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NASA NTRS1989

The orbital inclination of A0620 - 00 measured polarimetrically

The mass of the degenerate primary in A0620 - 00 is inferred from its spectroscopic mass function to be not less than 3.2 solar masses, making it an excellent candidate for a black hole. The exact value of the mass depends on the orbital inclination. The inclination of a binary system can be determined from the shape of its Stokes parameter light curves if the linear polarization of the system varies as a function of orbital phase. A0620 - 00 over one 8-hour binary period was observed with the 4.5-m equivalent MMT. Its polarization in the visible is variable with orbital phase. The standard theory of Brown et al. (1978) was used to derive an orbital inclination of i = 57 deg (+20 deg, -50 deg), where the error is the 90-percent confidence interval. An inclination of i = 57 deg corresponds to a mass of the compact primary of 6.6 solar masses, but the large uncertainty in the measured value of the inclination allows the derived mass of A0620 - 00 to be as low as 3.8 solar masses. If this is taken to be the maximum mass of any degenerate configuration consistent with general relativity except a black hole, then the mass of A0620 - 00 is still not well enough determined to conclude that it must be a black hole.

Dolan, Joseph F.↗

NASA NTRS2007

The ROSSI X-Ray Timing Explorer: Capabilities, Achievements and Aims

The prime scientific objectives of the Rossi X-Ray Timing Explorer (RXTE) were the study of astrophysical compact objects: black holes (galactic and extragalactic), many types of neutron stars, and accreting white dwarfs. RXTE was successful in achieving its original observing objectives of large area and high time resolution observations with broadband (2-200 keV) spectra, scheduled flexibly enough to enable observations of targets of opportunity on any timescale greater than a few hours. These capabilities enabled qualitatively new discoveries about dynamical timescale phenomena related to neutron stars and black holes, phenomena which probe basic physics in the most extreme environments of gravity, density, and magnetic fields. RXTE has extended its lifetime by applying the proportional counter area selectively and maintains schedule flexibility by making use of the distribution of targets around the sky. Proposed future observations emphasize opportunity to discover and study additional millisecond pulsars, pursue the high frequency quasi-periodic oscillations in black hole transients, and connect high frequency phenomena with longer term characteristics. RXTE will continue to strongly support, for both galactic and extragalactic targets, combining RXTE observations with other wavelengths (from IR to TeV) or with other capabilities, such as high spectral resolution.

Swank, J. H.↗

NASA NTRS2020

Tidal Disruptions of Main-sequence Stars. II. Simulation Methodology and Stellar Mass Dependence of the Character of Full Tidal Disruptions

This is the second in a series of papers presenting the results of fully general relativistic simulations of stellar tidal disruptions in which the stars' initial states are realistic main-sequence models. In the first paper, we gave an overview of this program and discussed the principal observational implications of our work. Here we describe our calculational method, which includes a new method for calculating fully relativistic stellar self-gravity, and provide details about the outcomes of full disruptions, focusing on the stellar mass dependence of the outcomes for a black hole of mass 106 M(⊙). We consider eight different stellar masses, from 0.15 M(⊙) to 10 M(⊙). We find that, relative to the traditional order-of-magnitude estimate r t, the physical tidal radius of low-mass stars (M(*) ≲ 0.7 M(⊙)) is larger by tens of percent, while for high-mass stars (M(*) ≲ 1 M(⊙)) it is smaller by a factor of 2–2.5. The traditional estimate of the range of energies found in the debris is ≈1.4× too large for low-mass stars, but is a factor of ~2 too small for high-mass stars; in addition, the energy distribution for high-mass stars has significant wings. For all stars undergoing tidal encounters, we find that mass loss continues for many stellar vibration times because the black hole's tidal gravity competes with the instantaneous stellar gravity at the star's surface until the star has reached a distance from the black hole ~O(10)r(t).

