Delay Time Distribution Research Articles

The RR Lyrae Delay-time Distribution: A Novel Perspective on Models of Old Stellar Populations

Abstract The delay-time distribution (DTD) is the occurrence rate of a class of objects as a function of time after a hypothetical burst of star formation. DTDs are mainly used as a statistical test of stellar evolution scenarios for supernova progenitors, but they can be applied to many other classes of astronomical objects. We calculate the first DTD for RR Lyrae variables using 29,810 RR Lyrae from the OGLE-IV survey and a map of the stellar age distribution (SAD) in the Large Magellanic Cloud (LMC). We find that ∼46% of the OGLE-IV RR Lyrae are associated with delay times greater than 8 Gyr (main-sequence progenitor masses less than 1 M ⊙), and consistent with existing constraints on their ages, but surprisingly about 51% of RR Lyrae appear to have delay times of 1.2–8 Gyr (main-sequence masses between 1 and 2 M ⊙ at LMC metallicity). This intermediate-age signal also persists outside the Bar region, where crowding is less of a concern, and we verified that without this signal the spatial distribution of the OGLE-IV RR Lyrae is inconsistent with the SAD map of the LMC. Since an intermediate-age RR Lyrae channel is in tension with the lack of RR Lyrae in intermediate-age clusters (noting issues with small-number statistics), and noting the age–metallicity constraints on LMC stars, our DTD result possibly indicates that systematic uncertainties may still exist in SAD measurements of old stellar populations, perhaps stemming from the construction methodology or the stellar evolution models used. We describe tests to further investigate this issue.

Statistical characteristics of spray autoignition of transient kerosene jet in cross flow

To study statistical characteristics of the random spray autoignition, aviation kerosene was injected transiently into non-vitiated air crossflow in a flow reactor with optical accesses. The operating conditions were relevant to gas turbine combustor: the air crossflow pressure and temperature were in the range of 1.4–1.7 MPa and 830–947 K, respectively, and the jet-to-crossflow momentum flux ratios were 20, 50 and 80. Statistical distributions of random ignition delay times with adequate convergence were estimated based on histograms. The dependences of the distributions on reactor pressure, temperature, and jet-to-crossflow momentum flux ratio were studied. The results show that the resulting distributions appear more concentrated with the increase of air temperature or jet-to-crossflow momentum flux ratio. And then the correlations for the mean and standard deviation of the ignition delay time sample data were developed based on the present results. Compared with the correlations of ignition delay time of homogeneous premixed gas-phase kerosene/air mixture reported in the literature, the results show a greater significance pressure dependence and lower temperature sensitivity of the ignition delay time of non-premixed kerosene spray.

Where Binary Neutron Stars Merge: Predictions from IllustrisTNG

Abstract The rate and location of binary neutron star (BNS) mergers are determined by a combination of the star formation history and the delay-time distribution (DTD) function. In this paper, we couple the star formation rate histories from the IllustrisTNG model to a series of varied assumptions for the BNS DTD to make predictions for the BNS merger host galaxy mass function. These predictions offer two outcomes: (i) in the near term they influence the BNS merger event follow-up strategy by scrutinizing where most BNS merger events are expected to occur, and (ii) in the long term they constrain the DTD for BNS merger events once the host galaxy mass function is observationally well determined. From our fiducial model analysis, we predict that 50% of BNS mergers will occur in host galaxies with stellar mass between 1010 and 1011 M ⊙, 68% between 4 × 109 and 3 × 1011 M ⊙, and 95% between 4 × 108 and 2 × 1012 M ⊙. We find that the details of the DTD employed do not have a strong effect on the peak of the host mass function. However, varying the DTD provides enough spread that the true DTD can be determined from enough electromagnetic observations of BNS mergers. Knowing the true DTD can help us determine the prevalence of BNS systems formed through highly eccentric and short-separation fast-merging channels and can constrain the dominant source of r-process material.

