SEARCH · Engineering Papers

Results for “Stars”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,459 records · Page 81

All sources NASA NTRS DOE OSTI

NASA NTRS2013

The Ultraviolet Radiation Environment around M Dwarf Exoplanet Host Stars

The spectral and temporal behavior of exoplanet host stars is a critical input to models of the chemistry and evolution of planetary atmospheres. Ultraviolet photons influence the atmospheric temperature profiles and production of potential biomarkers on Earth-like planets around these stars. At present, little observational or theoretical basis exists for understanding the ultraviolet spectra of M dwarfs, despite their critical importance to predicting and interpreting the spectra of potentially habitable planets as they are obtained in the coming decades. Using observations from the Hubble Space Telescope, we present a study of the UV radiation fields around nearby M dwarf planet hosts that covers both far-UV (FUV) and near-UV (NUV) wavelengths. The combined FUV+NUV spectra are publicly available in machine-readable format. We find that all six exoplanet host stars in our sample (GJ 581, GJ 876, GJ 436, GJ 832, GJ 667C, and GJ 1214) exhibit some level of chromospheric and transition region UV emission. No "UV-quiet" M dwarfs are observed. The bright stellar Lyman-alpha emission lines are reconstructed, and we find that the Lyman-alpha line fluxes comprise approximately 37%-75% of the total 1150-3100 A flux from most M dwarfs; approximately greater than 10(exp3) times the solar value. We develop an empirical scaling relation between Lyman-alpha and Mg II emission, to be used when interstellar H I attenuation precludes the direct observation of Lyman-alpha. The intrinsic unreddened flux ratio is F(Lyman-alpha)/F(Mg II) = 10(exp3). The F(FUV)/F(NUV) flux ratio, a driver for abiotic production of the suggested biomarkers O2 and O3, is shown to be approximately 0.5-3 for all M dwarfs in our sample, greather than 10(exp3) times the solar ratio. For the four stars with moderate signal-to-noise Cosmic Origins Spectrograph time-resolved spectra, we find UV emission line variability with amplitudes of 50%.500% on 10(exp2)-10(exp3) s timescales. This effect should be taken into account in future UV transiting planet studies, including searches for O3 on Earth-like planets. Finally, we observe relatively bright H2 fluorescent emission from four of the M dwarf exoplanetary systems (GJ 581, GJ 876, GJ 436, and GJ 832). Additional modeling work is needed to differentiate between a stellar photospheric or possible exoplanetary origin for the hot (T(H2) approximately equal to 2000-4000 K) molecular gas observed in these objects.

France, Kevin↗

NASA NTRS2013

Dust Production and Mass Loss in Cool Evolved Stars

Following the red giant branch phase and the subsequent core He-burning phase, the low- to intermediate-mass stars (0.8<M/M solar mass <8) begin to ascend the asymptotic giant branch (AGB). Pulsations levitate material from the stellar surface and provide density enhancements and shocks, which can encourage dust formation and re-processing. The dust composition depends on the atmospheric chemistry (abundance of carbon relative to oxygen), which is altered by dredging up newly formed carbon to the surface of the star. I will briefly review the current status of models that include AGB mass loss and relate them to recent observations of AGB stars from the Surveying the Agents of Galaxy Evolution (SAGE) Spitzer surveys of the Small and Large Magellanic Clouds, including measures of the total dust input to the interstellar medium from AGB stars.

