skip to main content


Title: Deep multi-task mining Calabi–Yau four-folds
Abstract

We continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi–Yau manifolds using deep learning. In this paper, we consider the dataset of all Calabi–Yau four-folds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by state-of-the-art computer vision architectures, we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using a multi-task architecture. With 30% (80%) training ratio, we reach an accuracy of 100% forh(1,1)and 97% forh(2,1)(100% for both), 81% (96%) forh(3,1), and 49% (83%) forh(2,2). Assuming that the Euler number is known, as it is easy to compute, and taking into account the linear constraint arising from index computations, we get 100% total accuracy.

 
more » « less
Award ID(s):
2019786
NSF-PAR ID:
10303335
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
IOP Publishing
Date Published:
Journal Name:
Machine Learning: Science and Technology
Volume:
3
Issue:
1
ISSN:
2632-2153
Page Range / eLocation ID:
Article No. 015006
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    We measure the CO-to-H2conversion factor (αCO) in 37 galaxies at 2 kpc resolution, using the dust surface density inferred from far-infrared emission as a tracer of the gas surface density and assuming a constant dust-to-metal ratio. In total, we have ∼790 and ∼610 independent measurements ofαCOfor CO (2–1) and (1–0), respectively. The mean values forαCO (2–1)andαCO (1–0)are9.35.4+4.6and4.22.0+1.9Mpc2(Kkms1)1, respectively. The CO-intensity-weighted mean is 5.69 forαCO (2–1)and 3.33 forαCO (1–0). We examine howαCOscales with several physical quantities, e.g., the star formation rate (SFR), stellar mass, and dust-mass-weighted average interstellar radiation field strength (U¯). Among them,U¯, ΣSFR, and the integrated CO intensity (WCO) have the strongest anticorrelation with spatially resolvedαCO. We provide linear regression results toαCOfor all quantities tested. At galaxy-integrated scales, we observe significant correlations betweenαCOandWCO, metallicity,U¯, and ΣSFR. We also find thatαCOin each galaxy decreases with the stellar mass surface density (Σ) in high-surface-density regions (Σ≥ 100Mpc−2), following the power-law relationsαCO(21)Σ0.5andαCO(10)Σ0.2. The power-law index is insensitive to the assumed dust-to-metal ratio. We interpret the decrease inαCOwith increasing Σas a result of higher velocity dispersion compared to isolated, self-gravitating clouds due to the additional gravitational force from stellar sources, which leads to the reduction inαCO. The decrease inαCOat high Σis important for accurately assessing molecular gas content and star formation efficiency in the centers of galaxies, which bridge “Milky Way–like” to “starburst-like” conversion factors.

     
    more » « less
  2. Abstract

    We use ALMA observations of CO(2–1) in 13 massive (M*≳ 1011M) poststarburst galaxies atz∼ 0.6 to constrain the molecular gas content in galaxies shortly after they quench their major star-forming episode. The poststarburst galaxies in this study are selected from the Sloan Digital Sky Survey spectroscopic samples (Data Release 14) based on their spectral shapes, as part of the Studying QUenching at Intermediate-z Galaxies: Gas, anguLarmomentum, and Evolution (SQuIGGLE) program. Early results showed that two poststarburst galaxies host large H2reservoirs despite their low inferred star formation rates (SFRs). Here we expand this analysis to a larger statistical sample of 13 galaxies. Six of the primary targets (45%) are detected, withMH2109M. Given their high stellar masses, this mass limit corresponds to an average gas fraction offH2MH2/M*7%or ∼14% using lower stellar masses estimates derived from analytic, exponentially declining star formation histories. The gas fraction correlates with theDn4000 spectral index, suggesting that the cold gas reservoirs decrease with time since burst, as found in local K+A galaxies. Star formation histories derived from flexible stellar population synthesis modeling support this empirical finding: galaxies that quenched ≲150 Myr prior to observation host detectable CO(2–1) emission, while older poststarburst galaxies are undetected. The large H2reservoirs and low SFRs in the sample imply that the quenching of star formation precedes the disappearance of the cold gas reservoirs. However, within the following 100–200 Myr, theSQuIGGLEgalaxies require the additional and efficient heating or removal of cold gas to bring their low SFRs in line with standard H2scaling relations.

