SIMULATOR FOR MICROLENS PLANET SURVEYSSergei Ipatov1, Keith Horne2, Khalid Alsubai3,

Dan Bramich4,  Martin  Dominik2,*, Markus Hundertmark2, Christine Liebig2, Colin Snodgrass5, Rachel Street6, Yiannis Tsapras6    

1) Alsubai Est. for Scientific Studies, Doha, Qatar; 2) Univ. of St. Andrews, St. Andrews, Scotland, United Kingdom; 3) Qatar Foundation, Doha, Qatar; 4) European Southern Observatory, Garching bei München, Germany; 5) Max Planck Institute for Solar System Research, Katlenburg-Lindau, Germany; 6) Las Cumbres Observatory Global Telescope Network, Santa Barbara, USA * Royal Society University Research Fellow†supported by Qatar National Research Fund (QNRF), member of Qatar Foundation (grant

NPRP 09-476-1-078)

This source file for the poster can be also found on http://star-www.st-and.ac.uk/~si8/doha2013s.ppt Contact: siipatov@hotmail.com

Abstract We summarize the status of a computer simulator for microlens planet surveys. The simulator generates synthetic light curves of microlensing events observed with specified networks of telescopes over specified periods of time. The main purpose is to assess the impact on planet detection capabilities of different observing strategies, and different telescope resources, and to quantify the planet detection efficiency of our actual observing network, so that we can use the observations to constrain planet abundance distributions. At this stage we have developed models for sky brightness and seeing, calibrated by fitting to data from the OGLE survey and RoboNet observations in 2011. Time intervals during which events are observable are identified by accounting for positions of the Sun, the Moon and other restrictions on telescope pointing. Simulated observations are then generated for an algorithm that adjusts target priorities in real time with the aim of maximizing planet detection zone area summed over all the available events. The efficiency of microlens observations with a use of different telescopes is discussed.

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Styding planets by microlensing Microlensing is unique in its sensitivity to wider-orbit (i.e. cool)

planetary-mass bodies .

The 15% blip lasting about 24 hrs that revealed 5-Earth-mass planet OGLE-2005-BLG-390 impressively demonstrated the sensitivity of ongoing microlensing efforts to Super-Earths. Had an Earth-mass planet been in the same spot, it would have been detectable from a 3% signal lasting 12 hrs. The detection of less massive planets requires photometry at the few per cent level on Galactic bulge main-sequence stars, which, given the crowding levels, becomes possible with images of angular resolution below about 0.4″. 3

•Detection zone at microlense observations•Based on the approach presented in [1], at

each time step for different events we calculate the detection zone area and the probability of detection of an exoplanet. The event with a maximum probability at a time step is chosen for observations. •We define the ‘detection zone’ as the

region on the lens plane (x,y) where the light curve anomaly δ(t,x,y,q) is large enough to be detected by the observations (q is the ratio of the planet to that of the star).

[1] Horne K., Snodgrass C., Tsapras Y., MNRAS, 2009, v. 396, 2087-2102

Detection zones on the lens plane indicate the regions where a planet with mass ratio q=m/M=10-3 is detected with Δχ2>25. The light curve A(t) has maximum magnification Ao=5, and the accuracy of the measurements is σ=(5/A1/2) per cent. 4

Maximizing planet detection zone area The photometric S/N (signal to noise) ratio and hence the area w of an isolated planet detection zone scales as the square root of the exposure time : S/N = (Δt /τ) 1/2 , w = g Δt 1/2 . Here τ is the exposure time required to reach S/N=1. The 'goodness' gi of an available target depends on the target's brightness and magnification, the telescope and detector characteristics, and observing conditions (air mass, sky brightness, seeing). The simulator evaluates 'goodness' of available targets in real time, and observes the one offering the greatest increase in w with exposure time. Moves to a new target occur when the increase in w for the new target is better than the current target, accounting for the slew time required to move to the new target. As the CCD camera takes a finite time tread to read out, and the telescope takes a finite time tslew to slew from one target and settle into position on the next, the on-target exposure time accumulated during an observation time t is Δt=t- tslew –n tread (tslew ~ 30-100 s, tread ~10-20 s). At a time step Δt the detection area of i-th event increases by gi[(Δt+tdone) 1/2 - tdone

1/2 ], where tdone is an exposure time already has been done. For a new target, the area is gi(Δt-tslew) 1/2. For a choice of a best event, we compared gi[(tplan+tdone) 1/2 - tdone

1/2 ] for a current target with gi[tslew

1/2] for a new target, where tplan=2tslew. All but one of the targets require slew time before the exposure can begin. See [1] for details. [1] Horne K., Snodgrass C., Tsapras Y., MNRAS, 2009, v. 396, 2087-2102. 5