Taeho Ryu↗

DOE OSTI2026

Quantum fate of the Choptuik naked singularity

Classical critical collapse provides a dynamical route from smooth initial data to a naked singularity, representing a sharper violation of predictability than ordinary black hole singularities. We argue that this distinction is erased by quantum backreaction. Building on the semiclassical interior analysis, where quantum self-energy of the collapsing matter generates a universal growing mode and a finite mass gap, we study the exterior naked singularity region that determines global visibility in the Einstein-scalar system. We analyze controlled exterior models in both $2+1$ and $3+1$ dimensions. In the former, smooth matching and physical boundary conditions analytically select a vacuum polarization state, whose backreaction cloaks the classically naked region by a quantum trapped branch. In the latter, numerical horizon tracing shows that near a quantum-shifted threshold the exterior develops finite-mass marginally trapped surfaces rather than a zero-mass naked endpoint. These results suggest a global quantum picture in which the Choptuik naked singularity shares the fate of an ordinary black hole singularity: quantum effects push the putative Cauchy horizon behind a quantum-generated horizon, thereby reducing the loss of predictability to the standard black hole evaporation problem.

FOS: Physical sciences↗

DOE OSTI2023

General relativistic simulations of collapsing binary neutron star mergers with Monte Carlo neutrino transport

Recent gravitational wave observations of neutron-star-neutron-star and neutron-star-black-hole binaries appear to indicate that massive neutron stars may not be too uncommon in merging systems. These discoveries have led to an increased interest in the simulation of merging compact binaries involving massive stars. In this paper, we present a first set of evolution of massive neutron star binaries using Monte Carlo radiation transport for the evolution of neutrinos. Here, we study a range of systems, from nearly symmetric binaries that collapse to a black hole before forming a disk or ejecting material, to more asymmetric binaries in which tidal disruption of the lower mass star leads to the production of more interesting postmerger remnants. For the latter type of systems, we additionally study the impact of viscosity on the properties of the outflows, and compare our results to two recent simulations of identical binaries performed with the whiskyTHC code. We find agreement on the black hole properties, disk mass, and mass and velocity of the outflows within expected numerical uncertainties, and some minor but noticeable differences in the evolution of the electron fraction when using a subgrid viscosity model, with viscosity playing a more minor role in our simulations. The method used to account for r-process heating in the determination of the outflow properties appears to have a larger impact on our result than those differences between numerical codes. We also use the simulation with the most ejected material to verify that our newly implemented Lagrangian tracers provide a reasonable sampling of the matter outflows as they leave the computational grid. We note that, given the lack of production of hot outflows in these mergers, the main role of neutrinos in these systems is to set the composition of the postmerger remnant. One of the main potential uses of our simulations is, thus, as improved initial conditions for longer evolutions of such remnants.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2006

The NASA Beyond Einstein Program

Einstein's legacy is incomplete, his theory of General relativity raises -- but cannot answer --three profound questions: What powered the big bang? What happens to space, time, and matter at the edge of a black hole? and What is the mysterious dark energy pulling the Universe apart? The Beyond Einstein program within NASA's Office of Space Science aims to answer these questions, employing a series of missions linked by powerful new technologies and complementary approaches towards shared science goals. The Beyond Einstein program has three linked elements which advance science and technology towards two visions; to detect directly gravitational wave signals from the earliest possible moments of the BIg Bang, and to image the event horizon of a black hole. The central element is a pair of Einstein Great Observatories, Constellation-X and LISA. Constellation-X is a powerful new X-ray observatory dedicated to X-Ray Spectroscopy. LISA is the first spaced based gravitational wave detector. These powerful facilities will blaze new paths to the questions about black holes, the Big Bang and dark energy. The second element is a series of competitively selected Einstein Probes, each focused on one of the science questions and includes a mission dedicated resolving the Dark Energy mystery. The third element is a program of technology development, theoretical studies and education. The Beyond Einstein program is a new element in the proposed NASA budget for 2004. This talk will give an overview of the program and the missions contained within it.

