A re-analysis of exomoon candidate MOA-2011-BLG-262lb using the Besançon Galactic Model

Size: px
Start display at page:

Download "A re-analysis of exomoon candidate MOA-2011-BLG-262lb using the Besançon Galactic Model"

Transcription

1 A re-analysis of exomoon candidate MOA-2011-BLG-262lb using the Besançon Galactic Model A dissertation submitted to the University of Manchester for the degree of Master of Science by Research in the Faculty of Science & Engineering 2017 By Parvin Mansour School of Physics and Astronomy

2 Contents Abstract 8 Declaration 9 Copyright 10 Acknowledgements 11 The Author 12 Dedication 13 Introduction 14 1 Microlensing Lens equation Binary lenses Caustics Optical depth and Event rate Planetary microlensing light curve Microlensing degeneracy FFPs Microlensing surveys Parvin Mansour 2

3 CONTENTS 2 MOA-2011-BLG-262lb Observation Light curve analysis The relative proper motion Source and lens magnitude Bayesian priors Probability distribution MOA-2011-BLG-262lb conclusion Analysing MOA-2011-BLG-262lb using the Besançon Model Besançon Galactic Model A brief description Interstellar extinction Initial catalogue parameters Accounting for the finite source effect Optical depth Average Einstein radius crossing time and event rate Comparison with MABµls microlensing maps Preliminary probability density maps Selection functions Application to MOA-2011-BLG-262lb Refining Besançon catalogues Final probability density maps Discussion/ Results 77 5 Conclusion/ Future direction 81 BIBLIOGRAPHY 83 Parvin Mansour 3

4 List of Tables 1.1 Microlensing parameters Model parameters for planet-moon solution Model parameters for star-planet solution The values for optical depth, event rate and average crossing time from our and MABµls simulations The χ 2 -weight for all four models (Bennett et al. 2014) Parvin Mansour 4

5 List of Figures 1.1 Simple geometry of a lensing system Geometry of a point mass lens Caustic configurations Planetary microlensing light curve Planetary microlensing light curve Parallax effect on the microlensing light curve MOA-2011-BLG-262 light curve K-band images from Kick-2 and VVV The magnitude-distance relation for both models Lens distance probability distribution The planet-moon lens distance probability distribution The star-planet lens distance probability distribution Simulated map of the optical depth Simulated map of the event rate Simulated map of the average crossing time Posterior probability map of Solar-mass lenses Posterior probability map of Jupiter-mass lenses Posterior probability map of solar-mass lenses including the selection functions Parvin Mansour 5

6 LIST OF FIGURES 3.7 Posterior probability map of Jupiter-mass lenses including the selection functions Plot of source magnitude versus source motion Plot of source distance versus lens distance for Solar-mass population Plot of source distance versus lens proper motion for Solar-mass population Plot of source distance versus source proper motion for Solar-mass population Plot of lens distance versus lens proper motion for Solar-mass population Plot of lens distance versus source proper motion for Solar-mass lens population Plot of lens proper motion versus source proper motion for Solarmass population Plot of source distance versus lens distance for Jupiter-mass population Plot of source distance versus lens proper motion for Jupiter-mass population Plot of source distance versus source proper motion for Jupitermass population Plot of lens distance versus lens proper motion for Jupiter-mass population Plot of lens distance versus source proper motion for Jupiter-mass lens population Plot of lens proper motion versus source proper motion for Jupitermass population Final posterior probability map of the 0.12 solar-mass lenses Final posterior probability map of the 3.6 Jupiter-mass lenses.. 71 Parvin Mansour 6

7 LIST OF FIGURES 3.23 Contour plot of probability distribution of 0.12 Solar-mass lens population Contour plot of probability distribution of 3.6 Jupiter-mass lens population Probability density map of Solar-mass lenses with the relative proper motion line Probability density map of Jupiter-mass lenses with the relative proper motion line Probability density map of Jupiter-mass lenses with a more relaxed distance Parvin Mansour 7

8 The University of Manchester ABSTRACT OF DISSERTATION submitted by Parvin Mansour for the Degree of Master of Science by Research and entitled Towards Real Time Selection of Computing Exoplanet Microlensing Models September 2017 Gravitational microlensing is the bending of star light due to gravitational influence of a massive compact object, known as the lens, along the line of sight. The presence of any planet orbiting the lens can be detected via the microlensing method. Due to the fact that it does not rely on detection of photon from the star or the planet, this method provides a powerful tool for detecting free floating planets and cool exoplanets orbiting a wide range of stars with distances of order of several kpc. The physical characteristics of the lens system can be determined by constructing a model that matches with the observed data. Unfortunately, typical microlensing models suffer from a two fold degeneracy, which means that the mass and distance of the lens cannot be disentangled. Finding the best parameters set that provide a good description of the observed microlensing light curve is a challenging task. Different model fits can produce similar light curves with reasonable agreement with the observation, therefore it is essential to be able to compute the probability density of different model fits. We developed a software, using the Besançon population synthesis model of the Galaxy, that can predict the probability density of different microlensing event model fits. We used this software to compute the probability density of two models describing the microlensing event MOA-2011-BLG-262-lb, a free floating planet-moon system and a star-planet system with a super Earth orbiting a star. We calculated the relative posterior probability of both model fits by incorporating selection functions for the Einstein radius crossing time, relative proper motion, source apparent magnitude and χ 2 from the MOA-2011-BLG-262-lb event and found that the ratio of the planet-moon model posterior probability to that of the star-planet model is in order of Parvin Mansour 8

9 Declaration No portion of the work referred to in this dissertation has been submitted in support of an application for another degree or qualification of this or any other university or other institution of learning. Parvin Mansour 9

10 Copyright The author of this dissertation (including any appendices and/or schedules to this dissertation) owns certain copyright or related rights in it (the Copyright ) and he has given The University of Manchester the right to use such Copyright, including for administrative, promotional, educational and/or teaching purposes. Copies of this dissertation, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the regulations of the John Rylands University Library of Manchester. Details of these regulations may be obtained from the Librarian. This page must form part of any such copies made. The ownership of any patents, designs, trade marks and any and all other intellectual property rights except for the Copyright (the Intellectual Property Rights ) and any reproductions of copyright works, for example graphs and tables ( Reproductions ), which may be described in this dissertation, may not be owned by the author and may be owned by third parties. Such Intellectual Property Rights and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property Rights and/or Reproductions. Further information on the conditions under which disclosure, publication and exploitation of this dissertation, the Copyright and any Intellectual Property Rights and/or Reproductions described in it may take place is available from the Head of School of Physics and Astronomy. Parvin Mansour 10

11 Acknowledgements I would like to thank my supervisor, Dr Eamonn Kerins, for his support over the past year. This work could not have been completed without his guidance and encouragement. I enjoyed our weekly meetings and discussions of the research and life in general. I also would like to thank Safa Al-Hakeem and Charlie Walker for proof-reading this dissertation. Their comments have improved this work. My family means the world to me and I could not have completed my journey without them. Special thanks to my husband, Nabil, for his ongoing support over the years. Parvin Mansour 11

12 The Author The author was born in Tehran, Iran where she completed a high school diploma before moving to UK in She started her Bachelor of science, Astronomy and planetary path away at the Open University in 2012 and graduated in She started her MSc in September 2016 at the University of Manchester. The result of the research she undertook during her MSc are presented in this thesis. Parvin Mansour 12

13 The sky Is a suspended blue ocean. The stars are the fish That swim. The planets are the white whales I sometimes hitch a ride on, And the sun and all light Have forever fused themselves Into my heart and upon My skin. There is only one rule On this Wild Playground, For every sign Hafiz has ever seen Reads the same. They all say, Have fun, my dear; my dear, have fun, In the Beloved s Divine Game. Hafiz For my beloved husband, Nabil and our children, Reem, Hassan and Rasha who helped me find my playground. Parvin Mansour 13

14 Introduction By the 19th century all of the planets within the solar system were known. However it was not until the late 1900s when a new planet, an exoplanet (a planet orbiting a star other than the sun) was discovered. Exoplanetary science is a relatively new field in astronomy and in recent years has witnessed a huge increase in the number of detected exoplanets in the Galaxy. New discoveries are announced almost every week. To date we have more than 3600 confirmed exoplanets 1 and this number is expected to increase significantly when all of the data from the Kepler satellite is analysed. The overwhelming majority of these exoplanets are discovered by the transit and radial velocity techniques (Perryman 2014). By combining the information gathered from both methods, the planet s radius, mass, density, orbital inclination and the atmospheric composition can be measured. However these methods are biased towards massive planets in close orbit around the host. In fact, the first exoplanet discovered (by radial velocity) orbiting a sun like star was a Jupiter-mass planet orbiting the host at an orbit closer than that of Mercury around the sun (Mayor & Queloz 1995). Hence to be able to detect planets further away from the host we need to use different techniques. Unlike other detection methods, the microlensing technique does not rely on detection of photons from the host star or the planet and is capable of detecting planets beyond the snow line (a region around the star where volatiles can exist in ice form and where according to core accretion theory (Safronov 1972) (Gol- 1 The Extrasolar Planets Encyclopaedia: Parvin Mansour 14

15 dreich & Ward 1973) many planets are formed). This method is also capable of detecting planets over a wide range of Galactic distances and around a wide range of stars, making it complementary to other techniques. Together they can produce the full map of planetary distribution within the Galaxy, helping us gain a better understanding of planet formation and evolution. Much like other methods microlensing also suffers from limitations, it is rare and unpredictable and suffers from degeneracies. To find a correct set of parameters to describe a microlensing event is a challenging task. A typical binary microlensing event is described by a model with several parameters, hence in order to re-construct a model of the observed light curve, it is necessary to search in a multi-dimensional parameter space. However, even if one does find a set of parameters which seems to provide a good description of the event, many other parameter sets may also provide similar and sometimes indistinguishable light curves. These degenerate models require extra investigation, for instance using Bayesian analysis based on different Galactic models, when performing microlensing modelling. The motivation behind this research was to develop software that can calculate the probability density of measured lens properties within the context of an assumed Galactic model. The software was used on one case, MOA-2011-BLG- 262lb, where the observed microlensing light curve had two solutions (Bennett et al. 2014), a free floating 2 planet-moon system, where an Earth-mass moon orbits a Jupiter-mass planet and a star-planet system, where a super-earth planet orbits a brown dwarf. The structure of this dissertation is as follows. The theoretical bases of microlensing, microlensing observation, surveys and significant discoveries are discussed in Chapter 1. Chapter 2 covers the MOA-2011-BLG-262lb case. The Besançon Galactic Model, which was used for the analysis is described in Chapter 3. Whereas, Chapter 4 and 5 cover the discussion and conclusion respectively. 2 Free Floating Planets will be described further in section 1.7. Parvin Mansour 15

16 Chapter 1 Microlensing Microlensing is the temporary magnification of a background star, known as the source, due to gravitational field of a foreground star, known as the lens. The presence of the lens results in multiple images of the source with a very small separation. The image separation is so small that it cannot be resolved by optical telescopes. However, microlensing events can be detected due to the combined magnification of these images (Gaudi 2010). As the apparent brightness of the source changes, the relative proper motion of the lens with respect to the source, µ rel, will produce a unique light curve known as the Paczynski light curve (Paczynski 1996). If the lens has a companion, there will be further perturbation in the light curve. Such features can be used to measure or constrain the physical parameters of the lensing system such as the mass, distance and transverse velocity, υ, which is the relative transverse velocity between the source and the lens. 1.1 Lens equation The simplest case of microlensing involves a point-mass lens. The geometry of a point-mass lens can be seen in figure 1.1. Parvin Mansour 16

17 1.1: LENS EQUATION Figure 1.1: The simple geometry of a lensing system and the angles and distances used to derive the lens equation are shown here (Mao 2012). The light ray is deflected by the lens, D by an angle α. β and θ are the true and observed angles between the lens and the source, S, respectively. ξ and η are the distances between the lens and the light ray and the source position respectively. D d, D s and D ds are the distance between the observer and lens, the observer and source and source and lens respectively. In 1915 Einstein derived the formula for the deflection angle of a light ray due to the gravitational field of a point-mass M (Schneider, Ehlers & Falco 1992) as α = 4 G M ξ c 2. (1.1) where G and c are the gravitational constant and speed of light respectively. Assuming a point source and small angle (ξ D d ) we have β = θ D ds D s α, (1.2) and θ = ξ D d. (1.3) Parvin Mansour 17

18 1.1: LENS EQUATION Using equations (1.1) and (1.3), equation (1.2) can be written as β = θ 4 G M D ds θ c 2 D s D d. (1.4) When β=0, the images will form a ring known as an Einstein ring with an angular size θ E = Dividing equation (1.4) by θ E gives 4 G M Dds c 2 D s D d. (1.5) r s = r 1 r, (1.6) where r s β θ E and r θ θ E. This equation has two solutions r ± = 1 2 ( r s ± ) rs (1.7) Figure 1.2: The two images created by the lens, M, of the source, S, are marked as I 1 corresponding to the minor image and I 2 corresponding to the major image. The Einstein radius is marked as a dashed circle (Paczynski 1996). Parvin Mansour 18

