Gen Relativ Gravit (2011) 43:989–1006DOI 10.1007/s10714-010-0964-x

RESEARCH ARTICLE

The gravitational bending of light by stars: a continuingstory of curiosity, scepticism, surprise, and fascination

Martin Dominik

Received: 18 December 2009 / Accepted: 24 February 2010 / Published online: 26 March 2010© Springer Science+Business Media, LLC 2010

Abstract Driven entirely by human curiosity, the effect of the gravitational bendingof light has evolved on unforeseen paths, in an interplay between shifts in prevail-ing paradigms and advance of technology, into the most unusual way to study planetpopulations. The confirmation of the bending angle predicted by Einstein with theSolar Eclipse measurements from 1919 marked the breakthrough of the theory ofGeneral Relativity, but it was not before the detection of the double image of thequasar 0957+561 that ‘gravitational lensing’ really entered the observational era. Theobservation of a characteristic transient brightening of a star caused by the gravitationaldeflection of its light by an intervening foreground star, constituting a ‘microlensingevent’, required even further advance in technology before it could first emerge in1993. While it required more patience in waiting before ‘Einstein’s blip’ for the firsttime revealed the presence of a planet orbiting a star other than the Sun, such detec-tions can now be monitored live, and gravitational microlensing is not only sensitive tomasses as low as that of the Moon, but can even reveal planets around stars in galaxiesother than the Milky Way.

Keywords Extra-solar planetary systems · Relativity and gravitation ·History of science · Science and government · Photography and photometry ·Gravitational lenses and luminous arcs

M. Dominik (B)SUPA, School of Physics and Astronomy, University of St Andrews,North Haugh, St Andrews KY16 9SS, UKe-mail: md35@st-andrews.ac.uk

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1 From the beginnings to Einstein’s ‘weird’ theory

Probably ever since its existence, mankind has been fascinated about all the pinpointsof light on the night sky, leading to wondering about what is going on out there, andwhether there are other worlds like ours, or rather quite unlike ours. Ancient mysticideas got replaced by the dominant concept in Greek philosophy for natural phenom-ena, which is geometry—going hand in hand with simplicity, symmetry, and beauty.These principles governed the view for several millennia, and were applied to all fieldsof science, famously reflected in the drawing of the human body by Leonardo da Vincifollowing the description by the Roman architect Vitruvius [1].1 While the Copernicanrevolution involved a paradigm shift away from the Ptolemaic model of a geocentricuniverse, Kepler’s description of the planetary orbits in a heliocentric system is still apurely geometric one [2–5].

The way we understand nature was only changed with a strict demand for causal-ity leading Newton to introduce the concept of forces, which allowed to formulate auniversal law of gravity with the gravitational constant G characterizing the strengthof the gravitational attraction between massive bodies [6].

In 1801, Johann Georg von Soldner [7], believing in light consisting of corpuscles,applied Newton’s theory to find a light ray grazing near the limb of the Sun to bedeflected by 0.84 arcsec, and concluded that such an effect would not be of practicalrelevance. Given that the competing wave theory of light was gaining more and morefollowers, he pointed out “Hopefully, nobody will get concerned that I treat a light rayjust as a massive body.”2 In fact, not only the inability to measure the predicted effect,but also the shortly following victory of the wave theory wiped away Soldner’s result.The timing of his findings could hardly have been worse.

Apparently unaware of earlier discussions of this topic, Albert Einstein wonderedabout the influence of gravity on the propagation of light first in 1907 [8], but lackof satisfaction with his discussion caused him to get back to it 3 years later. In orderto avoid “unnecessary complexity”, he abstained from applying the laws of SpecialRelativity [9], but instead based his calculations, published in 1911, which he consid-ered first-order approximations, on Newtonian mechanics and the Galilean principleof Relativity [10]. His presented thoughts about the equivalence between referenceframes that are accelerated with respect to each other, and thereby a local equivalencebetween accelerated frames and the effect of gravity formed a fundamental basis fordeveloping the theory of General Relativity, which was not completed before 1915[11,12]. Coincidentally, this theory replaces Newton’s forces back with geometry, butnow the geometry is linked to a cause, found on the other side of Einstein’s gravitationalfield equations.

