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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Mapping the Universe in hydrogen deuteride

Hydrogen deuteride (HD) is prevalent in a wide variety of astrophysical environments, and measuring its large-scale distribution at different epochs can, in principle, provide information about the properties of these environments. In this paper we explore the prospects for accessing this distribution using line-intensity mapping of emission from the lowest rotational transition in HD, focusing on observations of the epoch of reionization (z~6–10) and earlier. We find the signal from the epoch of reionization to be most promising, through cross correlations within existing [CII] intensity mapping surveys. While the signal we predict is out of reach for current-generation projects, planned future improvements should be able to detect reionization-era HD without any additional observations, and would help to constrain the properties of the star-forming galaxies thought to play a key role in reionization. We also investigate several avenues for measuring HD during “cosmic dawn” (z~10–30), a period in which HD could provide one of the only complementary observables to 21 cm intensity maps. We conclude that existing and planned facilities are poorly matched to the specifications desirable for a significant detection, though such a measurement may be achievable with sustained future effort. Finally, we explain why HD intensity mapping of the intergalactic medium during the cosmic dark ages (z≳30) appears to be out of reach of any conceivable experiment.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Radial Profiles of the Binary Fraction in Elliptical Galaxies

The radial profile of the binary fraction may vary with environment and is of significant importance for studying the formation mechanisms of binary stars and their dynamical evolution within globular clusters and galaxies. However, existing studies remain limited to the Milky Way and its neighboring galaxies. Leveraging the method proposed by Zhang et al. for estimating the variation in the binary fraction from integrated spectral features, we analyze a sample of 513 elliptical galaxies drawn from the Mapping Nearby Galaxies at Apache Point Observatory survey to measure their radial binary fraction profiles. Our results show that after accounting for the effect induced by radial variations in the stellar population (SP), the median SP-subtracted binary fraction, $r^{\textrm{med}}_{\textrm{b,sub}}$, becomes approximately flat. For nearly all elliptical galaxies in our sample, the variation in the binary fraction relative to the galaxy center at 1R e is less than 5%. No clear correlation is found between the ​​​​​gradient of the binary fraction and the gradients of the SP properties. Moreover, we also compare differences between ultraviolet (UV) upturn and non-UV upturn galaxies. The overall binary fraction profiles and the SP properties of the non-UV upturn galaxies in our sample are comparable to those of the UV upturn galaxies. This similarity may arise from the presence of residual star formation in the non-UV upturn systems.

Li, Xiejin [Chinese Academy of Sciences; Universit↗
DOE OSTI2023

The Local Cluster Survey II: disc-dominated cluster galaxies with suppressed star formation

We investigate the role of dense environments in suppressing star formation by studying $\rm \log _{10}(M_\star /M_\odot) \gt 9.7$ star-forming galaxies in nine clusters from the Local Cluster Survey (0.0137 < z < 0.0433) and a large comparison field sample drawn from the Sloan Digital Sky Survey. We compare the star formation rate (SFR) with stellar mass relation as a function of environment and morphology. After carefully controlling for mass, we find that in all environments, the degree of SFR suppression increases with increasing bulge-to-total (B/T) ratio. In addition, the SFRs of cluster and infall galaxies at a fixed mass are more suppressed than their field counterparts at all values of B/T. These results suggest a quenching mechanism that is linked to bulge growth that operates in all environments and an additional mechanism that further reduces the SFRs of galaxies in dense environments. We limit the sample to B/T ≤ 0.3 galaxies to control for the trends with morphology and find that the excess population of cluster galaxies with suppressed SFRs persists. Here, we model the time-scale associated with the decline of SFRs in dense environments and find that the observed SFRs of the cluster core galaxies are consistent with a range of models including a mechanism that acts slowly and continuously over a long (2–5 Gyr) time-scale, and a more rapid (<1 Gyr) quenching event that occurs after a delay period of 1–6 Gyr. Quenching may therefore start immediately after galaxies enter clusters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The Most Metal-poor Stars in the Inner Bulge