19 1.1: LENS EQUATION Figure 1.2 shows the position of the images produced during a microlensing event. The solution for r + corresponds to the major image outside the Einstein radius while the solution for r - gives the position of the minor image inside the Einstein radius on the opposite side of the lens (Gaudi 2012). The separation of these images is typically milliarcsecounds and cannot be resolved (Mao 2012). Nevertheless, the event can be observed through changing magnification of the images. The source brightness is conserved (Schneider, Ehlers & Falco 1992), therefore the magnification of each image (µ + and µ - ) is simply the ratio of image area to that of the source µ ± = θ dθ β dβ. (1.8) Using ( ) dθ dβ = 1 β 1 ±, (1.9) 2 β2 + 4 θe 2 the solution of equation (1.8) is The total magnification is given by µ ± = u u u ± 1 2. (1.10) µ = µ + + µ - = u2 + 2 u u 2 + 4, (1.11) where u is the lens-source separation. For u 1 the magnification scales as µ 1 u, (1.12) and for u 0 the magnification scales as µ u 4. (1.13) Parvin Mansour 19

20 1.2: BINARY LENSES Also as u, µ 1 and as u 1, µ diverges. Assuming a constant proper motion between the source and lens, the lens-source separation is given by u = ( ) 2 t u 2 t0 0 +, (1.14) t E where t 0 is the time of closest approach, u 0 is the minimum source-lens separation in units of θ E and t E is the Einstein radius crossing time (the time it takes the source to move by an angular distance equal to θ E ). Any Paczynski light curve can be described by these three parameters. t E is related to θ E and µ rel (the lens-source relative proper motion) as t E = θ E µ rel = R E υ, (1.15) where υ = µ rel D d, R E = θ E D d = 4 G M D d (D s D d ) c 2 D s. (1.16) 1.2 Binary lenses Derivation of the binary lens equation builds on that of the point-mass lens. The lens equation for an N point-mass lens can be written as β = ξ θ 2 E N i=1 m i ξ ξ i ξ ξ i 2, (1.17) where m i is the ratio of mass i to the total mass of the lens system (Mao 2012). Using the relation between the two-dimensional vectors and complex numbers, Witt (1990) shows that equation (1.17) can be written in a complex form by substituting the vectors with complex numbers as z s = z N i=1 m i z z i, (1.18) Parvin Mansour 20

21 1.2: BINARY LENSES where z and z s are the complex position of each point-like image and the source respectively and z i is the position of the i th mass component of the lens. For a binary system where the mass ratio is defined as equation (1.18) can be written as q = m 2 m 1, (1.19) Taking the complex conjugate of this equation gives z s = z m 1 z z 1 + m 2 z z 2. (1.20) z = z s + m 1 z z 1 + m 2 z z 2. (1.21) Substituting equation (1.21) into (1.20) will eliminate z and give a fifth order polynomial which can be solved numerically (Mao 2012). The solution to the binary lens equation and hence the number of images produced during the event depend on the position of the source relative to that of the lens (Gaudi 2012). Similarly to the point-mass lenses, the magnification of the images in binary lenses is the ratio of their area to that of the source. The magnification of the image is the inverse of the Jacobian determinant evaluated at the position of the image µ = 1 J, (1.22) where J is the determinant of Jacobian of the binary lens equation. J can be written as J = 1 m 1 (z z 1 ) 2 + m 2 (z z 2 ) 2 2. (1.23) Just as the single lens, the total magnification is the sum of the absolute magnification of all images. Parvin Mansour 21

22 1.3: CAUSTICS 1.3 Caustics From equation (1.22) the source will be infinitely magnified when J=0. In this case, equation (1.23) can be written as or more generally 1 = m 1 (z z 1 ) 2 + m 2 (z z 2 ) 2 e iφ = N i=1 2, (1.24) m i (z z i ) 2. (1.25) Solving equation (1.25) for 0 φ 2π will give a closed smooth curve in the lens plane known as a critical curve. The position of the corresponding curves in the source plane are known as caustics. The points where caustics meet are known as cusps (Gaudi 2012). Caustic number, size and shape is determined by the mass ratio, q, and the projected separation, s, of the binary lens (Griest & Safizadeh 1998). Gaudi (2008) puts caustics in three different configurations, close, resonant and wide (figure 1.3). The caustic closer to the massive component of the binary lens is known as the central caustic whilst the caustics further away from the massive component are known as the planetary caustics (Gaudi 2012). When a similar mass companion orbits the primary lens close to the Einstein ring, the central and planetary caustics merge and form a large caustic, close to the more massive component, known as the resonant caustic. During high magnification events (i.e. µ > 100), the probability of the source crossing the central caustic is very high (Griest & Safizadeh 1998). This makes high magnification events ideal for detecting planetary anomalies in the event light curve. Hearnshaw et al. (2006) state that as s increases, the size of the planetary caustic scales as s 2, however as s decreases the size of the caustic will scale as s 3. The central caustic size scale with s as (s + s 1 ) 2 (Chung et al. 2005). Parvin Mansour 22

23 1.4: OPTICAL DEPTH AND EVENT RATE Figure 1.3: The three caustic topologies, close (left), resonant (middle) and wide (right). The solid lines d c (q) and d w (q) separate these regions. The primary component of the binary is close to the diamond-shape/central caustic (Cassan 2008). 1.4 Optical depth and Event rate Mao (2012) defines the optical depth, τ, as the probability that at any given time any given source falls within the Einstein radius of any given lens. τ is therefore a cross section of θ E of all lenses between the observer and the source and is given by τ = Ds 0 N(D d ) D 2 d π θ E 2 dd d, (1.26) where N(D d ) is the number density of all lenses along the line of sight. In the simple limit of constant density along the line of sight equation (1.26) evaluates to τ = 2π G ρ 0 D s 2 3 c 2, (1.27) Parvin Mansour 23

24 1.5: PLANETARY MICROLENSING LIGHT CURVE whilst the measured optical depth towards the Galactic bulge is 10 6 (Sumi et al. 2013). The microlensing event rate, Γ, is the rate of microlensing events per unit time for a given star (Mao 2012). Γ is related to τ as Γ = 2 τ π < t E >, (1.28) where < t E > is the average microlensing event time scale. For sources with an apparent magnitude of I <20 at the Galactic positions b 3 o and 0 o l 2 o Sumi & Penny (2016) find Γ = star 1 year 1, and increasing slightly at lower latitudes. The small event rate means that in order to be able to detect a few hundred events each year, microlensing surveys need to monitor hundreds of millions of stars continuously. 1.5 Planetary microlensing light curve Planetary microlensing events occur when a planet orbits the primary lens near one of the images produced during the event. The gravitational field of the planet will distort the shape of the images and produce a detectable anomaly in the event light curve (as seen in figure 1.4). Unlike point-mass lenses, binary lens light curves are usually asymmetrical with some deviations from the Paczynski form. A typical single-lens microlensing event could last anywhere between a few weeks to a few months (with a typical duration of 20 days towards the Galactic bulge). Planetary microlensing events are much shorter lasting a few days, for Jupiter-mass planets and a few hours, for Earth-mass planets. Parvin Mansour 24

25 1.5: PLANETARY MICROLENSING LIGHT CURVE Figure 1.4: The left panel shows two images (blue disks) of the source (red circle) which are produced due to presence of the lens (black dot). The right panel shows the magnification as a function of time. Further perturbation in the light curve is due to the presence of a planet orbiting the host near one of the images (Paczynski 1996). Figure 1.5 shows the light curve of the microlensing event OGLE-2003-BLG- 235/ MOA-2003-BLG-53, the first microlensing planet discovery (Bond et al. 2004). During the planetary microlensing event, as the source enters the caustic region, the total number of images increases to five and the light curve exhibits a discontinuous increase in magnification, followed by a smooth decrease inside the caustic region. When the source exits the caustic, the light curve display the opposite behaviour with a smooth increase in magnification followed by a discontinuous decrease as the source crosses the caustic curve. The light curve then has two large peaks with a U-shape in between the peaks. This is particularly useful for planetary caustic crossings. The star-planet mass ratio can be inferred from the size of the U-shape base (Griest & Safizadeh 1998). Parvin Mansour 25

26 1.5: PLANETARY MICROLENSING LIGHT CURVE Figure 1.5: The light curve of the first planetary microlensing event OGLE-2003-BLG- 235/ MOA-2003-BLG-53. The U-shape feature is due to the source entering and exiting the caustic (Bond et al. 2004). In order to model the light curve of a planetary microlensing event in addition to t E, t 0, u 0, s and q we also need α, the angle of source trajectory relative to the binary lens axis (Gaudi 2012). The magnification map of the event can be generated by mapping from the image to the source plane for a trial values of s and q, using the inverse ray shooting technique (Wambsganss 1997). The model light curve is then generated using a numerical grid search with a fixed set of values for s, q and α whilst minimising χ 2 over the other parameters. Due to many local minima, finding the best model is a difficult and time consuming task. Blend flux One additional parameter needed for modelling the event light curve is the source flux, F s. The source-lens alignment is very small and can not be resolved, there- Parvin Mansour 26

27 1.6: MICROLENSING DEGENERACY fore instead of collecting the magnified flux of the source alone, the telescope will collect all sources of light (the source+lens flux). Furthermore, microlensing surveys take place towards the Galactic bulge which is very crowded, so the neighbouring stars also contribute to the observed flux. The total flux then is F t = F s + F B, (1.29) where F B is the blend flux which is the sum of lens flux and the flux from neighboring stars. F s and F B may be separable a few years after the microlensing event when the angular separation between the lens and source increases to a few milliarcsec (Bennett, Anderson & Gaudi 2007). 1.6 Microlensing degeneracy Out of the three parameters that describes a point-mass microlensing event light curve, t E is the only one that contains information about the lens s mass, distance and velocity. Different combinations of M, D s, D d and υ can give the same t E, this is known as microlensing degeneracy. Fortunately this degeneracy can be broken by measuring parallax and the finite source effect. Finite source effect In order to derive the lens equation we made the assumption that the source is a point-mass object, which is incorrect. Real stars have a finite angular size, therefore as the source moves near the centre of the lens, one part of it can be magnified more significantly than other parts. Subsequently, in order to measure the apparent brightness of the source correctly, it is necessary to integrate the product of the source magnification and intensity over the face of the star (Gould 1994). Mao (2012) states that once we measure the finite source effect we can then find t (the source crossing time) and therefore ρ, the ratio of angular source Parvin Mansour 27

28 1.6: MICROLENSING DEGENERACY radius to the angular Einstein radius ρ = t t E. (1.30) The source s colour and magnitude can be used to measure θ and in turn θ E since This then gives the relative proper motion θ E = θ ρ. (1.31) µ rel = θ E t E. (1.32) Therefore, finite source effect can be used to partially break the microlensing degeneracy. However in order to break the microlensing degeneracy completely we need additional information such as parallax. Parallax The other assumption we made in order to derive the lens equation was that the observer, lens and source are in a rectilinear motion. While this assumption holds for most microlensing events, the Earth orbit and acceleration becomes important when the microlensing duration is equal to a large fraction of the Earth orbital period (Gaudi 2008). Also the Earth rotation can result in a measurable difference in the timing of data points collected at different locations, thus making the socalled terrestrial parallax measurement possible. Parallax can also be measured if the event is simultaneously observed by a ground-based telescope and a satellite, orbiting the Earth at large orbital separation ( 1 AU). The measurement of this so-called space-based parallax is made possible by the fact that the relative lenssource position as seen from the Earth differs to that seen by a satellite. Parallax, π E, is given by π E = AU, (1.33) R E Parvin Mansour 28

29 1.6: MICROLENSING DEGENERACY where R E = 4 G M D d c 2 R E, (1.34) where R E is the linear Einstein radius in the lens plane and R E Einstein radius in the observer plane. is the projected Figure 1.6: The light curve of a microlensing event OGLE-2014-BLG-0939 which was observed by OGLE (black dots) and Spitzer (red dots) (Yee et al. 2015). Figure 1.6 shows the difference in t 0 and u 0 of two light curves for the microlensing event OGLE-2014-BLG-0939 observed by space-based satellite, Spitzer and ground-based telescope, OGLE (the Optical Gravitational Lensing Experiment). Using the difference between these light curves π E can be measured. Combining π E measurements with θ E, we can find the lens mass, proper motion Parvin Mansour 29