Target observability•The observability of a target is limited by its own position on the sky, as well as that of the Sun and the Moon, and telescopes moreover have pointing restrictions. Taking the LT (from http://telescope.livjm.ac.uk/) as example, we particularly require:•Air mass of target > 3 or•Cos (zenith of the Sun) < sin (-8.8o) or•Altitude of a target: alt<altmin=25o or alt>altmax=87o or•Hour angle: ha<hamin or ha>hamax. For LT there are no limits on ha: hamin=-12 h and hamax=12 h. For 1-m telescopes, hamin=-5 h and hamax=5 h.• Telescopes considered:•1.3m OGLE - The Optical Gravitational Lensing Experiment - Las Campanas, Chile.• 2m FTS - Faulkes Telescope South - Siding Springs, Australia.• 2m FTN - Faulkes Telescope North - Haleakela, Hawaii.• 2m LT - Liverpool Telescope - La Palma, Canary Islands.•Three 1m CTIO - Cerro Tololo Inter-American Observatory in Chile .•Three 1m SAAO - South African Astronomical Observatory.•Two 1m SSO - Siding Spring Observatory near Coonabarabran, New South Wales, Australia.•1m MDO - McDonald observatory in Texas. 6

•Observations analyzed for construction of sky model:•For studies of sky brightness for FTS, FTN, and LT, we considered those events observed in 2011 for which .dat files are greater than 1 kbt: FTS - 39 events; FTN - 19 events, LT – 20 events. For OGLE we considered 20 events (110251-110270).

•Calculations of Isky(0) and the coefficients (k1 and ko)

presented in the tables and on the plots were based on χ2 optimization of the straight line fit (y=k1·x+ko, χ2=∑[(yi-k1·xi-ko)/σi]2, σi

2 is variance).The value of Isky(0) (sky brightness at zenith) was chosen in such a way that the sum of squares of differences between observational and model sky brightness magnitudes were minimum in the case when the Moon is below the horizon. The used sky model was based mainly on [2] K. Krisciunas & B. Schaefer, 1991, PASP, v. 103, 1033-1039.

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Dependences of seeing on air mass and values of sky brightness at zenith obtained based on analysis of observations

•Values Isky(0) of sky brightness at zenith (I magnitude per square arcsec) and bo in the χ2 optimization b=b1·a+bo (where a is air mass) for the Moon below the horizon at throughput thruput=0.324 and an extinction coefficient extmag=0.05 (for extmag equal to 0 and 0.1, values of Isky(0) differed by less than 0.3%; Isky(0) is one of parameters of the model used):

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Telescope FTS FTN LT OGLEIsky(0) 19.0 18.7 19.6 18.1b0 18.8 18.3 19.0 18.0

Telescope FTS FTN LT OGLE ko 1.33 0.68 1.35 1.33 k1 0.52 0.21 0.42 0.29 σ 0.37 0.21 0.50 0.25

Seeing (FWHM in arcsec) vs. air mass (χ2 optimization): seeing=ko+k1×(airmass-1)

Seeing (in arcsec) vs. air mass. FTS observations of 39 events. A thick straight line is based on χ2 optimization (y= ko+ k1 (x-1), ko=1.334, k1=0.519). Thinner straight lines differ from this line by +/- Ϭ (Ϭ=0.367). Non-straight lines show mean and median values (the line for the mean value is thicker). 10

Sky brightness (mag) vs. air mass for Moon below the horizon. Different points are

for OGLE observations of 20 different events. The lines are for the χ2 optimization (b=b1·a+bo ) with different bo (different values for different events) and the same b1. The

most solid line is for the model for which bo is the same for all events. For Moon below the

horizon, the values of bo (which characterize sky zenith brightness near different events)

differ typically but not more that 1 mag. 11

Sky brightness residuals (mag) vs. air mass for the model with different bo for FTS observations of 39 events. Left plot is for all positions of the Moon and the Sun. Right plot is for the Moon below the horizon and solar elevation < - 18o. 12

Sky brightness residuals vs. solar elevation•The influence of solar elevation on sky brightness began to play a role at θSun>-14o, and was considerable at θSun>-7o. For example, if we consider only FTS observations with the Moon below the horizon, then sky brightness residual sbr can be up to -3 mag at -8o<θSun<-7o, sbr>-1 mag at θSun<-8o, and sbr>-0.4 mag at θSun<-14o.

•Sky brightness residuals (in mag.) vs. solar elevation for FTS observations of 39 events. Red signs are for the Moon below the horizon. 13

Time intervals when it is better observe events

Time intervals for events selected for observations with OGLE (at actual times of peaks of light curves). Considered events: 1110001-111562. 14

Light curves (with error bars) for events selected for observations with OGLE (at actual times of peaks of light curves). Considered events: 110001-111562. 15

Comparison of the efficiency of telescopes for microlense observations

Our simulator suggests what events it is better to observe at specific time intervals with a specific telescope in order to increase the probability of finding new exoplanets using microlense observations. For estimates of the probability, for best events we considered wsum =∑ gi[(Δt+tdone) 1/2 - tdone

