Early Supernova Research Articles

Mesiri: Mephisto Early Supernovae Ia Rapid Identifier

The early time observations of Type Ia supernovae (SNe Ia) play a crucial role in investigating and resolving longstanding questions about progenitor stars and the explosion mechanisms of these events. Colors of supernovae (SNe) in the initial days after the explosion can help differentiate between different types of SNe. However, the use of true color information to identify SNe Ia at the early-time explosion is still in its infancy. The Multi-channel Photometric Survey Telescope (Mephisto) is a photometric survey telescope equipped with three CCD cameras, capable of simultaneously imaging the same patch of sky in three bands (u, g, i or v, r, z), yielding real-time colors of astronomical objects. In this paper, we introduce a new time-series classification tool named Mephisto Early Supernovae Ia Rapid Identifier (Mesiri), which, for the first time, utilizes real-time color information to distinguish early-time SNe Ia from core-collapse supernovae. Mesiri is based on the deep learning approach and can achieve an accuracy of 96.75% ± 0.79%, and AUC of 98.87% ± 0.53% in case of single epoch random observation before the peak brightness. These values reach towards perfectness if additional data points on several night observations are considered. The classification with real-time color significantly outperforms that with pseudo-color, especially at the early time, i.e., with only a few points of observations. The BiLSTM architecture shows the best performance compared to others that have been tested in this work.

Virialized equation of state for warm and dense stellar plasmas in proto-neutron stars and supernova matter

ABSTRACT We present microscopic molecular dynamics simulations including the efficient Ewald sum procedure to study warm and dense stellar plasmas consisting of finite-size ion charges immerse in a relativistic neutralizing electron gas. For densities typical of Supernova matter and crust in a proto-neutron star, we select a representative single ion composition and obtain the virialized equation of state (vEoS). We scrutinize the finite-size and screening corrections to the Coulomb potential appearing in the virial coefficients B2, B3, and B4 as a function of temperature. In addition, we study the thermal heat capacity at constant volume, CV, and the generalized Mayer’s relation i.e. the difference CP − CV with CP being the heat capacity at constant pressure, obtaining clear features signalling the onset of the liquid–gas phase transition. Our findings show that microscopic simulations reproduce the discontinuity in CV, whose value lies between that of idealized gas and crystallized configurations. We study the pressure isotherms marking the boundary of the metastable region before the gaseous transition takes place. The resulting vEoS displays a behaviour where effective virial coefficients include extra density dependence showing a generalized density–temperature form. As an application we parametrize pressure as a function of density and temperature under the form of an artificial neural network showing the potential of machine learning for future regression analysis in more refined multicomponent approaches. This is of interest to size the importance of these corrections in the liquid–gas phase transition in warm and dense plasma phases contributing to the cooling behaviour of early Supernova phases and proto-neutron stars.

UV Signatures of Magnetar Formation and Their Crucial Role for GW Detection

The emission from shock breakouts (SBOs) represents the earliest electromagnetic (EM) signal emitted by cataclysmic events involving the formation or the merger of neutron stars (NSs). As such, SBOs carry unique information on the structure of their progenitors and on the explosion energy. The characteristic SBO emission is expected in the UV range, and its detection is one of the key targets of the ULTRASAT satellite. Among SBO sources, we focus on a specific class involving the formation of fast-spinning magnetars in the core-collapse of massive stars. Fast-spinning magnetars are expected to produce a specific signature in the early UV supernova light curve, powered by the extra spin energy quickly released by the NS. Moreover, they are considered as optimal candidates for the emission of long-transient gravitational wave (GW) signals, the detection of which requires early EM triggers to boost the sensitivity of dedicated GW search pipelines. We calculate early supernova UV light curves in the presence of a magnetar central engine, as a function of the explosion energy, ejecta mass, and magnetar parameters. We then estimate the ULTRASAT detection horizon (z < 0.15) as a function of the same physical parameters, and the overall expected detection rate, finding that magnetar-powered SBOs may represent up to 1/5 of the total events detected by ULTRASAT. Moreover, at the expected sensitivity of the LIGO/Virgo/Kagra O5 science run, one such event occurring within 5 Mpc will provide an ideal trigger for a GW long-transient search. Future GW detectors like the Einstein Telescope will push the horizon for joint EM-GW detections to 35–40 Mpc.

