Abstract
We developed a parametric Galactic model toward the Galactic bulge by fitting to spatial distributions of the Gaia DR2 disk velocity, VVV proper motion, BRAVA radial velocity, OGLE-III red ...clump star count, and OGLE-IV star count and microlens rate, optimized for use in microlensing studies. We include the asymmetric drift of Galactic disk stars and the dependence of velocity dispersion on Galactic location in the kinematic model, which has been ignored in most previous models used for microlensing studies. We show that our model predicts a microlensing parameter distribution significantly different from those typically used in previous studies. We estimate various fundamental model parameters for our Galaxy through our modeling, including the initial mass function (IMF) in the inner Galaxy. Combined constraints from star counts and the microlensing event timescale distribution from the OGLE-IV survey, in addition to a prior on the bulge stellar mass, enable us to successfully measure IMF slopes using a broken power-law form over a broad mass range,
α
bd
=
0.22
−
0.55
+
0.20
for
M
< 0.08
M
⊙
,
α
ms
=
1.16
−
0.15
+
0.08
for 0.08
M
⊙
≤
M
<
M
br
, and
α
hm
=
2.32
−
0.10
+
0.14
for
M
≥
M
br
, as well as a break mass at
M
br
=
0.90
−
0.14
+
0.05
M
⊙
. This is significantly different from the Kroupa IMF for local stars, but similar to the Zoccali IMF measured from a bulge luminosity function. We also estimate the dark matter mass fraction in the bulge region of 28% ± 7% which could be larger than a previous estimate. Because our model is purely parametric, it can be universally applied using the parameters provided in this paper. (A tool for microlensing simulation using our Galactic model has been published, Koshimoto & Ranc 2021, and can be downloaded at
https://github.com/nkoshimoto/genulens
.)
Abstract
The microlensing parallax campaign with the Spitzer space telescope aims to measure masses and distances of microlensing events seen toward the Galactic bulge, with a focus on planetary ...microlensing events. The hope is to measure how the distribution of planets depends on position within the Galaxy. In this paper, we compare 50 microlens parallax measurements from the 2015 Spitzer campaign to three different Galactic models commonly used in microlensing analyses, and we find that ≥74% of these events have microlensing parallax values higher than the medians predicted by Galactic models. The Anderson–Darling tests indicate probabilities of
p
AD
< 6.6 × 10
−5
for these three Galactic models, while the binomial probability of such a large fraction of large microlensing parallax values is <4.6 × 10
−4
. Given that many Spitzer light curves show evidence of large correlated errors, we conclude that this discrepancy is probably due to systematic errors in the Spitzer photometry. We find formally acceptable probabilities of
p
AD
> 0.05 for subsamples of events with bright source stars (
I
S
≤ 17.75) or Spitzer coverage of the light-curve peak. This indicates that the systematic errors have a more serious influence on faint events, especially when the light-curve peak is not covered by Spitzer. We find that multiplying an error bar renormalization factor of 2.2 by the reported error bars on the Spitzer microlensing parallax measurements provides reasonable agreement with all three Galactic models. However, corrections to the uncertainties in the Spitzer photometry itself are a more effective way to address the systematic errors.
Abstract
We present the first measurement of the mass function of free-floating planets (FFPs), or very wide orbit planets down to an Earth mass, from the MOA-II microlensing survey in 2006–2014. Six ...events are likely to be due to planets with Einstein radius crossing times
t
E
< 0.5 days, and the shortest has
t
E
= 0.057 ± 0.016 days and an angular Einstein radius of
θ
E
= 0.90 ± 0.14
μ
as. We measure the detection efficiency depending on both
t
E
and
θ
E
with image-level simulations for the first time. These short events are well modeled by a power-law mass function,
dN
4
/
d
log
M
=
(
2.18
−
1.40
+
0.52
)
×
(
M
/
8
M
⊕
)
−
α
4
dex
−1
star
−1
with
α
4
=
0.96
−
0.27
+
0.47
for
M
/
M
⊙
< 0.02. This implies a total of
f
=
21
−
13
+
23
FFPs or very wide orbit planets of mass 0.33 <
M
/
M
⊕
< 6660 per star, with a total mass of
80
−
47
+
73
M
⊕
star
−1
. The number of FFPs is
19
−
13
+
23
times the number of planets in wide orbits (beyond the snow line), while the total masses are of the same order. This suggests that the FFPs have been ejected from bound planetary systems that may have had an initial mass function with a power-law index of
α
∼ 0.9, which would imply a total mass of
171
−
52
+
80
M
⊕
star
−1
. This model predicts that Roman Space Telescope will detect
988
−
566
+
1848
FFPs with masses down to that of Mars (including
575
−
424
+
1733
with 0.1 ≤
M
/
M
⊕
≤ 1). The Sumi et al. large Jupiter-mass FFP population is excluded.