White, Nicholas E.↗

DOE OSTI2023

The active CGCG 077-102 NED02 galaxy within the Abell 2063 galaxy cluster

Context.Within the framework of investigating the link between the central super massive black holes in the cores of galaxies and the galaxies themselves, we detected a variable X-ray source in the center of CGCG 077-102 NED02, which is a member of the CGCG 077-102 galaxy pair within the Abell 2063 cluster of galaxies. Aims.Our goal is to combine X-ray and optical data to demonstrate that this object harbors an active super massive black hole in its core, and to relate this to the dynamical status of the galaxy pair within the Abell 2063 cluster. Methods.We usedChandraandXMM-Newtonarchival data to derive the X-ray spectral shape and variability. We also obtained optical spectroscopy to detect the expected emission lines that are typically found in active galactic nuclei. Finally, we used public ZTF imaging data to investigate the optical variability. Results.There is no evidence of multiple X-ray sources or extended components within CGCG 077-102 NED02. Single X-ray spectral models fit the source well. We detect significant, nonrandom inter-observation 0.5–10 keV X-ray flux variabilities, for observations separated by ∼4 days for short-term variations and by up to ∼700 days for long-term variations. Optical spectroscopy points toward a passive galaxy for CGCG 077-102 NED01 and a Seyfert for CGCG 077-102 NED02. The classification of CGCG 077-102 NED02 is also consistent with its X-ray luminosity of over 10 42 erg s −1 . We do not detect short-term variability in the optical ZTF light curves. However, we find a significant long-term stochastic variability in theg-band that can be well described by the damped random walk model with a best-fit characteristic damping timescale ofτ DRW = 30 −12 +28 days. Finally, the CGCG 077-102 galaxy pair is deeply embedded within the Abell 2063 potential, with a long enough history within this massive structure to have been affected by the influence of this cluster for a long time. Conclusions.Our observations point toward a moderately massive black hole in the center of CGCG 077-102 NED02 of ∼10 6 M ⊙ . As compared to another similar pair in the literature, CGCG 077-102 NED02 is not heavily obscured, perhaps because of the surrounding intracluster medium ram-pressure stripping.

Astronomy & Astrophysics↗

NASA NTRS2019

Multi-messenger Astrophysics with Pulsar Timing Arrays: Astro2020 Science White Paper

Pulsar timing arrays (PTAs) are on the verge of detecting low-frequency gravitational waves (GWs)from supermassive black hole binaries (SMBHBs). With continued observations of a large sampleof millisecond pulsars, PTAs will reach this major milestone within the next decade. Already,SMBHB candidates are being identied by electromagnetic surveys in ever-increasing numbers;upcoming surveys will enhance our ability to detect and verify candidates, and will be instrumentalin identifying the host galaxies of GW sources. Multi-messenger (GW and electromagnetic) obser-vations of SMBHBs will revolutionize our understanding of the co-evolution of SMBHs with theirhost galaxies, the dynamical interactions between binaries and their galactic environments, and thefundamental physics of accretion. Multi-messenger observations can also make SMBHBs `standardsirens' for cosmological distance measurements out to z ~ 0.5 LIGO has already ushered in break-through insights in our knowledge of black holes. The multi-messenger detection of SMBHBs withPTAs will be a breakthrough in the years 2020-2030 and beyond, and prepare us for LISA to helpcomplete our views of black hole demographics and evolution at higher redshifts.

Kelley, L. Z.↗

DOE OSTI2024

Fragmentation in Gravitationally Unstable Collapsar Disks and Subsolar Neutron Star Mergers

Abstract Although stable neutron stars (NSs) can in principle exist down to massesM ns ≈ 0.1M ⊙ , standard models of stellar core-collapse predict a robust lower limitM ns ≳ 1.2M ⊙ , roughly commensurate with the Chandrasekhar massM Ch of the progenitor’s iron core (electron fractionY e ≈ 0.5). However, this limit may be circumvented in sufficiently dense neutron-rich environments (Y e < 0.5) for which M Ch ∝ Y e 2 is reduced to ≲1M ⊙ . Such physical conditions could arise in the black hole accretion disks formed from the collapse of rapidly rotating stars (“collapsars”), as a result of gravitational instabilities and cooling-induced fragmentation, similar to models for planet formation in protostellar disks. We confirm that the conditions to form subsolar-mass NS (ssNS) may be marginally satisfied in the outer regions of massive neutrino-cooled collapsar disks. If the disk fragments into multiple ssNSs, their subsequent coalescence offers a channel for precipitating subsolar mass LIGO/Virgo gravitational-wave mergers that does not implicate primordial black holes. The model makes several additional predictions: (1) ∼Hz frequency Doppler modulation of the ssNS-merger gravitational-wave signals due to the binary’s orbital motion in the disk; (2) at least one additional gravitational-wave event (coincident within ≲hours), from the coalescence of the ssNS-merger remnant(s) with the central black hole; (3) an associated gamma-ray burst and supernova counterpart, the latter boosted in energy and enriched withr-process elements from the NS merger(s) embedded within the exploding stellar envelope (“kilonovae inside a supernova”).