The bulge is the oldest component of the Milky Way. Since numerous simulations of Milky Way formation have predicted that the oldest stars at a given metallicity are found on tightly bound orbits, the Galaxy’s oldest stars are likely metal-poor stars in the inner bulge with small apocenters (i.e., R {sub apo} ≲ 4 kpc). In the past, stars with these properties have been impossible to find due to extreme reddening and extinction along the line of sight to the inner bulge. We have used the mid-infrared metal-poor star selection of Schlaufman & Casey (2014) on Spitzer/Galactic Legacy Infrared Mid-Plane Survey Extraordinaire data to overcome these problems and target candidate inner bulge metal-poor giants for moderate-resolution spectroscopy with Anglo-Australian Telescope/AAOmega. We used those data to select three confirmed metal-poor giants ([Fe/H] = −3.15, −2.56, −2.03) for follow-up high-resolution Magellan/Magellan Inamori Kyocera Echelle spectroscopy. A comprehensive orbit analysis using Gaia DR2 astrometry and our measured radial velocities confirms that these stars are tightly bound inner bulge stars. We determine the elemental abundances of each star and find high titanium and iron-peak abundances relative to iron in our most metal-poor star. We propose that the distinct abundance signature we detect is a product of nucleosynthesis in the Chandrasekhar-mass thermonuclear supernova of a CO white dwarf accreting from a helium star with a delay time of about 10 Myr. Even though chemical evolution is expected to occur quickly in the bulge, the intense star formation in the core of the nascent Milky Way was apparently able to produce at least one Chandrasekhar-mass thermonuclear supernova progenitor before chemical evolution advanced beyond [Fe/H]∼−3.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Simulations of Tidal Disruption Events

Numerical simulations have historically played a major role in understanding the hydrodynamics of the tidal disruption process. Given the complexity of the geometry of the system, the challenges posed by the problem have indeed stimulated much work on the numerical side. Smoothed Particles Hydrodynamics methods, for example, have seen their very first applications in the context of tidal disruption and still play a major role to this day. Likewise, initial attempts at simulating the evolution of the disrupted star with the so-called affine method have been historically very useful. Here, we provide an overview of the numerical techniques used in the field and of their limitations, and summarize the work that has been done to simulate numerically the tidal disruption process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

JENSA: Past, present, and future

Nuclear reaction studies rely on three main physical components: the beam of nuclei provided by the facility, the detector systems used to measure the outgoing particles of interest, and the target. Target fabrication is thus a critical aspect of studying the reactions that power stars and probe the evolution of nuclear structure. The Jet Experiments in Nuclear Structure and Astrophysics (JENSA) gas jet target is the most dense helium jet target for rare isotope beam reaction studies in the world, providing targets of gaseous elements such as helium, nitrogen, and neon. A brief overview of the design and operation of JENSA, including commissioning and recent science experiments, and a discussion the future of JENSA coupled to the dedicated recoil separator SECAR, are presented.

Chipps, Kelly [ORNL] (ORCID:0000000330501298)↗
DOE OSTI2022

Exploring the MeV sky with a combined coded mask and Compton telescope: the Galactic Explorer with a Coded aperture mask Compton telescope (GECCO)

The sky at MeV energies is currently poorly explored. Here we present an innovative mission concept that builds upon the heritage of past and current missions improving the sensitivity and, very importantly, the angular resolution. This consists in combining a Compton telescope and a coded-mask telescope. We delineate the motivation for such a concept and we define the scientific goals for such a mission. The Galactic Explorer with a Coded Aperture Mask Compton Telescope (GECCO) is a novel concept for a next-generation telescope covering hard X-ray and soft gamma-ray energies. The potential and importance of this approach that bridges the observational gap in the MeV energy range are presented. With the unprecedented angular resolution of the coded mask telescope combined with the sensitive Compton telescope, a mission such as GECCO can disentangle the discrete sources from the truly diffuse emission. Individual Galactic and extragalactic sources are detected. This also allows to understand the gamma-ray Galactic center excess and the Fermi Bubbles, and to trace the low-energy cosmic rays, and their propagation in the Galaxy. Nuclear and annihilation lines are spatially and spectrally resolved from the continuum emission and from sources, addressing the role of low-energy cosmic rays in star formation and galaxy evolution, the origin of the 511 keV positron line, fundamental physics, and the chemical enrichment in the Galaxy. Such an instrument also detects explosive transient gamma-ray sources, which, in turn, enables identifying and studying the astrophysical objects that produce gravitational waves and neutrinos in a multi-messenger context. By looking at a poorly explored energy band it also allows discoveries of new astrophysical phenomena.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Prospects for Galactic and stellar astrophysics with asteroseismology of giant stars in the TESS continuous viewing zones and beyond