1 The ‘Vitruvian man’ can in fact be found on the obverse side of the standard 1 Euro coin issued by theItalian Republic.2 In German (original): “Hoffentlich wird es niemand bedenklich finden, dass ich einen Lichtstral geradezuals schweren Körper behandle.”

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Einstein’s numerical result of 0.83 arcsec coincided with the value predicted bySoldner a century earlier, but Einstein envisioned that this effect now could actuallybe measured. Despite of shortcomings of his treatment in quite relevant details, hewrote “I would hope that astronomers devoted attention to this emerging question,regardless of whether the presented considerations might lack of proper foundationsor even look audacious. Apart from any theory, one has to ask whether with today’smeans an influence of gravitational fields on the propagation of light can be estab-lished.”3

Excited about Einstein’s work, Erwin (Finlay-)Freundlich4 was “the first amongfellow-scientists who has taken the pains to put the theory to the test” (as remarkedby Einstein in 1919) [13]. His immense efforts led to the preparation of observationsof the Solar Eclipse of 21 August 1914 on the Crimea. This turned out to be anotherbad timing, because Freundlich got into the outbreak of the World War, and ended upin detention by the Russians. Apart from this, the weather was bad, anyway.

With the full theory of General Relativity, Einstein re-addressed the issue of thegravitational bending of light along with a discussion of the perihelion precession ofMercury, and found that the deflection angle should actually be twice of that predictedearlier on the basis of Newtonian mechanics [14].

The eclipse of 29 May 1919 provided an extraordinary opportunity to testEinstein’s predictions, with the Hyades cluster, the densest population of bright starsin the ecliptic plane, being behind the Sun. Consequently, two British expeditionsembarked to Sobral (Brazil) and the island of Principe, the latter led by the laterknighted Arthur Eddington. On the different possible outcomes of the observations,Eddington stated “The present eclipse expeditions may for the first time demonstratethe weight of light; or they may confirm Einsteins weird theory of non-Euclidean space;or they may lead to a result of yet more far-reaching consequences—no deflection.”[15] However, it was Einstein’s theory that was considered to be confirmed by themeasurements [16], and reporting to the Royal Astronomical Society after the expedi-tion, Eddington remarked “The generalized relativity theory is a most profound theoryof Nature, embracing almost all the phenomena of physics” [17].

While this marked the crucial breakthrough for its wide acceptance, we now knowthat the claimed accuracy of many measurements of the gravitational light bendingmade over almost 50 years [18] was corrupted by underestimated true systematic errorsrelated to the instruments available at that time. Notably, Freundlich’s observations atTakengon (North Sumatra) during the eclipse of 9 May 1929, which seemed to indi-cate a larger bending angle [19], overencouraged him to become a strong sceptic ofEinstein’s theory [20,21]. It was only after his death that this issue could be satisfac-torily settled in favour of General Relativity by means of radio interferometry [22].

3 In German (original): “Es wäre dringend zu wünschen, daß sich Astronomen der hier aufgerollten Frageannähmen, auch wenn die im vorigen gegebenen Überlegungen ungenügend fundiert oder gar abenteuerlicherscheinen sollten. Denn abgesehen von jeder Theorie muß man sich fragen, ob mit den heutigen Mittelnein Einfluß der Gravitationsfelder auf die Ausbreitung des Lichtes sich konstatieren läßt.”4 Later John Napier professor of Astronomy at the University of St Andrews (1951–1959).

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2 The gravitational ‘lens’

Einstein discussed the gravitational bending of starlight by stars other than the Sunalready in 1912, as his notes show [23], but despite the fact that the measurementsof the Solar bending angle were such a success, it needed intense persuasion by theCzech engineer and amateur scientist Mandl, to get Einstein to publish the relevantresults, which finally happened in 1936 [24].

All the physics about gravitational light bending is in the law describing the deflec-tion angle for a light ray passing a massive body of mass M at an impact parameter ξ ,namely

α(ξ) = 2RS

ξ, (1)

where RS denotes Schwarzschild’s gravitational radius, given by

RS = 2G M

c2 , (2)

where c is the vacuum speed of light.5 Everything else is just—geometry. For thebending of light received from a background source star due to the gravity of an inter-vening foreground star, one finds a unique characteristic scale, the angular Einsteinradius

θE =√

2RS

(D−1

L − D−1S

), (3)

which depends on the mass M of the foreground ‘lens’ star, and the distances DL andDS of the lens and source star, respectively, from the observer.

