An Extrasolar Planet Census with a Space-based Microlensing Survey
Microsoft Word - Bennett_space_microlensing.doc
An Extrasolar Planet Census with a Space-based 
Microlensing Survey 
D.P. Bennett
, J. Anderson
, J.-P. Beaulieu
, I. Bond
, E. Cheng
, K. Cook
, S. Friedman
, B.S. 
Gaudi
, A. Gould
, J. Jenkins
, R. Kimble
, D. Lin
, M. Rich
, K. Sahu
, D. Tenerelli
, A. 
Udalski
, and P. Yock
University of Notre Dame, Notre Dame, IN, USA 
 Rice University, Houston, TX, USA 
 Institut d’Astrophysique, Paris, France 
 Massey University, Auckland, New Zealand 
 Conceptual Analytics, LLC, Glen Dale, MD, USA 
 Lawrence Livermore National Laboratory, USA 
 Space Telescope Science Institute, Baltimore, MD, USA 
 Ohio State University, Columbus, OH, USA 
 SETI Institute, Mountain View, CA, USA 
 NASA/Goddard Space Flight Center, Greenbelt, MD, USA 
 University of California, Santa Cruz, CA, USA 
 University of California, Los Angeles, CA, USA 
 Lockheed Martin Space Systems Co., Sunnyvale, CA, USA 
 Warsaw University, Warsaw, Poland 
University of Auckland, Auckland, New Zealand 
ABSTRACT 
A space-based gravitational microlensing exoplanet survey will provide a statistical census of 
exoplanets with masses  0.1M  and orbital separations ranging from 0.5AU to . This includes 
analogs to all the Solar System’s planets except for Mercury, as well as most types of planets 
predicted by planet formation theories. Such a survey will provide results on the frequency of 
planets around all types of stars except those with short lifetimes. Close-in planets with 
separations < 0.5 AU are invisible to a space-based microlensing survey, but these can be found 
by Kepler. Other methods, including ground-based microlensing, cannot approach the 
comprehensive statistics on the mass and semi-major axis distribution of extrasolar planets that a 
space-based microlensing survey will provide. The terrestrial planet sensitivity of a ground-based 
microlensing survey is limited to the vicinity of the Einstein radius at 2-3 AU, and space-based 
imaging is needed to identify and determine the mass of the planetary host stars for the vast 
majority of planets discovered by microlensing. Thus, a space-based microlensing survey is 
likely to be the only way to gain a comprehensive understanding of the nature of planetary 
systems, which is needed to understand planet formation and habitability. The proposed 
Microlensing Planet Finder (MPF) mission is an example of a space-based microlensing survey 
that can accomplish these objectives with proven technology and a cost that fits comfortably 
under the NASA Discovery Program cost cap. 
1. Basics of the Gravitational Microlensing Method 
The physical basis of microlensing is the gravitational attraction of light rays by a star or 
planet. As illustrated in Fig. 1, if a “lens star” passes close to the line of sight to a more distant 
source star, the gravitational field of the lens star will deflect the light rays from the source star. 
The gravitational bending effect of the lens star “splits”, distorts, and magnifies the images of the 
source star. For Galactic microlensing, the image separation is  4 mas, so the observer sees a 
microlensing event as a transient brightening of the source as the lens star’s proper motion 
moves it across the line of sight. 
Gravitational microlensing events are characterized by the Einstein ring radius, 
= 2.0 AU
(1 kpc)
where ML is the lens star mass, and DL 
and DS are the distances to the lens and 
source, respectively. This is the radius of 
the ring image that is seen with perfect 
alignment between the lens and source 
stars. The lensing magnification is 
determined by the alignment of the lens 
and source stars measured in units of RE, 
so even low-mass lenses can give rise to 
high magnification microlensing events. 
The duration of a microlensing event is 
given by the Einstein ring crossing time, 
Fig. 1: The geometry of a microlensing planet search
towards the Galactic bulge. Main sequence stars in
the bulge are monitored for magnification due to
gravitational lensing by foreground stars and planets
in the Galactic disk and bulge. 