ABSTRACT The NASA Transiting Exoplanet Survey Satellite (NASA-TESS) mission presents a treasure trove for understanding the stars it observes and the Milky Way, in which they reside. We present a first look at the prospects for Galactic and stellar astrophysics by performing initial asteroseismic analyses of bright (G < 11) red giant stars in the TESS southern continuous viewing zone (SCVZ). Using three independent pipelines, we detect νmax and Δν in 41 per cent of the 15 405 star parent sample (6388 stars), with consistency at a level of $\sim \! 2{{\ \rm per\ cent}}$ in νmax and $\sim \! 5{{\ \rm per\ cent}}$ in Δν. Based on this, we predict that seismology will be attainable for ∼3 × 105 giants across the whole sky and at least 104 giants with ≥1 yr of observations in the TESS-CVZs, subject to improvements in analysis and data reduction techniques. The best quality TESS-CVZ data, for 5574 stars where pipelines returned consistent results, provide high-quality power spectra across a number of stellar evolutionary states. This makes possible studies of, for example, the asymptotic giant branch bump. Furthermore, we demonstrate that mixed ℓ = 1 modes and rotational splitting are cleanly observed in the 1-yr data set. By combining TESS-CVZ data with TESS-HERMES, SkyMapper, APOGEE, and Gaia, we demonstrate its strong potential for Galactic archaeology studies, providing good age precision and accuracy that reproduces well the age of high [α/Fe] stars and relationships between mass and kinematics from previous studies based on e.g. Kepler. Better quality astrometry and simpler target selection than the Kepler sample makes this data ideal for studies of the local star formation history and evolution of the Galactic disc. These results provide a strong case for detailed spectroscopic follow-up in the CVZs to complement that which has been (or will be) collected by current surveys.

Mackereth, J. Ted↗
DOE OSTI2022

TYC 2990-127-1: An Algol-type SB2 binary system of subgiant and red giant with a probable ongoing mass-transfer

ABSTRACT We present a study of the spectroscopic binary TYC 2990-127-1 from the LAMOST survey. We use full-spectrum fitting to derive radial velocities and spectral parameters. The high mass ratio indicates that the system underwent mass transfer in the past. We compute the orbital solution and find that it is a very close sub-giant/red giant pair on circular orbit, slightly inclined to the sky-plane. Fitting of the TESS photometrical data confirms this and suggests an inclination of i ∼ 39.8°. The light curve and spectrum around Hα show signs of irregular variability, which supports ongoing mass transfer. The binary evolution simulations suggest that the binary may experience non-conservative mass transfer with accretion efficiency 0.3, and the binary will enter into common envelope (CE) phase in the subsequent evolution. The remnant product after the ejection of CE may be a detached double helium white dwarf (He WD) or a merger.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Measurements of the thermal Sunyaev-Zel’dovich effect with ACT and DESI luminous red galaxies

