slug to those derived with a conventional non-stochastic fitting code, Yggdrasil. We show that slug's stochastic models are generally a better fit to the observations than the deterministic ones used by Yggdrasil. However, the overall properties of the cluster populations recovered by both codes are qualitatively similar.

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arXiv2015

Simulated Photoevaporative Mass Loss from Hot Jupiters in 3D

Ionizing stellar photons heat the upper regions of planetary atmospheres, driving atmospheric mass loss. Gas escaping from several hot, hydrogen-rich planets has been detected using UV and X-ray transmission spectroscopy. Because these planets are tidally locked, and thus asymmetrically irradiated, escaping gas is unlikely to be spherically symmetric. In this paper, we focus on the effects of asymmetric heating on local outflow structure. We use the Athena code for hydrodynamics to produce 3D simulations of hot Jupiter mass loss that jointly model wind launching and stellar heating via photoionization. Our fiducial planet is an inflated, hot Jupiter with radius $R_p=2.14 R_{\rm Jup}$ and mass $M_p = 0.53 M_{\rm Jup}$. We irradiate the initially neutral, atomic hydrogen atmosphere with 13.6 eV photons and compute the outflow's ionization structure. There are clear asymmetries in the atmospheric outflow, including a neutral shadow on the planet's nightside. Given an incident ionizing UV flux comparable to that of the Sun, we find a steady-state mass loss rate of ~$2\times10^{10}$ g s$^{-1}$. The total mass loss rate and the outflow substructure along the substellar ray show good agreement with earlier 1D models, for two different fluxes. Our 3D data cube can be used to generate the outflow's extinction spectrum during transit. As a proof of concept, we find absorption of stellar Lyman-alpha at Doppler-shifted velocities of up to $\pm 50$ km s$^{-1}$. Our work provides a starting point for further 3D models that can be used to predict observable signatures of hot Jupiter mass loss.

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arXiv2015

A Dynamical Model for the Formation of Gas Rings and Episodic Starbursts Near Galactic Centres

We develop a simple dynamical model for the evolution of gas in the centres of barred spiral galaxies, using the Milky Way's Central Molecular Zone (CMZ, i.e., the central few hundred pc) as a case study. We show that, in the presence of a galactic bar, gas in a disc in the central regions of a galaxy will be driven inwards by angular momentum transport induced by acoustic instabilities within the bar's inner Lindblad resonance. This transport process drives turbulence within the gas that temporarily keeps it strongly gravitationally stable and prevents the onset of rapid star formation. However, at some point the rotation curve must transition from approximately flat to approximately solid body, and the resulting reduction in shear reduces the transport rates and causes gas to build up, eventually producing a gravitationally-unstable region that is subject to rapid and violent star formation. For the observed rotation curve of the Milky Way, the accumulation happens $\sim 100$ pc from the centre of the Galaxy, in good agreement with the observed location of gas clouds and young star clusters in the CMZ. The characteristic timescale for gas accumulation and star formation is of order $10-20$ Myr. We argue that similar phenomena should be ubiquitous in other barred spiral galaxies.

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arXiv2015

SLUG -- Stochastically Lighting Up Galaxies. III: A Suite of Tools for Simulated Photometry, Spectroscopy, and Bayesian Inference with Stochastic Stellar Populations

Stellar population synthesis techniques for predicting the observable light emitted by a stellar population have extensive applications in numerous areas of astronomy. However, accurate predictions for small populations of young stars, such as those found in individual star clusters, star-forming dwarf galaxies, and small segments of spiral galaxies, require that the population be treated stochastically. Conversely, accurate deductions of the properties of such objects also requires consideration of stochasticity. Here we describe a comprehensive suite of modular, open-source software tools for tackling these related problems. These include: a greatly-enhanced version of the slug code introduced by da Silva et al. (2012), which computes spectra and photometry for stochastically- or deterministically-sampled stellar populations with nearly-arbitrary star formation histories, clustering properties, and initial mass functions; cloudy_slug, a tool that automatically couples slug-computed spectra with the cloudy radiative transfer code in order to predict stochastic nebular emission; bayesphot, a general-purpose tool for performing Bayesian inference on the physical properties of stellar systems based on unresolved photometry; and cluster_slug and sfr_slug, a pair of tools that use bayesphot on a library of slug models to compute the mass, age, and extinction of mono-age star clusters, and the star formation rate of galaxies, respectively. The latter two tools make use of an extensive library of pre-computed stellar population models, which are included the software. The complete package is available at http://www.slugsps.com.

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