The delay time distribution of Type-Ia supernovae in galaxy clusters: the impact of extended star-formation histories

ABSTRACT The delay time distribution (DTD) of Type-Ia supernovae (SNe Ia) is important for understanding chemical evolution, SN Ia progenitors, and SN Ia physics. Past estimates of the DTD in galaxy clusters have been deduced from SN Ia rates measured in cluster samples observed at various redshifts, corresponding to different time intervals after a presumed initial brief burst of star formation. A recent analysis of a cluster sample at z = 1.13–1.75 confirmed indications from previous studies of lower redshift clusters, that the DTD has a power-law form, DTD(t) = R1(t/Gyr)α, with amplitude R1, at delay $t=1\,\rm Gyr$, several times higher than measured in field-galaxy environments. This implied that SNe Ia are somehow produced in larger numbers by the stellar populations in clusters. This conclusion, however, could have been affected by the implicit assumption that the stars were formed in a single brief starburst at high z. Here, we re-derive the DTD from the cluster SN Ia data, but relax the single-burst assumption. Instead, we allow for a range of star-formation histories and dust extinctions for each cluster. Via MCMC modelling, we simultaneously fit, using stellar population synthesis models and DTD models, the integrated galaxy-light photometry in several bands, and the SN Ia numbers discovered in each cluster. With these more-realistic assumptions, we find a best-fitting DTD with power-law index $\alpha =-1.09_{-0.12}^{+0.15}$, and amplitude $R_1=0.41_{-0.10}^{+0.12}\times 10^{-12}\,{\rm yr}^{-1}\, {\rm M}_\odot ^{-1}$. We confirm a cluster-environment DTD with a larger amplitude than the field-galaxy DTD, by a factor ∼2–3 (at 3.8σ). Cluster and field DTDs have consistent slopes of α ≈ −1.1.

The effects of different Type Ia SN yields on Milky Way chemical evolution

ABSTRACT We study the effect of different Type Ia SN nucleosynthesis prescriptions on the Milky Way chemical evolution. To this aim, we run detailed one-infall and two-infall chemical evolution models, adopting a large compilation of yield sets corresponding to different white dwarf progenitors (near-Chandrasekar and sub-Chandrasekar) taken from the literature. We adopt a fixed delay time distribution function for Type Ia SNe, in order to avoid degeneracies in the analysis of the different nucleosynthesis channels. We also combine yields for different Type Ia SN progenitors in order to test the contribution to chemical evolution of different Type Ia SN channels. The results of the models are compared with recent LTE and NLTE observational data. We find that ‘classical’ W7 and WDD2 models produce Fe masses and [α/Fe] abundance patterns similar to more recent and physical near-Chandrasekar and sub-Chandrasekar models. For Fe-peak elements, we find that the results strongly depend either on the white dwarf explosion mechanism (deflagration-to-detonation, pure deflagration, double detonation) or on the initial white dwarf conditions (central density, explosion pattern). The comparison of chemical evolution model results with observations suggests that a combination of near-Chandrasekar and sub-Chandrasekar yields is necessary to reproduce the data of V, Cr, Mn and Ni, with different fractions depending on the adopted massive stars stellar yields. This comparison also suggests that NLTE and singly ionized abundances should be definitely preferred when dealing with most of Fe-peak elements at low metallicity.

Neutron stars mergers in a stochastic chemical evolution model: impact of time delay distributions

ABSTRACT We study the evolution of the [Eu/Fe] ratio in the Galactic halo by means of a stochastic chemical evolution model considering merging neutron stars as polluters of europium. We improved our previous stochastic chemical evolution model by adding a time delay distribution for the coalescence of the neutron stars, instead of constant delays. The stochastic chemical evolution model can reproduce the trend and the observed spread in the [Eu/Fe] data with neutron star mergers as unique producers if we assume: (i) a delay time distribution ∝t−1.5, (ii) an $M_{\boldsymbol{ Eu}}= 3 \times 10^{-6} \, \boldsymbol{M}_{\odot }$ per event, (iii) progenitors of neutron stars in the range $9\!-\!50\, \boldsymbol{M}_{\odot}$, and (iv) a constant fraction of massive stars in the initial mass function (0.02) that produce neutron star mergers. Our best model is obtained by relaxing point (iv) and assuming a fraction that varies with metallicity. We confirm that the mixed scenario with both merging neutron stars and supernovae as europium producers can provide a good agreement with the data relaxing the constraints on the distribution time delays for the coalescence of neutron stars. Adopting our best model, we also reproduce the dispersion of [Eu/Fe] at a given metallicity, which depends on the fraction of massive stars that produce neutron star mergers. Future high-resolution spectroscopic surveys, such as 4MOST and WEAVE, will produce the necessary statistics to constrain at best this parameter.