A massive object bending light is commonly referred to as a ‘gravitational lens’,but this is actually a misnomer. While for a lens, the deflection increases with distancefrom its centre, gravitational bending gets weaker, similar to what happens if lightpasses through the foot of a wine glass (see Fig. 1) [25,26]. Sir Oliver Joseph Lodge[27] remarked already in 1919 that it would be “impermissible to say that the solargravitational field acts as a lens, for it has no focal length”.

As illustrated in Fig. 2, light from an observed source star can pass on either sideof the deflecting lens star, which results in two images, one of them inside and theother outside the Einstein circle with radius θE around the lens star. While for stars, theseparation of the images is too small to resolve them with current optical telescopes,6

their distortion results in an observable transient brightening of a single blurred imagewhile the foreground star passes by, giving rise to a ‘gravitational microlensing event’.The closer the two stars get aligned, the larger the observed magnification. In fact, assource and lens star (almost) exactly line up as seen from the observer, the two imageseventually stretch out to form a thin ring around the Einstein circle.

5 To order RS/r , i.e. for weak gravitational fields, the trajectory is a hyperbola.6 But not with future interferometers.

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Fig. 1 The deflection of a bundle of parallel light rays by a convex (glass) lens and the foot of a wine glass,respectively. For the convex lens, the deflection is weaker for light rays closer to its centre, leading to a focus-ing of the light bundle. In contrast, the foot of a wine glass, similar to massive bodies, causes a strongerbending for light rays closer to the centre. Reproduced from http://www.artemis-uk.org/Microlensing_freefrom.html

Fig. 2 Left The two images I+ and I− that arise from the gravitational bending of light originating from acircular source S, located on either side of the lens star L and inside or outside, respectively, the Einsteincircle with angular radius θE around L . Right Apparent magnification of the source star, observed as thesource S passes the lens L at different impact parameters with proper motion μ. The closer the source andlens star approach each other on the sky, the larger magnification. The resulting microlensing light curves,with a characteristic time-scale tE = θE/μ, are symmetric with respect to a peak that corresponds to theclosest angular approach between lens and source star. Left panel reproduced from http://www.artemis-uk.org/Microlensing_freefrom.html

Einstein’s conclusion that “There is no great chance of observing this phenomenon”is a polite understatement of what he really thought. In his reply to the editor he wrote:“Let me also thank you for your cooperation with the little publication which MisterMandl squeezed out of me. It is of little value, but it makes the poor guy happy.”7 [23]He further pointed out that “this apparent amplification of q by the lens-like actionof the star B is a most curious effect, not so much for its becoming infinite, withx (which is the separation of the observer from the line connecting source and lens

7 In German (original): “Ich danke Ihnen noch sehr für Ihr Entgegenkommen bei der kleinen Publikation,die Herr Mandl aus mir herauspreßte. Sie ist wenig wert, aber dieser arme Kerl hat seine Freude davon.”[28].

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star) vanishing, but since with increasing distance D of the observer not only does itdecrease, but even increases proportionally to

√D.” [24] Mandl not only discussed

the potential significance of gravitational lensing with Einstein, but he also pointed theRussian-American inventor and engineer Vladimir Zworykin8 to it, who in turn askedthe Swiss astronomer Fritz Zwicky, who worked in the United States [29]. As a con-sequence, just a year after Einstein’s publication, namely in 1937, Zwicky remarkedthat gravitational lensing might well be observable if one considers whole galaxiesrather than stars as light sources and deflectors [30], for the two reasons that galaxiescan be resolved at much larger distances, and (more distant) lens galaxies can cause adeflection of the order of an arcsecond rather than less than a milli-arcsecond for starswithin the Milky Way. However, it seems that nobody has listened to him. . .