The Prevalence and Influence of Circumstellar Material around Hydrogen-rich Supernova Progenitors

Narrow transient emission lines (flash-ionization features) in early supernova (SN) spectra trace the presence of circumstellar material (CSM) around the massive progenitor stars of core-collapse SNe. The lines disappear within days after the SN explosion, suggesting that this material is spatially confined, and originates from enhanced mass loss shortly (months to a few years) prior to the explosion. We performed a systematic survey of H-rich (Type II) SNe discovered within less than 2 days from the explosion during the first phase of the Zwicky Transient Facility survey (2018–2020), finding 30 events for which a first spectrum was obtained within <2 days from the explosion. The measured fraction of events showing flash-ionization features (>36% at the 95% confidence level) confirms that elevated mass loss in massive stars prior to SN explosion is common. We find that SNe II showing flash-ionization features are not significantly brighter, nor bluer, nor more slowly rising than those without. This implies that CSM interaction does not contribute significantly to their early continuum emission, and that the CSM is likely optically thin. We measured the persistence duration of flash-ionization emission and find that most SNe show flash features for ≈5 days. Rarer events, with persistence timescales >10 days, are brighter and rise longer, suggesting these may be intermediate between regular SNe II and strongly interacting SNe IIn.

Timing and multi-channel: novel method for determining the neutrino mass ordering from supernovae

One of the few remaining unknowns in the standard three-flavor neutrino oscillation paradigm is the ordering of neutrino masses. In this work we propose a novel method for determining neutrino mass ordering using the time information on early supernova neutrino events. In a core-collapse supernova, neutrinos are produced earlier than antineutrinos and, depending on the mass ordering which affects the adiabatic flavor evolution, may cause earlier observable signals in νe detection channels than in others. Hence, the time differences are sensitive to the mass ordering. We find that using the time information on the detection of the first galactic supernova events at future detectors like DUNE, JUNO and Hyper-Kamiokande, the mass ordering can already be determined at∼ 2σ CL, while \U0001d4aa(10) events suffice for the discovery. Our method does not require high statistics and could be used within the supernova early warning system (SNEWS) which will have access to the time information on early supernova neutrino events recorded in a number of detectors. The method proposed in this paper also implies a crucial interplay between the mass ordering and the triangulation method for locating supernovae.

Fink: Early supernovae Ia classification using active learning

Context. The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will produce a continuous stream of alerts made of varying sources in the sky. This data flow will be publicly advertised and distributed to scientists via broker systems such as FINK, whose task is to extract scientific information from the stream. Given the complexity and volume of the data to be generated, LSST is a prime target for machine learning (ML) techniques. One of the most challenging stages of this task is the construction of appropriate training samples which enable learning based on a limited number of spectroscopically confirmed objects. Aims. We describe how the FINK broker early supernova Ia (SN Ia) classifier optimizes its ML classifications by employing an active learning (AL) strategy. We demonstrate the feasibility of implementing such strategies in the current Zwicky Transient Facility (ZTF) public alert data stream. Methods. We compared the performance of two AL strategies: uncertainty sampling and random sampling. Our pipeline consists of three stages: feature extraction, classification, and learning strategy. Starting from an initial sample of ten alerts, including five SNe Ia and five non-Ia, we let the algorithm identify which alert should be added to the training sample. The system was allowed to evolve through 300 iterations. Results. Our data set consists of 23 840 alerts from ZTF with a confirmed classification via a crossmatch with the SIMBAD database and the Transient Name Server (TNS), 1600 of which were SNe Ia (1021 unique objects). After the learning cycle was completed, the data configuration consisted of 310 alerts for training and 23 530 for testing. Averaging over 100 realizations, the classifier achieved ~89% purity and ~54% efficiency. From 01 November 2020 to 31 October 2021 FINK applied its early SN Ia module to the ZTF stream and communicated promising SN Ia candidates to the TNS. From the 535 spectroscopically classified FINK candidates, 459 (86%) were proven to be SNe Ia. Conclusions. Our results confirm the effectiveness of AL strategies for guiding the construction of optimal training samples for astronomical classifiers. It demonstrates in real data that the performance of learning algorithms can be highly improved without the need of extra computational resources or overwhelmingly large training samples. This is, to our knowledge, the first application of AL to real alert data.