30 1.6: MICROLENSING DEGENERACY and transverse velocity: where M = k θ E k π E, (1.35) 4 G c 2 AU, (1.36) µ l = µ E θ E + µ s, (1.37) and υ = µ E θ E + µ s π E θ E + π s, (1.38) where µ l, µ s, µ E and π s are the lens, source, Earth proper motions and the source parallax respectively (Gould 2000). For microlensing events where θ E measurement is not possible, a value for lens mass can still be obtained from π E measurement and source brightness (Bennett et al. 2006). Parallax measurements are the only way to find lens mass values for point-mass lenses. This fact becomes very important when we consider the distribution of isolated low-mass objects such as Free Floating Planets, FFPs, within the Galaxy. Xallarap and binary motion If the source or the lens are part of a binary system, the orbital motion of the companion can be detected in the event light curve. Unfortunately the effect of binary orbital motion due to the source companion, known as xallarap (Griest & Hu 1992) (Rahvar & Dominik 2009), and binary motion due to the lens companion (Dominik 1998) can mimic parallax which leads to difficulties pinpointing the true origin of the effect. On the positive note, however, when these effects are measured, they lead to direct constraints on physical parameters such as lens system s orbital parameters and separation between the lens component (Skowron et al. 2011). Parvin Mansour 30

31 1.7: FFPS 1.7 FFPs The microlensing method is most sensitive to planets orbiting the host at an orbital separation of a R E 2 AU (Griest & Safizadeh 1998). However, it is also sensitive to planets with orbital separation of a 0.5 AU- (Sumi et al. 2011), making this method ideal for detecting FFPs. FFPs are planets that do not orbit any star. Unfortunately, the processes of their formation are still unknown. Boss (2003) states that FFPs undergo a similar formation to stars (i.e. have formed due to gravitational collapse of gas clouds), whilst Lissauer, Levison & Duncan (1998) state that FFPs could form inside protoplanetary disks and be removed from the system via planet-planet interaction. Measurements such as the one made by Sumi et al. (2011) have put a strain on the latter theory. Sumi et al. (2011) claims that for each main-sequence star in the Galaxy there should be 2 FFPs. This means that each protoplanetary disk should produce 8 planets and nearly 40% of these planets should be ejected from the planetary system (Veras & Raymond 2012). Are all the protoplanetary disks in the Galaxy massive enough to produce this many planets? In order to be able to answer this question we need to gain a better understanding of the distribution of FFPs. Due to the fact that FFPs are not bound to any stars, other detection methods are not capable of detecting them (although young/ close-by FFPs can sometimes be detected by the direct imaging technique (Quanz et al. 2010)). FFPs can act as single-lenses and can be detected by the microlensing method. Sumi et al. (2011) show that the duration of an event scales with lens mass as t E M M J, (1.39) where M J is Jupiter mass. So while stellar microlensing events can last for weeks to months, the FFP event duration is much shorter (with a typical event duration of 1 day). Due to their short duration, space-based parallax measurement is the Parvin Mansour 31

32 1.8: MICROLENSING SURVEYS only way to obtain a mass value for FFPs. A summary of the main microlensing parameters are shown in table 1.1. Table 1.1: Microlensing parameters Parameters Description t E The Einstein radius crossing time t 0 The time of closest approach u 0 The minimum source-lens separation in units of θ E s Projected separation of the binary lens α The angle of the source trajectory relative to the binary lens axis q The binary lens mass ratio µ rel The relative proper motion of the lens with respect to the source θ E The Einstein radius The angular source radius θ 1.8 Microlensing surveys As mentioned in section 1.4, the microlensing event rate is However the probability of detecting a planetary perturbation in the light curve is 10 2 (Mao & Paczynski 1991) 1. Therefore billions of stars need to be monitored in order to detect few planets. To increase the number of stars observed, all microlensing surveys take place towards the Galactic bulge, which has the highest surface density of stars. These surveys monitor hundreds of square degrees continuously in order to observe a few events. Ground-based surveys such as OGLE with a 1.4 m telescope and a 1.4 deg 2 field of view (Udalski 2003), MOA-II, Microlensing Observation in Astrophysics, with a 1.8 m telescope and a 2.2 deg 2 field of view (Hearnshaw et al. 2006) and KMT- Net, the Korean Microlensing Telescope Network, with a network of three 1.6 m telescopes each covering a field of view of 4 deg 2, located in Chile, South Africa and Australia (Poteet et al. 2012) monitor the sky every night. Once an event is 1 Mao & Paczynski (1991) states that the probability of planetary microlensing is roughly equal to half of the width of the caustics region. Assuming every star in the Galaxy is orbited by a planet with a mass of 10 3 M star and an orbital distance of 1-10 AU, they show that the probability of planetary microlensing is 0.03 Parvin Mansour 32

33 1.8: MICROLENSING SURVEYS detected and identified, a warning alert will go off and a network of smaller telescopes such as PLANET (Probing Lensing Anomalies NETwork) (Albrow et al. 1998), RoboNet (Tsapras et al. 2009) and µfun 2 start round the clock coverage of the event. These follow up observations are essential for planetary microlensing events. Surveys such as MOA have a cadence (observation frequency) of 50 minutes. However, planetary microlensing events are very short and in order to obtain the full shape of the light curve, much shorter cadence are needed. Followup observation can provide a cadence of 3-5 minutes. Space-based telescopes, Spitzer and Kepler, have recently been used for microlensing surveys (Udalski et al. 2015) (Han et al. 2016). In addition to measuring parallax and breaking microlensing degeneracy, space-based surveys can have a much better resolution and can detect significantly more events than groundbased surveys (Bennett 2004). Faint main-sequence stars are more easily observed from space and their small angular size results in longer and sharper planetary anomalies in the event light curve (Bennett and Rhie 2002), increasing the planet detection sensitivity. Space-based telescopes are capable of detecting planets with mass as low as 0.1 M (Barry et al. 2011). Future surveys Space-based microlensing observations will be carried out by WFIRST (Barry et al. 2011), the Wide Field Infrared Survey Telescope, and Euclid (Penny et al. 2013). WFIRST which is due to launch in , will observe the Galactic bulge for 500 days, over a 6 year period, and is capable of detecting planets with mass of 0.1 M <M< few M J. WFIRST is predicted to detect around 5330 planets of which 2080 are FFPs. Euclid has a shorter observation period (around 180 days) but is capable of detecting Mars to Earth-mass planets WFIRST: Parvin Mansour 33

34 1.8: MICROLENSING SURVEYS Significant discoveries The first exoplanet discovered by the microlensing technique was observed simultaneously by OGLE and MOA in 2004 (Bond et al. 2004), with an event duration of 7 days. The event light curve was explained by a binary lens where a Jupiter-mass planet with a mass of 2.6 M J orbits a 0.63 M host at an orbital separation of around 4.3 AU. To date 59 exoplanets have been discovered by the microlensing method 4, including the first cool super-earth orbiting an M dwarf at an orbital separation of 2.6 AU (Beaulieu et al. 2006), a population of FFPs with t E < 2 days (Sumi et al. 2011), the first circumbinary planet (a planet orbiting both components of the binary system) (Bennett et al. 2016), a planetary microlensing event, where the source is part of a binary system (Bennett et al. 2017), a multiple-planet system (Gaudi et al. 2008) and even a planet possibly in the habitable zone of the host (Batista et al. 2014). 4 The Extrasolar Planets Encyclopaedia: Parvin Mansour 34

35 Chapter 2 MOA-2011-BLG-262lb MOA-2011-BLG-262lb is a very good example of microlensing degeneracy. The light curve of this event has two different solutions (Bennett et al. 2014). The first model fit is a free floating exoplanet-exomoon system with an Earth-mass moon orbiting a Jupiter-mass planet with a mass of around 4 M J. The second model fit is a star-planet system where a super-earth orbits a star. 2.1 Observation MOA-2011-BLG-262lb, located at l = -0.4 o and b = -3.9 o, was first observed by MOA-II 1.8 m telescope at Mt. John University Observatory (MJUO) in New Zealand on 26th June, 2011 (Hearnshaw et al. 2006). The data from MOA-II triggered the MOA alert system and follow up observations by the PLANET collaboration started immediately. In addition to MOA-II, the event was also observed by a 0.61 m telescope at MJUO, a 1.0 m telescope at Canopus observatory, the OGLE 1.3 m telescope, a 1.3 m telescope at CTIO (Cerro Tololo InterAmerican Observatory) and the FTS (Faulkes South Telescope) 2 m telescope, although CTIO and FTS did not cover the planetary anomaly. Due to the fact that the event was identified as a high magnification event with a short duration, the observing cadence on MOA-II was changed from every Parvin Mansour 35

36 2.1: OBSERVATION 50 minutes to every 2 minutes and later to every 7 minutes. MOA-2011-BLG- 262lb is a binary microlensing event with a mass ratio of q As the source limb entered the caustic MOA-II, MJUO and Canopus telescopes had started observing the event and continued to do so until well after the source exited the caustic. The event had a peak magnification of A max 75 and the observation was continued until the magnification fell below 30. The event light curve consists of 4884 observations in MOA red-band, 562 observations in I-band and 143 observations in V-band. Figure 2.1 shows the event light curve with the planet-moon and star-planet models indicated by the magenta and black curves respectively. Figure 2.1: The data from MOA-II, MJUO, Canopus, CTIO, OGLE and Faulkes telescopes are shown in red, green & cyan, blue, magenta, black and gold respectively. The magenta curve indicates the exoplanet-exomoon model and the star-exoplanet model is indicated by the black curve (Bennett et al. 2014). Parvin Mansour 36

37 2.2: LIGHT CURVE ANALYSIS 2.2 Light curve analysis As previously mentioned, this event was identified as a high magnification event. The majority of planetary microlensing events with high magnification suffer from a 2-fold s 1/s degeneracy (Griest & Safizadeh 1998). This degeneracy results in two solutions for s > 1 and s < 1. The parameters of both solutions are shown in table 2.1. Table 2.1: Model parameters for planet-moon solution Parameters s < 1 s > 1 t E ( days) t 0 ( HJD ) t ( days) u s I s V s fit χ This event also suffers from another degeneracy which results from the fact that the source radius crossing time, t, is similar to the caustic crossing time of the event. As a result of this degeneracy, two more model fits can also describe the observed light curve. The parameters of these solutions for s < 1 and s > 1 are given in table 2.2. Table 2.2: Model parameters for star-planet solution Parameters s < 1 s > 1 t E ( days) t 0 ( HJD ) t ( days) u s I s V s fit χ Parvin Mansour 37

38 2.3: THE RELATIVE PROPER MOTION 2.3 The relative proper motion The fact that this event had a sharp caustic feature and mass ratio of less than 10 3 ensured that the lens relative proper motion with respect to the source, µ rel, could be measured. As mentioned in Section 1.6, θ can be measured from the source brightness and colour using the method from (Kervella & Fouqué 2008). Bennett et al. (2014) obtained a value for planet-moon and star-planet models of θ = ± µas and θ = ± µas respectively. Using θ E = θ t E t, (2.1) and values for t E and t from table 2.1 and 2.2, yields an angular Einstein radii of ± mas and ± mas for planet-moon and star-planet models respectively. Equation (1.32) and these θ E values gives µ rel = 19.6 ± 1.6 mas/yr for the planet-moon model and µ rel = 11.6 ± 0.9 mas/yr for the starplanet model. Both of these high µ rel values are an indication of a nearby lensing system. Source proper motion Due to the crowded nature of the Galactic bulge, the proper motion measurements are usually restricted to stars with I s < 18 (Sumi et al. 2004). Although the MOA-2011-BLG-262lb source is a faint star with I s 19.9, it was possible to obtain a value for its proper motion, using a dipole-fitting method developed by Skowron et al. (2014), which gave a source proper motion of (-2.3, -0.9) ± (2.8, 2.6) mas/yr in a (North, East) Galactic heliocentric coordinate frame. Assuming D s = 8.3 kpc, Bennett et al. (2014) obtain a geocentric source proper motion of (-2.3, -1.7) ± (2.8, 2.6) mas/yr. This result strongly disfavours a bulge-lens for the planet-moon system whilst only slightly disfavouring a bulge lens for the star-planet system. Parvin Mansour 38

39 2.4: SOURCE AND LENS MAGNITUDE 2.4 Source and lens magnitude Nearly one year after the event was identified by MOA-II, the Keck-2 telescope 1 took an AO (Adoptive Optics) image of the event in the J, H and K-bands. The source star was no longer magnified. Figure 2.2 shows a comparison between the image in K-band taken by Keck-2 and VVV 2, where S1 indicates the position of the source+lens. Figure 2.2: The K-band image from the VVV survey is shown in the left panel. The middle panel shows the K-band image from Keck-2 and a zoom-in of the field, where the position of the source+lens is shown by the arrow. The right panel shows the source star, S1, and the four closest stars to it in an AO image (Bennett et al. 2014). The right panel in figure 2.2 shows a relatively uncrowded field, which means negligible contribution to the event magnitude from the neighbouring stars. The AO image (the right panel in figure 2.2) which was taken less than a year after the microlensing event peak magnification, suggests a source- lens separation of less than 20 mas. Therefore the S1 flux is the combined flux of the source and the lens. PSF photometry yields a magnitude of ± 0.10, ± 0.07 and ± 0.10 for S1 in J, H and K-band respectively. Using the H-band data from the CTIO telescope, taken during the event, gives the source magnitude in 1 Keck Observatory: observatory 2 The VVV survey: Parvin Mansour 39

