Models Of Star Formation History Research Articles

Time Delay of Fast Radio Burst Population with Respect to the Star Formation History

In spite of significant progress in the research of fast radio bursts (FRBs) in recent decades, their origin is still under extensive debate. Investigation of the population of FRBs can provide new insight into this interesting problem. In this paper, based on the first Canadian Hydrogen Intensity Mapping Experiment (CHIME)/FRB catalog, we construct a Bayesian framework to analyze the FRB population, with the selection effect of the CHIME telescope being properly taken into account. The energy function is modeled as the power law with an exponential cutoff. Four redshift distribution models are considered, i.e., the star formation history (SFH) model, and three time-delayed models (Gaussian delay, log-normal delay, and power-law delay). The free parameters are simultaneously constrained using the Bayesian inference method, and the Bayesian information criterion (BIC) is used in model comparison. According to the BIC, the log-normal delay model fits the data best. The power-law delay model and Gaussian delay model can also give reasonable fits, although they are not as good as the log-normal delay model. However, the SFH model is strongly disfavored compared with the three time-delayed models. The energy function is tightly constrained and is almost independent of the redshift models, with the best-fitting power-law index α ≈ 1.8 and cut-off energy log(Ec/erg)≈42 . The FRB population shows on average a 3 ∼ 5 billion yr time delay with respect to the SFH. Therefore, the hypothesis that the FRB population traces the SFH is conclusively ruled out.

Revised Constraints on the Fast Radio Burst Population from the First CHIME/FRB Catalog

In this paper, we investigate the fast radio burst (FRB) population using the first CHIME/FRB catalog. We first reconstruct the extragalactic dispersion measure–redshift relation (DME–z relation) from well-localized FRBs, then use it to infer the redshift and isotropic energy of the first CHIME/FRB catalog. The intrinsic energy distribution is modeled by the power law with an exponential cutoff, and the selection effect of the CHIME telescope is modeled by a two-parametric function of specific fluence. For the intrinsic redshift distribution, the star formation history (SFH) model and five other SFH-related models are considered. We construct the joint likelihood of fluence, energy, and redshift, and all the free parameters are constrained simultaneously using the Bayesian inference method. The Bayesian information criterion (BIC) is used to choose the model that best matches the observational data. For comparison, we fit our models with two data samples, i.e., the Full sample and the Gold sample. The power-law index and cutoff energy are tightly constrained to be 1.8 ≲ α ≲ 1.9 and log(Ec/erg)≈42 , which are almost independent of the redshift distribution model and the data sample we choose. The parameters involving the selection effect strongly depend on the data sample but are insensitive to the redshift distribution model. According to BIC, the pure SFH model is strongly disfavored by both the Full sample and Gold sample. For the other five SFH-related redshift distribution models, most of them can match the data well if the parameters are properly chosen. Therefore, with the present data, it is still premature to draw a conclusion on the FRB population.

Spectra of axions emitted from main sequence stars

We compute the detailed energy spectra of axions with two-photon coupling produced in stellar cores over a wide range of stellar masses. We focus on main sequence stars and base our calculations on the stellar interior profiles from MESA, for which we provide simple fits in an appendix. The obtained stellar axion spectra, combined with recent models of star formation history and stellar initial mass function, enable us to estimate the properties of the diffuse axion background sourced by all the stars in the universe. The fluxes of this stellar axion background and its decay photons are subdominant to but can in principle be disentangled from those expected from the Sun and the early universe based on their different spectral and spatial profiles.

The cosmological star formation history from the Local Cosmological Volume of galaxies and constraints on the matter homogeneity