3 Towards entering the observational era

28 years passed before Einstein’s ideas were brought up again, independently andquasi-simultaneously by two scientists working on different sides of the AtlanticOcean, who in 1964 arrived at similar conclusions. Sjur Refsdal [31] from Oslo,Norway, pointed out that “Due to progress in experimental technique we find, con-trary to Einstein, that the effect may be of practical interest”. Sidney Liebes [32] fromPrinceton, New Jersey, United States, considered a lot of different applications, andeven the detection of extra-solar planets, rightfully concluding that: “It seems thereforethat the primary effect of planetary deflectors bound to stars other than the sun wouldbe to slightly perturb the lens action of these stars”—and this is exactly what is beingexploiting now.

Already in the 1960s, the agenda listed: (1) random lensing between Milky Waystars, (2) lensing of globular cluster stars, (3) unobservable stars as deflectors, (4) lens-ing by asteroids and planets, (5) object stars in the Andromeda Galaxy, (6) scattering ofmicrolensing spikes off gas or dust, (7) lens effects among galaxies, (8) determinationof masses of galaxies and stars, (9) and the determination of the Hubble parameter, andcosmological models [31–35]. To summarize, almost everything that has been donesince then, has been thought about. But, for most of the applications, the technologywas not available—yet. The visionary view of Refsdal and Liebes was not widelyshared, and therefore no systematic search was conducted.

It took until 1979 to see gravitational lensing turning from a subject of theoreticalstudies to observational science. Just by chance, at Jodrell Bank near Manchester, twinimages of a quasar with strikingly similar spectra were detected, the first ever gravita-tionally-lensed object spotted (see Fig. 3) [36]. Despite the fact that this discovery wasstraightforward to happen with the considerations by Einstein and Zwicky, given thatquasars were the most distant objects known, it was actually one of the very few casesnot considered by Refsdal and Liebes. In the mid-1960s however, quasars were notgenerally accepted to be distant objects, and only a few hundreds were known, but thisactually did not stop the Russian scientist Alexei Byalko in 1967 from just suggesting

8 Best known as a pioneer of television technology.

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Fig. 3 The first detection of a gravitationally-lensed object: Images of the quasar 0957+561 (left) and theircorresponding spectra (right), pointing to these referring to the same object. Reprinted by permission fromMacmillan Publishers Ltd [36]

quasars as the most promising targets to look for brightness variations induced by starsin the central parts of the Milky Way [37].

Still in 1979, Kyongae Chang and Sjur Refsdal provided an explanation for differ-ences in the flux between the two quasar images of 0957+561, namely further imagesplitting by stars near the light path [38]. In fact, this interpretation is substantially inline with the original suggestion by Byalko. This formalism of macro-images beingsplit into unresolved micro-images, only resulting in brightness variations, refers tothe original definition of gravitational microlensing, where this term is now usedsomewhat sloppily: Each of the characteristics (1) gravitational bending of light bystars, (2) further splitting of macro-images into micro-images, (3) image separationsof a few µas, and (4) observed flux variation as a result of unresolved images, hasbeen used as the defining criterion. The concept of two deflectors of different massscales not only holds for stars within a Galaxy, but in full analogy for planets orbit-ing stars. Thereby, unaware of it at that time, Chang and Refsdal have provided thefoundation to the theory of gravitational lensing by planets in orbit around their hoststar.

4 Gravitational microlensing surveys in the quest for missing matter

Findings tabled by Vera Rubin [39,40] in 1975 revealed that the rotation curves ofspiral galaxies tend to become flat when moving outwards from the centre, incompat-ible with the mass associated with observed stars. The problem of missing (‘dark’)matter was however brought up already in 1933, by Fritz Zwicky [41], following hisinvestigation of the Coma cluster of galaxies. Another of his great suggestions had notbeen taken seriously.

Several interpretations for the missing dark matter (or at least part of it) have beensuggested: Unseen baryonic matter might exist in the form of Massive Compact Halo

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Objects (MACHOs) within galaxies, Weakly-Interacting Massive Particles (WIMPs)might constitute a non-baryonic dark matter candidate, or one might consider revis-ing the law of gravitation.9 Given that there appear to be different amounts of mattermissing on different scales, it might well be the case that the dark matter problem doesnot have a single simple solution. In particular, baryonic dark matter cannot accountfor all of the missing mass.