40 2.4: SOURCE AND LENS MAGNITUDE H-band for both models as H planet moon = ± and H star planet = ± Subtracting these values from S1 flux, gives a lens flux of ± 1.10 and ± 1.00 for the planet-moon and star-planet models respectively. Figure 2.3: The magnitude-distance relation for the planet-moon model (left) and the star-planet model (right). The black, dashed curves shows the magnitude-distance relation based on two different extinction laws and the shaded area is the allowed region. The range for brown dwarfs and super Jupiters are indicated by the red, dashed lines. The blue curves (top right corner) indicates some isochrones for main-sequence stars obtained using methods from An et al. (2007) (Bennett et al. 2014). Figure 2.3 shows the lens absolute magnitude-distance relations and limits for both models. The black, dashed curves shows the magnitude-distance relation based on two different extinction laws from Gonzalez et al. (2011) and Cardelli, Clayton & Mathis (1989) where the shaded area is the allowed region. The red dashed lines show the range for stars with M=0.07 M and planets with M=13 M J. The blue curve indicates some isochrones for main-sequence stars obtained using methods from An et al. (2007). The position of the isochrone curve requires a lens distance of 7 and 7.7 kpc for the planet-moon and star-planet models respectively. These values implies a host mass and transverse velocity of 0.36 M and 677 km/s for the planet-moon model and 0.41 M and 442 km/s for the Parvin Mansour 40

41 2.5: BAYESIAN PRIORS star-planet model respectively. At a distance of 0.5 kpc (the favoured planet-moon distance), stars would have ( J-K) 1 and would be very red, low-mass stars, which exclude any of the neighboring stars in the AO image as a possible host for the planet-moon system. Hence if the planet-moon model is the correct solution, it must be a free floating system. 2.5 Bayesian priors Apart from including a prior on source proper motion in the Bayesian analysis, Bennett et al. (2014) also made three prior assumptions, the relative proper motion, the host mass function and the fact that the mass of the primary lens has no effect on the probability of the host having a companion with the observed mass ratio, q and at a host-companion separation of a R E. The relative proper motion The average proper motion of stars in the Galactic bulge is given by < µ star > = υ D, (2.2) where υ and D are the Galactic rotation speed and the distance to the centre of the Galaxy respectively. For a star in the bulge, equation (2.2) will give a mean proper motion of 6.4 mas/yr. Following the method given by Koz lowski et al. (2006), if both the source and the lens reside in the bulge, the relative proper motion is around 5.2 mas/yr. If the lens is a disk lens (D l < 2.7 kpc), the mean proper motion difference between the bulge and the disk will result in µ rel of around 8.2 mas/yr. Both of these values are smaller than the relative proper motion of the star-planet and planet-moon systems, which means a disk lens at D l < 2.7 kpc is preferred. However the planet-moon solution favours a disk Parvin Mansour 41

42 2.5: BAYESIAN PRIORS lens more than the star-planet solution. The proper motion value for the planetmoon model is about 3.5 times larger than the two bulge star s proper motion dispersion (which is around 5.6 mas/yr), whilst the measured proper motion for the star-planet model is only 2.1 times larger than the bulge-bulge proper motion dispersion. Mass function Bennett et al. (2014) use a mass function in their Bayesian analysis which follows the broken law with dn d logm = M 1 α, (2.3) α = 2.0 for 0.7 < M M 1 = 1.3 for 0.08 < M M 0.7 = 0.49 for 0.01 < M M 0.08 (2.4) = 1.3 for 10 5 < M M This will give the ratio of stars to brown dwarfs to planets as 1 : 0.73 : 5.5. Assuming all planets have a mass of 1 M J, the Bayesian analysis gives similar densities for stars and planets, but this does not imply an equal lensing probability. From equation (1.16), we have R E M. (2.5) The fact that the lensing probability for stars is greater than that of planets, and the stellar density in the bulge is about 5 times larger than that of the disk means that the Bayesian analysis favours the star-planet solution over the planet-moon solution. Parvin Mansour 42

43 2.6: PROBABILITY DISTRIBUTION 2.6 Probability distribution The result of the Bennett et al. (2014) Bayesian analysis, including all solutions, is shown in Figure 2.4. Figure 2.5 and 2.6 show the lens distance probability for the planet-moon and star-planet models respectively. Figure 2.4: The probability distribution for planet-moon and star-planet models weighted by Galactic priors (Bennett et al. 2014). Figure 2.5: The lens distance probability distribution for the planet-moon model (Bennett et al. 2014). Parvin Mansour 43

44 2.7: MOA-2011-BLG-262LB CONCLUSION Figure 2.6: The probability distribution for star-planet model (Bennett et al. 2014). Figure 2.4 shows two distinct distributions, one for the planetary host at a distance of 0.64 kpc and one for the stellar host in the Galactic bulge at a distance of 7 kpc. The planetary mass distribution gives the host and companion masses and their separation as M h 3.6 M J, M c 0.54 M and a 0.13 AU respectively. For the stellar host distribution, M h, M c and a are approximately 0.12 M, 18 M and 0.84 AU respectively. 2.7 MOA-2011-BLG-262lb conclusion The data from this event is well fit by two different solutions with similar likelihoods. The best-fit model has a large relative proper motion, µ rel = 19.6 ± 1.6 mas/yr which implies a close lens distance of 0.56 kpc and a Jupiter-mass planet with M 3.6 M J as the primary lens. The other solution which is disfavoured by χ 2 = 2.91 has a lower relative proper motion, µ rel = 11.6 ± 0.9 mas/yr and a distance of D l = 7.2 ± 0.8 kpc, where a star with M= 0.12 M is the primary lens. Parvin Mansour 44

45 2.7: MOA-2011-BLG-262LB CONCLUSION Unfortunately even though the result from Skowron et al. (2014) moderately disfavours the star-planet model, the lack of parallax measurement has resulted in a great uncertainty in the Bayesian analysis, making it impossible to favour one model over the other. The 2000 km separation between the MJUO telescope in New Zealand and Canopus telescope in Tasmania would have been sufficient enough for measuring this event s terrestrial parallax. Unfortunately due to telescope hardware problems, the images obtained by the Canopus telescope were of poor quality and the photometry was not precise enough for parallax measurement. Therefore the only light curve parameters available for constraining the lensing system mass, distance and transverse velocity were t E and θ. Lensing systems with stellar-mass primaries would have a larger Einstein radius, therefore the mass function in the Bayesian analysis would prefer the star-planet over the planet-moon model. Hence Bennett et al. (2014) chose the star-planet model, stating that the probability of a free floating exoplanet-exomoon system is much less than the star-exoplanet solution of this event. Parvin Mansour 45

46 Chapter 3 Analysing MOA-2011-BLG-262lb using the Besançon Model We have re-analyzed MOA-2011-BLG-262lb using Galactic priors based on the Besançon Galaxy Population Synthesis Model (Robin et al. 2003, 2012). We used the latest version of the Besançon Galactic Model (Robin et al. 2014) to generate stellar catalogues and carry out a series of microlensing simulations. We calculated the posterior probability distribution of microlensing events with respect to the relative proper motion, µ rel, and lens distance, D l, for two different lens host populations with mass of 1M and 1M J. We also measured the probability density of both models which describe the MOA-2011-BLG-262lb microlensing event light curve. An overview of the Besançon model, the microlensing simulations, the preliminary probability density maps and the result of its application to the MOA-2011-BLG-262lb event are presented here. Parvin Mansour 46

47 3.1: BESANÇON GALACTIC MODEL 3.1 Besançon Galactic Model A brief description The Besançon Galactic population synthesis model is a simulation tool which uses a theoretical model of the Galaxy, including stellar and Galactic evolution and dynamics, in order to constrain the observable parameters of the stellar population of the Galaxy. The Besançon model is used to produce catalogues of stars containing stellar information such as distance, mass, magnitude, proper motion and radius amongst other parameters. The Besançon model assumes four distinct stellar populations; a thin disk, a thick disk, a bulge and a stellar halo. Each population is modelled based on a set of evolutionary tracks, an initial mass function (IMF) and a star formation rate (Haywood, Robin & Creze 1997). The Besançon model is constantly refined as new physical constraints become available. We have used version 1307 of Besançon model (Robin et al. 2012, 2014) for our work. Thin disk The thin disk, which comprises seven components aged between 0-10 Gyr, is divided into two parts, the young disc, defined by a population of stars with age < 0.15 Gyr and the old disk which is defined by the other six components. The young and old disk density distributions are modelled based on the Einasto (1979) density law and the distribution of the components of both disks are defined by an ellipsoid. The functions describing the density law of the ellipsoid can be found in Robin et al. (2003). The disk has a scale length of 2.2 kpc and a large hole at its centre with a scale length of 1.3 kpc, therefore the maximum density of its population is located at 2.3 kpc from the centre of the Galaxy. The total mass of the thin disk is Parvin Mansour 47

48 3.1: BESANÇON GALACTIC MODEL M with the IMF modeled by the following power law dn dm = M α, (3.1) where α = -1.6 for M < 1 M and α = -3 for M > 1 M. Thick disk Unlike the thin disk populations, which are formed during separate periods of star formation, the thick disk stars are assumed to be formed during a short period of time and age between Gyr. The disk kinematics are described by observational constrains from Ojha et al. (1996). The thick disk has a much lower density compared to the thin disk and the bulge becomes significant only at Galactic latitude b < 8 o. The low density of the thick disk at lower latitudes means that it only lightly contributes to microlensing optical depth and event rate measurements. The bulge Covering a region of 20 o < l < 20 o, 10 o < b < 10 o and assuming a Sun- Galactocentric radius of 8 kpc, Robin et al. (2012) revisited the stellar density, luminosity function and bulge structure analysis by Picaud & Robin (2004) and showed that the bulge has two main components: the bar extending to latitudes of 5 o and the thick bulge which dominates the star counts at latitudes above 5 o. The exact nature of the thick bulge is not well understood, it is either a flattened spheroid or a counter part of the local thick disk. The bar is modelled by a boxy, S-shaped ellipsoid with scale length along the principle axis with ratio of 1.46:0.49:0.39 kpc and a position angle of 13 o with respect to the Sun-Galactic centre direction. The thick bulge is modelled by another ellipsoid with scale length of 4.44:1.31:0.80 kpc. The bulge IMF is also modelled by the equation (3.1) but with α= for mass above 0.7 M. The total mass of the bar and Parvin Mansour 48

49 3.2: INITIAL CATALOGUE PARAMETERS the thick bulge is M and M respectively. The age of the bulge stellar population is 8 Gyr with the bar population having a higher metallicity compared to that of the thick bulge. Stellar halo The stellar halo and faint stellar remnants (i.e. white dwarfs) are believed to be an important part of the dark matter halo (Robin et al. 2004). The stellar halo is made up of a population of metal-poor stars with an age of 14 Gyr formed during a single, short period of star formation. Robin, Reylé & Crézé (2000) states that the stellar halo IMF also is modelled by the equation (3.1) with α = -1.9 ± 0.2 for mass of 0.1 M M 0.8 M. 95% of the stellar halo has a Galactocentric distance of less than 25 kpc (Robin et al. 2014). The stellar halo contribution to the microlensing optical depth and event rate is not significant due to its small density near the Galactic centre Interstellar extinction Interstellar extinction is the effect (absorbing and scattering) of dust on electromagnetic radiation, which results in reddening and dimming of stars. The extinction distribution along any line of sight can be computed, using a comparison between simulated, unreddened stars and observed, reddened stars. To achieve a realistic model Robin et al. (2012) adopts the method used by Marshall et al. (2006), where extinction is measured as a function of distance in the Galactic longitude l < 100 o and latitude b < 10 o. 3.2 Initial catalogue parameters Using the Besançon model, we produced a pair of source/lens catalogues for four different line of sights with l = 1 o and b = 1 o, 2 o, 3 o and 4 o. In order to Parvin Mansour 49

50 3.3: ACCOUNTING FOR THE FINITE SOURCE EFFECT ensure good statistics as well as a reasonable computational time, we choose the solid angle, Ω, in each catalogue so that every source catalogue contains around 2000 stars whilst every lens catalogue has around stars 1. All catalogues are truncated at a stellar distance of 15 kpc. We measured the average optical depth, average Einstein radius crossing time and average event rate. The parameters used for the microlensing calculations include, apparent magnitude in K-band along with I-K colour, proper motion in l and b, stellar mass, distance and radius (the latter was used in order to measure the finite source effect). The source catalogue was generated with a cut of in I-band, ensuring that even stars four magnitudes fainter than ground-based detectability limits are included, whilst the lens catalogue was drawn with no cut since even the faintest stars and remnants can act as lenses. 3.3 Accounting for the finite source effect For source-lens pairs with u θ E 3 θ, the impact parameter, the finite source effect becomes important. Normally the rate and optical depth are computed for events with minimum impact parameter u 0 1, corresponding to magnification A 0 3/ 5. For finite source events we explicitly compute u 0 corresponding to A 0 3/ 5 for all source-lens pairs with 0.01 < ρ < 3.16, where ρ is the ratio of angular source radius to the angular Einstein radius, using a 2-D pre-computed look-up table of source magnification versus ρ and u. Otherwise we assume a point-mass source, point-mass lens model. The look-up table was produced for stars of uniform surface brightness by generating a grid of u and ρ, where each (u and ρ) bin is associated with a magnification, µ, obtained using the equation µ = 2 π ρ 2 ρ 0 π 0 A ρ dρ dφ, (3.2) 1 These numbers give around 10 6 lensing systems in each simulation and although a better statistic is always more desirable, however to achieve a reasonable computational time we had to limit ourselves to these numbers. Parvin Mansour 50