Boyer, M. L.↗

NASA NTRS2013

BD-22deg3467, a DAO-type Star Exciting the Nebula Abell 35

Spectral analyses of hot, compact stars with non-local thermodynamical equilibrium (NLTE) model-atmosphere techniques allow the precise determination of photospheric parameters such as the effective temperature (T(sub eff)), the surface gravity (log g), and the chemical composition. The derived photospheric metal abundances are crucial constraints for stellar evolutionary theory. Aims. Previous spectral analyses of the exciting star of the nebula A35, BD-22deg3467, were based on He+C+N+O+Si+Fe models only. For our analysis, we use state-of-the-art fully metal-line blanketed NLTE model atmospheres that consider opacities of 23 elements from hydrogen to nickel. We aim to identify all observed lines in the ultraviolet (UV) spectrum of BD-22deg3467 and to determine the abundances of the respective species precisely. Methods. For the analysis of high-resolution and high signal-to-noise ratio (S/N) far-ultraviolet (FUSE) and UV (HST/STIS) observations, we combined stellar-atmosphere models and interstellar line-absorption models to fully reproduce the entire observed UV spectrum. Results. The best agreement with the UV observation of BD-22deg3467 is achieved at T(sub eff) = 80 +/- 10 kK and log g = 7.2 +/- 0.3. While T(sub eff) of previous analyses is verified, log g is significantly lower. We re-analyzed lines of silicon and iron (1/100 and about solar abundances, respectively) and for the first time in this star identified argon, chromium, manganese, cobalt, and nickel and determined abundances of 12, 70, 35, 150, and 5 times solar, respectively. Our results partially agree with predictions of diffusion models for DA-type white dwarfs. A combination of photospheric and interstellar line-absorption models reproduces more than 90% of the observed absorption features. The stellar mass is M approx. 0.48 Solar Mass. Conclusions. BD.22.3467 may not have been massive enough to ascend the asymptotic giant branch and may have evolved directly from the extended horizontal branch to the white dwarf state. This would explain why it is not surrounded by a planetary nebula. However, the star, ionizes the ambient interstellar matter, mimicking a planetary nebula.

Ziegler, M.↗

NASA NTRS2013

Constraints on the Neutron Star and Inner Accretion Flow in Serpens X-1 Using Nustar

We report on an observation of the neutron star low-mass X-ray binary Serpens X-1, made with NuSTAR. The extraordinary sensitivity afforded by NuSTAR facilitated the detection of a clear, robust, relativistic Fe K emission line from the inner disk. A relativistic profile is required over a single Gaussian line from any charge state of Fe at the 5 sigma level of confidence, and any two Gaussians of equal width at the same confidence. The Compton back-scattering "hump" peaking in the 10-20 keV band is detected for the first time in a neutron star X-ray binary. Fits with relativistically blurred disk reflection models suggest that the disk likely extends close to the innermost stable circular orbit (ISCO) or stellar surface. The best-fit blurred reflection models constrain the gravitational redshift from the stellar surface to be ZnS (is) greater than 0.16. The data are broadly compatible with the disk extending to the ISCO; in that case,ZnS(is) greater than 0.22 and RNS (is) less than12.6 km (assuming MnS = 1.4 solar mass and a = 0, where a = cJ/GM2). If the star is as large or larger than its ISCO, or if the effective reflecting disk leaks across the ISCO to the surface, the redshift constraints become measurements. We discuss our results in the context of efforts to measure fundamental properties of neutron stars, and models for accretion onto compact objects.

accretion↗

NASA NTRS2013

A Panchromatic View of the Restless SN 2009ip Reveals the Explosive Ejection of a Massive Star Envelope

The double explosion of SN 2009ip in 2012 raises questions about our understanding of the late stages of massive star evolution. Here we present a comprehensive study of SN 2009ip during its remarkable rebrightenings. High-cadence photometric and spectroscopic observations from the GeV to the radio band obtained from a variety of ground-based and space facilities (including the Very Large Array, Swift, Fermi, Hubble Space Telescope, and XMM) constrain SN 2009ip to be a low energy (E (is) approximately 10(exp 50) erg for an ejecta mass approximately 0.5 solar mass) and asymmetric explosion in a complex medium shaped by multiple eruptions of the restless progenitor star. Most of the energy is radiated as a result of the shock breaking out through a dense shell of material located at approximately 5 × 10( exp 14) cm with M approximately 0.1 solar mass, ejected by the precursor outburst approximately 40 days before the major explosion. We interpret the NIR excess of emission as signature of material located further out, the origin of which has to be connected with documented mass-loss episodes in the previous years. Our modeling predicts bright neutrino emission associated with the shock break-out if the cosmic-ray energy is comparable to the radiated energy. We connect this phenomenology with the explosive ejection of the outer layers of the massive progenitor star, which later interacted with material deposited in the surroundings by previous eruptions. Future observations will reveal if the massive luminous progenitor star survived. Irrespective of whether the explosion was terminal, SN 2009ip brought to light the existence of new channels for sustained episodic mass loss, the physical origin of which has yet to be identified.