Cosmic Microwave Background (CMB) photons scatter off the free-electron gas in galaxies and clusters, allowing us to use the CMB as a backlight to probe the gas in and around low-redshift galaxies. The thermal Sunyaev-Zel’dovich effect, sourced by hot electrons in high-density environments, measures the thermal pressure of the target objects, shedding light on halo thermodynamics and galaxy formation, and providing a path toward understanding the baryon distribution around cosmic structures. We use a combination of high-resolution CMB maps from the Atacama Cosmology Telescope and photometric luminous red galaxy catalogs from the Dark Energy Spectroscopic Instrument to measure the thermal Sunyaev-Zel’dovich signal in four redshift bins from 𝑧 = 0.4 to 𝑧 = 1.2, with a combined detection significance of 19⁢𝜎 when stacking on the fiducial CMB Compton-𝑦 map. We discuss possible sources of contamination, finding that residual dust emission associated with the target galaxies is important and limits current analyses. We discuss several mitigation strategies and quantify the residual modeling uncertainty. Furthermore, this work complements closely related measurements of the kinematic Sunyaev-Zel’dovich and weak lensing of the same galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Backlighting extended gas halos around luminous red galaxies: Kinematic Sunyaev-Zel’dovich effect from DESI Y1 and ACT data

The gas density profile around galaxies, shaped by feedback and affecting the galaxy lensing signal, is imprinted on the cosmic microwave background (CMB) by the kinematic Sunyaev-Zel’dovich effect (kSZ). We precisely measure this effect (𝑆/𝑁 ≈ 10) via velocity stacking with 825,283 spectroscopically confirmed luminous red galaxies (LRG) from the Dark Energy Spectroscopic Instrument Year 1 (DESI Y1) survey, which overlap with the Atacama Cosmology Telescope (ACT) Data Release 6 temperature maps over ≥ 4,000 deg 2 . We explore the kSZ dependence with various galaxy parameters and find no significant trend with redshift but clear trends with stellar mass and absolute magnitude in 𝑔, 𝑟, and 𝑧 bands. Our analysis suggests that the gas extends beyond the dark matter halo (99.5% confidence level, i.e., probability to exceed (PTE)⁢ = 0.005). We find a tentative preference for hydrodynamical simulation models with stronger feedback that drives gas further out (Illustris 𝑧 = 0.5, PTE⁢ = 0.37) over weaker-feedback cases (IllustrisTNG 𝑧 = 0.8, PTE⁢ = 0.045), though with limited statistical significance. In all cases, a free multiplicative amplitude was fit to the simulated profiles, and further modeling work is required to firm up these conclusions. We find consistency between kSZ profiles around spectroscopic and photometric LRG, with comparable statistical power, thus increasing our confidence in the photometric analysis. Additionally, we present the first kSZ measurement around the DESI Y1 bright galaxy sample (BGS) and the emission-line galaxies (ELG) whose features match qualitative expectations. Finally, we forecast 𝑆/𝑁 ∼ 50 for future stacked kSZ measurements using data from the ACT, the DESI Y3, and the Rubin Observatory. Furthermore, these measurements will serve as an input for galaxy formation models and baryonic uncertainties in galaxy lensing.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

A Continuous Galactic Line Source of Axions: The Remarkable Case of 23 Na

Here, we argue that $^{23}$Na is a potentially significant source of galactic axions. For temperatures $\gtrsim 7 \times 10^8$K -- characteristic of carbon burning in the massive progenitors of supernovae and ONeMg white dwarfs -- the 440 keV first excited state of $^{23}$Na is thermally populated, with its repeated decays pumping stellar energy into escaping axions. Odd-A nuclear abundances are typically very low in high-temperature stellar environments (or absent entirely due to burn-up). $^{23}$Na is an exception: $\approx 0.1 M_\odot$ of the isotope is synthesized during carbon burning then maintained at $\approx 10^9$K for times ranging up to $6 \times 10^4$y. Using MESA simulations, a galactic model, and sampling over progenitor masses, locations, and evolutionary stages, we find a continuous flux at earth of $\langle ϕ_a \rangle \approx 22$/cm$^2$s for $g^\mathrm{eff}_{aNN} = 10^{-9}$. Some fraction of these axions convert to photons as they propagate through the galactic magnetic field, producing a distinctive 440 keV line $γ$ ray detectable by all-sky detectors like the Compton Spectrometer and Imager (COSI). Assuming a 1$μ$G galactic magnetic field and a sufficiently light axion mass, we find that COSI will be able to probe $| g_{aNN}^\mathrm{eff} g_{a γγ} | \gtrsim1.8 \times 10^{-22}$ GeV$^{-1}$ at $3σ$ after two years of surveying.