51 3.4: OPTICAL DEPTH where A = u 2 + ρ 2 2 ρ cosφ + 2 u2 + ρ 2 2 u ρ cosφ u 2 + ρ 2 2 u ρ cosφ + 4. (3.3) Here u is the distance between the lens and the point on the source face which is magnified, ρ is the distance between the source centre and the point and φ is the angle between u and ρ. The look-up table covered 1500 ρ and u values in ranges and respectively. To include the finite source correction in our computation we added u i to the rate weighting of each source-lens pair as w = µ rel D 2 l θ E u i, (3.4) where u i is the impact parameter corresponding to A > 3 5 for microlensing events with finite source effect and w is proportional to the overall rate contribution from lenses with parameters µ rel, D l, θ E and u i (Kerins, Robin & Marshall 2009). 3.4 Optical depth The source optical depth is calculated for all source-lens pairs with D l < D s, τ = N(D L <D s) i π θ 2 E,i u2 i Ω l, (3.5) where Ω l is the solid angle over which the lens catalogues are selected. The source-averaged microlensing optical depth of all sources along the line of sight was calculated as τ = Ns i N(DL <D s) i Ns i u 2 i where N s is the number of catalogue sources. π θ 2 E,i u2 i Ω l, (3.6) Parvin Mansour 51

52 3.5: AVERAGE EINSTEIN RADIUS CROSSING TIME AND EVENT RATE 3.5 Average Einstein radius crossing time and event rate In order to calculate the average Einstein radius crossing time, < t E measured t E for each lens-source pair as >, we t E = θ E µ rel, (3.7) where µ rel is calculated using stellar proper motions from the Besançon model µ rel = (µ l l µs l )2 + (µ l b µs b )2, (3.8) where µ l l and µs l are the lens and source proper motions in l respectively and µ l b and µ s b are lens and source proper motion in b respectively. The average crossing time is then calculated using the rate weighted t E < t E > = = N(DL <D s) i N(DL <D s) i w i N(DL <D s) i w i t E,i µ i Dl,i 2 θ E,i u i t E,i N(DL <D s) i µ i Dl,i 2 θ. E,i u i (3.9) The average event rate over all source stars is then simply Γ = 2 τ π < t E >. (3.10) 3.6 Comparison with MABµls microlensing maps To check our computation accuracy and before producing the probability density maps for different populations, we compared our values for average optical depth (τ s ), event rate (Γ s ) and Einstein radius crossing time (< t E > s ) along four differ- Parvin Mansour 52

53 3.6: COMPARISON WITH MABµLS MICROLENSING MAPS ent line of sights with the MABµls 2 simulated maps. MABµls, the Manchester- Besançon microlensing Simulator, is a multi-wavelength microlensing simulator (Penny et al. 2013) which calculates the optical depth, event rate, Einstein radius crossing time and generates microlensing maps of the inner Galaxy. Table 3.1 shows our results for optical depth, event rate and crossing time along four line of sights with l= 1 o, compared to that obtained from MABµls simulated maps 3. Table 3.1: The values for optical depth, event rate and average crossing time from our and MABµls simulations b τ s τ MAB Γ s Γ MAB < t E > s < t E > MAB b = 4 o days 23 days b = 3 o days 24 days b = 2 o days 24 days b = 1 o days 25 days Figures 3.1, 3.2 and 3.3 show the simulated microlensing maps of optical depth, event rate and average crossing time respectively. These maps cover the central regions of the Galaxy with 0 o < l < 2 o and 5 o < b < 0 o. Overall there is good agreement with MABµls but there are some differences due to different IMF assumptions and difference in finite source treatment and source counting. 2 the Manchester-Besançon microlensing Simulator: 3 All values in the table are approximate values. Parvin Mansour 53

54 3.6: COMPARISON WITH MABµLS MICROLENSING MAPS Figure 3.1: The simulated map of the optical depth towards the Galactic longitude 0 o < l < 2 o and latitude 5 o < b < 0 o from the MABµls simulation. Parvin Mansour 54

55 3.6: COMPARISON WITH MABµLS MICROLENSING MAPS Figure 3.2: The simulated map of the event rate towards the Galactic longitude 0 o < l < 2 o and latitude 5 o < b < 0 o from the MABµls simulation. Parvin Mansour 55

56 3.6: COMPARISON WITH MABµLS MICROLENSING MAPS Figure 3.3: The simulated map of the average crossing time in days towards the Galactic longitude 0 o < l < 2 o and latitude 5 o < b < 0 o from the MABµls simulation. Parvin Mansour 56

57 3.7: PRELIMINARY PROBABILITY DENSITY MAPS 3.7 Preliminary probability density maps In our computation of the microlensing optical depth, event rate and average duration, we used the masses generated by the Besançon model. To calculate the probability of the model fits from MOA-2011-BLG-262lb case, we replaced all lens masses with 3.6 M J and 0.12 M, the primary lens mass of the planetmoon and star-planet models respectively. We generated a new catalogue with l = 0.4 o, b = 3.9 o, the Galactic coordinates for the MOA-2011-BLG-262lb event, and calculated the rate-weight of each source-lens pair. Figures 3.4 and 3.5 show the posterior probability map of 0.12 M and 3.6 M J lenses respectively. Figure 3.4: The posterior probability map of Solar-mass lenses is shown here. Parvin Mansour 57

58 3.7: PRELIMINARY PROBABILITY DENSITY MAPS Figure 3.5: The posterior probability map of Jupiter-mass lenses is shown here. The highest posterior probability of 0.12 M lenses are about an order of magnitude larger than that of 3.6 M J lenses with significant weights corresponding to lens distance of around 4.5 kpc D l 9.5 kpc and relative proper motion of around 1 mas/yr µ rel < 10.5 mas/yr for both lens populations Selection functions To improve our calculation we constrain our model further by adding a selection function to the rate-weight of each source-lens pair. The selection function is Parvin Mansour 58

59 3.8: APPLICATION TO MOA-2011-BLG-262LB given by ψ = i = i P i exp ( 1 2 ( ) X i sim Xobs i 2 ), σ(x obs ) (3.11) where i is the product sum of all selection functions included in our computation and Xsim i and Xobs i are the simulated and observed parameters respectively. the σ(x obs ) is the uncertainty in the observed parameter. Since the impact parameter u 0 distribution is uniform and does not enter probability ratios, we remove it from rate-weight calculation before applying our model to the MOA-2011-BLG-262lb microlensing event. Therefore the rate-weight of each lensing system summed over all lenses j is simply Ψ = j ψ j θ E,j D 2 l,j µ j. (3.12) For a complete representation of the posterior probability of each model we consider all the available constraints, which for MOA-2011-BLG-262lb includes t E, I s and µ rel. 3.8 Application to MOA-2011-BLG-262lb The posterior probability maps in figures 3.4 and 3.5 were produced with ψ=1. However, for this event we need to constrain our model further by adding selection functions to the rate-weight, using the observed parameters given by Bennett et al. (2014). The MOA alert system gives the relative error of t E for this event, so we set t E = ± days and I s = ± Figures 3.6 and 3.7 shows the new posterior probability maps for 0.12 solar-mass and 3.6 Jupiter-mass lens populations with constraints in event crossing time and source magnitude. Parvin Mansour 59

60 3.8: APPLICATION TO MOA-2011-BLG-262LB Figure 3.6: The posterior probability map of 0.12 M lenses with a constraint in Einstein radius crossing time and source magnitude. Parvin Mansour 60

61 3.8: APPLICATION TO MOA-2011-BLG-262LB Figure 3.7: The posterior probability map of 3.6 M J lenses with a constraint in Einstein radius crossing time and source magnitude. The mass, t E and I s constraints decrease the maximum posterior probability for 0.12 M and 3.6 M J populations by nearly 4 and 3 order of magnitude, respectively. Adding these constraints had no effect on the 0.12 M lens population distance range, but the lenses have a higher proper motion of 4 µ rel 14.5 mas/yr. For 3.6 M J lenses, these effects are more significant. The model now favours a population of lenses with a much lower relative proper motion of 1 µ rel 7 mas/yr and a D l region extending to a distance of 3 kpc D l 9 kpc. Parvin Mansour 61

62 3.8: APPLICATION TO MOA-2011-BLG-262LB Refining Besançon catalogues In order to constrain our model further, we made more cuts in the source catalogue. Figure 3.8 shows the plot of source apparent magnitude versus source proper motion for all the lensing systems with significant contributions to the rate-weight, where the source magnitude is given by the catalogue K and I-K values I s = K + (I K). (3.13) The significant rate-weights correspond to a source magnitude of and a proper motion of mas/yr, so we produced a new larger source catalogue restricted to these cuts. Figure 3.8: The plot of source apparent magnitude versus source proper motion. The sources with significant contribution to the weight have µ s 14.5 mas/yr and 19.5 < I s < We computed the rate-weight of all lensing systems for the new source catalogue and used plots of D s vs D l, µ l and µ s, D l vs µ l and µ s and µ l vs µ s to make further cuts in our source and lens catalogues. Figures show these plots Parvin Mansour 62

63 3.8: APPLICATION TO MOA-2011-BLG-262LB for the 0.12 M population, whilst figures show the plots for the 3.6 M J population. All rate-weighted systems that contribute significantly to the posterior probability fall within lens and source distance of 2-14 kpc for both populations and have a source proper motion of mas/yr. Therefore the final lens catalogue used in our computation had a cut in D l = 2 14 kpc, whilst the source catalogue had the following cuts in D s = 2 14 kpc, I s = and µ s = mas/yr. With these restrictions we can re-run a larger simulation sampling only regions of significant microlens weighting. Figure 3.9: Plot of source distance versus lens distance for the 0.12 solar-mass population. All sources and lenses which contribute significantly to the weight have a distance of 2-14 kpc. Parvin Mansour 63

64 3.8: APPLICATION TO MOA-2011-BLG-262LB Figure 3.10: Plot of source distance versus lens proper motion for the 0.12 solar-mass lens population. The source-lens pairs with significant contribution to the weight have 2 D s 14 kpc and µ l < 19 mas/yr. Figure 3.11: Plot of source distance versus source proper motion for the 0.12 solar-mass lens population. Sources with significant contribution to the weight have a distance and proper motion of 2 D s 14 kpc and µ s < 14.5 mas/yr respectively. Parvin Mansour 64

65 3.8: APPLICATION TO MOA-2011-BLG-262LB Figure 3.12: Plot of lens distance versus lens proper motion for the 0.12 solar-mass lens population. Lenses with significant contribution to the weight have a distance and proper motion of 2 D l 14 kpc and µ l < 19 mas/yr respectively. Figure 3.13: Plot of lens distance versus source proper motion for the 0.12 solar-mass lens population. The source-lens pairs with significant contribution to the weight have 2 D l 14 kpc and µ s < 14.5 mas/yr. Parvin Mansour 65

66 3.8: APPLICATION TO MOA-2011-BLG-262LB Figure 3.14: Plot of source proper motion versus lens proper motion for the 0.12 solarmass lens population. The source-lens pairs with significant contribution to the weight have µ s < 14.5 and µ l < 19mas/yr. Figure 3.15: Plot of source distance versus lens distance for the 3.6 M J lens population. All sources and lenses which contribute significantly to the weight have a distance of kpc. Parvin Mansour 66

67 3.8: APPLICATION TO MOA-2011-BLG-262LB Figure 3.16: Plot of source distance versus lens proper motion for the 3.6 M J lens population.the source-lens pairs with significant contribution to the weight have 1.7 D s 14 kpc and µ l < 18 mas/yr. Figure 3.17: Plot of source distance versus source proper motion for the 3.6 M J lens population. Sources with significant contribution to the weight have a distance and proper motion of 1.7 D s 14 kpc and µ s < 14.5 mas/yr respectively. Parvin Mansour 67

68 3.8: APPLICATION TO MOA-2011-BLG-262LB Figure 3.18: Plot of lens distance versus lens proper motion for the 3.6 M J lens population. Lenses with significant contribution to the weight have a distance and proper motion of 2 D l 14 kpc and µ l < 18 mas/yr respectively. Figure 3.19: Plot of lens distance versus source proper motion for the 3.6 M J lens population. The source-lens pairs with significant contribution to the weight have 2 D l 14 kpc and µ s < 14.5 mas/yr. Parvin Mansour 68