ABSTRACT The Lilly–Madau plot is commonly interpreted as the history of the cosmic star formation of the Universe by showing the co-moving star formation rate density (SFRD) over cosmic time. Therefore, the Lilly–Madau plot is sensitive not only to the star formation history (SFH) but also to the number density of galaxies. Assessing the Catalogue of Neighbouring Galaxies, we reconstruct the SFHs of galaxies located in the Local Cosmological Volume (LV) based on delayed-τ and power-law SFH models. Galaxies with stellar masses of $M_{*} \gtrsim 10^{10}\, {\rm M_{\odot }}$ typically evolve according to the delayed-τ model by having first increasing followed by exponentially declining SFRs, while the majority of less massive star-forming galaxies have an almost constant or increasing SFH. Deducing the cosmic SFRD evolution of the LV reveals that the SFHs of local galaxies are inconsistent with the Lilly–Madau plot. The SFRDs of the LV are significantly lower at redshifts of $z \lesssim 3$ underestimating the Lilly–Madau peak at z = 1.86 by a factor of 2.16 ± 0.32 (delayed-τ model) and 5.90 ± 0.88 (power-law model). Assuming the delayed-τ model for galaxies with $M_{*} \ge 10^{10}\, {\rm M_{\odot }}$ and a power-law model for less massive galaxies, the SFRD is 2.22 ± 0.33 lower than measured at z = 1.86. This inconsistency between the evolution of the local and global SFRD has cosmological implications. Since the Lilly–Madau plot also constrains the cosmological matter field, the near-constancy of SFHs of LV galaxies could imply that the peak of the Lilly–Madau plot at z = 1.86 is the imprint of an ≈5 co-moving Gpc-scale inhomogeneity.

Constraints on Fluctuating Star Formation Rates for Intermediate-mass Galaxies with Hα and UV Luminosities

We study the recent star formation histories (SFHs) of 575 intermediate-mass galaxies (IMGs, 109 ≤ M/M ⊙ ≤ 1010) in COSMOS at 0.3 < z < 0.4 by comparing their Hα and UV luminosities. These two measurements trace star formation rates (SFRs) on different timescales and together reveal fluctuations in recent activity. We compute L Hα from Magellan IMACS spectroscopy, while L UV is derived from rest-frame 2800 Å photometry. Dust corrections are applied to each band independently. We compare the deviation of L Hα and L UV from their respective star-forming sequences (i.e., and ), and after accounting for observational uncertainties we find a small intrinsic scatter between the two quantities (σ δ ≲ 0.03 dex). This crucial observational constraint precludes strong fluctuations in the recent SFHs of IMGs: simple linear SFH models indicate that a population of IMGs would be limited to only factors of ≲2 change in SFR over 200 Myr and ≲30% on shorter timescales of 20 Myr. No single characteristic SFH for IMGs, such as an exponentially rising/falling burst, can reproduce the individual and joint distribution of and . Instead, an ensemble of SFHs is preferred. Finally, we find that IMG SFHs predicted by recent hydrodynamic simulations, in which feedback drives rapid and strong SFR fluctuations, are inconsistent with our observations.

No Need for Extreme Stellar Masses at z ∼ 7: A Test-case Study of COS-87259

Recent controversy regarding the existence of massive () galaxies at z > 6 poses a challenge for galaxy formation theories. Hence, it is of critical importance to understand the effects of SED fitting methods on stellar mass estimates of Epoch of Reionization galaxies. In this work, we perform a case study on the AGN host galaxy candidate COS-87259, with spectroscopic redshift z spec = 6.853, that is claimed to have an extremely high stellar mass of . We test a suite of different SED fitting algorithms and stellar population models on our independently measured photometry in 17 broad bands for this source. Between five different code setups, the stellar mass estimates for COS-87259 span –11.00, while the reduced χ 2 values of the fits are all close to unity within , such that the quality of the SED fits is basically indistinguishable. Only when we adopt a nonparametric star formation history model within Prospector do we retrieve a stellar mass exceeding . Although the derived stellar masses change when using previously reported photometry for this source, the nonparametric SED-fitting method always yields the highest values. As these models are becoming increasingly popular for James Webb Space Telescope high-redshift science, we stress the absolute importance of testing various SED fitting routines particularly on apparently very massive galaxies at such high redshifts.

Timing the r-process Enrichment of the Ultra-faint Dwarf Galaxy Reticulum II

The ultra-faint dwarf galaxy Reticulum II (Ret II) exhibits a unique chemical evolution history, with % of its stars strongly enhanced in r-process elements. We present deep Hubble Space Telescope photometry of Ret II and analyze its star formation history. As in other ultra-faint dwarfs, the color–magnitude diagram is best fit by a model consisting of two bursts of star formation. If we assume that the bursts were instantaneous, then the older burst occurred around the epoch of reionization, forming ∼80% of the stars in the galaxy, while the remainder of the stars formed ∼3 Gyr later. When the bursts are allowed to have nonzero durations, we obtain slightly better fits. The best-fitting model in this case consists of two bursts beginning before reionization, with approximately half the stars formed in a short (100 Myr) burst and the other half in a more extended period lasting 2.6 Gyr. Considering the full set of viable star formation history models, we find that 28% of the stars formed within 500 ± 200 Myr of the onset of star formation. The combination of the star formation history and the prevalence of r-process-enhanced stars demonstrates that the r-process elements in Ret II must have been synthesized early in its initial star-forming phase. We therefore constrain the delay time between the formation of the first stars in Ret II and the r-process nucleosynthesis to be less than 500 Myr. This measurement rules out an r-process source with a delay time of several Gyr or more, such as GW170817.