In 1981, Maria Petrou [43] proposed in her PhD thesis at the University of Cam-bridge to use gravitational microlensing as a probe of a potential brown-dwarf haloof the Milky Way, and quantified Einstein’s “not-a-great” chance to be about one in amillion. Unfortunately, she was then discouraged by her supervisor to proceed alongthat line of research.

Consequently, her contribution is not well-known, in sharp contrast to the ratherfamous paper written by Bohdan Paczynski [44] in 1986, 5 years later, in which heindependently arrives at essentially the same conclusions. Again, a period of quies-cence has been followed by more than one person coming up with the same idea atapproximately the same time.

In the 1980s, for the first time, the required technology for carrying out micro-lensing surveys is within sight, and as a consequence of Paczynski’s paper, the firstcampaigns to observe the transient brightening of stars due to the gravitational bend-ing of their light by an intervening star started operating. The first such gravitationalmicrolensing surveys, namely EROS (Experience de la Recherche d’Objets Sombres)and MACHO, focused on target stars in the Magellanic Clouds for probing the MilkyWay halo [45,46]. Following a further suggestion by Bohdan Paczynski [47,48], inorder to distinguish the absence of MACHOs from a failure of the applied technique,observations on targets in the Milky Way bulge, which would probe known compactdeflectors in the form of disk and bulge stars, by the OGLE (Optical GravitationalLensing Experiment) survey started shortly thereafter [49].

Looking back to 1964, the potential to detect unobservable stars or other compactmassive objects by means of them causing an observable brightening of backgroundstars had already mentioned by Sidney Liebes [32]. The massive data-processing ven-ture required was however impossible still with the computer technology of the 1970s,not even talking about 1936, where there were not any computers at all. Not possiblewithout more than half a century of unforeseeable advance in technology after thepublication of Einstein’s paper on the “lens-like action of a star by the deviation oflight in the gravitational field” [24], the detection of microlensing events turned intoa reality in 1993 with MACHO LMC-1 (see Fig. 4) [50].

9 Kim Griest had argued for massive astrophysical dark matter candidates such as brown dwarfs,Jupiters, or black hole remnants of an early generation of stars to “be collectively called massive astrophys-ical compact halo objects (MACHOs)”, given that the name ‘WIMP’ for the major alternative was alreadywell-established [42]. However, following the title of his respective paper which does not contain the word‘astrophysical’, the acronym MACHO is now commonly understood to stand for MAssive Compact HaloObject.

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Fig. 4 Data and model lightcurve of MACHO LMC-1,showing the event magnificationobtained simultaneously in twospectral passbands. This was thefirst reported microlensingevent, with an event time-scalet = 2tE = 33.9 days. The lowestpanel illustrates theachromaticity of the observedsignal. Reprinted by permissionfrom Macmillan Publishers Ltd[50]

5 Planets from Einstein’s blip—live to your home

5.1 Detecting unseen planets around unseen stars

However, when looking at the acquired data of MACHO LMC-1 carefully, it becamestriking that the most discrepant points are clustered around the peak. For both of thecolour filters, the two points closest to the peak show the largest discrepancies, andthere is even a third one that looks suspicious. If one replaces the single lens star witha binary system, one obtains a far more convincing fit to the observed data [51,52],and this is not just pulling three additional parameters from the hat in order to explainthree data points. Since the measurements are independently registered on two differ-ent CCDs behind a beam splitter, and explicitly testing for correlations gave a negativeresult, it is actually six discrepant data points. Unfortunately, this event also providesa prominent case for model ambiguities and parameter degeneracies in gravitationalmicrolensing events, by being compatible with almost any mass ratio between thetwo components of the lens binary, including the possibility of the secondary being aplanet [53]. So, somewhat unfortunately, this event did not turn into the first reporteddetection of a planet orbiting a star other than the Sun (this was 1993!!).

In the meantime, Bohdan Paczynski and his then-student Shude Mao [54], discov-ered that the detectability of planets orbiting their host stars in gravitationalmicrolensing is aided by a resonance effect if the planet separation coincides with theangular Einstein radius of its host star. Gould and Loeb [55] derived some quantitative

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Fig. 5 Probability density and cumulative distribution function (bold) for the mass of the lens star ofongoing microlensing events, which correspond to adopted kinematic models of the Milky Way involvinga tilted barred bulge and a double-exponential disk, and mass functions of bulge and disk stars [56]. Forsimplification, a typical direction and source star distance has been assumed. Reproduced from M. Dominiket al. [57]

estimates and recovered the formalism of Chang and Refsdal [38] in this context. Atthe end, a concept for the detection of planets along the thoughts of Sidney Liebesresulted.