Photometric Classification of Early-time Supernova Light Curves with SCONE

Abstract In this work, we present classification results on early supernova light curves from SCONE, a photometric classifier that uses convolutional neural networks to categorize supernovae (SNe) by type using light-curve data. SCONE is able to identify SN types from light curves at any stage, from the night of initial alert to the end of their lifetimes. Simulated LSST SNe light curves were truncated at 0, 5, 15, 25, and 50 days after the trigger date and used to train Gaussian processes in wavelength and time space to produce wavelength–time heatmaps. SCONE uses these heatmaps to perform six-way classification between SN types Ia, II, Ibc, Ia-91bg, Iax, and SLSN-I. SCONE is able to perform classification with or without redshift, but we show that incorporating redshift information improves performance at each epoch. SCONE achieved 75% overall accuracy at the date of trigger (60% without redshift), and 89% accuracy 50 days after trigger (82% without redshift). SCONE was also tested on bright subsets of SNe (r &lt; 20 mag) and produced 91% accuracy at the date of trigger (83% without redshift) and 95% five days after trigger (94.7% without redshift). SCONE is the first application of convolutional neural networks to the early-time photometric transient classification problem. All of the data processing and model code developed for this paper can be found in the SCONE software package 1 1 github.com/helenqu/scone located at github.com/helenqu/scone (Qu 2021).

PSR J1709-4429's Proper Motion and Its Relationship to SNR G343.1–2.3

Abstract We have obtained a deep (670 ks) CXO ACIS image of the remarkable pulsar wind nebula (PWN) of PSR J1709−4429, in four epochs during 2018–2019. Comparison with an archival 2004 data set provides a pulsar proper motion μ = 13 ± 3 mas yr−1 at a PA of 86° ± 9° (1σ combined statistical and systematic uncertainties), precluding birth near the center of SNR G343.1−2.3. At the pulsar’s characteristic age of 17 kyr, the association can be preserved through a combination of progenitor wind, birth kick, and PWN outflow. Associated TeV emission may, however, indicate an explosion in an earlier supernova. Inter-epoch comparison of the X-ray images shows that the PWN is dynamic, but we are unable to conclusively measure flow speeds from blob motion. The pulsar has generated a radio/X-ray wind bubble, and we argue that the PWN’s long narrow jets are swept back by shocked pulsar wind venting from this cavity. These jets may trace the polar magnetic field lines of the PWN flow, an interesting challenge for numerical modeling.

ALMA Lensing Cluster Survey: a strongly lensed multiply imaged dusty system at z ≥ 6

ABSTRACT We report the discovery of an intrinsically faint, quintuply-imaged, dusty galaxy MACS0600-z6 at a redshift z = 6.07 viewed through the cluster MACSJ0600.1–2008 (z = 0.46). A ≃ 4σ dust detection is seen at 1.2mm as part of the ALMA Lensing Cluster Survey (ALCS), an on-going ALMA Large programme, and the redshift is secured via [C ii] 158 μm emission described in a companion paper. In addition, spectroscopic follow-up with GMOS/Gemini-North shows a break in the galaxy’s spectrum, consistent with the Lyman break at that redshift. We use a detailed mass model of the cluster and infer a magnification μ ≳ 30 for the most magnified image of this galaxy, which provides an unprecedented opportunity to probe the physical properties of a sub-luminous galaxy at the end of cosmic reionization. Based on the spectral energy distribution, we infer lensing-corrected stellar and dust masses of $\rm {2.9^{+11.5}_{-2.3}\times 10^9}$ and $\rm {4.8^{+4.5}_{-3.4}\times 10^6}$$\rm {M_{\odot }}$, respectively, a star formation rate of $\rm {9.7^{+22.0}_{-6.6} \, M_{\odot } \, yr^{-1}}$, an intrinsic size of $\rm {0.54^{+0.26}_{-0.14}}$ kpc, and a luminosity-weighted age of 200 ± 100 Myr. Strikingly, the dust production rate in this relatively young galaxy appears to be larger than that observed for equivalent, lower redshift sources. We discuss if this implies that early supernovae are more efficient dust producers and the consequences for using dust mass as a probe of earlier star formation.