Recovering the Star Formation Histories of Recently Quenched Galaxies: The Impact of Model and Prior Choices

Accurate models of the star formation histories (SFHs) of recently quenched galaxies can provide constraints on when and how galaxies shut down their star formation. The recent development of nonparametric SFH models promises the flexibility required to make these measurements. However, model and prior choices significantly affect derived SFHs, particularly for post-starburst galaxies (PSBs), which have sharp changes in their recent SFH. In this paper, we create mock PSBs, then use the Prospector SED fitting software to test how well four different SFH models recover key properties. We find that a two-component parametric model performs well for our simple mock galaxies, but is sensitive to model mismatches. The fixed- and flexible-bin nonparametric models included in Prospector are able to rapidly quench a major burst of star formation, but systematically underestimate the post-burst age by up to 200 Myr. We develop a custom SFH model that allows for additional flexibility in the recent SFH. Our flexible nonparametric model is able to constrain post-burst ages with no significant offset and just ∼90 Myr of scatter. Our results suggest that while standard nonparametric models are able to recover first-order quantities of the SFH (mass, SFR, average age), accurately recovering higher-order quantities (burst fraction, quenching time) requires careful consideration of model flexibility. These mock recovery tests are a critical part of future SFH studies. Finally, we show that our new, public SFH model is able to accurately recover the properties of mock star-forming and quiescent galaxies and is suitable for broader use in the SED fitting community. https://github.com/bd-j/prospector

Surrogate modelling the Baryonic Universe II: On forward modelling the colours of individual and populations of galaxies

ABSTRACT Among the properties shaping the light of a galaxy, the star formation history (SFH) is one of the most challenging to model due to the variety of correlated physical processes regulating star formation. In this work, we leverage the stellar population synthesis model fsps, together with SFHs predicted by the hydrodynamical simulation IllustrisTNG and the empirical model universemachine, to study the impact of star formation variability on galaxy colours. We start by introducing a model-independent metric to quantify the burstiness of a galaxy formation model, and we use this metric to demonstrate that universemachine predicts SFHs with more burstiness relative to IllustrisTNG. Using this metric and principal component analysis, we construct families of SFH models with adjustable variability, and we show that the precision of broad-band optical and near-infrared colours degrades as the level of unresolved short-term variability increases. We use the same technique to demonstrate that variability in metallicity and dust attenuation presents a practically negligible impact on colours relative to star formation variability. We additionally provide a model-independent fitting function capturing how the level of unresolved star formation variability translates into imprecision in predictions for galaxy colours; our fitting function can be used to determine the minimal SFH model that reproduces colours with some target precision. Finally, we show that modelling the colours of individual galaxies with per cent-level precision demands resorting to complex SFH models, while producing precise colours for galaxy populations can be achieved using models with just a few degrees of freedom.

Improving z ∼ 7–11 Galaxy Property Estimates with JWST/NIRCam Medium-band Photometry

Abstract The past decade has seen impressive progress in the detection of z &gt; 7 galaxies with the Hubble Space Telescope; however, little is known about their properties. The James Webb Space Telescope will revolutionize the high-z field by providing near-IR (i.e., rest-frame optical) data of unprecedented depth and spatial resolution. Measuring galaxy quantities such as resolved stellar ages or gas metallicity gradients traditionally requires spectroscopy, as broadband imaging filters are generally too coarse to fully isolate diagnostics such as the 4000 Å (rest-frame) break, continuum emission from aged stars, and key emission lines (e.g., [O ii], [O iii], Hβ). However, in this paper, we show that adding NIRCam images through a strategically chosen medium-band filter to common wide-band filter sets adopted by ERS and GTO programs delivers tighter constraints on these galactic properties. To constrain the choice of filter, we perform a systematic investigation of which combinations of wide-band filters from ERS and GTO programs and single medium-band filters offer the tightest constraints on several galaxy properties at redshifts z ∼ 7–11. We employ the JAGUAR extragalactic catalogs to construct statistical samples of physically motivated mock photometry and conduct SED-fitting procedures to evaluate the accuracy of galaxy property (and photo-z) recovery with a simple star formation history model. We find that adding &gt;4.1 μm medium filters at comparable depth to the broadband filters can significantly improve photo-zs and yield close to order-of-magnitude improvements in the determination of quantities such as stellar ages, metallicities, SF-related quantities, and emission-line fluxes at z ∼ 8. For resolved sources, the proposed approach enables the spatially resolved determination of these quantities that would be prohibitive with slit spectroscopy.