Dark matter↗
DOE OSTI2020

Early structure formation constraints on the ultralight axion in the postinflation scenario

Many works have concentrated on the observable signatures of the dark matter being an ultralight axion-like particle (ALP). We concentrate on a particularly dramatic signature in the late-time cosmological matter power spectrum that occurs if the symmetry breaking that establishes the ALP happens after inflation -- white-noise density fluctuations that dominate at small scales over the adiabatic fluctuations from inflation. Here, these fluctuations alter the early history of nonlinear structure formation. We find that for symmetry breaking scales of f A ~ 10 13 – 10 15 GeV, which requires a high effective maximum temperature after inflation, ALP dark matter with particle mass of m A ~ 10 –13 – 10 –20 eV could significantly change the number of high-redshift dwarf galaxies, the reionization history, and the Lyα forest. We consider all three observables. We find that the Lyα forest is the most constraining of current observables, excluding f A ≳ 10 15 GeV (m A ≲ 10 –17 eV) in the simplest model for the ALP and considerably lower values in models coupled to a hidden strongly interacting sector (f A ≳ 10 13 GeV and m A ≲ 10 –13 eV). Observations that constrain the extremely high-redshift tail of reionization may disfavor similar levels of isocurvature fluctuations as the forest. Future z ~ 20–30 21cm observations have the potential to improve these constraints further using that the supersonic motions of the isocurvature-enhanced abundance of ~10 4 M ⊙ halos would shock heat the baryons, sourcing large BAO features.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Oscillations and random walk of the soliton core in a fuzzy dark matter halo

We report that a fuzzy dark matter halo consists of a soliton core close to the center and a Navarro-Frenk-White–like density profile in the outer region. Previous investigations found that the soliton core exhibits temporal oscillations and random walk excursions around the halo center. Analyzing a set of numerical simulations, we show that both phenomena can be understood as the results of wave interference - a suitable superposition of the ground (solitonic) state and excited states in a fixed potential suffices to account for the main features of these phenomena. Such an eigenmode analysis can shed light on the evolution of a satellite halo undergoing tidal disruption. As the outer halo is stripped away, reducing the amplitudes of the excited states, the ground state evolves adiabatically. This suggests diminished soliton oscillations and random walk excursions, an effect to consider in deducing constraints from stellar heating.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Atacama Cosmology Telescope: Combined kinematic and thermal Sunyaev-Zel’dovich measurements from BOSS CMASS and LOWZ halos

The scattering of cosmic microwave background (CMB) photons off the free-electron gas in galaxies and clusters leaves detectable imprints on high resolution CMB maps: the thermal and kinematic Sunyaev-Zel’dovich effects (tSZ and kSZ respectively). We use combined microwave maps from the Atacama Cosmology Telescope DR5 and Planck in combination with the CMASS (mean redshift $\langle z \rangle$ = 0.55 and host halo mass $\langle M_{vir} \rangle$ = 3 × 10 13 M ⊙ ) and LOWZ ( $\langle z \rangle$ = 0.31 , $\langle M_{vir} \rangle$ = 5 × 10 13 M ⊙ ) galaxy catalogs from the Baryon Oscillation Spectroscopic Survey (BOSS DR10 and DR12), to study the gas associated with these galaxy groups. Using individual reconstructed velocities, we perform a stacking analysis and reject the no-kSZ hypothesis at 6.5σ, the highest significance to date. This directly translates into a measurement of the electron number density profile, and thus of the gas density profile. Despite the limited signal to noise, the measurement shows at high significance that the gas density profile is more extended than the dark matter density profile, for any reasonable baryon abundance (formally > 90 σ for the cosmic baryon abundance). We simultaneously measure the tSZ signal, i.e., the electron thermal pressure profile of the same CMASS objects, and reject the no-tSZ hypothesis at 10σ. We combine tSZ and kSZ measurements to estimate the electron temperature to 20% precision in several aperture bins, and find it comparable to the virial temperature. In a companion paper, we analyze these measurements to constrain the gas thermodynamics and the properties of feedback inside galaxy groups. We present the corresponding LOWZ measurements in this paper, ruling out a null kSZ (tSZ) signal at 2.9 (13.9) σ , and leave their interpretation to future work. This paper and the companion paper demonstrate that current CMB experiments can detect and resolve gas profiles in low mass halos and at high redshifts, which are the most sensitive to feedback in galaxy formation and the most difficult to measure any other way. They will be a crucial input to cosmological hydrodynamical simulations, thus improving our understanding of galaxy formation. These precise gas profiles are already sufficient to reduce the main limiting theoretical systematic in galaxy-galaxy lensing: baryonic uncertainties. Future such measurements will thus unleash the statistical power of weak lensing from the Rubin, Euclid and Roman observatories. Finally, our stacking software ThumbStackis publicly available and directly applicable to future Simons Observatory and CMB-S4 data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Modifying PyUltraLight to model scalar dark matter with self-interactions