view↗

NASA NTRS2015

CSI 2264: Characterizing Young Stars in NGC 2264 With Short-Duration Periodic Flux Dips in Their Light Curves

We identify nine young stellar objects (YSOs) in the NGC 2264 star-forming region with optical CoRoT light curves exhibiting short-duration, shallow, periodic flux dips. All of these stars have infrared (IR) excesses that are consistent with their having inner disk walls near the Keplerian corotation radius. The repeating photometric dips have FWHM generally less than one day, depths almost always less than 15%, and periods (3 < P < 11 days) consistent with dust near the Keplerian co-rotation period. The flux dips vary considerably in their depth from epoch to epoch, but usually persist for several weeks and, in two cases, were present in data collected on successive years. For several of these stars, we also measure the photospheric rotation period and find that the rotation and dip periods are the same, as predicted by standard \disk-locking" models. We attribute these flux dips to clumps of material in or near the inner disk wall, passing through our line of sight to the stellar photosphere. In some cases, these dips are also present in simultaneous Spitzer IRAC light curves at 3.6 and 4.5 microns. We characterize the properties of these dips, and compare the stars with light curves exhibiting this behavior to other classes of YSO in NGC 2264. A number of physical mechanisms could locally increase the dust scale height near the inner disk wall, and we discuss several of those mechanisms; the most plausible mechanisms are either a disk warp due to interaction with the stellar magnetic field or dust entrained in funnel- ow accretion columns arising near the inner disk wall.

CSI 2264↗

NASA NTRS2016

Demonstrating the Likely Neutron Star Nature of Five M31 Globular Cluster Sources with Swift-NuSTAR Spectroscopy

We present the results of a joint Swift-NuSTAR spectroscopy campaign on M31. We focus on the five brightest globular cluster X-ray sources in our fields. Two of these had previously been argued to be black hole candidates on the basis of apparent hard-state spectra at luminosities above those for which neutron stars are in hard states. We show that these two sources are likely to be Z-sources (i.e. low magnetic field neutron stars accreting near their Eddington limits), or perhaps bright atoll sources (low magnetic field neutron stars which are just a bit fainter than this level) on the basis of simultaneous Swift and NuSTAR spectra which cover a broader range of energies. These new observations reveal spectral curvature above 6-8 keV that would be hard to detect without the broader energy coverage the NuSTAR data provide relative to Chandra and XMM-Newton. We show that the other three sources are also likely to be bright neutron star X-ray binaries, rather than black hole X-ray binaries. We discuss why it should already have been realized that it was unlikely that these objects were black holes on the basis of their being persistent sources, and we re-examine past work which suggested that tidal capture products would be persistently bright X-ray emitters. We discuss how this problem is likely due to neglecting disc winds in older work that predict which systems will be persistent and which will be transient.

globular clusters: general↗

NASA NTRS2016

The Far-Ultraviolet Spectra of Two Hot PG1159 Stars

PG 1159 stars are hot, hydrogen-deficient (pre-) white dwarfs with atmospheres mainly composed of helium, carbon, and oxygen. The unusual surface chemistry is the result of a late helium-shell flash. Observed element abundances enable us to test stellar evolution models quantitatively with respect to their nucleosynthesis products formed near the helium-burning shell of the progenitor asymptotic giant branch stars. Because of the high effective temperatures (T(sub eff)), abundance determinations require ultraviolet spectroscopy and non-local thermodynamic equilibrium model atmosphere analyses. Up to now, we have presented results for the prototype of this spectral class and two cooler members (T(sub eff) in the range 85,000-140,000 K). Here we report on the results for two even hotter stars (PG 1520+525 and PG 1144+005, both with T(sub eff) = 150,000 K) which are the only two objects in this temperature-gravity region for which useful far-ultraviolet spectra are available, and revisit the prototype star. Previous results on the abundances of some species are confirmed, while results on others (Si, P, S) are revised. In particular, a solar abundance of sulphur is measured in contrast to earlier claims of a strong S deficiency that contradicted stellar evolution models. For the first time, we assess the abundances of Na, Al, andCl with newly constructed non-LTE model atoms. Besides the main constituents (He, C, O), we determine the abundances (or upper limits) of N, F, Ne, Na, Al, Si, P, S, Cl, Ar, and Fe. Generally, good agreement with stellar models is found.