Evolution of Galaxy Star Formation and Metallicity: Impact on Double Compact Object Mergers

Abstract In this paper, we study the impact of different galaxy statistics and empirical metallicity scaling relations on the merging rates and properties of compact object binaries. Firstly, we analyze the similarities and differences of using the star formation rate functions versus stellar mass functions as galaxy statistics for the computation of cosmic star formation rate density. We then investigate the effects of adopting the Fundamental Metallicity Relation versus a classic Mass Metallicity Relation to assign metallicity to galaxies with given properties. We find that when the Fundamental Metallicity Relation is exploited, the bulk of the star formation occurs at relatively high metallicities, even at high redshift; the opposite holds when the Mass Metallicity Relation is employed, since in this case the metallicity at which most of the star formation takes place strongly decreases with redshift. We discuss the various reasons and possible biases giving rise to this discrepancy. Finally, we show the impact of these different astrophysical prescriptions on the merging rates and properties of compact object binaries; specifically, we present results for the redshift-dependent merging rates and for the chirp mass and time delay distributions of the merging binaries.

A Sketching Framework for Reduced Data Transfer in Photon Counting Lidar

Single-photon lidar has become a prominent tool for depth imaging in recent years. At the core of the technique, the depth of a target is measured by constructing a histogram of time delays between emitted light pulses and detected photon arrivals. A major data processing bottleneck arises on the device when either the number of photons per pixel is large or the resolution of the time stamp is fine, as both the space requirement and the complexity of the image reconstruction algorithms scale with these parameters. We solve this limiting bottleneck of existing lidar techniques by sampling the characteristic function of the time of flight (ToF) model to build a compressive statistic, a so-called sketch of the time delay distribution, which is sufficient to infer the spatial distance and intensity of the object. The size of the sketch scales with the degrees of freedom of the ToF model (number of objects) and not, fundamentally, with the number of photons or the time stamp resolution. Moreover, the sketch is highly amenable for on-chip online processing. We show theoretically that the loss of information for compression is controlled and the mean squared error of the inference quickly converges towards the optimal Cram\'er-Rao bound (i.e. no loss of information) for modest sketch sizes. The proposed compressed single-photon lidar framework is tested and evaluated on real life datasets of complex scenes where it is shown that a compression rate of up-to 150 is achievable in practice without sacrificing the overall resolution of the reconstructed image.

A procedure for deriving new ODE models: Using the generalized linear chain trick to incorporate phase-type distributed delay and dwell time assumptions

Ordinary differential equations models have a wide variety of applications in the fields of mathematics, statistics, and the sciences. Though they are widely used, these models are sometimes viewed as inflexible with respect to the incorporation of time delays. The Generalized Linear Chain Trick (GLCT) serves as a way for modelers to incorporate much more flexible delay or dwell time distribution assumptions than the usual exponential and Erlang distributions. In this paper we demonstrate how the GLCT can be used to generate new ODE models by generalizing or approximating existing models to yield much more general ODEs with phase-type distributed delays or dwell times.

The delay time distribution of supernovae from integral-field spectroscopy of nearby galaxies

ABSTRACT Constraining the delay time distribution (DTD) of different supernova (SN) types can shed light on the time-scales of galaxy chemical enrichment and feedback processes affecting galaxy dynamics, and SN progenitor properties. Here, we present an approach to recover SN DTDs based on integral-field spectroscopy (IFS) of their host galaxies. Using a statistical analysis of a sample of 116 SNe in 102 galaxies, we evaluate different DTD models for SN types Ia (73), II (28), and Ib/c (15). We find the best SN Ia DTD fit to be a power law with an exponent α = −1.1 ± 0.3 (50 per cent confidence interval (C.I.)), and a time delay (between star formation and the first SNe) $\Delta = 50^{+100}_{-35}~\mathrm{Myr}$ (50 per cent C.I.). For core collapse (CC) SNe, both of the Zapartas et al. DTD models for single and binary stellar evolution are consistent with our results. For SNe II and Ib/c, we find a correlation with a Gaussian DTD model with $\sigma = 82^{+129}_{-23}~\mathrm{Myr}$ and $\sigma = 56^{+141}_{-9}~\mathrm{Myr}$ (50 per cent C.I.), respectively. This analysis demonstrates that IFS opens a new way of studying SN DTD models in the local Universe.

