MOA-2010-BLG-353Lb A Possible Saturn Revealed
N. J. Rattenbury, D. P. Bennett, T. Sumi, N. Koshimoto, I. A. Bond, A. Udalski, F. Abe, A. Bhattacharya, M. Freeman, A.Fukui, Y. Itow, M. C. A. Li, C. H. Ling, K. Masuda, Y. Matsubara, Y. Muraki, K. Ohnishi, To. Saito, A. Sharan, D. J. Sullivan, D. Suzuki, P. J. Tristram, S. Kozlowski, P. Mroz, P. Pietrukowicz, G. Pietrzynski, R. Poleski, D. Skowron, J. Skowron, I. Soszynski, M. K. Szymanski, K. Ulaczyk, L. Wyrzykowski
MMon. Not. R. Astron. Soc. , 000–000 (2015) Printed 13 August 2018 (MN L A TEX style file v2.2)
MOA-2010-BLG-353Lb: A Possible Saturn Revealed
N. J. Rattenbury ,A(cid:63) , D. P. Bennett ,A , T. Sumi ,A , N. Koshimoto ,A ,I. A. Bond ,A , A. Udalski ,B , F. Abe ,A , A. Bhattacharya ,A , M. Freeman ,A ,A. Fukui ,A , Y. Itow ,A , M. C. A. Li ,A , C. H. Ling ,A , K. Masuda ,A ,Y. Matsubara ,A , Y. Muraki ,A , K. Ohnishi ,A , To. Saito ,A , A. Sharan ,A ,D. J. Sullivan ,A , D. Suzuki ,A , P. J. Tristram ,A , S. Koz(cid:32)lowski ,B ,P. Mr´oz ,B , P. Pietrukowicz ,B , G. Pietrzy´nski , ,B , R. Poleski , ,B ,D. Skowron ,B J. Skowron ,B , I. Soszy´nski ,B , M. K. Szyma´nski ,B ,K. Ulaczyk ,B , (cid:32)L. Wyrzykowski ,B Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA Department of Earth and Space Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka,Osaka 560-0043, Japan Institute of Natural and Mathematical Sciences, Massey University, Private Bag 102-904, North Shore Mail Centre,Auckland, New Zealand Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa, Poland Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya, 464-8601, Japan School of Physics, The University of New South Wales, Sydney NSW 2052, Australia Okayama Astrophysical Observatory, National Astronomical Observatory, 3037-5 Honjo, Kamogata, Asakuchi, Okayama719-0232, Japan Department of Physics, Konan University, Nishiokamoto 8-9-1, Kobe 658-8501, Japan Nagano National College of Technology, Nagano 381-8550, Japan Tokyo Metropolitan College of Industrial Technology, Tokyo 116-8523, Japan School of Chemical and Physical Sciences, Victoria University, Wellington, New Zealand Mt. John Observatory, P.O. Box 56, Lake Tekapo 8770, New Zealand Universidad de Concepci´on, Departamento de Astronomia, Casilla 160-C, Concepci´on, Chile Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, OH 43210,USA A Microlensing Observations in Astrophysics (MOA) Collaboration B Optical Gravitational Lensing Experiment (OGLE) Group
Accepted ........ Received .......; in original form ......
ABSTRACT
We report the discovery of a possible planet in microlensing event MOA-2010-BLG-353. This event was only recognised as having a planetary signal after the microlensingevent had finished, and following a systematic analysis of all archival data for binarylens microlensing events collected to date. Data for event MOA-2010-BLG-353 wereonly recorded by the high cadence observations of the OGLE and MOA survey groups.If we make the assumptions that the probability of the lens star hosting a planet ofthe measured mass ratio is independent of the lens star mass or distance, and thatthe source star is in the Galactic bulge, a probability density analysis indicates theplanetary system comprises a 0 . +1 . − . M Saturn mass planet orbiting a 0 . +0 . − . M (cid:12) red dwarf star, 6 . +1 . − . kpc away. The projected separation of the planet from thehost star is 1 . +0 . − . AU. Under the additional assumption that the source is on thefar side of the Galactic bulge, the probability density analysis favours a lens systemcomprising a slightly lighter planet.
