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Paper text:
gravitational microlensing can be used to detect extra - solar planets orbiting distant stars @xcite with relatively large photometric signals as long as the angular planetary einstein ring radius is not much smaller than the angular size of the source star @xcite . for giant source stars in the galactic bulge , however , the signals of earth - mass planets are largely washed out by their large angular size , but galactic bulge main sequence stars are small enough to allow the detection of planets with masses as low as @xmath2 .    this fact has led to suggestions that ground - based microlensing surveys might be able to measure the abundance of earth - like planets @xcite . however , the initial estimates of the sensitivity of such a survey neglected the blending of main sequence source stars in the bulge that is illustrated in fig .
[ fig - image ] .
the brightness of the source stars was over - estimated , and it was not realized that the actual source stars were blended with several other stars of similar brightness in ground - based images .
more realistic estimates of the sensitivity of the proposed ground - based extra - solar planet searches indicated very poor sensitivity to terrestrial planets @xcite , and suggested that only a space - based survey @xcite could discover a significant number of earth - like planets .    in this paper
, we simulate the most capable ground - based microlensing survey that could reasonably be attempted : a network of three 2-m class wide field - of - view telescopes spanning the globe in the southern hemisphere that are dedicated to the microlensing planet search survey for four years .
many of the details of our simulations have been described in @xcite , but there are additional details that must be added to describe the observing conditions at ground - based observatories .
i assume that the microlensing survey telescopes are located at the best existing observatory sites in chile ( paranal ) , south africa ( sutherland ) , and australia ( siding springs ) . for paranal , actual seeing and cloud cover records are available from the eso web site .
the sutherland site in south africa has conditions similar to la silla in chile ( peter martinez , private communication ) , so the eso records for la silla ( offset by 1 year ) were used as a proxy for sutherland .
standard airmass and wavelength correction formulae @xcite were used to convert the eso seeing data to seeing estimates for bulge observations in the i - band , and the sky brightness was calculated following @xcite .    for the observations from australia ,
the 1997 - 1999 seeing records from the macho project have been used since the mt .
stromlo observatory and siding springs have very similar seeing . to compensate for the optical effects of the macho telescope , 0.8 
was subtracted in quadrature from all the macho telescope seeing values .
the number of clear nights was adjusted slightly to meet the long term averages for each site as listed in @xcite .
an important input to this simulation is the systematic crowded field photometry errors that are assigned .
the ogle - iii ews data @xcite provides a set of photometry for stars with brightness varying in a predictable way ( due to microlensing ) using the most accurate crowded field photometry method devised to date @xcite . by fitting to point - source ,
single - lens light curves to the 2002 ogle - iii ews data for stars brighter than @xmath3 , we find an assumed systematic error of 0.7% of the total flux at the psf peak of each star seems to give fit @xmath4 .
the systematic errors appear to be larger for fainter stars or for other data sets , but i adopt this as a systematic error estimation formula .
this systematic error implies a limit to the useful size of a microlensing planet search survey telescope .
once the systematic error dominates , it is no longer useful to go to a larger telescope .
our simulation results yield an optimal telescope aperture of about 2-m with a 6 sq .
deg .  field - of - view ( fov ) .
larger telescopes could detect some more planets by cycling between two or more fields , but the gain is not large because of the rapid decrease in the microlensing rate away from the central galactic bulge .
[ fig - bad - lc1 ] shows an example of two light curves that would be considered planet detections by the criteria of @xcite for a space - based survey ( a @xmath5 improvement for the planetary lensing model over the best single lens model ) .
but the uneven data quality due to seeing variations and cloud cover imply that the planetary parameters can not be constrained .
thus , while the planetary signal is detectable for these events , terrestrial planets can not be discovered with data like this .
the situation is only slightly better for the events shown in fig .
[ fig - bad - lc2 ] , where the poor seeing in australia , and low s / n of the planetary deviation conspire to prevent determinations of the planetary masses .
of course , sometimes a planetary signal will be seen during good observing conditions , yielding light curves that can accurately determine the planetary parameters .
this is the case for the two events shown in fig .
[ fig - good - lc ] .
generally , such events have planetary deviations that occur at high magnification , such as the event on the left or have large amplitude deviations like the event on the right .
intermediate between the poorly covered planetary detections shown in figs .
[ fig - bad - lc1][fig - bad - lc2 ] and the well covered planetary discoveries shown in figs .