Astronomy & Astrophysics↗

NASA NTRS1997

The Evolving Universe: Structure and Evolution of the Universe Roadmap 2000-2020

The Roadmap for the Structure and Evolution of the Universe (SEU) theme embraces three fundamental, scientific quests: (1) To explain structure in the Universe and forecast our cosmic destiny. (2) To explore the cycles of matter and energy in the evolving Universe. (3) To examine the ultimate limits of gravity and energy in the Universe. These quests are developed into six, focused research campaigns addressing the objectives of one or more quests: Identify dark matter and learn how it shapes galaxies and systems of galaxies; Find out where and when the chemical elements were made; Understand the cycles in which matter, energy, and magnetic field are exchanged between stars and the gas between stars; Discover how gas flows in disks and how cosmic jets are formed; Identify the sources of gamma-ray bursts and high-energy cosmic rays; and Measure how strong gravity operates near black holes and how it affects the early Universe. These campaigns lead to a portfolio of future major missions of strong scientific and popular appeal, strongly endorsed by the scientific community and which has undergone significant initial study. Some of these missions are in a state of readiness that makes ideal candidates for the present Office of Space Science Strategic Plan; others may well feature in the next Strategic Plan. Each provides a golden scientific opportunity to advance our understanding of the Universe. Our highest priority science objectives are addressed by five Observatory Class Missions, unranked by science, but in approximate order of readiness: A high-energy gamma-ray facility that will observe relativistic jets and study the sources of cosmic gamma ray bursts; An ultra-sensitive X-ray telescope, optimized for spectroscopy, to examine the hot gas linked with clusters of galaxies, the disks around black holes, and supernova explosions; A large, radio telescope in deep space to map central regions of distant quasars and perform astrometric investigations; An orbiting gravitational coalescing, massive black holes and test how gravity waves distort spacetime; A pair of Earth-orbiting, optical telescopes that will detect flashes of light produced when ultra high-energy cosmic rays impact the upper atmosphere so as to determine their arrival directions and energies. A new program for supporting pertinent international collaboration is strongly endorsed and maintaining a strong Explorer program is important. The flexibility to exploit exceptional opportunities, such as attaching payloads to space station, should also be acquired. A strong technology development program must be initiated now to enable this mission set.

Source record↗

DOE OSTI2024

Mid-Range Science Objectives for the Event Horizon Telescope

The first images of the black holes in Sagittarius A* and M87* have created a wide range of new scientific opportunities in gravitational physics, compact objects, and relativistic astrophysics. We discuss here the scientific opportunities that arise from the rich data sets that have already been obtained and the new data sets that will be obtained, exploiting a wide range of technical advances, including observational agility, receiver upgrades, and the addition of new stations. This document provides a 5-year framework for Event Horizon Telescope (EHT) science structured around four fundamental questions that are used to prioritize the analysis of existing data, guide technical upgrades, and determine the optimal use of future observational opportunities with EHT, ALMA, and multi-wavelength facilities. Through enhancements over this period, the EHT will create the first movie of M87* connecting black hole and jet physics, provide detailed studies of the structure and dynamics of Sgr A*, characterize the magnetospheres of both systems through polarimetric imaging, and explore the spacetime properties of black holes with greater precision and range.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2011

Accretion States of the Galactic Micro Quasar GRS 1758-258

We present the results of a radio and X-ray study of the Galactic micro quasar GRS 1758-258, using unpublished archival data and new observations. We focus in particular on the 2000-2002 state transitions, and on its more quiet behaviour in 2008-2009. Our spectral and timing analysis of the XMM-Newton data shows that the source was in the canonical intermediate, soft and hard states in 2000 September 19,2001 March 22 and 2002 September 28, respectively. We estimate the disk size, luminosity and temperature, which are consistent with a black hole mass approx.10 Solar Mass, There is much overlap between the range of total X-ray luminosities (on average approx. 0.02L(sub Edd)) in the hard and soft states, and probably between the corresponding mass accretion rates; in fact, the hard state is often more luminous. The extended radio lobes seen in 1992 and 1997 are still present in 2008-2009. The 5-GHz radio core flux density has shown variability between approx. 0.1-0.5 mJy over the last two decades. This firmly places GRS 1758-258 in the radio-quiet sequence of Galactic black holes, in the radio/X-ray plane. We note that this dichotomy is similar to the dichotomy between the radio/X-ray sequences of Seyfert and radio galaxies. We propose that the different radio efficiency of the two sequences is due to relativistic electron/positron jets in radio-loud black holes, and sub-relativistic, thermally dominated outflows in radio-quiet sources.