Key words: stars: individual (MOA-2010-BLG-353); planetary systems: detection (cid:63) e-mail: [email protected] (cid:13) a r X i v : . [ a s t r o - ph . E P ] O c t Rattenbury, N. J. et al.
As a planet detection technique, microlensing is unique inthat the peak sensitivity of microlensing to planets falls be-yond the host star’s snow line. The snow line is defined asthe radius in the midplane of the protoplanetary disk wherethe temperature is below the sublimation temperature forwater. Crossing the snow line, the density of solid materialincreases by a factor of a few (Gaudi 2012). Understandingthe population of planets that form at or near the snow lineis important for the core-accretion theory of planet forma-tion (Ida and Lin 2005). Microlensing searches have discov-ered cold planets orbiting their hosts stars (see e.g. Sumiet al. (2010), Gaudi (2012)) and has also provided evidencefor a large population of free-floating planets – planets with-out a host star or at least separated by a very large distancefrom a potential host (Sumi et al. 2011).Three survey groups now routinely monitor dense stel-lar fields, looking for microlensing events. These groups andtheir operations are briefly described below.The Microlensing Observations in Astrophysics collab-oration (MOA, Bond et al. (2001), Sumi et al. (2003)) usesthe 1.8 metre MOA-II telescope at the Mount John Uni-versity Observatory, Tekapo, New Zealand. The MOA-cam3camera (Sako et al. 2008) mounted on the MOA-II telescopehas a 2.2 square degree field of view and is able to observe50 square degrees of the Galactic bulge every hour.The Optical Gravitational Lensing Experiment (OGLE,Udalski et al. (2015)) observe crowded stellar fields using the1.3 metre Warsaw telescope at Las Campanas, Chile. Thefourth phase of the OGLE project – OGLE-IV – is currentlyin operation and monitors over 3000 degrees of the sky. Boththe MOA and OGLE survey operations include high cadenceobservations ( <
60 minutes) for a subset of their fields. Suchhigh cadence observations led to the discovery of the popu-lation of free-floating planets mentioned above and reportedby Sumi et al. (2011).The OGLE survey detects ∼ ∼
600 eventsper year. Most of the MOA detections have an OGLE coun-terpart and the longitudinal separation of Las Campanasand Tekapo means that these events can be well-sampled intime by these two survey groups. Both the MOA and OGLEgroups issue real time alerts as new events are discovered.The Korean Microlensing Network (KMTNet, Parket al. (2012)) of three wide field-of-view telescopes located inSouth Africa, Australia and Chile has also recently startedsurvey operations.During each year’s microlensing “season” – during thesouthern hemisphere winter – microlensing event data aremonitored for evidence of a deviation from that expected as-suming a single mass is acting as the gravitational lens. Suchdeviations are found in real time by human observers, andby the expert system ARTEMiS (Dominik et al. 2008, 2010)and the community alerted to the presence of an anomalythat may be owing to a second mass – possibly a planet – inthe lens system. Preliminary models are circulated, includ-ing those generated automatically by the RTModel system(Bozza 2010; Bozza et al. 2012) . In response to anomaly alerts, one or more follow-up collaborations proceed to in-vest their observational resources to monitor events of par-ticular interest. The follow-up groups, which include µ FUN(Gould et al. 2010), PLANET (Albrow et al. 1998), RoboNet(Tsapras et al. 2009) and MiNDSTEp (Dominik et al. 2010)monitor anomalous events as intensely as deemed necessary.These data, combined with the survey data, are used toconstrain models of the lens system which could be foundto include one or more planets. To date, 28 microlensingplanets have been found by microlensing, and the reader isdirected to the NASA Exoplanet Archive for details.Follow-up data were obtained for most microlensingevents which showed evidence of a planet or planets. Incontrast, some planets have been discovered using surveydata alone, e.g. events MOA-2007-BLG-197 (Bennett et al.2008) and MOA-2008-BLG-379 (Suzuki et al. 2014). Whilefollow-up data were collected for event MOA-2011-BLG-293, the survey data alone were sufficient to characterisethe planetary system (Yee et al. 2012). The planet foundin event MOA-2011-BLG-322 was found using survey datafrom the MOA and OGLE groups and the Wise Observa-tory (Shvartzvald et al. 2014). This present work reportsanother planet found using microlensing survey data alone.That the data contained a planet anomaly was only discov-ered after the event, once a systematic search over the binarylens parameter space was made for all archival binary lensmicrolensing data light curves.In this paper, we present the analysis of microlensingevent MOA-2010-BLG-353. In Sections 2 and 3 we describethe data and their treatment, respectively. The results ofmodelling the observed light curve data with a binary lensmodel are presented in Section 4. An analysis of the back-ground source star is given in Section 5. The planet param-eters estimated from a probability density analysis is pre-sented in Section 6 and Section 7 comprises our discussionand conclusion. Microlensing event MOA-2010-BLG-353 was discovered at(RA, Dec) = (18 h m . s