69 3.8: APPLICATION TO MOA-2011-BLG-262LB Figure 3.20: Plot of source proper motion versus lens proper motion for the 3.6 M J lens population. The source-lens pairs with significant contribution to the weight have µ s < 14.5 and µ l < 18 mas/yr Final probability density maps Figures 3.21 and 3.22 show the posterior probability maps for 0.12 M and 3.6 M J lens populations using source/lens catalogues with all the cuts. It can be seen from these figures that our model strongly favours a stellar bulge lens with µ rel > 5 mas/yr, however, at lower proper motion, a disk/bulge Jupiter-mass lens is favoured. Parvin Mansour 69

70 3.8: APPLICATION TO MOA-2011-BLG-262LB Figure 3.21: The final posterior probability map of the 0.12 solar-mass lenses is shown here. Parvin Mansour 70

Gravitational microlensing: an original technique to detect exoplanets

Gravitational microlensing: an original technique to detect exoplanets Gravitational microlensing: an original technique to detect exoplanets Gravitational lens effect Microlensing and exoplanets 4 Time variation 5 Basic equations θ E (mas) = 2.854 M 1/2 1/2 L D OL R E (AU)

More information

Detecting Planets via Gravitational Microlensing

Detecting Planets via Gravitational Microlensing Detecting Planets via Gravitational Microlensing -- Toward a Census of Exoplanets Subo Dong Institute for Advanced Study Collaborators: Andy Gould (Ohio State) [MicroFUN], Andrzej Udalski (Warsaw) [OGLE],

More information

Microlensing (planet detection): theory and applications

Microlensing (planet detection): theory and applications Microlensing (planet detection): theory and applications Shude Mao Jodrell Bank Centre for Astrophysics University of Manchester (& NAOC) 19/12/2009 @ KIAA Outline What is (Galactic) microlensing? Basic

More information

Searching for extrasolar planets using microlensing

Searching for extrasolar planets using microlensing Searching for extrasolar planets using microlensing Dijana Dominis Prester 7.8.2007, Belgrade Extrasolar planets Planets outside of the Solar System (exoplanets) Various methods: mostly massive hot gaseous

More information

Scott Gaudi The Ohio State University. Results from Microlensing Searches for Planets.

Scott Gaudi The Ohio State University. Results from Microlensing Searches for Planets. Scott Gaudi The Ohio State University Results from Microlensing Searches for Planets. Collaborative Efforts. Worldwide Collaborations: μfun MiNDSTEP MOA OGLE PLANET RoboNet Microlensing is a cult. -Dave

More information

Microlensing Parallax with Spitzer

Microlensing Parallax with Spitzer Microlensing Parallax with Spitzer Pathway to the Galactic Distribution of Planets 2015 Sagan/Michelson Fellows Symposium May 7-8, 2015 Caltech Sebastiano Calchi Novati Sagan Visiting Fellow NExScI (Caltech),

More information

Conceptual Themes for the 2017 Sagan Summer Workshop

Conceptual Themes for the 2017 Sagan Summer Workshop Conceptual Themes for the 2017 Sagan Summer Workshop Authors: Jennifer C. Yee (SAO) & Calen B. Henderson (JPL) Theme 1: The Scale of the Einstein Ring Microlensing is most sensitive to planets near the

More information

The Gravitational Microlensing Planet Search Technique from Space

The Gravitational Microlensing Planet Search Technique from Space The Gravitational Microlensing Planet Search Technique from Space David Bennett & Sun Hong Rhie (University of Notre Dame) Abstract: Gravitational microlensing is the only known extra-solar planet search

More information

Microlensing Planets (and Beyond) In the Era of Large Surveys Andy Gould (OSU)

Microlensing Planets (and Beyond) In the Era of Large Surveys Andy Gould (OSU) Microlensing Planets (and Beyond) In the Era of Large Surveys Andy Gould (OSU) Einstein (1912) [Renn, Sauer, Stachel 1997, Science 275, 184] Mao & Paczynski Microlens Planet Searches Gould & Loeb Survey

More information

Rachel Street. K2/Campaign 9: Microlensing

Rachel Street. K2/Campaign 9: Microlensing C2 C9 C7 Rachel Street K2/Campaign 9: Microlensing Probing Cool Planets Value of probing colder population Rocky planets Icy planets Gas giants Beyond snowline: Giant planet formation(?) Icy planets/planetesimals

More information

The Demographics of Extrasolar Planets Beyond the Snow Line with Ground-based Microlensing Surveys

The Demographics of Extrasolar Planets Beyond the Snow Line with Ground-based Microlensing Surveys The Demographics of Extrasolar Planets Beyond the Snow Line with Ground-based Microlensing Surveys White Paper for the Astro2010 PSF Science Frontier Panel B. Scott Gaudi The Ohio State University gaudi@astronomy.ohio-state.edu

More information

Frequency of Exoplanets Beyond the Snow Line from 6 Years of MOA Data Studying Exoplanets in Their Birthplace

Frequency of Exoplanets Beyond the Snow Line from 6 Years of MOA Data Studying Exoplanets in Their Birthplace Frequency of Exoplanets Beyond the Snow Line from 6 Years of MOA Data Studying Exoplanets in Their Birthplace David Bennett University of Notre Dame Analysis to appear in Suzuki et al. (2015) MicroFUN

More information

The frequency of snowline planets from a 2 nd generation microlensing survey

The frequency of snowline planets from a 2 nd generation microlensing survey The frequency of snowline planets from a 2 nd generation microlensing survey Yossi Shvartzvald Tel-Aviv University with Dan Maoz, Matan Friedmann (TAU) in collaboration with OGLE, MOA, µfun Microlensing

More information

L2 point vs. geosynchronous orbit for parallax effect by simulations

L2 point vs. geosynchronous orbit for parallax effect by simulations L point vs. geosynchronous orbit for parallax effect by simulations Lindita Hamolli Physics Dept. Faculty of Natyral Science lindita.hamolli@fshn.edu.al Mimoza Hafizi Physics Dept. Faculty of Natyral Science

More information

arxiv:astro-ph/ v1 21 Jul 2003

arxiv:astro-ph/ v1 21 Jul 2003 Signs of Planetary Microlensing Signals Cheongho Han Department of Physics, Institute for Basic Science Research, Chungbuk National University, Chongju 361-763, Korea; cheongho@astroph.chungbuk.ac.kr arxiv:astro-ph/0307372v1

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION doi:10.1038/nature10684 1 PLANET microlensing data 2002-2007 1.1 PLANET observing strategy 2002-2007 Since the discovery of the first extrasolar planet orbiting a main-sequence

More information

Investigating the free-floating planet mass by Euclid observations

Investigating the free-floating planet mass by Euclid observations Investigating the free-floating planet mass by Euclid observations Lindita Hamolli 1 Mimoza Hafizi 1 Francesco De Paolis,3 Achille A. Nucita,3 1- Department of Physics, University of Tirana, Albania. -

More information

Refining Microlensing Models with KECK Adaptive Optics. Virginie Batista

Refining Microlensing Models with KECK Adaptive Optics. Virginie Batista Refining Microlensing Models with KECK Adaptive Optics Virginie Batista Institut d Astrophysique de Paris Centre National d Etudes Spatiales Collaborators : J.-P. Beaulieu, D. Bennett, A. Bhattacharya,

More information

The Wellington microlensing modelling programme

The Wellington microlensing modelling programme , Aarno Korpela and Paul Chote School of Chemical & Physical Sciences, Victoria University of Wellington, P O Box 600, Wellington, New Zealand. E-mail: denis.sullivan@vuw.ac.nz, a.korpela@niwa.co.nz, paul@chote.net

More information

Exoplanet Microlensing Surveys with WFIRST and Euclid. David Bennett University of Notre Dame

Exoplanet Microlensing Surveys with WFIRST and Euclid. David Bennett University of Notre Dame Exoplanet Microlensing Surveys with WFIRST and Euclid David Bennett University of Notre Dame Why Space-based Microlensing? Space-based microlensing is critical for our understanding of exoplanet demographics

More information

Microlensing with Spitzer

Microlensing with Spitzer Microlensing with Spitzer uncover lens masses and distances by parallax measurements Wide-field InfraRed Surveys 2014 November 17th-20th 2014 Pasadena, CA Sebastiano Calchi Novati NExScI (Caltech), Univ.

More information

MICROLENSING PLANET DISCOVERIES. Yossi Shvartzvald NPP Fellow at JPL

MICROLENSING PLANET DISCOVERIES. Yossi Shvartzvald NPP Fellow at JPL MICROLENSING PLANET DISCOVERIES Yossi Shvartzvald NPP Fellow at JPL Prehistory MACHO LMC-1 Alcock et al. 1993 Prehistory MACHO LMC-1 Alcock et al. 1993 Dominik & Hirshfeld 1994 Prehistory Dominik & Hirshfeld

More information

Gravitational microlensing. Exoplanets Microlensing and Transit methods

Gravitational microlensing. Exoplanets Microlensing and Transit methods Gravitational microlensing Exoplanets Microlensing and s Planets and Astrobiology (2016-2017) G. Vladilo May take place when a star-planet system crosses the visual of a background star, as a result of

More information

A CHARACTERISTIC PLANETARY FEATURE IN DOUBLE-PEAKED, HIGH-MAGNIFICATION MICROLENSING EVENTS

A CHARACTERISTIC PLANETARY FEATURE IN DOUBLE-PEAKED, HIGH-MAGNIFICATION MICROLENSING EVENTS The Astrophysical Journal, 689:53Y58, 2008 December 10 # 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A. A CHARACTERISTIC PLANETARY FEATURE IN DOUBLE-PEAKED, HIGH-MAGNIFICATION

More information

Ground Based Gravitational Microlensing Searches for Extra-Solar Terrestrial Planets Sun Hong Rhie & David Bennett (University of Notre Dame)

Ground Based Gravitational Microlensing Searches for Extra-Solar Terrestrial Planets Sun Hong Rhie & David Bennett (University of Notre Dame) Ground Based Gravitational Microlensing Searches for Extra-Solar Terrestrial Planets Sun Hong Rhie & David Bennett (University of Notre Dame) Abstract: A gravitational microlensing terrestrial planet search

More information

Is the Galactic Bulge Devoid of Planets?

Is the Galactic Bulge Devoid of Planets? Is the Galactic Bulge Devoid of Planets? Matthew Penny Ohio State University penny@astronomy.ohio-state.edu There's Something Going On with Our Distance Estimates There's Something Going On with Our Distance

More information

Keck Key Strategic Mission Support Program for WFIRST

Keck Key Strategic Mission Support Program for WFIRST Keck Key Strategic Mission Support Program for WFIRST David Bennett January 26, 2018 NASA Goddard Space Flight Center 1 Why complete the census? A complete census is needed to understand planet formation

More information

Simple Point Lens 3 Features. & 3 Parameters. t_0 Height of Peak. Time of Peak. u_0 Width of Peak. t_e

Simple Point Lens 3 Features. & 3 Parameters. t_0 Height of Peak. Time of Peak. u_0 Width of Peak. t_e Exoplanet Microlensing III: Inverting Lightcurves, lens vs. world Andy Gould (Ohio State) Simple Point Lens 3 Features & 3 Parameters Time of Peak t_0 Height of Peak u_0 Width of Peak t_e Simple Planetary

More information

arxiv:astro-ph/ v1 9 Aug 2001

arxiv:astro-ph/ v1 9 Aug 2001 Mon. Not. R. Astron. Soc. 000, 000 000 (0000) Printed 2 October 2018 (MN LATEX style file v1.4) Properties of Planet-induced Deviations in the Astrometric Microlensing Centroid Shift Trajectory Cheongho

More information

Microlensing by Multiple Planets in High Magnification Events

Microlensing by Multiple Planets in High Magnification Events Microlensing by Multiple Planets in High Magnification Events B. Scott Gaudi Ohio State University, Department of Astronomy, Columbus, OH 43210 gaudi@astronomy.ohio-state.edu Richard M. Naber and Penny

More information

The Galactic Exoplanet Survey Telescope (GEST)

The Galactic Exoplanet Survey Telescope (GEST) The Galactic Exoplanet Survey Telescope (GEST) D. Bennett (Notre Dame), J. Bally (Colorado), I. Bond (Auckland), E. Cheng (GSFC), K. Cook (LLNL), D. Deming, (GSFC) P. Garnavich (Notre Dame), K. Griest

More information

arxiv:astro-ph/ v1 14 Nov 2006

arxiv:astro-ph/ v1 14 Nov 2006 Characterization of Gravitational Microlensing Planetary Host Stars David P. Bennett 1, Jay Anderson 2, and B. Scott Gaudi 3 ABSTRACT arxiv:astro-ph/0611448v1 14 Nov 2006 The gravitational microlensing

More information

arxiv:astro-ph/ v2 4 Nov 1999

arxiv:astro-ph/ v2 4 Nov 1999 Gravitational Microlensing Evidence for a Planet Orbiting a Binary Star System D.P. Bennett, S.H. Rhie, A.C. Becker, N. Butler, J. Dann, S. Kaspi, E.M. Leibowitz, Y. Lipkin, D. Maoz, H. Mendelson, B.A.