Cobalt and copper abundances in 56 Galactic bulge red giants

Context. The Milky Way bulge is an important tracer of the early formation and chemical enrichment of the Galaxy. The abundances of different iron-peak elements in field bulge stars can give information on the nucleosynthesis processes that took place in the earliest supernovae. Cobalt (Z = 27) and copper (Z = 29) are particularly interesting. Aims. We aim to identify the nucleosynthesis processes responsible for the formation of the iron-peak elements Co and Cu. Methods. We derived abundances of the iron-peak elements cobalt and copper in 56 bulge giants, 13 of which were red clump stars. High-resolution spectra were obtained using FLAMES-UVES at the ESO Very Large Telescope by our group in 2000–2002, which appears to be the highest quality sample of optical high-resolution data on bulge red giants obtained in the literature to date. Over the years we have derived the abundances of C, N, O, Na, Al, Mg; the iron-group elements Mn and Zn; and neutron-capture elements. In the present work we derive abundances of the iron-peak elements cobalt and copper. We also compute chemodynamical evolution models to interpret the observed behaviour of these elements as a function of iron. Results. The sample stars show mean values of [Co/Fe] ~ 0.0 at all metallicities, and [Cu/Fe] ~ 0.0 for [Fe/H] ≥−0.8 and decreasing towards lower metallicities with a behaviour of a secondary element. Conclusions. We conclude that [Co/Fe] varies in lockstep with [Fe/H], which indicates that it should be produced in the alpha-rich freezeout mechanism in massive stars. Instead [Cu/Fe] follows the behaviour of a secondary element towards lower metallicities, indicating its production in the weak s-process nucleosynthesis in He-burning and later stages. The chemodynamical models presented here confirm the behaviour of these two elements (i.e. [Co/Fe] vs. [Fe/H] ~constant and [Cu/Fe] decreasing with decreasing metallicities).

Presupernova Neutrinos: Directional Sensitivity and Prospects for Progenitor Identification

Abstract We explore the potential of current and future liquid scintillator neutrino detectors of kt mass to localize a presupernova neutrino signal in the sky. In the hours preceding the core collapse of a nearby star (at distance kpc), tens to hundreds of inverse beta decay events will be recorded, and their reconstructed topology in the detector can be used to estimate the direction to the star. Although the directionality of inverse beta decay is weak (∼8% forward−backward asymmetry for currently available liquid scintillators), we find that for a fiducial signal of 200 events (which is realistic for Betelgeuse), a positional error of ∼60° can be achieved, resulting in the possibility to narrow the list of potential stellar candidates to less than 10, typically. For a configuration with improved forward−backward asymmetry (∼40%, as expected for a lithium-loaded liquid scintillator), the angular sensitivity improves to ∼15°, and—when a distance upper limit is obtained from the overall event rate—it is in principle possible to uniquely identify the progenitor star. Any localization information accompanying an early supernova alert will be useful to multimessenger observations and to particle physics tests using collapsing stars.

The explosion energy of the type IIP supernova SN 2013fs with a confined dense circumstellar shell

ABSTRACT The recent study of the SN 2013fs flash spectrum suggests an enormous explosion energy for SNe IIP, far beyond the possibilities of the neutrino mechanism. The issue of the explosion energy of SN 2013fs is revisited, making use of the effects of the early supernova interaction with the dense circumstellar shell. The velocity of the cold dense shell between reverse and forward shocks is inferred from the analysis of the broad He ii 4686 Å on day 2.4. This velocity, alongside other observables, provides us with an alternative energy estimate of ∼1.8 × 1051 erg for the preferred mass of ∼10 M⊙. The inferred value is within the range of neutrino-driven explosions.

Early Supernova Emission: Logarithmic Corrections to the Planar Phase

Abstract When the shock wave generated in a supernova explosion breaks out of the stellar envelope, the first photons, typically in the X-ray-to-UV range, escape to the observer. Following this breakout emission, radiation from deeper shells diffuses out of the envelope as the supernova ejecta expands. Previous studies have shown that the radiation throughout the planar phase (i.e., before the expanding envelope has doubled its radius) originates in the same mass coordinate, called the “breakout shell.” We derive a self-similar solution for the radiation inside the envelope and show that this claim is incorrect and that the diffusion wave propagates logarithmically into the envelope (in a Lagrangian sense), rather than remaining at a fixed mass coordinate. The logarithmic correction implies that the luminosity originates in regions where the density is ∼10 times higher than previously thought, where the photon production rate is increased and helps thermalization. We show that this result has significant implications for the observed temperature. In our model, the radiation emitted from blue supergiant and Wolf–Rayet explosions is still expected to be out of thermal equilibrium during the entire planar phase, but the observed temperature will decrease by 2 orders of magnitude, contrary to previous estimates. Considering the conditions at the end of the planar phase, we also find how the temperature and luminosity transition into the spherical phase.