If one looks towards the Galactic bulge, source stars are at a typical distance of8.5 kpc, whereas lens stars—-2/3 in the bulge and 1/3 in the disk—are at about 6.5 kpc[47,48,56]. With the mass functions of bulge and disk stars, one finds microlensingevents preferentially being caused by M-dwarf stars of around 0.3 Solar masses, dueto their large abundance as compared to Solar-mass stars (see Fig. 5). This means thatthe angular Einstein radius roughly becomes

θE ∼ 300 µas

(M

0.3M�

)1/2

, (4)

which corresponds to a physical radius at the distance DL of the lens star

rE = DLθE ∼ 2 AU

(M

0.3M�

)1/2

. (5)

Given that the kinematics of the Milky Way result in a typical proper motion μ betweenlens and source star of about 15µ as per day, the event time-scale tE ≡ θE/μ becomes

tE ∼ 20 d

(M

0.3M�

)1/2

. (6)

If a planet were an isolated object of mass Mp, the planetary deviation would last

tp = (Mp/M)1/2 tE, (7)

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which evaluates to about a day for a Jupiter-mass and about 1.5 h for an Earth-massplanet. However, the tidal gravitational field of the parent star at the position of theplanet aids its detection, and in particular increases the signal duration by a fair factor.Moreover, due to the finite radius R� = DSθ� of the observed star, the signal durationcannot fall below

2t� = 2R�

DSμ∼ 2h

(R�

R�

). (8)

As long as the observed source stars can be approximated as point-like, the signalamplitude can reach any level regardless of the planet mass, while just the signal dura-tion and the probability for a signal of given amplitude to occur decreases towardssmaller masses. Only if Mp/M � 4(θ�/θE)2 = 4(t�/tE)2, the finite angular size of thesource star causes a reduced signal amplitude along with an increased signal duration.

To summarize, microlensing events typically last about a month, the technique ismost sensitive to detecting planets at about 2 AU from their host star with M ∼ 0.3M�,planetary signals last between days and hours, and the hard limit to the mass of detect-able planets arises from the finite size of the observed source stars.

5.2 Implementing an efficient three-step strategy

In 1994, the Early-Warning System implemented by OGLE [58] for the first timeoffered the opportunity to detect microlensing events while still in progress; and real-time photometric data were provided to the scientific community. This allowed toadopt a three-step strategy of survey, follow-up, and anomaly monitoring [59], whichmakes efficient use of facilities. The first aim is to detect a substantial number ofmicrolensing events by means of a survey of hundreds of millions of stars with at leastdaily sampling. The most promising ongoing microlensing events are then monitoredabout hourly with precise photometry using telescope networks over which the Sunnever rises and which will always keep you in the dark. Whenever these data indicate adeviation from an ordinary microlensing light curve that might be due to the presenceof a planet orbiting the lens star, basically any potential site on the globe (or in space)can be asked for almost continuous observations of the respective target.

The deployment of the Probing Lensing Anomalies NETwork (PLANET) of 1 m-class telescopes in 1995 was the first systematic effort into monitoring microlensingevents to be able to characterize planetary signals [60]. An intended sampling every1.5–2.5 h with 1–2% accuracy was considered to be well-suited to characterize signalscaused by Jupiter-mass planets, whereas Earth-mass planets were thought to be outof reach [61]. From 42 well-covered events between 1995 and 1999, and the absenceof any planetary signals, PLANET data revealed that less than a third of the lens starsthat caused these events harbour Jupiter-like planets in orbits between 1.5 and 4 AU[62,63]. Given that we now know that the abundance is much smaller, this was a ratherweak limit, but it was the first one for low-mass stars ever published.