More information

Microlensing Surveys for Exoplanets

Microlensing Surveys for Exoplanets Annu. Rev. Astron. Astrophys. 2012. 50:411 53 First published online as a Review in Advance on June 15, 2012 The Annual Review of Astronomy and Astrophysics is online at astro.annualreviews.org This article

More information

Importance of the study of extrasolar planets. Exoplanets Introduction. Importance of the study of extrasolar planets

Importance of the study of extrasolar planets. Exoplanets Introduction. Importance of the study of extrasolar planets Importance of the study of extrasolar planets Exoplanets Introduction Planets and Astrobiology (2017-2018) G. Vladilo Technological and scientific spin-offs Exoplanet observations are driving huge technological

More information

MICROLENSING BY MULTIPLE PLANETS IN HIGH-MAGNIFICATION EVENTS B. Scott Gaudi. and Richard M. Naber and Penny D. Sackett

MICROLENSING BY MULTIPLE PLANETS IN HIGH-MAGNIFICATION EVENTS B. Scott Gaudi. and Richard M. Naber and Penny D. Sackett The Astrophysical Journal, 502:L33 L37, 1998 July 20 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A. MICROLENSING BY MULTIPLE PLANETS IN HIGH-MAGNIFICATION EVENTS B. Scott

More information

Exploring the shortest microlensing events

Exploring the shortest microlensing events Exploring the shortest microlensing events Przemek Mróz Warsaw University Observatory 25.01.2018 Outline Update on short-timescale events from 2010-15 from OGLE Short-timescale binary events Short-timescale

More information

Towards the Galactic Distribution of Exoplanets

Towards the Galactic Distribution of Exoplanets Towards the Galactic Distribution of Exoplanets Spitzer and the Microlensing Parallax May 23, 2016 ExEP Science Briefing, JPL, Pasadena Sebastiano Calchi Novati IPAC/NExScI, Caltech credit: NASA/JPL OUTLINE

More information

REANALYSIS OF THE GRAVITATIONAL MICROLENSING EVENT MACHO-97-BLG-41 BASED ON COMBINED DATA

REANALYSIS OF THE GRAVITATIONAL MICROLENSING EVENT MACHO-97-BLG-41 BASED ON COMBINED DATA DRAFT VERSION MARCH 26, 2013 Preprint typeset using LATEX style emulateapj v. 5/2/11 REANALYSIS OF THE GRAVITATIONAL MICROLENSING EVENT MACHO-97-BLG-41 BASED ON COMBINED DATA YOUN KIL JUNG 1, CHEONGHO

More information

Extrasolar Planets. Methods of detection Characterization Theoretical ideas Future prospects

Extrasolar Planets. Methods of detection Characterization Theoretical ideas Future prospects Extrasolar Planets Methods of detection Characterization Theoretical ideas Future prospects Methods of detection Methods of detection Methods of detection Pulsar timing Planetary motion around pulsar

More information

Observations of gravitational microlensing events with OSIRIS. A Proposal for a Cruise Science Observation

Observations of gravitational microlensing events with OSIRIS. A Proposal for a Cruise Science Observation Observations of gravitational microlensing events with OSIRIS A Proposal for a Cruise Science Observation Michael Küppers, Björn Grieger, ESAC, Spain Martin Burgdorf, Liverpool John Moores University,

More information

Planet abundance from PLANET observations

Planet abundance from PLANET observations Planet abundance from PLANET 2002-07 observations Collaborations : PLANET OGLE Arnaud Cassan Institut d Astrophysique de Paris Université Pierre et Marie Curie Ground-based microlensing : alert + follow-up

More information

Transiting Hot Jupiters near the Galactic Center

Transiting Hot Jupiters near the Galactic Center National Aeronautics and Space Administration Transiting Hot Jupiters near the Galactic Center Kailash C. Sahu Taken from: Hubble 2006 Science Year in Review The full contents of this book include more

More information

How Common Are Planets Around Other Stars? Transiting Exoplanets. Kailash C. Sahu Space Tel. Sci. Institute

How Common Are Planets Around Other Stars? Transiting Exoplanets. Kailash C. Sahu Space Tel. Sci. Institute How Common Are Planets Around Other Stars? Transiting Exoplanets Kailash C. Sahu Space Tel. Sci. Institute Earth as viewed by Voyager Zodiacal cloud "Pale blue dot" Look again at that dot. That's here.

More information

EUCLID,! the planet hunter

EUCLID,! the planet hunter EUCLID,! the planet hunter Jean-Philippe Beaulieu, Eamonn Kerins & Matthew Penny Pascal Fouqué, Virginie Batista, Arnaud Cassan, Christian Coutures & Jean-Baptiste Marquette Institut d Astrophysique de

More information

arxiv:astro-ph/ v1 5 Apr 1996

arxiv:astro-ph/ v1 5 Apr 1996 Einstein Radii from Binary-Source Events arxiv:astro-ph/9604031v1 5 Apr 1996 Cheongho Han Andrew Gould 1 Dept. of Astronomy, The Ohio State University, Columbus, OH 43210 cheongho@payne.mps.ohio-state.edu

More information

Lecture 12: Extrasolar planets. Astronomy 111 Monday October 9, 2017

Lecture 12: Extrasolar planets. Astronomy 111 Monday October 9, 2017 Lecture 12: Extrasolar planets Astronomy 111 Monday October 9, 2017 Reminders Star party Thursday night! Homework #6 due Monday The search for extrasolar planets The nature of life on earth and the quest

More information

arxiv: v1 [astro-ph] 12 Nov 2008

arxiv: v1 [astro-ph] 12 Nov 2008 Self-Organizing Maps. An application to the OGLE data and the Gaia Science Alerts Łukasz Wyrzykowski, and Vasily Belokurov arxiv:0811.1808v1 [astro-ph] 12 Nov 2008 Institute of Astronomy, University of

More information

Detectability of extrasolar moons as gravitational microlenses. C. Liebig and J. Wambsganss

Detectability of extrasolar moons as gravitational microlenses. C. Liebig and J. Wambsganss DOI: 10.1051/0004-6361/200913844 c ESO 2010 Astronomy & Astrophysics Detectability of extrasolar moons as gravitational microlenses C. Liebig and J. Wambsganss Astronomisches Rechen-Institut, Zentrum für

More information

Project Observations and Analysis in 2016 and Beyond

Project Observations and Analysis in 2016 and Beyond Project Observations and Analysis in 2016 and Beyond David Bennett NASA Goddard Statistical Results from MOA Survey Mass ratio function survey sensitivity Suzuki et al. (2016) MOA-II analysis, 29 planets

More information

HD Transits HST/STIS First Transiting Exo-Planet. Exoplanet Discovery Methods. Paper Due Tue, Feb 23. (4) Transits. Transits.

HD Transits HST/STIS First Transiting Exo-Planet. Exoplanet Discovery Methods. Paper Due Tue, Feb 23. (4) Transits. Transits. Paper Due Tue, Feb 23 Exoplanet Discovery Methods (1) Direct imaging (2) Astrometry position (3) Radial velocity velocity Seager & Mallen-Ornelas 2003 ApJ 585, 1038. "A Unique Solution of Planet and Star

More information

Observations of extrasolar planets

Observations of extrasolar planets Observations of extrasolar planets 1 Mercury 2 Venus radar image from Magellan (vertical scale exaggerated 10 X) 3 Mars 4 Jupiter 5 Saturn 6 Saturn 7 Uranus and Neptune 8 we need to look out about 10 parsecs

More information

Fig 2. Light curves resulting from the source trajectories in the maps of Fig. 1.

Fig 2. Light curves resulting from the source trajectories in the maps of Fig. 1. Planet/Binary Degeneracy I High-magnification events with double-peak structure Not only planets but also very wide or very close binaries can also produce such a perturbations. Can we distinguish them

More information

MASS FUNCTION OF STELLAR REMNANTS IN THE MILKY WAY

MASS FUNCTION OF STELLAR REMNANTS IN THE MILKY WAY MASS FUNCTION OF STELLAR REMNANTS IN THE MILKY WAY (pron: Woocash Vizhikovsky) Warsaw University Astronomical Observatory Wednesday Seminar, IoA Cambridge, 8 July 2015 COLLABORATORS Krzysztof Rybicki (PhD

More information

(x 2 + ξ 2 ) The integral in (21.02) is analytic, and works out to 2/ξ 2. So. v = 2GM ξc

(x 2 + ξ 2 ) The integral in (21.02) is analytic, and works out to 2/ξ 2. So. v = 2GM ξc Gravitational Lenses [Schneider, Ehlers, & Falco, Gravitational Lenses, Springer-Verlag 199] Consider a photon moving past a point of mass, M, with an starting impact parameter, ξ. From classical Newtonian

More information

Can We See Them?! Planet Detection! Planet is Much Fainter than Star!

Can We See Them?! Planet Detection! Planet is Much Fainter than Star! Can We See Them?! Planet Detection! Estimating f p! Not easily! Best cases were reported in late 2008! Will see these later! Problem is separating planet light from star light! Star is 10 9 times brighter

More information

Extrasolar planets detections and statistics through gravitational microlensing

Extrasolar planets detections and statistics through gravitational microlensing Extrasolar planets detections and statistics through gravitational microlensing Arnaud Cassan To cite this version: Arnaud Cassan. Extrasolar planets detections and statistics through gravitational microlensing.

More information

arxiv: v1 [astro-ph] 9 Jan 2008

arxiv: v1 [astro-ph] 9 Jan 2008 Discovery and Study of Nearby Habitable Planets with Mesolensing Rosanne Di Stefano & Christopher Night Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 arxiv:0801.1510v1

More information

MOA-2011-BLG-322Lb: a second generation survey microlensing planet

MOA-2011-BLG-322Lb: a second generation survey microlensing planet Advance Access publication 2014 January 30 doi:10.1093/mnras/stt2477 MOA-2011-BLG-322Lb: a second generation survey microlensing planet Y. Shvartzvald, 1 D. Maoz, 1 S. Kaspi, 1 T. Sumi, 2,3 A. Udalski,

More information

Sub-Saturn Planet MOA-2008-BLG-310Lb: Likely To Be In The Galactic Bulge

Sub-Saturn Planet MOA-2008-BLG-310Lb: Likely To Be In The Galactic Bulge Sub-Saturn Planet MOA-2008-BLG-310Lb: Likely To Be In The Galactic Bulge A Senior Honors Thesis Presented in Partial Fulfillment of the Requirements for graduation with research distinction in Astronomy

More information

Detectability of Orbital Motion in Stellar Binary and Planetary Microlenses

Detectability of Orbital Motion in Stellar Binary and Planetary Microlenses Mon. Not. R. Astron. Soc., () Printed July 3 (MN LaT E X style file v.) Detectability of Orbital Motion in Stellar Binary and Planetary Microlenses microlensing events per year, of which, of order ten

More information

Gravitational Lensing: Strong, Weak and Micro

Gravitational Lensing: Strong, Weak and Micro P. Schneider C. Kochanek J. Wambsganss Gravitational Lensing: Strong, Weak and Micro Saas-Fee Advanced Course 33 Swiss Society for Astrophysics and Astronomy Edited by G. Meylan, P. Jetzer and P. North

More information

Binary Lenses in OGLE-III EWS Database. Season 2004

Binary Lenses in OGLE-III EWS Database. Season 2004 ACTA ASTRONOMICA Vol. 56 (2006) pp. 307 332 Binary Lenses in OGLE-III EWS Database. Season 2004 by M. J a r o s z y ń s k i, J. S k o w r o n, A. U d a l s k i, M. K u b i a k, M. K. S z y m a ń s k i,

More information

The Microlensing Event MACHO-99-BLG-22/OGLE-1999-BUL-32: An Intermediate Mass Black Hole, or a Lens in the Bulge

The Microlensing Event MACHO-99-BLG-22/OGLE-1999-BUL-32: An Intermediate Mass Black Hole, or a Lens in the Bulge The Microlensing Event MACHO-99-BLG-22/OGLE-1999-BUL-32: An Intermediate Mass Black Hole, or a Lens in the Bulge D.P. Bennett 1, A.C. Becker 2, J.J. Calitz 3, B.R. Johnson 4,C.Laws 5,J.L.Quinn 1,S.H.Rhie

More information

TrES Exoplanets and False Positives: Finding the Needle in the Haystack

TrES Exoplanets and False Positives: Finding the Needle in the Haystack Transiting Extrasolar Planets Workshop ASP Conference Series, Vol. 366, 2007 C. Afonso, D. Weldrake and Th. Henning TrES Exoplanets and False Positives: Finding the Needle in the Haystack F. T. O Donovan

More information

Gravitational Microlensing: A Powerful Search Method for Extrasolar Planets. July 23, ESA/FFG Summer School Alpbach

Gravitational Microlensing: A Powerful Search Method for Extrasolar Planets. July 23, ESA/FFG Summer School Alpbach Gravitational Microlensing: A Powerful Search Method for Extrasolar Planets Joachim Wambsganss Zentrum für Astronomie der Universität Heidelberg July 23, 2009 ESA/FFG Summer School Alpbach 1 Gravitational

More information

Photon Statistics Limits for Earth-Based Parallax Measurements of MACHO Events

Photon Statistics Limits for Earth-Based Parallax Measurements of MACHO Events arxiv:astro-ph/9503039v2 12 Mar 1995 Photon Statistics Limits for Earth-Based Parallax Measurements of MACHO Events Daniel E. Holz and Robert M. Wald Enrico Fermi Institute and Department of Physics University

More information

Planets and Brown Dwarfs

Planets and Brown Dwarfs Extra Solar Planets Extra Solar Planets We have estimated there may be 10 20 billion stars in Milky Way with Earth like planets, hospitable for life. But what evidence do we have that such planets even

More information

Planet Detection! Estimating f p!