94, -27 ◦ m . s
64) and an alert wasissued by the MOA collaboration on July 28th, 2010. TheMOA collaboration observed the field in which MOA-2010-BLG-353 was discovered with a median cadence of 20 min-utes over the course of the event. The MOA observationswere made in the custom MOA-red filter, which has a pass-band corresponding to the sum of the standard I- and V-filters.During the period between May 2009 and May 2011, theOGLE survey team were not issuing alerts to the communityas it was upgrading both their camera and Early WarningSystem (EWS) software (Udalski 2003). However, the OGLEteam did record I-band data for this event, with a mediancadence of 60 minutes, using the OGLE-IV camera (Udalskiet al. 2015). exoplanetarchive.ipac.caltech.edu/index.htmlc (cid:13) , 000–000 OA-2010-BLG-353Lb: A Possible Saturn Revealed The images obtained by the MOA telescope were reducedusing the difference imaging pipeline of Bond et al. (2001).When analysing a crowded stellar field using difference imag-ing, a neighbouring star, of a different colour to the targetstar, can affect the photometry of the target star through thedifferential refraction effect of the atmosphere. The degreeto which the source star’s photometry is affected dependson the amplitude and direction of the differential refraction.In addition to discarding extreme outliers, the MOA datawere corrected for differential refraction. The final MOAlight curve comprised 9130 data points.The OGLE data set for this event comprises 3248 I-bandobservations, generated from the OGLE difference imaginganalysis pipeline (Udalski 2003). It was not necessary toapply a correction for differential refraction to the OGLEdata.
An initial best-fitting binary lens model to the observationaldata was found from a large-scale grid search over the basicbinary lens parameter space. Initial values were found forthe mass ratio, q = M p /M L , where M p and M L are planetand host lens masses respectively, the binary lens separation, s , in units of the Einstein ring radius, the source star trackorientation angle α , the minimum impact parameter u , theEinstein radius crossing time t E , the epoch t correspondingto the source star being positioned at u and the relativeangular source star radius ρ = θ (cid:63) /θ E , where θ (cid:63) and θ E arethe angular sizes of the source star and Einstein ring radiirespectively.Starting from the initial best-fitting binary lens solutionfound from the grid search, we refined the solution using avariant of the image-centred ray shooting method of Bennett(2010).We used a linear limb-darkening profile for the sourcestar and chose limb-darkening coefficients based on an es-timate of the source star’s (V-I) colour. This (V-I) colourestimate is model-dependent. For this reason, we iteratedthe steps of finding the best-fitting binary lens model us-ing our MCMC algorithm, deriving the corresponding (V-I)colour for the source and therefrom the source star limb-darkening coefficients, until the values of the limb-darkeningcoefficients ceased to change. The details of how we esti-mated the source colour are presented in Section 5, alongwith the limb-darkening coefficients used in the final modelfor this event.The motion of the Earth in its orbit around the Suncan impart a parallax signal for some microlensing events(Gould 1992; Alcock et al. 1995). This additional effect isgenerally a desirable one – allowing a more accurate esti-mate of the lens star mass and distance, and thereby a moreaccurate estimate of the absolute values of the mass and or-bital radius of planetary lens components. Parallax is morelikely to be seen in microlensing events with large values of t E . This event has t E (cid:39)
11 days, and is therefore a priori unlikely to to show any parallax signal. Despite this, we at-tempted to include microlensing parallax in our models. Notunsurprisingly, we were unable to detect any parallax signalfor this event.