Abstract
The PRime-focus Infrared Microlensing Experiment (PRIME) will be the first to conduct a dedicated near-infrared microlensing survey by using a 1.8 m telescope with a wide field of view of ...1.45 deg
2
at the South African Astronomical Observatory. The major goals of the PRIME microlensing survey are to measure the microlensing event rate in the inner Galactic bulge to help design the observing strategy for the exoplanet microlensing survey by the Nancy Grace Roman Space Telescope and to make a first statistical measurement of exoplanet demographics in the central bulge fields where optical observations are very difficult owing to the high extinction in these fields. Here we conduct a simulation of the PRIME microlensing survey to estimate its planet yields and determine the optimal survey strategy, using a Galactic model optimized for the inner Galactic bulge. In order to maximize the number of planet detections and the range of planet mass, we compare the planet yields among four observation strategies. Assuming the Cassan et al. mass function as modified by Penny et al., we predict that PRIME will detect planetary signals for 42–52 planets (1–2 planets with
M
p
≤ 1
M
⊕
, 22−25 planets with mass 1
M
⊕
<
M
p
≤ 100
M
⊕
, 19–25 planets 100
M
⊕
<
M
p
≤ 10, 000
M
⊕
), per year depending on the chosen observation strategy.
We present adaptive optics imaging from the NIRC2 instrument on the Keck II telescope that resolves the exoplanet host (and lens) star as it separates from the brighter source star. These ...observations yield the K-band brightness of the lens and planetary host star, as well as the lens-source relative proper motion, , in the heliocentric reference frame. The measurement allows for the determination of the microlensing parallax vector, , which had only a single component determined by the microlensing light curve. The combined measurements of and KL provide the masses of the host star, , and planet, mp = 3.27 0.32MJupiter with a projected separation of 3.4 0.5 au. This confirms the tentative conclusion of a previous paper that this super-Jupiter mass planet, OGLE-2005-BLG-071Lb, orbits an M dwarf. Such planets are predicted to be rare by the core accretion theory and have been difficult to find with other methods, but there are two such planets with firm mass measurements from microlensing, and an additional 11 planetary microlens events with host mass estimates and planet mass estimates >2 Jupiter masses that could be confirmed by high angular follow-up observations. We also point out that OGLE-2005-BLG-071L has separated far enough from its host star that it should be possible to measure the host-star metallicity with spectra from a high angular resolution telescope such as Keck, the Very Large Telescope, the Hubble Space Telescope, or the James Webb Space Telescope.
We compare the planet-to-star mass-ratio distribution measured by gravitational microlensing to core accretion theory predictions from population synthesis models. The core accretion theory's runaway ...gas accretion process predicts a dearth of intermediate-mass giant planets that is not seen in the microlensing results. In particular, the models predict ∼10 × fewer planets at mass ratios of than inferred from microlensing observations. This tension implies that gas giant formation may involve processes that have hitherto been overlooked by existing core accretion models or that the planet-forming environment varies considerably as a function of host-star mass. Variation from the usual assumptions for the protoplanetary disk viscosity and thickness could reduce this discrepancy, but such changes might conflict with microlensing results at larger or smaller mass ratios, or with other observations. The resolution of this discrepancy may have important implications for planetary habitability because it has been suggested that the runaway gas accretion process may have triggered the delivery of water to our inner solar system. So, an understanding of giant planet formation may help us to determine the occurrence rate of habitable planets.
Abstract
We measured the precise masses of the host and planet in the OGLE-2003-BLG-235 system, when the lens and source were resolving, with 2018 Keck high resolution images. This measurement is in ...agreement with the observation taken in 2005 with the Hubble Space Telescope (HST). In the 2005 data, the lens and sources were not resolved and the measurement was made using color-dependent centroid shift only. The Nancy Grace Roman Space Telescope will measure masses using data typically taken within 3–4 yr of the peak of the event, which is a much shorter baseline when compared to most of the mass measurements to date. Hence, the color-dependent centroid shift will be one of the primary methods of mass measurements for the Roman telescope. Yet, mass measurements of only two events (OGLE-2003-BLG-235 and OGLE-2005-BLG-071) have been done using the color-dependent centroid shift method so far. The accuracy of the measurements using this method are neither completely known nor well studied. The agreement of the Keck and HST results, as shown in this paper, is very important because this agreement confirms the accuracy of the mass measurements determined at a small lens-source separation using the color-dependent centroid shift method. It also shows that with >100 high resolution images, the Roman telescope will be able to use color-dependent centroid shift at a 3–4 yr time baseline and produce mass measurements. We find that OGLE-2003-BLG-235 is a planetary system that consists of a 2.34 ± 0.43
M
Jup
planet orbiting a 0.56 ± 0.06
M
⊙
K-dwarf host star at a distance of 5.26 ± 0.71 kpc from the Sun.