Weighing Milky Way satellites with LISA

ABSTRACT White dwarf stars are a well-established tool for studying Galactic stellar populations. Two white dwarfs in a tight binary system offer us an additional messenger – gravitational waves – for exploring the Milky Way and its immediate surroundings. Gravitational waves produced by double white dwarf (DWD) binaries can be detected by the future Laser Interferometer Space Antenna (LISA). Numerous and widespread DWDs have the potential to probe shapes, masses, and formation histories of the stellar populations in the Galactic neighbourhood. In this work we outline a method for estimating the total stellar mass of Milky Way satellite galaxies based on the number of DWDs detected by LISA. To constrain the mass we perform a Bayesian inference using binary population synthesis models and considering the number of detected DWDs associated with the satellite and the measured distance to the satellite as the only inputs. Based on a fiducial binary population synthesis model we find that for large satellites the stellar masses can be recovered to within (1) a factor 2 if the star formation history (SFH) is known and (2) an order of magnitude when marginalizing over different SFH models. For smaller satellites we can place upper limits on their stellar mass. Gravitational wave observations can provide mass measurements for large satellites that are comparable, and in some cases more precise, than standard electromagnetic observations.

How Well Can We Measure the Stellar Mass of a Galaxy: The Impact of the Assumed Star Formation History Model in SED Fitting

Abstract The primary method for inferring the stellar mass (M *) of a galaxy is through spectral energy distribution (SED) modeling. However, the technique rests on assumptions such as the galaxy star formation history (SFH) and dust attenuation law that can severely impact the accuracy of derived physical properties from SED modeling. Here we examine the effect that the assumed SFH has on the stellar properties inferred from SED fitting by ground-truthing them against mock observations of high-resolution cosmological hydrodynamic galaxy formation simulations. Classically, SFHs are modeled with simplified parameterized functional forms, but these forms are unlikely to capture the true diversity of galaxy SFHs and may impose systematic biases with underreported uncertainties on results. We demonstrate that flexible nonparametric SFHs outperform traditional parametric forms in capturing variations in galaxy SFHs and, as a result, lead to significantly improved stellar masses in SED fitting. We find a decrease in the average bias of 0.4 dex with a delayed-τ model to a bias under 0.1 dex for the nonparametric model, though this is heavily dependent on the choice of prior for the nonparametric model. Similarly, using nonparametric SFHs in SED fitting results in increased accuracy in recovered galaxy star formation rates and stellar ages.

Radial Star Formation Histories in 32 Nearby Galaxies

Abstract The spatially resolved star formation histories are studied for 32 normal star-forming galaxies drawn from the Spitzer Extended Disk Galaxy Exploration Science survey. At surface brightness sensitivities fainter than 28 mag arcsec−2, the new optical photometry is deep enough to complement archival ultraviolet and infrared imaging and to explore the properties of the emission well beyond the traditional optical extents of these nearby galaxies. Fits to the spectral energy distributions using a delayed star formation history model indicate a subtle but interesting average radial trend for the spiral galaxies: the inner stellar systems decrease in age with increasing radius, consistent with inside-out disk formation, but the trend reverses in the outermost regions with the stellar age nearly as old as the innermost stars. These results suggest an old stellar outer disk population formed through radial migration and/or the cumulative history of minor mergers and accretions of satellite dwarf galaxies. The subset of S0 galaxies studied here show the opposite trend compared to what is inferred for spirals: characteristic stellar ages that are increasingly older with radius for the inner portions of the galaxies, and increasingly younger stellar ages for the outer portions. This result suggests that either S0 galaxies are not well modeled by a delayed-τ model, and/or that S0 galaxies have a more complicated formation history than spiral galaxies.