Fig. 2: MPF is sensitive to planets above the 
purple curve in the mass vs. semi-major axis 
plane. The gold, green and cyan regions 
indicates the sensitivities of radial velocity 
surveys, SIM and Kepler, respectively. The 
location of our Solar System’s planets and many 
extrasolar planets are indicated, with ground-
based microlensing discoveries in red. 
which is typically 1-3 months for stellar lenses and a few days or less for a planet. 
Planets are detected via light curve deviations that differ from the normal stellar lens light 
curves (Mao & Paczynski 1991). Usually, the signal occurs when one of the two images due to 
lensing by the host star passes close to the location of the planet, as indicated in Fig. 1 (Gould & 
Loeb 1992), but planets can also be detected at very high magnification where the gravitational 
field of the planet destroys the symmetry of the Einstein ring (Griest & Safizadeh 1998). 
2. Capabilities of the Microlensing Method 
Planets down to one tenth of an Earth mass can be detected. The probability of a 
detectable planetary signal and its duration both scale as RE ~M p
, but given the optimum 
alignment, planetary signals from low-mass 
planets can be quite strong. The limiting 
mass for the microlensing method occurs 
when the planetary Einstein radius becomes 
smaller than the projected radius of the 
source star (Bennett & Rhie 1996). The 
~5.5 M  planet detected by Beaulieu et al. 
(2006) is near this limit for a giant source 
star, but most microlensing events have G 
or K-dwarf source stars with radii that are 
at least 10 times smaller than this. So, the 
sensitivity of the microlensing method 
extends down to < 0.1M , as the results of a 
detailed simulation of the MPF mission 
(Bennett & Rhie 2002) show in Fig. 2. 
Microlensing is sensitive to a wide 
range of planet-star separations and host 
star types. The host stars for planets 
detected by microlensing are a random 
sample of stars that happen to pass close to 
the line-of-sight to the source stars in the 
Galactic bulge, so all common types of 
stars are surveyed, including G, K, and M-
dwarfs, as well as white dwarfs and brown 
dwarfs. Microlensing is most sensitive to planets at a separation of ~RE (usually 2-3 AU) due to 
the strong stellar lens magnification at this separation, but the sensitivity extends to arbitrarily 
large separations. It is only planets well inside RE that are missed because the stellar lens images 
that would be distorted by these inner planets have very low magnifications and a very small 
contribution to the total brightness. These features can be seen in Fig. 2, which compares the 
sensitivity of the MPF mission with expectations for other planned and current programs. Other 
ongoing and planned programs can detect, at most, analogs of two of the Solar System’s planets, 
while a space-based microlensing survey can detect seven—all but Mercury. The only method 
with comparable sensitivity to MPF is the Kepler space-based transit survey, which complements 
the microlensing method with sensitivity at semi-major axes, a  1. The sensitivities of MPF and 
Kepler overlap at separations of ~1 AU, which corresponds to the habitable zone for G and K 
stars.  
The red crosses in Fig. 2 indicate the two gas 
giant (Bond et al. 2004; Udalski et al. 2005) and 
two ~10M  “super-earth” planets in orbits of ~3 
AU discovered by ground-based microlensing 
(Beaulieu et al. 2006; Gould et al. 2006). A 
preliminary analysis suggests that about one 
third of all stars are likely to have a super-earth 
at 1.5-4AU whereas radial velocity surveys find 
that only about 3% of stars have gas giants in 
this region (Butler et al. 2006). 
 Microlensing light curves yield 
unambiguous planet parameters. For the great 
majority of events, the basic planet parameters 
(planet:star mass ratio, planet-star separation) 
can be “read off” the planetary deviation
(Gould 
& Loeb 1992; Bennett & Rhie 1996; 
Wambsganss 1997). Possible ambiguities in the 
interpretation of planetary microlensing events 
have been studied in detail (Gaudi & Gould 
1997; Gaudi 1998), and these can be resolved 
with good quality, continuous light curves that 
will be routinely acquired with a space-based 
microlensing survey. A space-based survey will 
also detect most of the planetary host stars, 
which generally allows the host star mass, 
approximate spectral type, and the planetary 
mass and separation to be determined (Bennett 
et al. 2007). The distance to the planetary 
system is determined when the host star is 
identified, so a space-based microlensing survey 
will also measure how the properties of exoplanet systems change as a function of distance from 
the Galactic Center. There is usually some redundancy in the measurements that determine the 
properties of the host stars, and so the determination is robust to complicating factors, such as a 
binary companion to the background source star. 