While in the earlier years of microlensing follow-up, simply every reasonable eventwas monitored, the ever increasing number of events detected by the surveys triggered

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the question of which events are the most promising for detecting planetary signals.Kim Griest and Neda Safizadeh [64] pointed out that the quality of angular alignmenthas a crucial effect on the detection probability, while Keith Horne [65] developed apriority algorithm based on a worth factor that depends on the current event magnifi-cation and the event magnitude. The fully-automated prioritisation of ongoing eventsformed a prerequisite for the scheduling of microlensing observations on the RoboNetnetwork of UK-built 2m robotic telescopes that was put into place from 2004 onwards[66].

The excitement about the first clear detection of a planet by microlensing, withabout 1.5 Jupiter masses, in event OGLE-2003-BLG-235/MOA-2003-BLG-53, wasmixed with some demoralization for the follow-up campaigns, because it was basedon data that solely came from the survey campaigns [67], while the respective eventwas not considered a promising target for follow-up monitoring.

5.3 Planet detections that changed the view about our home

It was however a good decision not to give up with the follow-up monitoring, becausethe real excitement came on the 10th of August 2005. As part of the PLANET observa-tions at the Danish 1.54 m telescope at ESO LaSilla, two deviating points were detected.Due to a rather low degree of belief in an ongoing planetary deviation amongst thePLANET team (and despite minority opinions more in favour of something impor-tant happening), the opportunity to observe this target with the Canopus 1.0 m nearHobart was missed, but some further data at Perth Observatory were acquired (seeFig. 6). Fortunately, these were sufficient to nail down the planetary nature of thedeviation. It was quite a surprise that the planet, with the snappy name OGLE-2005-BLG-390Lb, turned out to be just about 5 times as massive as the Earth (with afactor 2 uncertainty), and thereby—despite its hostile conditions for life—was themost Earth-like extra-solar planet known at that time, and a first observational hintthat Earth-like planets are common in the Universe [68,69]. Not undeservedly, thisdiscovery made ESO’s top news story in 2006 [70]. This major result arose from a1.5 m (i.e. small) telescope, which is not widely expected to yield a forefront scientificresult.

A year later came another surprise. A quite complex light curve, constituting eventOGLE-2006-BLG-109, with lots of features, pointing not only to one, but two planets(see Fig. 7). Orbiting a star half as massive as the Sun, those planets have comparablemasses and surface temperatures to Jupiter and Saturn, but half-sized orbits, and halfthe orbital periods [71,72].

With the small chance of detecting gas-giant planets around low-mass stars, onefinds that those should not come alone, but rather with family and friends, so thatplanetary systems should be considered the rule rather than the exception. Given thaton one of the very few occasions where a look-alike of the Solar system with respectto outer gas giants could have been detected it was actually detected, one should startliving with the idea that the Solar system is far from unique in the Universe; if one notalready believed this before.

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Fig. 6 Model light curve and data acquired with six different telescopes (colour-coded) for microlensingevent OGLE-2005-BLG-390, which shows a 15–20% deviation over about a day caused by a planet roughlyfive times as massive as the Earth (with an uncertainty factor of 2). An Earth-mass planet in the same spotwould have been detectable from a 3% signal lasting about 12 h, provided that dense monitoring had startedwith the first suspicion of an ongoing anomaly arising from hourly monitoring and real-time photometry.Artist’s impression of planet OGLE-2005-BLG-390Lb ©ESO

Fig. 7 Model light curve along with data collected at various sites for the microlensing event OGLE-2006-BLG-109, revealing two gas-giant planets by means of five features, where feature #4 is the only one relatedto the inner, more massive, planet OGLE-2006-BLG-109Lb. Insets A and B show the caustic (at the timeof features #1, #3, and #5) along with source trajectory, where the circle indicates the angular source size.The source trajectory is curved due to annual parallax (i.e. the revolution of the Earth around the Sun), andthe shape and orientation of the caustic alters due to the orbital motion of the outer, less massive, planetOGLE-2006-BLG-109Lc. The portion of the caustic affected by OGLE-2006-BLG-109Lb is shown in red.From Gaudi et al. [71]. Reprinted with permission from AAAS

5.4 From the state of the art to future challenges

With the discovery of OGLE-2005-BLG-390Lb, we were not for at all from detectingan Earth-mass planet. Had such been in the same spot, it would have led to a 3%

