OSCULATING VERSUS INTERSECTING CIRCLES IN SPACE-BASED MICROLENS PARALLAX DEGENERACIES

Andrew Gould 한국천문학회 2019 Journal of The Korean Astronomical Society Vol.52 No.4

I investigate the origin of arc degeneracies in satellite microlens parallax π E measurements with only late time data, e.g., t > t 0 + t E as seen from the satellite. I show that these are due to partial overlap of a series of osculating, exactly circular, degeneracies in the π E plane, each from a single measurement. In events with somewhat earlier data, these long arcs break up into two arclets, or (with even earlier data) two points, because these earlier measurements give rise to intersecting rather than osculating circles. The two arclets (or points) then constitute one pair of degeneracies in the well-known four-fold degeneracy of space-based microlens parallax. Using this framework of intersecting circles, I show that next-generation microlens satellite experiments could yield good π E determinations with only about five measurements per event, i.e., about 30 observations per day to monitor 1500 events per year. This could plausibly be done with a small (hence cheap, in the spirit of Gould & Yee 2012) satellite telescope, e.g., 20 cm.

RIGOROUS "RICH ARGUMENT" IN MICROLENSING PARALLAX

Gould, Andrew The Korean Astronomical Society 2020 Journal of The Korean Astronomical Society Vol.53 No.5

I show that when the observables (π_E, t_E, θ_E, π_s, µ_s) are well measured up to a discrete degeneracy in the microlensing parallax vector π_E, the relative likelihood of the different solutions can be written in closed form P_i = KH_iB_i, where H_i is the number of stars (potential lenses) having the mass and kinematics of the inferred parameters of solution i and B_i is an additional factor that is formally derived from the Jacobian of the transformation from Galactic to microlensing parameters. Here t_E is the Einstein timescale, θ_E is the angular Einstein radius, and (π_s, µ_s) are the (parallax, proper motion) of the microlensed source. The Jacobian term B_i constitutes an explicit evaluation of the "Rich Argument", i.e., that there is an extra geometric factor disfavoring large-parallax solutions in addition to the reduced frequency of lenses given by H_i. I also discuss how this analytic expression degrades in the presence of finite errors in the measured observables.

New Advances in Gravitational Microlensing

Andrew Gould 한국우주과학회 2000 한국우주과학회보 Vol.9 No.2

MICROLENS MASSES FROM 1-D PARALLAXES AND HELIOCENTRIC PROPER MOTIONS

Andrew Gould 한국천문학회 2014 Journal of The Korean Astronomical Society Vol.47 No.6

One-dimensional (1-D) microlens parallaxes can be combined with heliocentric lens-sourcerelative proper motion measurements to derive the lens mass and distance, as suggested by Ghosh et al. (2004). Here I present the first mathematical anlysis of this procedure, which I show can be represented asa quadratic equation. Hence, it is formally subject to a two-fold degeneracy. I show that this degeneracycan be broken in many cases using the relatively crude 2-D parallax information that is often availablefor microlensing events. I also develop an explicit formula for the region of parameter space where it ismore difficult to break this degeneracy. Although no mass/distance measurements have yet been madeusing this technique, it is likely to become quite common over the next decade.

GAIA PARALLAX ZERO POINT FROM RR LYRAE STARS

Andrew Gould,Juna A. Kollmeier 한국천문학회 2017 Journal of The Korean Astronomical Society Vol.50 No.1

Like Hipparcos, Gaia is designed to give absolute parallaxes, independent of any astrophysical reference system. And indeed, Gaia's internal zero-point error for parallaxes is likely to be smaller than any individual parallax error. Nevertheless, due in part to mechanical issues of unknown origin, there are many astrophysical questions for which the parallax zero-point error $\sigma(\pi_0)$ will be the fundamentally limiting constraint. These include the distance to the Large Magellanic Cloud and the Galactic Center. We show that by using the photometric parallax estimates for RR Lyrae stars (RRL) within 8kpc, via the ultra-precise infrared period-luminosity relation, one can independently determine a hyper-precise value for $\pi_{0}$. Despite their paucity relative to bright quasars, we show that RRL are competitive due to their order-of-magnitude improved parallax precision for each individual object relative to bright quasars. We show that this method is mathematically robust and well-approximated by analytic formulae over a wide range of relevant distances.

FREE-FLOATING PLANETS, THE EINSTEIN DESERT, AND 'OUMUAMUA

Gould, Andrew,Jung, Youn Kil,Hwang, Kyu-Ha,Dong, Subo,Albrow, Michael D.,Chung, Sun-Ju,Han, Cheongho,Ryu, Yoon-Hyun,Shin, In-Gu,Shvartzvald, Yossi,Yang, Hongjing,Yee, Jennifer C.,Zang, Weicheng,Cha, S The Korean Astronomical Society 2022 Journal of The Korean Astronomical Society Vol.55 No.5