Detailed simulations indicate a large number of planet detections. Bennett & Rhie (2002) 
and Gaudi (unpublished) have independently simulated space-based microlensing surveys. These 
simulations included variations in the assumed mission capabilities that allow us to explore how 
changes in the mission design will affect the scientific output, and they form the basis of our 
predictions in Figs. 2-4. In order to predict the number of planets that will be detected by a 
space-based microlensing survey, we must make assumptions regarding the frequency of 
exoplanets. Figs. 3 and 4 show the expected number of planets that MPF would detect at orbital 
separations 1-2.5 AU and  (i.e. free-floating planets) assuming one such planet per star. The 
range 1-2.5 AU is presented because this is just outside the range of Kepler and inside the region 
of highest sensitivity for ground-based microlensing surveys. It also corresponds to the outer part 
of the habitable zone for G and K stars and contains the “snow-line” for part of the history of 
lower mass stars (Kennedy et al. 2006). Free-floating planets are expected to be a common by-
Fig. 3: The expected number of MPF planet 
discoveries as a function of the planet mass if 
every star has a single planet at a separation 
of 1.0-2.5 AU. 
Fig. 4: The expected number of MPF free-
floating planet discoveries. 
product of most planet formation scenarios (Levison 
et al. 1998; Goldreich et al. 2004), and only a space-
based microlensing survey can detect free-floating 
planets of  1M . 
3. A Space-based Microlensing Survey Is Needed 
Microlensing relies upon the high density of 
source and lens stars towards the Galactic bulge to 
generate the stellar alignments that are needed to 
generate microlensing events, but this high star 
density also means that the bulge main sequence 
source stars are not generally resolved in ground-
based images, as Fig. 5 demonstrates. This means 
that the precise photometry needed to detect planets 
of  1M  is not possible from the ground unless the magnification due to the stellar lens is 
moderately high. This, in turn, implies that ground-based microlensing is only sensitive to 
terrestrial planets located close to the Einstein ring (at ~2-3 AU). The full sensitivity to terrestrial 
planets in all orbits from 0.5 AU to  comes only from a space-based survey. 
 Planetary host star detection from space yields precise star and planet parameters. For 
all but a small fraction of planetary microlensing events, space-based imaging is needed to detect 
the planetary host stars, and the detection of the host stars allows the star and planet masses and 
separation in physical units to be determined. This can be accomplished with HST observations 
for a small number of planetary microlensing events (Bennett et al. 2006), but space-based 
survey data will be needed for the detection of host stars for hundreds or thousands of planetary 
microlensing events. Fig. 6 shows the distribution of planetary host star masses and the predicted 
uncertainties in the masses and separation of the planets and their host stars (Bennett et al. 2007) 
from simulations of the MPF mission. The host stars with masses determined to better than 20% 
are indicated by the red histogram in Fig. 6(a), and these are primarily the host stars that can be 
detected in MPF images. 
Ground-based microlensing surveys also suffer significant losses in data coverage and quality 
due to poor weather and seeing. As a result, a significant fraction of the planetary deviations seen 
Fig. 6: (a) The simulated distribution of stellar masses for stars with detected terrestrial planets. 
The red histogram indicates the subset of this distribution for which the masses can be 
determined to better than 20%. (b) The distribution of uncertainties in the projected star-planet 
separation. (c) The distribution of uncertainties in the star and planet masses. 
Fig. 5: A comparison between an image 
of the same star field in the Galactic bulge 
from CTIO in 1” seeing and a simulated 
MPF frame (based on an HST image). 
The indicated star is a microlensed main 
sequence source star. 