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Fig. 8 The ‘Catch-a-planet’ microlensing live display, powered by ARTEMiS (Automated Robotic Terres-trial Exoplanet Microlensing Search) in the foyer of the Physics and Astronomy building of the Universityof St Andrews, providing real-time information about the ongoing events and explaining the applied tech-nique and observing campaigns. It formed part of an exhibit “Is there anybody out there? Looking for newworlds”, which has been shown at the 2008 Royal Society Summer Science Exhibition [79], Techfest 2009at the IIT Bombay, and the 2009 Edinburgh International Science Festival. Photograph by Martin Dominik©2008

signal lasting about 12 h (see Fig. 6). A dense anomaly monitoring after a first triggercould have revealed it, provided that suitable telescopes are available. However, thesuccessful realisation of such a goal in a three-step strategy of survey, follow-up, andanomaly monitoring requires 1.5-hourly follow-up monitoring on a sufficient numberof targets, the real-time interchange of information, modelling, and identification ofongoing anomalies, as well as an immediate activation of anomaly monitoring within5–10 min [73]. The mass of the Earth is not the hard limit even for ground-basedobservations, but in principle one could get down to the mass of the Moon [74,75],albeit that the probability for such a detection with current observational capabilitiesis small.

In order to realize ambitions towards the detection of planets of Earth mass andbelow in a global effort, ARTEMiS (Automated Robotic Terrestrial ExoplanetMicrolensing Search) has started with the operation of a first version of an expertsystem that provides each telescope site with the most promising target to be observedat a given time in order to optimally fulfill the science goals [76,77]. Based on theprinciples of innovation, cooperation, and communication, it not only interacts bothwith electronic systems and human observers, but moreover allows for getting in touchwith the public on current research. By showing current data and model light curvesjust minutes after the data have been acquired, a phenomenon with no great chanceto be observed has been turned into a public live event at the forefront of science.While the microlensing hunt for planets is live on the web [78], it also featured as partof a successful exoplanet exhibit that toured several major science exhibitions (seeFig. 8).

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While there are still individual planets with unprecedented exciting properties wait-ing to be discovered, gravitational microlensing, as well as any other planet detectiontechnique, has to evolve into a means for studying the planet population statistics. Inorder to be able to draw meaningful conclusions, it is necessary to know what couldhave been detected and what has been missed, quantified by the detection efficiency ofthe observing campaign, which projects the underlying population onto the observeddistribution [57,80]. The need to know the statistics of target selection and anomalydetection calls for strictly-deterministic procedures, which allow to carry out statisti-cally representative simulations. Such procedures are adopted by the automated targetselection of RoboNet-II [81] or that being communicated by ARTEMiS, and the auto-mated anomaly detection provided by SIGNALMEN [73], one of the ARTEMiS coretechnologies. In contrast, human decisions, by their unpredictability and irreproduc-ibility, are the enemy of proper planet population statistics, and in fact, any planetdetection being the result of such needs to be discarded from a proper statistical anal-ysis. The MiNDSTEp (Microlensing Network for the Detection of Small TerrestrialExoplanets) consortium, a successor project of PLANET, has successfully realized apilot study in 2008 using the Danish 1.5 m telescope at ESOs site in La Silla (Chile)with a fully-deterministic microlensing observing strategy [82].

As Einstein pointed out in 1936, the ‘most curious’ phenomenon of gravitationalmicrolensing prefers larger distances. This preference however has to compete againstincreasing crowding and decreasing brightness. Nevertheless, modern image-subtrac-tion techniques allow even the real-time detection of microlensing events on stars inthe Andromeda Galaxy (M31) [83], and detecting planets there is within the reach ofcurrent or upcoming technology [84,85]. In fact, one of the observed signals mightinvolve a signature caused by a planet orbiting a star in M31 [86,87].

6 Gravitational light bending and the evolution of science

Let me conclude by pointing out that the story of the gravitational bending of lightillustrates some general characteristics of evolutionary processes in science: Sciencedoes not evolve on straight paths, its development critically depends on the environ-ment at a given time, and its progress is—by its nature—unpredictable. Scientificresearch most importantly is about people, and their creative potential. Major advanceis frequently the result of casting doubt on long-standing traditions, while on the otherhand one should be less sceptical about upcoming new ideas, even if they look ‘weird’,‘audacious’, or ‘just crazy’ at first sight.

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