Modeling the flight departure delay using survival analysis in South Korea

The air transportation industry in South Korea has been growing since the 2000s. Although the number of air passengers has continuously increased, the flight delay rate has fluctuated from year to year. In this study, a survival analysis was conducted to compare each flight delay in terms of airport/time slot and to evaluate the actual impacts of major variables on flight delays. We performed multiple analyses using survival analysis methodologies, including the Kaplan–Meier estimator, log-rank test, and Cox proportional hazards model. In particular, we applied a turnaround buffer as a key variable in Cox proportional hazards model analysis. The survival curve showed that more international flights departed earlier than scheduled or with minimal delay than domestic flights. However, international flights tended to have more long-term delays. The log-rank test indicated that international flights had a wider distribution of delay times than domestic flights. In the Cox proportional hazards analysis, under the condition in which the actual flight turnaround time was less than 120 min, the results indicated that the longer the actual turnaround buffer was, the less frequently the delays occurred. By using these analyses, we could numerically verify the actual delay trends in South Korea. The results can be used as fundamental resources for political and economic decision-making processes in the aviation industry.

The Binary–Host Connection: Astrophysics of Gravitational-Wave Binaries from Host Galaxy Properties

Abstract Gravitational waves from the merger of binary neutron stars (BNSs) are accompanied by electromagnetic counterparts, making it possible to identify the associated host galaxy. In this work, we explore how properties of the hosts relate to the astrophysical processes leading to the mergers. It is thought that the BNS merger rate within a galaxy at a given epoch depends primarily on the galaxy’s star formation history, as well as the underlying merger time-delay distribution of the binary systems. The stellar history of a galaxy, meanwhile, depends on the cosmological evolution of the galaxy through time, and is tied to the growth of structure in the universe. We study the hosts of BNS mergers in the context of structure formation by populating the UniverseMachine simulations with gravitational wave (GW) events, based on a simple time-delay model. We find that different time-delay distributions predict different properties of the associated host galaxies, including the distributions of stellar mass, star formation rate, halo mass, and local and large-scale clustering of hosts. Moreover, BNSs merging today with short delay times occur preferentially in hosts with high star formation rates, while those with long delay times live in dense regions within massive halos that have low star formation. We show that with events from current GW detector networks, it is possible to make preliminary distinctions between formation channels which trace stellar mass, halo mass, or star formation rate. We also find that strategies to follow-up GW events with electromagnetic telescopes can be significantly optimized using the clustering properties of their hosts.

Predicted rates of merging neutron stars in galaxies

ABSTRACT We compute rates of merging neutron stars (MNS) in different galaxies, as well as the cosmic MNS rate in different cosmological scenarios. Our aim is to provide predictions of kilonova rates for future observations both at low and high redshift. In the adopted galaxy models, the production of r-process elements either by MNS or core-collapse supernovae is taken into account. To compute the MNS rates, we adopt either a constant total time delay for merging (10 Myr) or a distribution function of such delays. We conclude (i) the observed present time MNS rate in our Galaxy is well reproduced either with a constant time delay or a distribution function ∝t−1. (ii) The [Eu/Fe] versus [Fe/H] relation can be well reproduced with only MNS, if the time delay is short and constant. If a distribution function of delays is adopted, core-collapse supernovae are also required. (iii) The present time cosmic MNS rate can be well reproduced in several cosmological scenarios. (iv) Spiral galaxies are the major contributors to the cosmic MNS at all redshifts in hierarchical scenarios. In the pure luminosity evolution scenario, the spirals are the major contributors locally, whereas at high redshift ellipticals dominate. (v) The predicted cosmic MNS rate well agrees with the cosmic rate of short gamma-ray bursts, if the distribution function of delays is adopted in a cosmological hierarchical scenario observationally derived. (vi) Future observations of kilonovae in ellipticals will allow us to disentangle among constant or a distribution of time delays and among different cosmological scenarios.