Werner, K.↗

NASA NTRS2016

Exocomet Signatures Around the A-shell Star Phi Leonis

We present an intensive monitoring of high-resolution spectra of the Ca II K line in the A7IV shell star Phi Leonis at very short (minutes, hours), short (night to night), and medium (weeks, months) timescales. The spectra show remarkable variable absorptions on timescales of hours, days, and months. The characteristics of these sporadic events are very similar to most that are observed toward the debris disk host star Beta Pictoris, which are commonly interpreted as signs of the evaporation of solid, comet-like bodies grazing or falling onto the star. Therefore, our results suggest the presence of solid bodies around Phi Leonis. To our knowledge, with the exception of Beta Pictoris, our monitoring has the best time resolution at the mentioned timescales for a star with events attributed to exocomets. Assuming the cometary scenario and considering the timescales of our monitoring, our results indicate that Phi Leonis presents the richest environment with comet-like events known to date, second only to Beta Pictoris.

high-resolution spectra of the Ca II K line↗

NASA NTRS2015

Exoplanet Coronagraph Shaped Pupil Masks and Laboratory Scale Star Shade Masks: Design, Fabrication and Characterization

Star light suppression technologies to find and characterize faint exoplanets include internal coronagraph instruments as well as external star shade occulters. Currently, the NASA WFIRST-AFTA mission study includes an internal coronagraph instrument to find and characterize exoplanets. Various types of masks could be employed to suppress the host star light to about 10 -9 level contrast over a broad spectrum to enable the coronagraph mission objectives. Such masks for high contrast internal coronagraphic imaging require various fabrication technologies to meet a wide range of specifications, including precise shapes, micron scale island features, ultra-low reflectivity regions, uniformity, wave front quality, achromaticity, etc. We present the approaches employed at JPL to produce pupil plane and image plane coronagraph masks by combining electron beam, deep reactive ion etching, and black silicon technologies with illustrative examples of each, highlighting milestone accomplishments from the High Contrast Imaging Testbed (HCIT) at JPL and from the High Contrast Imaging Lab (HCIL) at Princeton University. We also present briefly the technologies applied to fabricate laboratory scale star shade masks.

black silicon↗

NASA NTRS2017

Optical Design of the STAR-X Telescope

Top-level science goals of the Survey and Time-domain Astrophysical Research eXplorer (STAR-X) include: investigations of most violent explosions in the universe, study of growth of black holes across cosmic time and mass scale, and measure how structure formation heats majority of baryons in the universe. To meet these goals, the field-of-view of the telescope should be about 1 square-degree, the angular resolution should be 5 arc-seconds or below across large part of the field-of-view. The on-axis effective area at 1 KeV should be about 2,000 sq cm. Payload cost and launch considerations limit the outer diameter, focal length, and mass to 1.3 meters, 5 meters, and 250 kilograms, respectively. Telescope design is based on a segmented meta-shell approach we have developed at Goddard Space Flight Center for the STAR-X telescope. The telescope shells are divided into 30-degree segments. Individual telescopes and meta-shells are nested inside each other to meet the effective area requirements in 0.5 - 6.0 KeV range. We consider Wolter-Schwarzschild, and Modified-Wolter-Schwarzschild telescope designs as basic building blocks of the nested STAR-X telescope. These designs offer an excellent resolution over a large field of views. Nested telescopes are vulnerable to stray light problems. We have designed a multi-component baffle system to eliminate direct and single-reflection light paths inside the telescopes. Large number of internal and external baffle vane structures are required to prevent stray rays from reaching the focal plane. We have developed a simple ray-trace based tool to determine the dimensions and locations of the baffles. In this paper, we present the results of our trade studies, baffle design studies, and optical performance analyses of the STAR-X telescope.