Soria, Roberto↗

DOE OSTI2025

New Tests of Low-Scale Quantum Gravity with Cosmic-Ray Collisions

Cosmic ray collisions at high center of mass energy could enable graviton and black hole production as expected in theories of low-scale quantum gravity, such as extra-dimensions, many species, or some versions of string theory. Here we propose three novel phenomenological tests of these theories. We first consider the collision of cosmic rays with ambient protons, electrons and photons in Active Galactic Nuclei (AGN), finding that high-energy neutrino data from the blazar TXS 0506+056 places a constraint on the fundamental scale of gravity of $M_f \gtrsim 0.3$ TeV, and future high-energy neutrino data could raise this bound to $M_f \gtrsim 200$ TeV. We then point out that collisions of pairs of cosmic rays could occur at a sizable rate in AGN where the accelerated cosmic rays are not collimated, or on supermassive black hole binaries. This consideration could potentially let us test unprecedented large fundamental scales of $M_f \gtrsim 2$ PeV. We further compute the corresponding thermal neutrino emission arising from the Hawking evaporation of black holes produced in cosmic ray collisions, finding a spectrum that clearly differs from that expected in meson decays. Finally, we speculate with an scenario which would produce high-energy neutrino and gamma-ray emission from regions in the sky where no multi-wavelength counterparts would be expected, via graviton propagation from a different brane, which then decays in our Universe.

Ettengruber, Manuel [IPhT, Saclay]↗

NASA NTRS1997

The Structure of Active Galactic Nuclei

We are continuing our systematic investigation of the nuclear structure of nearby active galactic nuclei (AGN). Upon completion, our study will characterize hypothetical constructs such as narrow-line clouds, obscuring tori, nuclear gas disks. and central black holes with physical measurements for a complete sample of nearby AGN. The major scientific goals of our program are: (1) the morphology of the NLR; (2) the physical conditions and dynamics of individual clouds in the NLR; (3) the structure and physical conditions of the warm reflecting gas; (4) the structure of the obscuring torus; (5) the population and morphology of nuclear disks/tori in AGN; (6) the physical conditions in nuclear disks; and (7) the masses of central black holes in AGN. We will use the Hubble Space Telescope (HST) to obtain high-resolution images and spatially resolved spectra. Far-UV spectroscopy of emission and absorption in the nuclear regions using HST/FOS and the Hopkins Ultraviolet Telescope (HUT) will help establish physical conditions in the absorbing and emitting gas. By correlating the dynamics and physical conditions of the gas with the morphology revealed through our imaging program, we will be able to examine mechanisms for fueling the central engine and transporting angular momentum. The kinematics of the nuclear gas disks may enable us to measure the mass of the central black hole. Contemporaneous X-ray observations using ASCA will further constrain the ionization structure of any absorbing material. Monitoring of variability in the UV and X-ray absorption will be used to determine the location of the absorbing gas, possibly in the outflowing warm reflecting gas, or the broad-line region, or the atmosphere of the obscuring torus. Supporting ground-based observations in the optical, near-IR, imaging polarimetry, and the radio will complete our picture of the nuclear structures. With a comprehensive survey of these characteristics in a complete sample of nearby AGN, our conclusions should be more reliably extended to AGN as a class.

Kriss, Gerard A.↗

NASA NTRS2020

Comparing X-ray Color Selection in Separating X-ray Binary Classes using Color-Color-Intensity Diagrams

X-ray binaries exhibit a wide range of properties but there are few accepted methods to determine the nature of the compact object. Color-Color-Intensity diagrams have been suggested as a means of distinguishing between systems containing black holes from those containing neutron stars. However, this technique has been verified with data from only one instrument (RXTE/ASM) with a single set of X-ray colors defined using data available only in pre-determined energy bands. We test a selection of X-ray colors with a more sensitive instrument to determine the reliability of this method. We use data from the MAXI/Gas Slit Camera, which allows users to specify energy-bands. We test X-ray colors that have been previously defined in the literature as well as ones that we define specifically in this paper. A representative set of systems are used to construct Color-Color-Intensity diagrams in each set of colors to determine which are best for separating different classes. For studying individual sources certain bands are more effective than others. For a specified energy range, the separation of soft states in black hole binaries was possible only where both soft and hard colors included information from the lowest energy band. We confirm that Color-Color-Intensity diagrams can distinguish between systems containing black holes or neutron stars in all X-ray colors tested; this suggests an universality in the accretion processes governing these different classes. We suggest possible physical processes driving different classes of X-ray binaries to different locations in Color-Color-Intensity diagrams.