Planet Detection! Estimating f p! Planet Detection! Estimating f p! Can We See Them?! Not easily! Best cases were reported in late 2008! Will see these later! Problem is separating planet light from star light! Star is 10 9 times brighter

More information

DATA ANALYSIS OF MOA FOR GRAVITATIONAL MICROLENSING EVENTS WITH DURATIONS LESS THAN 2 DAYS BY USING BROWN DWARF POPULATION

DATA ANALYSIS OF MOA FOR GRAVITATIONAL MICROLENSING EVENTS WITH DURATIONS LESS THAN 2 DAYS BY USING BROWN DWARF POPULATION RevMexAA (Serie de Conferencias), 48, 129 133 (2016) DATA ANALYSIS OF MOA FOR GRAVITATIONAL MICROLENSING EVENTS WITH DURATIONS LESS THAN 2 DAYS BY USING BROWN DWARF POPULATION Sh. Hassani 1 RESUMEN Las

More information

arxiv: v2 [astro-ph.ep] 14 Aug 2018

arxiv: v2 [astro-ph.ep] 14 Aug 2018 Draft version August 16, 2018 Typeset using L A TEX manuscript style in AASTeX61 AN ICE GIANT EXOPLANET INTERPRETATION OF THE ANOMALY IN MICROLENSING EVENT OGLE-2011-BLG-0173 arxiv:1805.00049v2 [astro-ph.ep]

More information

Architecture and demographics of planetary systems

Architecture and demographics of planetary systems Architecture and demographics of planetary systems Struve (1952) The demography of the planets that we detect is strongly affected by detection methods psychology of the observer Understanding planet demography

More information

arxiv: v1 [astro-ph] 18 Aug 2007

arxiv: v1 [astro-ph] 18 Aug 2007 Microlensing under Shear Yoon-Hyun Ryu and Myeong-Gu Park arxiv:0708.2486v1 [astro-ph] 18 Aug 2007 Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 702-701, Korea

More information

Microlensing Planets: A Controlled Scientific Experiment From Absolute Chaos Andy Gould (OSU)

Microlensing Planets: A Controlled Scientific Experiment From Absolute Chaos Andy Gould (OSU) Microlensing Planets: A Controlled Scientific Experiment From Absolute Chaos Andy Gould (OSU) Generation 1 Liebes 1964, Phys Rev, 133, B835 Refsdal 1964, MNRAS, 128, 259 Mass measurement of Isolated Star

More information

NOT ENOUGH MACHOS IN THE GALACTIC HALO. Éric AUBOURG EROS, CEA-Saclay

NOT ENOUGH MACHOS IN THE GALACTIC HALO. Éric AUBOURG EROS, CEA-Saclay NOT ENOUGH MACHOS IN THE GALACTIC HALO Éric AUBOURG EROS, CEA-Saclay Experimental results 1- Galactic disk 2- Small masses (LMC/SMC) 10-7 10-2 M o 3- SMC 4- LMC GRAVITATIONAL MICROLENSING (Paczynski, 1986)

More information

Review of results from the EROS microlensing search for massive compact objects

Review of results from the EROS microlensing search for massive compact objects Author manuscript, published in "IDM008 - identification of dark matter 008, Stockholm : Sweden (008)" Review of results from the EROS microlensing search for massive compact objects Laboratoire de l Accélérateur

More information

arxiv:astro-ph/ v1 18 Nov 2003

arxiv:astro-ph/ v1 18 Nov 2003 Gravitational Microlensing: A Tool for Detecting and Characterizing Free-Floating Planets Cheongho Han, Sun-Ju Chung, Doeon Kim Department of Physics, Institute for Basic Science Research, Chungbuk National

More information

Gravitational Microlensing Observations. Grant Christie

Gravitational Microlensing Observations. Grant Christie Gravitational Microlensing Observations Optical Astronomy from an Urban Observatory Grant Christie Stardome Observatory, Auckland New Zealand and the Beginnings of Radio Astronomy Orewa, Jan 30-31, 2013

More information

Planets Around Other Stars Extrasolar Planet Detection Methods. February, 2006

Planets Around Other Stars Extrasolar Planet Detection Methods. February, 2006 Planets Around Other Stars Extrasolar Planet Detection Methods February, 2006 Distribution of this File Extrasolar_planet_detection.ppt This Powerpoint presentation was put together for the purpose of

More information

Microlensing and the Physics of Stellar Atmospheres

Microlensing and the Physics of Stellar Atmospheres Microlensing 2000: A New Era of Microlensing Astrophysics ASP Conference Series, Vol 000, 2000 JW Menzies and PD Sackett, eds Microlensing and the Physics of Stellar Atmospheres Penny D Sackett Kapteyn

More information

MOA-2011-BLG-293Lb: A testbed for pure survey microlensing. planet detections

MOA-2011-BLG-293Lb: A testbed for pure survey microlensing. planet detections MOA-2011-BLG-293Lb: A testbed for pure survey microlensing planet detections J.C. Yee 1. Introduction Microlensing uses gravitational lensing of individual stars to detect planets. In a microlensing event,

More information

Microlensing towards the Galactic Centre with OGLE

Microlensing towards the Galactic Centre with OGLE Microlensing towards the Galactic Centre with OGLE Łukasz Wyrzykowski (pron.: woo-cash vi-zhi-kov-ski) Warsaw University Astronomical Observatory, Poland Institute of Astronomy, University of Cambridge,

More information

arxiv:astro-ph/ v2 2 Mar 2000

arxiv:astro-ph/ v2 2 Mar 2000 1 The Optical Gravitational Lensing Experiment. Catalog of Microlensing Events in the Galactic Bulge arxiv:astro-ph/0002418v2 2 Mar 2000 A. U d a l s k i 1, K. Ż e b r u ń 1 M. S z y m a ń s k i 1, M.

More information

16th Microlensing Season of the Optical Gravitational Lensing Experiment

16th Microlensing Season of the Optical Gravitational Lensing Experiment 16th Microlensing Season of the Optical Gravitational Lensing Experiment A. Udalski Warsaw University Observatory 1 OGLE: The Optical Gravitational Lensing Experiment (1992 -.) http://ogle.astrouw.edu.pl

More information

arxiv: v2 [astro-ph.ep] 26 Dec 2013

arxiv: v2 [astro-ph.ep] 26 Dec 2013 arxiv:131.8v2 [astro-ph.ep] 26 Dec 213 Mon. Not. R. Astron. Soc., () Printed 5 April 218 (MN LATEX style file v2.2) MOA-211-BLG-322Lb: a second generation survey microlensing planet Y. Shvartzvald 1, D.

More information

II Planet Finding.

II Planet Finding. II Planet Finding http://sgoodwin.staff.shef.ac.uk/phy229.html 1.0 Introduction There are a lot of slides in this lecture. Much of this should be familiar from PHY104 (Introduction to Astrophysics) and

More information

Other planetary systems

Other planetary systems Exoplanets are faint! Other planetary systems Planets are seen only by reflected light at optical wavelengths At the distance of another star the faint light of a planet is lost in the glare of the star

More information

Articles publiés par Nature & Science «Discovery of a Jupiter/Saturn Analog with Gravitational Microlensing»

Articles publiés par Nature & Science «Discovery of a Jupiter/Saturn Analog with Gravitational Microlensing» Articles publiés par Nature & Science 1. Gaudi B.S., et al., 2008, «Discovery of a Jupiter/Saturn Analog with Gravitational Microlensing», Science 319, 927 2. Cassan A., Kubas D., Beaulieu J.P., et al.,

More information

Exoplanet Search Techniques: Overview. PHY 688, Lecture 28 April 3, 2009

Exoplanet Search Techniques: Overview. PHY 688, Lecture 28 April 3, 2009 Exoplanet Search Techniques: Overview PHY 688, Lecture 28 April 3, 2009 Course administration final presentations Outline see me for paper recommendations 2 3 weeks before talk see me with draft of presentation

More information

Planets & Life. Planets & Life PHYS 214. Please start all class related s with 214: 214: Dept of Physics (308A)

Planets & Life. Planets & Life PHYS 214. Please start all class related  s with 214: 214: Dept of Physics (308A) Planets & Life Planets & Life PHYS 214 Dr Rob Thacker Dept of Physics (308A) thacker@astro.queensu.ca Please start all class related emails with 214: 214: Today s s lecture Assignment 1 marked will hand

More information

arxiv: v1 [astro-ph.ep] 7 Sep 2018

arxiv: v1 [astro-ph.ep] 7 Sep 2018 WFIRST Exoplanet Mass Measurement Method Finds a Planetary Mass of 39 ± 8M for OGLE-2012-BLG-0950Lb arxiv:1809.02654v1 [astro-ph.ep] 7 Sep 2018 A. Bhattacharya 1,2, J.P. Beaulieu 3,4, D.P. Bennett 1,2,

More information

Data from: The Extrasolar Planet Encyclopaedia.

Data from: The Extrasolar Planet Encyclopaedia. Data from: The Extrasolar Planet Encyclopaedia http://exoplanet.eu/ 2009->10 Status of Exoplanet Searches Direct Detection: 5->9 planets detected Sensitive to large planets in large orbits around faint

More information

Planets are plentiful

Planets are plentiful Extra-Solar Planets Planets are plentiful The first planet orbiting another Sun-like star was discovered in 1995. We now know of 209 (Feb 07). Including several stars with more than one planet - true planetary

More information

THE LAST 25 YEARS OF EXOPLANETS AND THE ESSENTIAL CONTRIBUTIONS OF

THE LAST 25 YEARS OF EXOPLANETS AND THE ESSENTIAL CONTRIBUTIONS OF THE LAST 25 YEARS OF EXOPLANETS AND THE ESSENTIAL CONTRIBUTIONS OF Celebrating 25 Years of the OGLE Project July 25, 2017 Warsaw University Scott Gaudi The Ohio State University THE LAST 29 YEARS OF EXOPLANETS

More information

Lecture 20: Planet formation II. Clues from Exoplanets

Lecture 20: Planet formation II. Clues from Exoplanets Lecture 20: Planet formation II. Clues from Exoplanets 1 Outline Definition of a planet Properties of exoplanets Formation models for exoplanets gravitational instability model core accretion scenario

More information

The phenomenon of gravitational lenses

The phenomenon of gravitational lenses The phenomenon of gravitational lenses The phenomenon of gravitational lenses If we look carefully at the image taken with the Hubble Space Telescope, of the Galaxy Cluster Abell 2218 in the constellation

More information

Searching for Other Worlds

Searching for Other Worlds Searching for Other Worlds Lecture 32 1 In-Class Question What is the Greenhouse effect? a) Optical light from the Sun is reflected into space while infrared light passes through the atmosphere and heats

More information

arxiv:astro-ph/ v1 12 Apr 1997

arxiv:astro-ph/ v1 12 Apr 1997 Bright Lenses and Optical Depth Robert J. Nemiroff Department of Physics, Michigan Technological University, Houghton, MI 49931 arxiv:astro-ph/9704114v1 12 Apr 1997 Received ; accepted Submitted to The

More information

Extrasolar Planet Detection Methods. Tom Koonce September, 2005

Extrasolar Planet Detection Methods. Tom Koonce September, 2005 Extrasolar Planet Detection Methods Tom Koonce September, 2005 Planets Around Other Stars? How is it possible to see something so small, so far away? If everything is aligned perfectly, we can see the

More information

Space-Based Exoplanet Microlensing Surveys. David Bennett University of Notre Dame

Space-Based Exoplanet Microlensing Surveys. David Bennett University of Notre Dame Space-Based Exoplanet Microlensing Surveys David Bennett University of Notre Dame The Physics of Microlensing Foreground lens star + planet bend light of source star Multiple distorted images Only total

More information