Saha, Timo T.↗

NASA NTRS2017

Design of the STAR-X Telescope

Saha, Timo T.↗

NASA NTRS2017

Objective Assessment Method for RNAV STAR Adherence

Flight crews and air traffic controllers have reported many safety concerns regarding area navigation standard terminal arrival routes (RNAV STARs). Specifically, optimized profile descents (OPDs). However, our information sources to quantify these issues are limited to subjective reporting and time consuming case-by-case investigations. This work is a preliminary study into the objective performance of instrument procedures and provides a framework to track procedural concepts and assess design specifications. We created a tool and analysis methods for gauging aircraft adherence as it relates to RNAV STARs. This information is vital for comprehensive understanding of how our air traffic behaves. In this study, we mined the performance of 24 major US airports over the preceding three years. Overlaying 4D radar track data onto RNAV STAR routes provided a comparison between aircraft flight paths and the waypoint positions and altitude restrictions. NASA Ames Supercomputing resources were utilized to perform the data mining and processing. We assessed STARs by lateral transition path (full-lateral), vertical restrictions (full-lateral/full-vertical), and skipped waypoints (skips). In addition, we graphed frequencies of aircraft altitudes relative to the altitude restrictions. Full-lateral adherence was always greater than Full-lateral/ full- vertical, as it is a subset, but the difference between the rates was not consistent. Full-lateral/full-vertical adherence medians of the 2016 procedures ranged from 0% in KDEN (Denver) to 21% in KMEM (Memphis). Waypoint skips ranged from 0% to nearly 100% for specific waypoints. Altitudes restrictions were sometimes missed by systematic amounts in 1,000 ft. increments from the restriction, creating multi-modal distributions. Other times, altitude misses looked to be more normally distributed around the restriction. This tool may aid in providing acceptability metrics as well as risk assessment information.

Stewart, Michael↗

NASA NTRS2017

The Fundamental Stellar Parameters of FGK Stars in the SEEDS Survey Norman, OK 73071, USA

Large exoplanet surveys have successfully detected thousands of exoplanets to-date. Utilizing these detections and non-detections to constrain our understanding of the formation and evolution of planetary systems also requires a detailed understanding of the basic properties of their host stars. We have determined the basic stellar properties of F, K and G stars in the Strategic Exploration of Exoplanets and Disks with Subaru (SEEDS) survey from Echelle spectra taken at the Apache Point Observatory's 3.5m telescope. Using ROBOSPECT to extract line equivalent widths and Temperature Gravity microtrubulent Velocity ITerations to calculate the fundamental parameters, we have computed T(sub eff), log(g), v(sub t), [Fe/H], chromospheric activity and the age for our sample. Our methodology was calibrated against previously published results for a portion of our sample. The distribution of [Fe/H] in our sample is consistent with that typical of the Solar neighbourhood. Additionally, we find the ages of most of our sample are less than 500 Myr, but note that we cannot determine robust ages from significantly older stars via chromospheric activity age indicators. The future meta-analysis of the frequency of wide stellar and sub-stellar companions imaged via the SEEDS survey will utilize our results to constrain the occurrence of detected comoving companions with the properties of their host stars.

Strategic Exploration of Exoplanets and Disks with↗

NASA NTRS2017

Characterizing K2 Candidate Planetary Systems Orbiting Low-Mass Stars. II. Planetary Systems Observed During Campaigns 1-7

We recently used near-infrared spectroscopy to improve the characterization of 76 low-mass stars around which K2 had detected 79 candidate transiting planets. 29 of these worlds were new discoveries that had not previously been published. We calculate the false positive probabilities that the transit-like signals are actually caused by non-planetary astrophysical phenomena and reject five new transit-like events and three previously reported events as false positives. We also statistically validate 17 planets (7 of which were previously unpublished), confirm the earlier validation of 22 planets, and announce 17 newly discovered planet candidates. Revising the properties of the associated planet candidates based on the updated host star characteristics and refitting the transit photometry, we find that our sample contains 21 planets or planet candidates with radii smaller than 1.25 solar radii, 18 super-Earths (1.25-2 solar radii), 21 small Neptunes (2-4 solar radii), three large Neptunes (4-6 solar radii), and eight giant planets (greater than 6 solar radii). Most of these planets are highly irradiated, but EPIC 206209135.04 (K2-72e, 1.29 from plus 0.19 to minus 0.18 solar radii), EPIC 211988320.01 (perihelion radius equals 2.86 from plus 0.16 to minus 0.15 solar radii), and EPIC 212690867.01 (2.20 from plus 0.19 to minus 0.18 solar radii) orbit within optimistic habitable zone boundaries set by the "recent Venus" inner limit and the "early Mars" outer limit. In total, our planet sample includes eight moderately irradiated 1.5-3 solar radii planet candidates (planetary flux greater than or approximately 20 times Earth's flux) orbiting brighter stars (Ks less than 11) that are well-suited for atmospheric investigations with the Hubble, Spitzer, and/or James Webb Space Telescopes. Five validated planets orbit relatively bright stars (Kp less than 12.5) and are expected to yield radial velocity semi-amplitudes of at least 2 meters per second. Accordingly, they are possible targets for radial velocity mass measurement with current facilities or the upcoming generation of red optical and near-infrared high-precision RV (Radial Velocity) spectrographs.