Painlevé V and the Hankel determinant for a singularly perturbed Jacobi weight

We study the Hankel determinant generated by a singularly perturbed Jacobi weightw(x,t):=(1−x2)αe−tx2,x∈[−1,1],α>0,t≥0. If t=0, it is reduced to the classical symmetric Jacobi weight. For t>0, the factor e−tx2 induces an infinitely strong zero at the origin. This Hankel determinant is related to the Wigner time-delay distribution in chaotic cavities.In the finite n dimensional case, we obtain two auxiliary quantities Rn(t) and rn(t) by using the ladder operator approach. We show that the Hankel determinant has an integral representation in terms of Rn(t), where Rn(t) is closely related to a particular Painlevé V transcendent. Furthermore, we derive a second-order nonlinear differential equation and also a second-order difference equation for the logarithmic derivative of the Hankel determinant. This quantity can be expressed in terms of the Jimbo-Miwa-Okamoto σ-function of a particular Painlevé V. Then we consider the asymptotics of the Hankel determinant under a suitable double scaling, i.e. n→∞ and t→0 such that s=2n2t is fixed. Based on previous results by using the Coulomb fluid method, we obtain the large s and small s asymptotic behaviors of the scaled Hankel determinant, including the constant term in the asymptotic expansion.

Constraining delay time distribution of binary neutron star mergers from host galaxy properties

ABSTRACT Gravitational wave (GW) observatories are discovering binary neutron star mergers (BNSMs), and in at least one event we were able to track it down in multiple wavelengths of light, which allowed us to identify the host galaxy. Using a catalogue of local galaxies with inferred star formation histories and adopting a BNSM delay time distribution (DTD) model, we investigate the dependence of BNSM rate on an array of galaxy properties. Compared to the intrinsic property distribution of galaxies, that of BNSM host galaxies is skewed towards galaxies with redder colour, lower specific star formation rate, higher luminosity, and higher stellar mass, reflecting the tendency of higher BNSM rates in more massive galaxies. We introduce a formalism to efficiently make forecast on using host galaxy properties to constrain DTD models. We find comparable constraints from the dependence of BNSM occurrence distribution on galaxy colour, specific star formation rate, and stellar mass, all better than those from dependence on r-band luminosity. The tightest constraints come from using individual star formation histories of host galaxies, which reduces the uncertainties on DTD parameters by a factor of three or more. Substantially different DTD models can be differentiated with about 10 BNSM detections. To constrain DTD parameters at 10 per cent precision level requires about one hundred detections, achievable with GW observations on a decade time-scale.

Constraining the Delay Time Distribution of Compact Binary Objects from the Stochastic Gravitational-wave Background Searches

Abstract The initial separation of massive star binaries sets the timescale over which their compact remnants merge through the emission of gravitational waves. We show that the delay time distribution (DTD) of binary neutron stars or black holes can be inferred from the stochastic gravitational wave background (SGWB). If the DTD of a population is long, most of the mergers take place at low redshifts and the background would be rather quiet compared to a scenario in which the DTD is short leading to few individual detections at low redshift but a rather loud background. We show that different DTDs predict a factor of 5 difference in the magnitude of the gravitational wave background energy density ( ) and have the dominant effect on over other factors such as the mass function of the primary BH mass, , the maximum considered BH mass ( ), and the effective spin of the black hole ( ). A nondetection of such a background can rule out the short DTD scenario. We show that SGWB searches can rule out the short DTD scenario for the BBHs within about four years of observing time at advanced LIGO design sensitivity for a local merger rate of 30 assuming , and .