Here we introduce a modification of the pysiultralight code that models the dynamical evolution of ultralight axionlike scalar dark matter fields. Our modified code, pysiultralight, adds a quartic, self-interaction term to reflect the one which arises naturally in axionlike particle models. Using a particle mass of 10−22 eV/c 2 , we show that pysiultralight produces spatially oscillating solitons, exploding solitons, and collapsing solitons which prior analytic work shows will occur with attractive self-interactions. Using our code we calculate the oscillation frequency as a function of soliton mass and equilibrium radius in the presence of attractive self-interactions. We show that when the soliton mass is below the critical mass ($M_c$ = $\frac{\sqrt{3}}{2} M_{max}$) described by Chavanis and the initial radius is within a specific range, solitons are unstable and explode. We test the maximum mass criteria described by Chavanis and Chavanis and Delfini for a soliton to collapse when attractive self-interactions are included. We also analyze both binary soliton collisions and a soliton rotating around a central mass with attractive and repulsive self-interactions. We find that when attractive self-interactions are included, the density profiles get distorted after a binary collision. We also find that a soliton is less susceptible to tidal stripping when attractive self-interactions are included. We find that the opposite is true for repulsive self-interactions in that solitons would be more easily tidally stripped. Including self-interactions might therefore influence the survival timescales of infalling solitons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Construction of wave dark matter halos: Numerical algorithm and analytical constraints

Here we present a wave generalization of the classic Schwarzschild method for constructing self-consistent halos—such a halo consists of a suitable superposition of waves instead of particle orbits, chosen to yield a desired mean density profile. As an illustration, the method is applied to spherically symmetric halos. We derive an analytic relation between the particle distribution function and the wave superposition amplitudes and show how it simplifies in the high-energy (WKB) limit. We verify the stability of such constructed halos by numerically evolving the Schrödinger-Poisson system. The algorithm provides an efficient and accurate way to simulate the time-dependent halo substructures from wave interference. We use this method to construct halos with a variety of density profiles, all of which have a core from the ground-state wave function, though the core-halo relation need not be the standard one.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Tidal disruption of solitons in self-interacting ultralight axion dark matter

We report ultralight axions (ULAs) are promising dark matter candidates that can have a distinct impact on the formation and evolution of structure on nonlinear scales relative to the cold, collisionless dark matter (CDM) paradigm. However, most studies of structure formation in ULA models do not include the effects of self-interactions, which are expected to arise generically. Here, we study how the tidal evolution of solitons is affected by ULA self-interaction strength and sign. Specifically, using the pseudospectral solver UltraDark.jl, we simulate the tidal disruption of self-interacting solitonic cores as they orbit a 10 11 M ⊙ Navarro-Frenk-White CDM host halo potential for a range of orbital parameters, assuming a fiducial ULA particle mass of 10 -22 eV . We find that repulsive (attractive) self-interactions significantly accelerate (decelerate) soliton tidal disruption. We also identify a degeneracy between the self-interaction strength and soliton mass that determines the efficiency of tidal disruption, such that disruption timescales are affected at the ~ 50 % level for variations in the dimensionless ULA self-coupling from λ = -10 -92 to λ = 10 -92 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