1/2] (where Δt=2tslew for an event observed at a current time, and Δt=tslew and tdone=0 for other events) and rwsumt=(wsum/wsumOGLE)/(tsum/tsumOGLE) , where tsum is the total time during considered time interval when it is possible to observe at least one event. For best events we also calculated wsumo=∑gi[(ts+tdone)1/2 - tdone

1/2] and rwsumto=(wsumo/wsumoOGLE)/(tsum/tsumOGLE) with ts =20 s. For a typical run, the value of tsum/tsumOGLE is about 0.66, 0.56, and 0.62 for FTN, LT, and MDO, respectively, but it can vary for different considered time intervals. For other considered sites, the ratio differed from 1 by less than 0.1. In our calculations, rwsumt and rwsumto for observations with a 1-m telescope (located at CTIO, SAAO, SSO, or MDO) equipped with the Sinistro ccd, and with a 2-m telescope (FTS, FTN, or LT) were mainly in the range 0.8-1.2 and 1.4-2.2 of that for OGLE, respectively (see the plot below). The ratio of wsum for FTS and SSO located at the same site usually was about 2 . For the SBIG ccd, the values of wsum (and wsumo) were smaller by a factor of ~1.2 than those for the Sinistro ccd. The difference in wsum is about 5% if for SSO we use the values of Isky(0) and the dependence of seeing vs. air mass as those for OGLE, compared to those for FTS. 16

The values of rwsumt=(wsum/wsumOGLE)/(tsum/tsumOGLE) (the left plot) and rwsumto=(wsumo/wsumoOGLE )/(tsum /tsumOGLE) (the right plot), which characterize the efficiency of microlense observations, vs. the number Nt of a telescope in the case when 1-m telescopes (equipped with the Sinistro ccd) located at the same site observe different events at the same time. See details on the next slide. 17

Designations to the above plot:The values of rwsumt=(wsum/wsumOGLE)/(tsum/tsumOGLE) (the left plot) and rwsumto=(wsumo/wsumoOGLE)/(tsum/tsumOGLE) (the right plot), which characterize the efficiency of microlense observations, vs. the number Nt of a telescope in the case when 1-m telescopes (equipped with the Sinistro ccd) located at the same site observe different events at the same time. Considered time interval equals T=90 days.The signs for calculations with actual values of t0 (the time corresponding to the peak of a light-curve) and with random values of t0 (t0 = RNDM∙(tmx+2tE )- tE+to, where tE is the time scale equal to the ratio of the angular Einstein radius to the relative proper motion, RNDM is a random value between 0 and 1, tmx is the duration of the considered time interval, to is the beginning of the interval) for 1562 events are black and red, respectively. Crests are for the time interval beginning from May 2, circles are for the interval beginning from August 1. 18Nt 1 2 3 4 5-7 8 9-11 12-13

FTS FTN LT OGLE

CTIO MDO SAAO SSO

Comparison of the efficiency of 2-m telescopes with that of OGLE for a search of exoplanets

OGLE observed a little more than 200 galactic bulge fields. For 1500 events in 2011, it means that typically there could be ~10 events in one field (the ratio 1500/200 is 7.5). For telescopes other than OGLE (exclusive for LT), typically there can be only one event in the field of view. In our calculations for 1562 events (and 90 days time interval), the value of wsum (or wsumo) for the best events chosen for observations was usually considerably greater than for typical 10 other events (which are not the best at the current moment of time).Therefore, we can use the values of wsum (or wsumo) calculated only for the best events for comparison of the efficiency of different telescopes for a search of new exoplanets. Of course, telescopes with a wider field of view are more effective for a search of new events. Nevertheless, the obtained results show that, for a search of exoplanets based on already discovered events, a 2-m LCOGT telescope on average is more effective (per unit of time of observations) than OGLE and the efficiency of a 1-m telescope with Sinistro ccd can be close to that of OGLE, as the ratio of values of wsum (or wsumo) per unit of time for the 2-m telescopes to that for OGLE usually is in the range of 1.4-2.2, and that for 1-m telescopes is mainly in the range of 0.8-1.2. 19

Comparison of the efficiency of observations with the use of 1-m telescopes located at the same site.

In our test calculations, the values of wsum (and wsumo) at diameter of a telescope equal to 2 m were usually greater by a factor of 1.5 -1.7 than those for 1-m telescope if the difference was only in the diameter d of a telescope. Such factors correspond to s0.3 - s0.4 , there s is the effective area of a telescope. For two or three telescopes located at the same site for observations of the same event, the ratio of wsum (or wsumo) to that for one telescope is about 20.3=1.25 to 20.4=1.32 or about 30.3=1.4 to 30.4=1.55, respectively. Analysis of our calculations shows that most of the time it is better to observe different events using the telescopes located at the same site than to observe the same event with two or three telescopes, but at a time close to a light-curve peak often it is better to observe the same event with all telescopes located at the same site.

For 1562 events during 90 days (or larger) interval, a considerable (up to more than ½) contribution to wsum was during short time intervals corresponding to peaks of light curves, if this telescope is allowed to observe all events. 20