N Islam↗

DOE OSTI2024

Observational prospects of self-interacting scalar superradiance with next-generation gravitational-wave detectors

Abstract Current- and next-generation gravitational-wave observatories may reveal new, ultralight bosons. Through the superradiance process, these theoretical particle candidates can form clouds around astrophysical black holes and result in detectable gravitational-wave radiation. In the absence of detections, constraints—contingent on astrophysical assumptions—have been derived using LIGO-Virgo-KAGRA data on boson masses. However, the searches for ultralight scalars to date have not adequately considered self-interactions between particles. Self-interactions that significantly alter superradiance dynamics are generically present for many scalar models, including axion-like dark matter candidates and string axions. We implement the most complete treatment of particle self-interactions available to determine the gravitational-wave signatures expected from superradiant scalar clouds and revisit the constraints obtained in a past gravitational-wave search targeting the black hole in Cygnus X-1. We also project the reach of next-generation gravitational-wave observatories to scalar particle parameter space in the mass-coupling plane. We find that while proposed observatories have insufficient reach to self-interactions that can halt black hole spin-down, next-generation observatories are essential for expanding the search beyond gravitational parameter space and can reach a mass and interaction scale of ∼ 10 − 13 –10 −12 eV / c 2 and ≳ 10 17 GeV, respectively.

Collaviti, Spencer (ORCID:0009000372808236)↗

DOE OSTI2023

Holographic thermal correlators: a tale of Fuchsian ODEs and integration contours

We analyze real-time thermal correlation functions of conserved currents in holographic field theories using the grSK geometry, which provides a contour prescription for their evaluation. We demonstrate its efficacy, arguing that there are situations involving components of conserved currents, or derivative interactions, where such a prescription is, in fact, essential. To this end, we first undertake a careful analysis of the linearized wave equations in AdS black hole backgrounds and identify the branch points of the solutions as a function of (complexified) frequency and momentum. All the equations we study are Fuchsian with only regular singular points that for the most part are associated with the geometric features of the background. Special features, e.g., the appearance of apparent singular points at the horizon, whence outgoing solutions end up being analytic, arise at higher codimension loci in parameter space. Using the grSK geometry, we demonstrate that these apparent singularities do not correspond to any interesting physical features in higher-point functions. We also argue that the Schwinger-Keldysh collapse and KMS conditions, implemented by the grSK geometry, continue to hold even in the presence of such singularities. For charged black holes above a critical charge, we furthermore demonstrate that the energy density operator does not possess an exponentially growing mode, associated with ‘pole-skipping’, from one such apparent singularity. Our analysis suggests that the connection between the scrambling physics of black holes and energy transport has, at best, a limited domain of validity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Amplification of primordial perturbations from the rise or fall of the inflaton

The next generation of cosmic microwave background, gravitational wave, and large scale structure, experiments will provide an unprecedented opportunity to probe the primordial power spectrum on small scales. An exciting possibility for what lurks on small scales is a sharp rise in the primordial power spectrum: this can lead to the formation of primordial black holes, providing a dark matter candidate or the black holes observed by the LIGO-Virgo collaboration. In this study we develop a mechanism for the amplification of the small-scale primordial power spectrum, in the context of single-field inflation with a step-like feature in the inflaton potential. Specifically, we consider both the upward and the downward step in the potential. We also discuss the possibility of the strong coupling between perturbations because the rapid changes of the potential derivatives with the time-dependent field value, caused by the step-like feature, could make the coupling stronger. As a result, we find that the perturbations can remain weakly coupled yet sufficiently enhanced if the step realizes the rapid changes of the potential derivatives in some fraction of an e-fold, Script O(P R 1/2) ≲ ΔN < 1, where P R is the power spectrum of the curvature perturbation at that time. We also discuss the PBH formation rate from the inflaton trapping at the local minimum, which can occur in the potential with an upward step.

79 ASTRONOMY AND ASTROPHYSICS↗