(a) (b) (c) 
in a ground-based microlensing survey will have poorly constrained planet parameters due to 
poor light curve coverage (Peale 2003). 
4. A Space-Based Microlensing Survey Constrains Planet Formation Theories 
Rapid advancement in exoplanet research is driven by both extensive observational searches 
around mature stars as well as the construction of planet formation and evolution models. 
Perhaps the most surprising discovery so far is the great diversity in the planets' dynamical 
properties, but these results are largely confined to planets that are unusually massive or reside in 
very close orbits. The core accretion theory suggests most planets are much less massive than gas 
giants and that the critical region for understanding planet formation is the “snow-line”, located 
in the region (1.5-4 AU) of greatest microlensing sensitivity (Ida & Lin 2005; Kennedy et al. 
2006). Early results from ground-based microlensing searches (Beaulieu et al. 2006; Gould et al. 
2006) appear to confirm these expectations. A space-based microlensing survey would extend 
the current sensitivity of the microlensing method down to masses of ~0.1M  over a large range 
(0.5AU- ) in separation, and in combination with Kepler, such a mission provides sensitivity to 
sub-Earth mass planets at all separations. The semi-major axis region probed by space-
microlensing provides a cleaner test of planet formation theories than the close-in planets 
detected by other methods, because planets discovered at > 0.5 AU are more likely to have 
formed in situ than the close-in planets. The sensitivity region for space-microlensing includes 
the outer habitable zone for G and K stars through the “snow-line” and beyond, and the lower 
sensitivity limit reaches the regime of planetary embryos at ~0.1M . It may be that such planets 
are much more common than planets of 1M  because their type-1 migration time is much longer.  
Space-microlensing tests core accretion. The space-microlensing census of low-mass 
planets should also provide direct evidence of features of the proto-planetary disk predicted by 
the core accretion theory. There are several physical processes that control the development of 
planetary embryos and planets in the proto-planetary disk. In the inner disk, the size of planetary 
embryos is controlled by the isolation mass, and the isolation mass is expected to jump by an 
order of magnitude across the “snow-line” because of the increased surface density of solids in 
the disk. But the number of gas giant and super-earth planets is also expected to increase beyond 
the snow line, while the planetary growth time increases. This means that it is more likely for the 
growth of outer planets to be terminated via gravitational scattering of planetesimals or the proto-
planets themselves. Scattering would also result in the removal of lower mass planets into very 
distant orbits or even out of the gravitational influence of the host stars altogether, but space-
based microlensing can still detect planets in these locations. The frequency of planets of 
different masses and separations that a space-based microlensing survey provides will yield a 
unique insight into the planetary formation process and will allow us to determine the importance 
of these processes. 
The habitability of a planet depends on its formation history. The suitability of a planet 
for life depends on a number of factors, such as the average surface temperature, which 
determines if the planet resides in the habitable zone. However, there are many other factors that 
also may be important, such as the presence of sufficient water and other volatile compounds 
necessary for life (Raymond et al. 2004; Lissauer 2007). Thus, a reasonable understanding of 
planet formation is an important foundation for the search for nearby habitable planets and life. 
5. Overview of the Microlensing Planet Finder Mission  
Key requirements of the MPF mission are summarized in table 1. MPF continuously observes 
four 0.65 sq. deg. fields in the central Galactic Bulge using an inclined geostationary orbit to 
provide a continuous view of the Galactic Bulge 
fields and a continuous downlink. MPF will use a 
dedicated ground station co-located with other 
NASA facilities at White Sands, NM. Spacecraft 
commanding and on-board processing are 
minimized because of the simple observation plan and orbit design. 