We present Keck/NIRC2 adaptive optics imaging of planetary microlensing event MOA-2007-BLG-400 that resolves the lens star system from the source. We find that the MOA-2007-BLG-400L planetary system ...consists of a 1.71 ± 0.27M(sub Jup) planet orbiting a 0.69 ± 0.04M⨀ K-dwarf host star at a distance of 6.89 ± 0.77 kpc from the Sun. So, this planetary system probably resides in the Galactic bulge. The planet–host star projected separation is only weakly constrained due to the close-wide light-curve degeneracy; the 2σ projected separation ranges are 0.6–1.0 au and 4.7–7.7 au for close and wide solutions, respectively. This host mass is at the top end of the range of masses predicted by a standard Bayesian analysis. Our Keck follow-up program has now measured lens-source separations for six planetary microlensing events, and five of these six events have host star masses above the median prediction under the assumption that assumes that all stars have an equal chance of hosting planets detectable by microlensing. This suggests that more massive stars may be more likely to host planets of a fixed mass ratio that orbit near or beyond the snow line. These results also indicate the importance of host star mass measurements for exoplanets found by microlensing. The microlensing survey imaging data from NASA’s Nancy Grace Roman Space Telescope (formerly WFIRST) mission will be doing mass measurements like this for a huge number of planetary events.
Abstract We measure the dependence of planet frequency on host star mass, M L , and distance from the Galactic center, R L , using a sample of planets discovered by gravitational microlensing. We ...compare the two-dimensional distribution of the lens-source proper motion, μ rel , and the Einstein radius crossing time, t E , measured for 22 planetary events from Suzuki et al. with the distribution expected from Galactic model. Assuming that the planet-hosting probability of a star is proportional to M L m R L r , we calculate the likelihood distribution of ( m , r ). We estimate that r = 0.10 − 0.37 + 0.51 and m = 0.50 − 0.70 + 0.90 under the assumption that the planet-hosting probability is independent of the mass ratio. We also divide the planet sample into subsamples based on their mass ratio, q , and estimate that m = − 0.08 − 0.65 + 0.95 for q < 10 −3 and 1.25 − 1.14 + 1.07 for q > 10 −3 . Although uncertainties are still large, this result implies a possibility that, in orbits beyond the snowline, massive planets are more likely to exist around more massive stars whereas low-mass planets exist regardless of their host star mass.
Abstract
We present an adaptive optics (AO) analysis of images from the Keck II telescope NIRC2 instrument of the planetary microlensing event MOA-2009-BLG-319. The ∼10 yr baseline between the event ...and the Keck observations allows the planetary host star to be detected at a separation of 66.5 ± 1.7 mas from the source star, consistent with the light-curve model prediction. The combination of the host star brightness and light-curve parameters yields host star and planet masses of
M
host
= 0.524 ± 0.048
M
⊙
and
m
p
= 67.3 ± 6.2
M
⊕
at a distance of
D
L
= 7.1 ± 0.7 kpc. The star−planet projected separation is 2.03 ± 0.21 au. The planet-to-star mass ratio of this system,
q
= (3.857 ± 0.029) × 10
−4
, places it in the predicted “planet desert” at 10
−4
<
q
< 4 × 10
−4
according to the runaway gas accretion scenario of the core accretion theory. Seven of the 30 planets in the Suzuki et al. sample fall in this mass ratio range, and this is the third with a measured host mass. All three of these host stars have masses of 0.5 ≤
M
host
/
M
⊙
≤ 0.7, which implies that this predicted mass ratio gap is filled with planets that have host stars within a factor of two of 1
M
⊙
. This suggests that runaway gas accretion does not play a major role in determining giant planet masses for stars somewhat less massive than the Sun. Our analysis has been accomplished with a modified DAOPHOT code that has been designed to measure the brightness and positions of closely blended stars. This will aid in the development of the primary method that the Nancy Grace Roman Space Telescope mission will use to determine the masses of microlens planets and their hosts.
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