Signatures of an eruptive phase before the explosion of the peculiar core-collapse SN 2013gc

We present photometric and spectroscopic analysis of the peculiar core-collapse SN 2013gc, spanning seven years of observations. The light curve shows an early maximum followed by a fast decline and a phase of almost constant luminosity. At +200 days from maximum, a brightening of 1 mag is observed in all bands, followed by a steep linear luminosity decline after +300 d. In archival images taken between 1.5 and 2.5 years before the explosion, a weak source is visible at the supernova location, with mag$\approx$20. The early supernova spectra show Balmer lines, with a narrow ($\sim$560 km s$^{-1}$) P-Cygni absorption superimposed on a broad ($\sim$3400 km s$^{-1}$) component, typical of type IIn events. Through a comparison of colour curves, absolute light curves and spectra of SN 2013gc with a sample of supernovae IIn, we conclude that SN 2013gc is a member of the so-called type IId subgroup. The complex profile of the H$\alpha$ line suggests a composite circumstellar medium geometry, with a combination of lower velocity, spherically symmetric gas and a more rapidly expanding bilobed feature. This circumstellar medium distribution has been likely formed through major mass-loss events, that we directly observed from 3 years before the explosion. The modest luminosity ($M_I\sim-16.5$ near maximum) of SN 2013gc at all phases, the very small amount of ejected $^{56}$Ni (of the order of $10^{-3}$ M$_\odot$), the major pre-supernova stellar activity and the lack of prominent [O I] lines in late-time spectra support a fall-back core-collapse scenario for the massive progenitor of SN~2013gc.

The High-Cadence Transient Survey (HiTS): Early Supernova Light-Curves

AbstractSupernovae (SNe) are cosmic explosions which are usually represented in a small region of the luminosity–time-scale diagram when discussing the variable sky. However, there are different time-scales involved in the evolution of SNe that are not reflected by that representation. This talk reviewed some of the physical mechanisms driving the SN light-curve diversity, especially at early times. It then discussed our efforts in the astroinformatics laboratory at CMM and at MAS to discover very young SNe using large etendue telescopes such as Blanco/DECam; those efforts led to the real-time discovery of more than one hundred SNe, some of them very young, under the High cadence Transient Survey (HiTS). We showed that, by comparing hydrodynamical models in the literature with HiTS SNe using Markov Chain Monte Carlo to sample from the posterior in a Bayesian approach, we can constrain the physical parameters that are driving the early time-evolution of these events. We also discussed how these data are being used for different projects, such as the discovery of asteroids and variable stars, and for testing different machine-learning algorithms in an interdisciplinary approach.

Laboratory transition probabilities for studies of nucleosynthesis of Fe-group elements1

The synthesis of iron (Fe-) group elements was different in the early Galaxy than it is today. Measurements of the relative Fe-group elemental abundances in old metal-poor stars yield information on the Galactic chemical evolution and some information on early supernovae (SNe). Improved laboratory data on transition probabilities is essential to this effort. It is also essential to understand and map the limits of standard photospheric models based on one-dimensional and local thermodynamic equilibrium approximations.

Light-travel-time diagnostics in early supernova spectra: substantial mass-loss of the IIb progenitor of SN 2013cu through a superwind

The progenitors of type-IIb supernovae (SNe) are believed to have lost their H-rich envelopes almost completely in the direct pre-SN phase. Recently the first 'flash spectrum' of a SN IIb (SN2013cu) has been presented, taken early enough to study its immediate circumstellar medium (CSM). Similar to a previous study by Groh (2014) we analyse the structure and chemical composition of the optically-thick CSM using non-LTE model atmospheres. For the first time we take light-travel time (LTT) effects on the spectrum formation into account, which affect the shapes and strengths of the observable emission lines, as well as the inferred SN luminosity. Based on the new CSM parameters we estimate a lower limit of ~0.3Msun for the CSM mass, which is a factor 10-100 higher than previous estimates. The spectral fit implies a CSM in the form of a homogeneous and spherically symmetric superwind whose mass-loss rate exceeds common expectations by up to two orders of magnitude. The derived chemical composition is in agreement with a progenitor that has just left, or is just about to leave the Red-Supergiant (RSG) stage, confirming the standard picture for the origin of SNe IIb. Due to its extreme mass loss the SN progenitor will likely appear as extreme RSG, Luminous Blue Variable (LBV), or Yellow Hypergiant (YHG). The direct detection of a superwind, and the high inferred CSM mass suggest that stellar wind mass loss may play an important role in the formation of SNe IIb.