How to Measure Galaxy Star Formation Histories. I. Parametric Models

Abstract Parametric models for galaxy star formation histories (SFHs) are widely used, though they are known to impose strong priors on physical parameters. This has consequences for measurements of the galaxy stellar-mass function, star formation rate density (SFRD), and star-forming main sequence (SFMS). We investigate the effects of the exponentially declining, delayed exponentially declining, lognormal, and double power-law SFH models using Bagpipes. We demonstrate that each of these models imposes strong priors on specific star formation rates (SFRs), potentially biasing the SFMS, and also imposes a strong prior preference for young stellar populations. We show that stellar mass, SFR, and mass-weighted age inferences from high-quality mock photometry vary with the choice of SFH model by at least 0.1, 0.3, and 0.2 dex, respectively. However, the biases with respect to the true values depend more on the true SFH shape than the choice of model. We also demonstrate that photometric data cannot discriminate between SFH models, meaning that it is important to perform independent tests to find well-motivated priors. We finally fit a low-redshift, volume-complete sample of galaxies from the Galaxy and Mass Assembly (GAMA) Survey with each model. We demonstrate that our stellar masses and SFRs at redshift z ∼ 0.05 are consistent with other analyses. However, our inferred cosmic SFRDs peak at z ∼ 0.4, approximately 6 Gyr later than direct observations suggest, meaning that our mass-weighted ages are significantly underestimated. This makes the use of parametric SFH models for understanding mass assembly in galaxies challenging. In a companion paper, we consider nonparametric SFH models.

Galaxy properties derived with spectral energy distribution fitting in the Hawaii-Hubble Deep Field-North

We compile multi-wavelength data from ultraviolet to infrared (IR) bands as well as redshift and source-type information, for a large sample of 178 341 sources in the Hawaii-Hubble Deep Field-North field. A total of 145 635 sources among the full sample are classified/treated as galaxies and have redshift information available. We derive physical properties for these sources utilizing the spectral energy distribution fitting code CIGALE that is based on Bayesian analysis. Through various consistency and robustness checks, we find that our stellar-mass and star-formation rate (SFR) estimates are reliable, which is mainly due to two facts. Firstly, we adopt the most up-to-date and accurate redshifts and point spread function-matched photometry; and secondly, we make sensible parameter choices with the CIGALE code and take into account the influences of mid-IR/far-IR data, star-formation history models, and AGN contribution. We release our catalog of galaxy properties publicly (including, e.g., redshift, stellar mass, SFR, age, metallicity, dust attenuation). It is the largest of its kind in this field and should facilitate future relevant studies on the formation and evolution of galaxies.

SNITCH: seeking a simple, informative star formation history inference tool

Deriving a simple, analytic galaxy star formation history (SFH) using observational data is a complex task without the proper tool to hand. We therefore present SNITCH, an open source code written in Python, developed to quickly (~2 minutes) infer the parameters describing an analytic SFH model from the emission and absorption features of a galaxy spectrum dominated by star formation gas ionisation. SNITCH uses the Flexible Stellar Population Synthesis models of Conroy et al. (2009), the MaNGA Data Analysis Pipeline and a Markov Chain Monte Carlo method in order to infer three parameters (time of quenching, rate of quenching and model metallicity) which best describe an exponentially declining quenching history. This code was written for use on the MaNGA spectral data cubes but is customisable by a user so that it can be used for any scenario where a galaxy spectrum has been obtained, and adapted to infer a user-defined analytic SFH model for specific science cases. Herein we outline the rigorous testing applied to SNITCH and show that it is both accurate and precise at deriving the SFH of a galaxy spectra. The tests suggest that SNITCH is sensitive to the most recent epoch of star formation but can also trace the quenching of star formation even if the true decline does not occur at an exponential rate. With the use of both an analytical SFH and only five spectral features, we advocate that this code be used as a comparative tool across a large population of spectra, either for integral field unit data cubes or across a population of galaxy spectra.

Comment on "An excess of massive stars in the local 30 Doradus starburst".

Schneider et al (Reports, 5 January 2018, p. 69) used an ad hoc statistical method in their calculation of the stellar initial mass function. Adopting an improved approach, we reanalyze their data and determine a power-law exponent of [Formula: see text] Alternative assumptions regarding dataset completeness and the star formation history model can shift the inferred exponent to [Formula: see text] and [Formula: see text], respectively.