We complete the survey for finite-source/point-lens (FSPL) giant-source events in 2016-2019 KMTNet microlensing data. The 30 FSPL events show a clear gap in Einstein radius, 9 𝜇as < 𝜃_E < 26 𝜇as, which is consistent with the gap in Einstein timescales near t_E ~ 0.5 days found by Mróz et al. (2017) in an independent sample of point-source/point-lens (PSPL) events. We demonstrate that the two surveys are consistent. We estimate that the 4 events below this gap are due to a power-law distribution of free-floating planet candidates (FFPs) dN_FFP/d log M = (0.4 ± 0.2) (M/38 M_⊕)^-p/star, with 0.9 ≲ p ≲ 1.2. There are substantially more FFPs than known bound planets, implying that the bound planet power-law index 𝛾 = 0.6 is likely shaped by the ejection process at least as much as by formation. The mass density per decade of FFPs in the Solar neighborhood is of the same order as that of 'Oumuamua-like objects. In particular, if we assume that 'Oumuamua is part of the same process that ejected the FFPs to very wide or unbound orbits, the power-law index is p = 0.89 ± 0.06. If the Solar System's endowment of Neptune-mass objects in Neptune-like orbits is typical, which is consistent with the results of Poleski et al. (2021), then these could account for a substantial fraction of the FFPs in the Neptune-mass range.

KMT-2018-BLG-0029LB: A VERY LOW MASS-RATIO Spitzer MICROLENS PLANET

Andrew Gould,류윤현,Sebastiano Calchi Novati,Weicheng Zang,Michael D. Albrow,정선주,CHEONGHOHAN,황규하,정연길,신인구,Yossi Shvartzvald,Jennifer C. Yee,차상목,Dong-Jin Kim,김현우,김승리,이정욱,Dong-Joo Lee,이용석,Byeong-Gon Park,Ri 한국천문학회 2020 Journal of The Korean Astronomical Society Vol.53 No.1

At q = 1.81+/-0.20*10^{-5}, KMT-2018-BLG-0029Lb has the lowest planet-host mass ratio q of any microlensing planet to date by more than a factor of two. Hence, it is the first planet that probes below the apparent "pile-up" at q = 5-10*10^{-5}. The event was observed by Spitzer, yielding a microlens-parallax pi_E measurement. Combined with a measurement of the Einstein radius theta_E from finite-source effects during the caustic crossings, these measurements imply masses of the host M_host = 1.14+0.10-0.12 M_sun and planet M_planet = 7.59+0.75-0.69 M_Earth, system distance D_L = 3.38+0.22-0.26 kpc and projected separation a_p = 4.27+0.21-0.23 au. The blended light, which is substantially brighter than the microlensed source, is plausibly due to the lens and could be observed at high resolution immediately.

WFIRST ULTRA-PRECISE ASTROMETRY II: ASTEROSEISMOLOGY

Andrew Gould,Daniel Huber,Matthew Penny,Dennis Stello 한국천문학회 2015 Journal of The Korean Astronomical Society Vol.48 No.2

WFIRST microlensing observations will return high-precision parallaxes, σ(π) . 0.3 μas, for the roughly 1 million stars with H < 14 in its 2.8 deg2 field toward the Galactic bulge. Combined with its 40,000 epochs of high precision photometry (∼ 0.7 mmag at Hvega = 14 and ∼ 0.1 mmag at H = 8), this will yield a wealth of asteroseismic data of giant stars, primarily in the Galactic bulge but including a substantial fraction of disk stars at all Galactocentric radii interior to the Sun. For brighter stars, the astrometric data will yield an external check on the radii derived from the two asteroseismic parameters, the large-frequency separation hνnli and the frequency of maximum oscillation power νmax, while for the fainter ones, it will enable a mass measurement from the single measurable asteroseismic parameter νmax. Simulations based on Kepler data indicate that WFIRST will be capable of detecting oscillations in stars from slightly less luminous than the red clump to the tip of the red giant branch, yielding roughly 1 million detections.

MICROLENSING BY KUIPER, OORT, AND FREE-FLOATING PLANETS

Andrew Gould 한국천문학회 2016 Journal of The Korean Astronomical Society Vol.49 No.4

Microlensing is generally thought to probe planetary systems only out to a few Einstein radii. Microlensing events generated by bound planets beyond about 10 Einstein radii generally do not yield any trace of their hosts, and so would be classified as free floating planets (FFPs). I show that it is already possible, using adaptive optics (AO), to constrain the presence of potential hosts to FFP candidates at separations comparable to the Oort Cloud. With next-generation telescopes, planets at Kuiper-Belt separations can be probed. Next generation telescopes will also permit routine vetting for all FFP candidates, simply by obtaining second epochs 4--8 years after the event.At present, the search for such hosts is restricted to within the ``confusion limit'' of $\theta_\confus\sim 0.25^{\prime\prime}$, but future {\it WFIRST} (Wide Field Infrared Survey Telescope) observations will allow one to probe beyond this confusion limit as well.

A New Method to Calibrate the Stellar Color/Surface-Brightness Relation

Andrew Gould 한국천문학회 2014 Journal of The Korean Astronomical Society Vol.47 No.4

I show that the standard microlensing technique to measure the angular radius of a star using color/surface-brightness relations can be inverted, via late-time proper motion measurements, to calibrate these relations. The method is especially useful for very metal-rich stars because such stars are in short supply in the solar neighborhood where other methods are most effective, but very abundant in Galactic bulge microlensing fields. I provide a list of eight spectroscopically identified high-metallicity bulge stars with the requisite finite-source effects, seven of which will be suitable calibrators when the Giant Magellan Telescope comes on line. Many more such sources can be extracted from current and future microlensing surveys.