Observable fractions of core-collapse supernova light curves brightened by binary companions

Many core-collapse supernova progenitors are presumed to be in binary systems. If a star explodes in a binary system, the early supernova light curve can be brightened by the collision of the supernova ejecta with the companion star. The early brightening can be observed when the observer is in the direction of the hole created by the collision. Based on a population synthesis model, we estimate the fractions of core-collapse supernovae in which the light-curve brightening by the collision can be observed. We find that 0.19% of core-collapse supernova light curves can be observed with the collisional brightening. Type Ibc supernova light curves are more likely to be brightened by the collision (0.53%) because of the high fraction of the progenitors being in binary systems and their proximity to the companion stars. Type II and IIb supernova light curves are less affected (~1e-3% and ~1e-2%, respectively). Although the early, slow light-curve declines of some Type IIb and Ibc supernovae are argued to be caused by the collision with the companion star (e.g. SN 2008D), the small expected fraction, as well as the unrealistically small separation required, disfavour the argument. The future transient survey by the Large Synoptic Survey Telescope is expected to detect ~10 Type Ibc supernovae with the early collisional brightening per year, and they will be able to provide information on supernova progenitors in binary systems.

Under the sword of Damocles: plausible regeneration of dark matter cusps at the smallest galactic scales

Abstract We study the evolution of the dark matter (DM) halo profiles of dwarf galaxies driven by the accretion of DM substructures through controlled N-body experiments. Our initial conditions assume that early supernova feedback erases the primordial DM cusps of haloes with z = 0 masses of 109 − 1010 M⊙. The orbits and masses of the infalling substructures are borrowed from the Aquarius cosmological simulations. Our experiments show that a fraction of haloes that undergo 1:3 down to 1:30 mergers are susceptible to reform a DM cusp by z ≈ 0. Cusp regrowth is driven by the accretion of DM substructures that are dense enough to reach the central regions of the main halo before being tidally disrupted. The infall of substructures on the mean of the reported mass–concentration relation and a mass ratio above 1:6 systematically leads to cusp regrowth. Substructures with 1:6–1:8, and 1:8–1:30 only reform DM cusps if their densities are 1σ and 2σ above the mean, respectively. The merging time-scales of these dense, low-mass substructures is relatively long (5 − 11 Gyr), which may pose a time-scale problem for the longevity of DM cores in dwarfs galaxies and possibly explain the existence of dense dwarfs-like Draco. These results suggest that within cold dark matter a non-negligible level of scatter in the mass profiles of galactic haloes acted on by feedback is to be expected given the stochastic mass accretion histories of low-mass haloes and the diverse star formation histories observed in the Local Group dwarfs.

Supernova dust formation and the grain growth in the early universe: the critical metallicity for low-mass star formation

We investigate the condition for the formation of low-mass second-generation stars in the early Universe. It has been proposed that gas cooling by dust thermal emission can trigger fragmentation of a low-metallicity star-forming gas cloud. In order to determine the critical condition in which dust cooling induces the formation of low-mass stars, we follow the thermal evolution of a collapsing cloud by a one-zone semi-analytic collapse model. Earlier studies assume the dust amount in the local Universe, where all refractory elements are depleted on to grains, and/or assume the constant dust amount during gas collapse. In this paper, we employ the models of dust formation and destruction in early supernovae to derive the realistic dust compositions and size distributions for multiple species as the initial conditions of our collapse calculations. We also follow accretion of heavy elements in the gas phase on to dust grains, i.e. grain growth, during gas contraction. We find that grain growth well alters the fragmentation property of the clouds. The critical conditions can be written by the gas metallicity Zcr and the initial depletion efficiency fdep,0 of gas-phase metal on to grains, or dust-to-metal mass ratio, as (Zcr/10−5.5 Z⊙) = (fdep,0/0.18)−0.44 with small scatters in the range of Zcr = [0.06–3.2] × 10−5 Z⊙. We also show that the initial dust composition and size distribution are important to determine Zcr.