MPF system. MPF uses a 1.1m Three-Mirror Anastigmat (TMA) telescope feeding a 145 
Mpixel HgCdTe focal plane residing on a standard spacecraft bus as shown in Fig. 7. The MPF 
design leverages existing hardware and design concepts, many of which are already 
demonstrated on-orbit and/or flight qualified. The spacecraft bus is a near-identical copy of that 
used for Spitzer and has demonstrated performance that meets MPF requirements. The telescope 
system leverages Ikonos and NextView commercial Earth-observing telescope designs that 
provide extensive diffraction-limited images. The focal plane design taps proven technologies 
developed for JWST. All elements are at TRL 6 or better. The focal plane design uses common 
non-destructive readout CMOS multiplexers for two detector technologies that cover the visible 
and the near-IR. The MPF focal plane can track up to 35 guide stars in the field, providing a 
built-in fine guidance capability. The focal plane gains additional advantages from using the 
Teledyne SIDECAR™ application specific integrated circuit (ASIC) that condenses all the 
control and readout electronics into a “system-on-a-chip” implementation. This approach 
dramatically simplifies the support electronics while minimizing wire-count challenges. 
Cost and Schedule. The total cost for the MPF mission is (FY06) $390M including 30% 
contingency during development. The team that developed the costs included NASA GSFC, 
Lockheed Martin, ITT, STScI, Teledyne and University of Notre Dame. 
6. Discussion and Summary 
A space-based microlensing survey provides a census of extrasolar planets that is complete (in 
a statistical sense) down to 0.1M  at orbital separations  0.5 AU, and when combined with the 
results of the Kepler mission a space-based microlensing survey will give a comprehensive 
Property Value Units  
Launch Vehicle 7920-9.5 Delta II 
Orbit Inclined GEO 
28.7 
degrees 
Mission Lifetime 4.0 years 
Telescope Aperture 1.1 meters (diam.) 
Field of View 0.95x0.68 degrees 
Spatial Resolution 0.240 arcsec/pixel 
Pointing Stability 0.048 arcsec 
Focal Plane Format 145 Megapixels 
Spectral Range 600 – 1700 nm in 3 bands 
Quantum Efficiency > 75% 
> 55% 
900-1400 nm 
700-1600 nm 
Dark Current < 1 e-/pixel/sec 
Readout Noise < 30 e-/read 
Photometric 
Accuracy 
1 or better % at J=20.5. 
Data Rate 50.1 Mbits/sec 
Table 1: Key MPF Mission Requirements 
Fig. 7: MPF On-Orbit Configuration 
picture of all types of extrasolar planets with masses down to well below an Earth mass. This 
complete coverage of planets at all separations can be used to calibrate the poorly understood 
theory of planetary migration. This fundamental exoplanet census data is needed to gain a 
comprehensive understanding of processes of planet formation and migration, and this 
understanding of planet formation is an important ingredient for the understanding of the 
requirements for habitable planets and the development of life on extrasolar planets. 
A subset of the science goals can be accomplished with an enhanced ground-based 
microlensing program (Gould et al. 2007), which would be sensitive to Earth-mass planets in the 
vicinity of the “snow-line”. But such a survey would have its sensitivity to Earth-like planets 
limited to a narrow range of semi-major axes, so it would not provide the complete picture of the 
frequency of exoplanets down to 0.1M  that a space-based microlensing survey would provide. 
Furthermore, a ground-based survey would not be able to detect the planetary host stars for most 
of the events, and so it will not provide the systematic data on the variation of exoplanet 
properties as a function of host star type that a space-based survey will provide. 
The basic requirements for a space-based microlensing survey are a 1-m class wide field-of-
view space telescope that can image the central Galactic bulge in the near-IR or optical almost 
continuously for periods of at least several months at a time. This can be accomplished as a 
NASA Discovery mission, as the example of the MPF mission shows, but there are a number of 
other proposed missions with similar requirements, such as a number of JDEM concept missions 
or a stare-mode astrometry mission (Johnston et al. 2007) that makes use of the same type of 
detectors as the MPF mission. Such an astrometry mission could complement the statistical 
planetary results from microlensing survey with data on nearby planets. Thus, a space-based 
microlensing survey could be accomplished with a standalone Discovery class mission or a joint 
mission with another project. As Fig. 2 shows, there is no other planned mission that can 
duplicate the science return of a space-based microlensing survey, and our knowledge of 
exoplanets and their formation will remain incomplete until such a mission is flown. 
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