Dressing, Courtney D.↗

NASA NTRS2013

A Panchromatic View of the Restless SN 2009ip Reveals the Explosive Ejection of a Massive Star Envelope

The double explosion of SN 2009ip in 2012 raises questions about our understanding of the late stages of massive star evolution. Here we present a comprehensive study of SN 2009ip during its remarkable rebrightenings. High-cadence photometric and spectroscopic observations from the GeV to the radio band obtained from a variety of ground-based and space facilities (including the Very Large Array, Swift, Fermi, Hubble Space Telescope, and XMM) constrain SN 2009ip to be a low energy (E approximating 10(exp 50) ergs for an ejecta mass approximating 0.5 M solar mass) and asymmetric explosion in a complex medium shaped by multiple eruptions of the restless progenitor star. Most of the energy is radiated as a result of the shock breaking out through a dense shell of material located at approximately 5 times 10 (exp 14) cm with M approximating 0.1 solar mass, ejected by the precursor outburst approximately 40 days before the major explosion. We interpret the NIR (Near Infrared) excess of emission as signature of material located further out, the origin of which has to be connected with documented mass-loss episodes in the previous years. Our modeling predicts bright neutrino emission associated with the shock break-out if the cosmic-ray energy is comparable to the radiated energy. We connect this phenomenology with the explosive ejection of the outer layers of the massive progenitor star, which later interacted with material deposited in the surroundings by previous eruptions. Future observations will reveal if the massive luminous progenitor star survived. Irrespective of whether the explosion was terminal, SN 2009ip brought to light the existence of new channels for sustained episodic mass loss, the physical origin of which has yet to be identified.

massive↗

NASA NTRS2018

Do Close-in Giant Planets Orbiting Evolved Stars Prefer Eccentric Orbits?

The NASA Kepler and K2 Missions have recently revealed a population of transiting giant planets orbiting moderately evolved, low-luminosity red giant branch stars. Here, we present radial velocity (RV) measurements of three of these systems, revealing signiﬁcantly non-zero orbital eccentricities in each case. Comparing these systems with the known planet population suggests that close-in giant planets around evolved stars tend to have more eccentric orbits than those around main sequence stars. We interpret this as tentative evidence that the orbits of these planets pass through a transient, moderately eccentric phase where they shrink faster than they circularize due to tides raised on evolved host stars. Additional RV measurements of currently known systems, along with new systems discovered by the recently launched NASA Transiting Exoplanet Survey Satellite (TESS) mission, may constrain the timescale and mass dependence of this process.

Thomas Barclay↗

NASA NTRS2020

Spitzer Microlensing Parallax Reveals Two Isolated Stars in the Galactic Bulge

We report the mass and distance measurements of two single-lens events from the 2017 Spitzer microlensing campaign. The ground-based observations yield the detection of finite-source effects, and the microlens parallaxes are derived from the joint analysis of ground-based observations and Spitzer observations. We find that the lens of OGLE-2017-BLG-1254 is a 0.60 ± 0.03 M⊙ star with D(LS) = 0.53 ± 0.11 kpc, where D(LS) is the distance between the lens and the source. The second event, OGLE-2017-BLG-1161, is subject to the known satellite parallax degeneracy, and thus is either a 0.51(sup +0.12, sub 3-0.10)M⊙ star with D(LS) = 0.40 ± 0.12 kpc or a 0.38(sup +0.13, sub -0.12) M⊙ star with D(LS) = 0.53 ± 0.19 kpc. Both of the lenses are therefore isolated stars in the Galactic bulge. By comparing the mass and distance distributions of the eight published Spitzer finite-source events with the expectations from a Galactic model, we find that the Spitzer sample is in agreement with the probability of finite-source effects occurring in single-lens events.

Weicheng Zang↗