Table 1.
Best-fitting binary lens model parameters for plane-tary microlensing event MOA-2010-BLG-353. Each quoted erroris the average of the upper and lower errors determined from thecorresponding MCMC parameter state distribution.Parameter Value t . ± .
06 HJD - 2450000 t E . ± . u − . ± . R E q (1 . ± . × − s . ± . R E α . ± .
02 rad ρ (2 . ± . × − The best-fitting binary lens model has the following pa-rameters for the binary lens mass ratio and binary lens sep-aration: q = (1 . ± . × − and s = (1 . ± . t E = (11 . ± .
7) days.Table 1 lists these and the other parameters in the best-fitting model. The light curve data during the microlensingevent MOA-2010-BLG-353, along with the best-fitting lightcurve, is shown in Figures 1 and 2. The critical and causticcurves and source star track are shown in Figure 3.The best-fitting planetary microlensing model is sys-tematically above the OGLE data points at t (cid:39) t (cid:39) t (cid:39) Characterising the source star in a microlensing event leadsto an estimate of the angular size of the Einstein ring inthe lens plane, θ E . This in turn allows tighter constraintsto be placed on the binary lens masses and lens separation,see e.g. Suzuki et al. (2014). The value of ρ = θ (cid:63) /θ E is pro-vided by the best-fitting model to the observed light curve,and an estimate of θ (cid:63) may be made from known relationsbetween optical colour and stellar radius. Determining thesource star’s optical colour therefore leads to our desiredestimate of θ E .The first step in determining the source star’s opticalcolour was to cross-match MOA field stars in the 2 ar-cmin region surrounding the co-ordinates of event MOA-2010-BLG-353, with stars in the calibrated OGLE-III cat-alogue (Udalski et al. 2008). This led to a colour-colourrelationship between the instrumental MOA and OGLE- c (cid:13)000
7) days.Table 1 lists these and the other parameters in the best-fitting model. The light curve data during the microlensingevent MOA-2010-BLG-353, along with the best-fitting lightcurve, is shown in Figures 1 and 2. The critical and causticcurves and source star track are shown in Figure 3.The best-fitting planetary microlensing model is sys-tematically above the OGLE data points at t (cid:39) t (cid:39) t (cid:39) Characterising the source star in a microlensing event leadsto an estimate of the angular size of the Einstein ring inthe lens plane, θ E . This in turn allows tighter constraintsto be placed on the binary lens masses and lens separation,see e.g. Suzuki et al. (2014). The value of ρ = θ (cid:63) /θ E is pro-vided by the best-fitting model to the observed light curve,and an estimate of θ (cid:63) may be made from known relationsbetween optical colour and stellar radius. Determining thesource star’s optical colour therefore leads to our desiredestimate of θ E .The first step in determining the source star’s opticalcolour was to cross-match MOA field stars in the 2 ar-cmin region surrounding the co-ordinates of event MOA-2010-BLG-353, with stars in the calibrated OGLE-III cat-alogue (Udalski et al. 2008). This led to a colour-colourrelationship between the instrumental MOA and OGLE- c (cid:13)000 , 000–000 Rattenbury, N. J. et al. A m p li f i c a t i on Figure 1.