     
    more » « less
  3. Abstract

    We present13CO(J= 1 → 0) observations for the EDGE-CALIFA survey, which is a mapping survey of 126 nearby galaxies at a typical spatial resolution of 1.5 kpc. Using detected12CO emission as a prior, we detect13CO in 41 galaxies via integrated line flux over the entire galaxy and in 30 galaxies via integrated line intensity in resolved synthesized beams. Incorporating our CO observations and optical IFU spectroscopy, we perform a systematic comparison between the line ratio12/13I[12CO(J=10)]/I[13CO(J=10)]and the properties of the stars and ionized gas. Higher12/13values are found in interacting galaxies compared to those in noninteracting galaxies. The global12/13slightly increases with infrared colorF60/F100but appears insensitive to other host-galaxy properties such as morphology, stellar mass, or galaxy size. We also present azimuthally averaged12/13profiles for our sample up to a galactocentric radius of 0.4r25(∼6 kpc), taking into account the13CO nondetections by spectral stacking. The radial profiles of12/13are quite flat across our sample. Within galactocentric distances of 0.2r25, the azimuthally averaged12/13increases with the star formation rate. However, Spearman rank correlation tests show the azimuthally averaged12/13does not strongly correlate with any other gas or stellar properties in general, especially beyond 0.2r25from the galaxy centers. Our findings suggest that in the complex environments in galaxy disks,12/13is not a sensitive tracer for ISM properties. Dynamical disturbances, like galaxy interactions or the presence of a bar, also have an overall impact on12/13, which further complicates the interpretations of12/13variations.

     
    more » « less
  4. Abstract

    We present a Keck/MOSFIRE rest-optical composite spectrum of 16 typical gravitationally lensed star-forming dwarf galaxies at 1.7 ≲z≲ 2.6 (zmean= 2.30), all chosen independent of emission-line strength. These galaxies have a median stellar mass oflog(M*/M)med=8.290.43+0.51and a median star formation rate ofSFRHαmed=2.251.26+2.15Myr1. We measure the faint electron-temperature-sensitive [Oiii]λ4363 emission line at 2.5σ(4.1σ) significance when considering a bootstrapped (statistical-only) uncertainty spectrum. This yields a direct-method oxygen abundance of12+log(O/H)direct=7.880.22+0.25(0.150.06+0.12Z). We investigate the applicability at highzof locally calibrated oxygen-based strong-line metallicity relations, finding that the local reference calibrations of Bian et al. best reproduce (≲0.12 dex) our composite metallicity at fixed strong-line ratio. At fixedM*, our composite is well represented by thez∼ 2.3 direct-method stellar mass—gas-phase metallicity relation (MZR) of Sanders et al. When comparing to predicted MZRs from the IllustrisTNG and FIRE simulations, having recalculated our stellar masses with more realistic nonparametric star formation histories(log(M*/M)med=8.920.22+0.31), we find excellent agreement with the FIRE MZR. Our composite is consistent with no metallicity evolution, at fixedM*and SFR, of the locally defined fundamental metallicity relation. We measure the doublet ratio [Oii]λ3729/[Oii]λ3726 = 1.56 ± 0.32 (1.51 ± 0.12) and a corresponding electron density ofne=10+215cm3(ne=10+74cm3) when considering the bootstrapped (statistical-only) error spectrum. This result suggests that lower-mass galaxies have lower densities than higher-mass galaxies atz∼ 2.

     
    more » « less
  5. Abstract

    Cosmic reionization was the last major phase transition of hydrogen from neutral to highly ionized in the intergalactic medium (IGM). Current observations show that the IGM is significantly neutral atz> 7 and largely ionized byz∼ 5.5. However, most methods to measure the IGM neutral fraction are highly model dependent and are limited to when the volume-averaged neutral fraction of the IGM is either relatively low (x¯HI103) or close to unity (x¯HI1). In particular, the neutral fraction evolution of the IGM at the critical redshift range ofz= 6–7 is poorly constrained. We present new constraints onx¯HIatz∼ 5.1–6.8 by analyzing deep optical spectra of 53 quasars at 5.73 <z< 7.09. We derive model-independent upper limits on the neutral hydrogen fraction based on the fraction of “dark” pixels identified in the Lyαand Lyβforests, without any assumptions on the IGM model or the intrinsic shape of the quasar continuum. They are the first model-independent constraints on the IGM neutral hydrogen fraction atz∼ 6.2–6.8 using quasar absorption measurements. Our results give upper limits ofx¯HI(z=6.3)<0.79±0.04(1σ),x¯HI(z=6.5)<0.87±0.03(1σ), andx¯HI(z=6.7)<0.940.09+0.06(1σ). The dark pixel fractions atz> 6.1 are consistent with the redshift evolution of the neutral fraction of the IGM derived from Planck 2018.

     
    more » « less