The Impact of Star Formation Histories on Stellar Mass Estimation: Implications from the Local Group Dwarf Galaxies

Abstract Building on the relatively accurate star formation histories (SFHs) and metallicity evolution of 40 Local Group (LG) dwarf galaxies derived from resolved color–magnitude diagram modeling, we carried out a comprehensive study of the influence of SFHs, metallicity evolution, and dust extinction on the UV-to-near-IR color–mass-to-light ratio (color– (λ)) distributions and M ⋆ estimation of local universe galaxies. We find that (1) the LG galaxies follow color– (λ) relations that fall in between the ones calibrated by previous studies; (2) optical color– (λ) relations at higher [M/H] are generally broader and steeper; (3) the SFH “concentration” does not significantly affect the color– (λ) relations; (4) light-weighted ages and metallicities together constrain (λ) with uncertainties ranging from ≲0.1 dex for the near-IR up to 0.2 dex for the optical passbands; (5) metallicity evolution induces significant uncertainties to the optical but not near-IR (λ) at a given and ; (6) the V band is the ideal luminance passband for estimating (λ) from single colors, because the combinations of (V) and optical colors such as B − V and g − r exhibit the weakest systematic dependences on SFHs, metallicities, and dust extinction; and (7) without any prior assumption on SFHs, M ⋆ is constrained with biases ≲0.3 dex by the optical-to-near-IR SED fitting. Optical passbands alone constrain M ⋆ with biases ≲0.4 dex (or ≲0.6 dex) when dust extinction is fixed (or variable) in SED fitting. SED fitting with monometallic SFH models tends to underestimate M ⋆ of real galaxies. M ⋆ tends to be overestimated (or underestimated) at the youngest (or oldest) .

Star formation quenching in green valley galaxies at 0.5 ≲ z ≲ 1.0 and constraints with galaxy morphologies

We calculate the star formation quenching timescales in green valley galaxies at intermediate redshifts ($z\sim0.5-1$) using stacked zCOSMOS spectra of different galaxy morphological types: spheroidal, disk-like, irregular and merger, dividing disk-like galaxies further into unbarred, weakly-barred and strongly-barred, assuming a simple exponentially-decaying star formation history model and based on the H$_{\delta}$ absorption feature and the $4000$ \AA ~break. We find that different morphological types present different star formation quenching timescales, reinforcing the idea that the galaxy morphology is strongly correlated with the physical processes responsible for quenching star formation. Our quantification of the star formation quenching timescale indicates that disks have typical timescales $60\%$ to 5 times longer than that of galaxies presenting spheroidal, irregular or merger morphologies. Barred galaxies in particular present the slowest transition timescales through the green valley. This suggests that although secular evolution may ultimately lead to gas exhaustion in the host galaxy via bar-induced gas inflows that trigger star formation activity, secular agents are not major contributors in the rapid quenching of galaxies at these redshifts. Galaxy interaction, associated with the elliptical, irregular and merger morphologies contribute, to a more significant degree, to the fast transition through the green valley at these redshifts. In the light of previous works suggesting that both secular and merger processes are responsible for the star formation quenching at low redshifts, our results provide an explanation to the recent findings that star formation quenching happened at a faster pace at $z\sim0.8$.

The challenging task of determining star formation rates: the case of a massive stellar burst in the brightest cluster galaxy of Phoenix galaxy cluster

Star formation in galaxies at the center of cooling-flow galaxy clusters is an important phenomenon in the context of formation and evolution of massive galaxies in the Universe. Yet, star formation rates (SFRs) in such systems continue to be elusive. We use our Bayesian-motivated spectral energy distribution (SED)-fitting code, BAYESCOOL, to estimate the plausible SFR values in the brightest cluster galaxy of a massive, X-ray luminous galaxy cluster, Phoenix. Previous studies of Phoenix have resulted in the highest measurement of SFR for any galaxy, with the estimates reaching up to 1000 solar masses/yr. However, a very small number of models have been considered in those studies. BAYESCOOL allows us to probe a large parameter space. We consider two models for star formation history, instantaneous bursts and continuous star formation, a wide range of ages for the old and the young stellar population, along with other discrete parameters, such as the initial mass function, metallicities, internal extinction and extinction law. We find that in the absence of any prior except that the maximum cooling rate < 3000 solar masses/yr, the SFR lies in the range (2230-2890) solar masses/yr. If we impose an observational prior on the internal extinction, E(B-V) < 0.6, the best-fit SFR lies in (454-494) solar masses/yr, and we consider this as the most probable range of SFR values for Phoenix. The SFR dependence on the extinction is a reflection of the standard age-extinction degeneracy, which can be overcome by using a prior on one of the two quantities in question.