Neutron Star Mergers as the Main Source of r-process: Natal Kicks and Inside-out Evolution to the Rescue

Abstract Binary neutron star mergers (BNSMs) are currently the most promising source of r-process thanks to the detection of GW170817. The estimated occurring frequency and the amount of mass ejected per merger indicate that BNSMs by themselves can account for all the r-process enrichment in the Galaxy. However, the decreasing trend of [Eu/Fe] versus [Fe/H] of disk stars for [Fe/H] ≳ −1 in the solar neighborhood is inconsistent with the flat trend expected from BNSMs with a standard delay time distribution (DTD) ∝ t −1. This has led to the suggestion that either additional sources or modification to the DTD of BNSMs is required to match the observations. We investigate the effects of natal kicks received during the birth of neutron star binaries on the chemical evolution of r-process element Eu in the Milky Way by combining the results from the galactic dynamics code galpy with a one-zone Galactic chemical evolution model omega. We show that when key inputs from simulations of the inside-out disk evolution are combined with natal kicks, BNSMs can naturally reproduce the observed decreasing trend of [Eu/Fe] with [Fe/H] in the solar neighborhood without the need for modification to the DTD or additional r-process sources.

High rate of gravitational waves mergers from flyby perturbations of wide black hole triples in the field

ABSTRACT Ultrawide triple black holes (TBHs; with an outer orbit >103 au) in the field can be considerably perturbed by flyby encounters with field stars through the excitation of their outer orbit eccentricities. We study the cumulative effect of such flybys, and show them to be conductive for the production of gravitational-wave (GW) sources. Flyby encounters with TBHs can destabilize them, leading to binary–single resonant encounters between the outer black hole (BH) and the inner binary. These encounters can result in either a prompt GW merger of two of the TBH components during the resonant phase, or the disruption of the TBH. In the latter case, a more compact binary is left behind, while the third BH is ejected. Such compact remnant binaries may still inspiral through GW emission, producing delayed GW mergers, with a significant fraction of these merging in less than a Hubble time. We find a volumetric merger rate of ∼3–10 Gpc−3 yr−1 contributed by the (former) prompt-merger TBH channel and ${\sim} 100\!-\!250\,{\rm {\rm Gpc^{-3}\,yr^{-1}}}$ contributed by the (latter) delayed-merger TBH channel. The prompt channel gives rise to eccentric mergers in the aLIGO band, while the majority of the delayed GW mergers are circularized when enter the aLIGO band. We find the total eccentric volumetric merger rate to be ∼1–10 Gpc−3 yr−1 from both channels. We expect these mergers to show no significant spin–orbit alignment, and uniform delay-time distribution.

Coupled analysis to probe the effect of angular assignments on the secondary electron yield (SEY) from copper electrodes

Secondary electron emission from copper is probed utilizing Monte Carlo simulations that take account of elastic scattering based on the Mott theory and inelastic collisions based on energy-dependent energy loss functions. The loss function and stopping power were obtained through first-principles density functional theory. Angular assignment of electrons following elastic scattering or the creation of secondaries is shown to affect the energy-dependent secondary electron yield (SEY). A good match of the simulation results (with a peak SEY of ∼180% at around 300 eV and less than 10% deviation over the 0 to 1000 eV energy range) to available experimental data is shown based on an energy and momentum conservation scheme. Also, the distribution of delay times for the generation of secondaries, the SEY behavior at different incident angles, the energy distribution of emergent secondaries, and their creation profiles as a function of depth are computed to provide a more complete picture of the governing mechanisms and predicted responses.

Searching for Balmer-dominated Type Ia Supernova Remnants in M33

Abstract We searched for Balmer-dominated Type Ia supernova remnants (SNRs) in M33 by selecting thermal X-ray sources with L X ≥ 5 × 10 35 erg s−1, identifying associated Hα emission features, and checking their [S ii] and [O iii] emission properties. Our search did not find any Balmer-dominated Type Ia SNRs in M33. This result is puzzling because M33 is 2–3 times more massive than the Large Magellanic Cloud (LMC), yet the LMC hosts five Balmer-dominated Type Ia SNRs and M33 has none. We have considered observational biases; interstellar densities and ionization conditions; the Type Ia SN rate expected from the star formation history and Type Ia SN delay time distribution function; and the metallicity effect. None of these can explain the absence of X-ray-bright Balmer-dominated Type Ia SNRs in M33. It is intriguing that the Galaxy has X-ray-bright and thermal Type Ia SNRs (Kepler and Tycho), as well as X-ray-faint and nonthermal Type Ia SNRs (G1.9+0.3, SN1006, and RCW86), while the LMC does not have the X-ray-faint and nonthermal ones and M33 does not have the X-ray-bright and thermal ones.