[ fig - good - lc ] are the light curves shown in fig .  [ fig - fair - lc ] . in both cases ,
the planetary parameters can be formally determined .
however for the event on the left , the source star brightness is only @xmath6 .
if the photometry errors are not random , as is likely for systematic errors , then the brightness of the source star can not be determined from the light curve fit .
hence , the planetary parameters will be poorly constrained . for the light curve on the right
, the parameters can be determined despite the relatively poor coverage of the deviation because the deviation shape contains redundant information .
however , the poor light curve coverage means that the redundancy can not be used to confirm the interpretation of the event .
this is a serious drawback because the planet discovery can not be confirmed in any other way .
it is clear from figs .
[ fig - bad - lc1]-[fig - good - lc ] it is sensible to consider two different categories of detected planetary events : `` detected '' planets and `` discovered '' planets .
the `` detected '' category includes all planets with planetary signals that provide at least a @xmath7 improvement over the best single lens fit .
clearly , the events shown in fig .  [ fig - good - lc ] should be in the `` discovered '' while those shown in figs .
[ fig - bad - lc1 ] and [ fig - bad - lc2 ] should not be in this category .
we define the planet `` discovered '' category with the following criteria .
each planetary light curve deviation is split up into 1 - 3 separate deviation regions of positive or negative magnification with respect to the single lens curve with the same parameters .
the first and last regions are considered be begin and end when the deviation reaches the with 10% of the maximum planetary deviation or 0.3% of single lens magnification . for a planet `` discovery '' , each the observations must cover at least 40% of each planetary deviation region , and at least 60% of each total deviation .
all measurements are considered to contribute the light curve coverage unless their error estimates are larger than one third of the maximum planetary deviation .
also , because a significant component of the error estimates is a systematic error , we also require that each  discovery " light curve have at least one measurement that detected the stellar microlensing event by @xmath8 and one measurement that detects the planetary deviation by @xmath9 . with these definitions , about one third of the detected planets
pass the planet discovery threshold including both the events in fig .
[ fig - good - lc ] and the light curve on the left side of fig .
[ fig - fair - lc ] .
[ fig - det_sep ] compares the sensitivity of a 3-site network of 2m - class ground - based microlensing planet search telescopes vs.  a space - based microlensing planet search telescope that would be appropriate for nasa s discovery program @xcite . at present
, the cost cap for a discovery mission is $ 360 m , and the ground - based network that i have simulated would be roughly one fifth that cost , including all software development and operational expenses .
the ground - based survey does the best at separations of 23 au where the planet is near the einstein ring and is detectable in high magnification events .
the ground - based survey would have about 30 times fewer planet discoveries and 10 times fewer raw detections of terrestrial planets at these separations . at 1 au
, the advantage of space for planet discoveries is a factor of 100 .
the number of planet detections as a function of planetary mass fraction are shown in fig .
[ fig - det_eps ] for planets in earth - like orbits and planets in all orbits .
the left hand panel indicates that even if earth - like planets in earth - like orbits are quite abundant , the 3-site ground - based survey would only expect to find one with good light curve coverage .
the ground - based results in fig .  [ fig - det_eps ] are somewhat misleading for @xmath10 because these events can generally be detected with giant source stars , which have not been included in this simulation .
these would add significantly to the ground - based detections , but would add little to the space - based detections .
so , for planets with mass fractions about ten times that of the earth , the ground - based survey may have an advantage .
i have carried out detailed simulations of the most capable ground - based microlensing terrestrial planet search program that could plausibly be attempted .
the simulated survey employs three 2 m class telescopes spanning the globe in the southern hemisphere which observe the galactic bulge whenever possible for a period of 4 years .
such a network is about 100 times less sensitive than a space - based survey which might only cost 5 times as much .
so , without some dramatic improvement in ground - based crowded field photometry , it will not be possible to conduct a microlensing survey to determine the abundance of terrestrial planets in the inner galaxy .    for a gravitational census of terrestrial planets
, a space - based survey will be required @xcite . as fig .
[ fig - n_vs_sep ] indicates , such a mission would complete the survey for terrestrial planets that will be started by the kepler mission @xcite which is sensitive to earth - like planets at separations @xmath11au using the transit method .
a space - based microlensing survey would overlap kepler with sensitivity at @xmath12au , and extend sensitivity to terrestrial planets to all separations including free - floating planets , which may have been ejected from their parent stars during the planetary formation process .
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i compare an aggressive ground - based gravitational microlensing survey for terrestrial planets to a space - based survey . 
 the ground - based survey assumes a global network of very wide field - of - view @xmath0 m telescopes that monitor fields in the central galactic bulge . 
 i find that such a space - based survey is @xmath1 times more effective at detecting terrestrial planets in earth - like orbits . 
 the poor sensitivity of the ground - based surveys to low - mass planets is primarily due to the fact that the main sequence source stars are unresolved in ground - based images of the galactic bulge . 
 this gives rise to systematic photometry errors that preclude the detection of most of the planetary light curve deviations for low mass planets .