Observed data from the MOA (gray) and OGLE(red) microlensing survey groups for event MOA-2010-BLG-353.Binned MOA data points are shown as black points. The best-fitting binary lens model is also shown (black line). The param-eters for this model are given in Table 1. The epoch when theMOA collaboration issued an alert for this event is indicated witha black arrow. A m p li f i c a t i on Figure 2.
This is a close-up view of the light curve for MOA-2010-BLG-353 as shown in Figure 1, highlighting the planetaryperturbation. The single lens, finite source star model is shownwith a dashed blue line.
III colours, ( R MOA − I OGLE3 ) and the calibrated OGLE-IIIcolour ( V − I ) OGLE3 . We similarly cross-matched MOA fieldstars with OGLE-IV field stars and found the relationshipbetween ( R MOA − I OGLE4 ) and ( V − I ) OGLE4 . Using the in-strumental source colour, ( R MOA − I OGLE4 ) S , obtained fromthe best-fitting model, we used this last relation to esti-mate the instrumental source colour in the OGLE-IV pho-tometric scale, ( V − I ) OGLE4 , S . Cross-matching OGLE-IIIand OGLE-IV field stars, we fitted a straight line of theform ( I OGLE3 − I OGLE4 ) = a ( V − I ) OGLE4 + b . This rela-tion, allows us to obtain ( R MOA − I OGLE3 ) S and with ourfirst colour-colour relationship, find an estimate of the source E ) y ( R E ) Figure 3.
The critical (blue) and caustic (red) curves correspond-ing to the best-fitting model for planetary microlensing eventMOA-2010-BLG-353. The source star track is also shown (black),and the direction of the source star is indicated with an arrow. colour ( V − I ) OGLE3 , S and magnitude I OGLE3 , S3 : I S = 17 . ± . V − I ) S = 2 . ± . I RCG = 15 . ± . V − I ) RCG = 1 . ± . I RCG , =14 . ± .
04 with the colour of the red clump being centredat ( V − I ) RCG , = 1 .
06 with dispersion 0 . A I , E ( V − I )) = (1 . , . ± (0 . , . I, V − I ) S , =(16 . , . ± (0 . , . As the OGLE-III colours are calibrated, we will delete theOGLE-III subscript. c (cid:13) , 000–000
OA-2010-BLG-353Lb: A Possible Saturn Revealed OGLE 3 I OG L E Figure 4.
Colour magnitude diagram of the OGLE-III field starsfor event MOA-2010-BLG-353. The centre of the red clump isindicated (asterisk) as is the location of the source star. is consistent with a K5 subgiant in the Galactic bulge. FromTable 5 of (Bessell et al. 1998), we estimate the surfacetemperature of a giant star with ( V − I ) = 1 .
98 to be T eff (cid:39) I and R MOA bandsof ( c I , c R MOA ) = (0 . , . c R MOA is computedas the average of the limb-darkening coefficients in the R and I bands. The limb-darkening coefficients differ only veryslightly if we assume a subgiant source star with a cooler T eff = 3500 K.With the intrinsic source colour in hand, we can use therelationship between optical colour and brightness-radius inKervella and Fouqu´e (2008) to estimate the source star’sangular radius: θ (cid:63) = 3 . ± . µ as. Combined with themodel value of the source star angular radius relative to theangular Einstein ring radius, ρ = θ (cid:63) /θ E = (2 . ± . × − , we derive a value of angular Einstein ring radius, θ E =0 . ± .
089 mas.
Without a measurement of microlensing parallax in eventMOA-2010-BLG-353, we have to appeal to statistical argu-ments in order to provide an estimate of the lens mass anddistance. We followed a similar analysis to that of Beaulieuet al. (2006) to generate probability densities for the lensmass and lens and source distances.The modelled t E and the calculated Einstein ring ra-dius θ E are related to the lens and source distances from theobserver – D L and D S respectively – and the lens mass M L ,via the relation θ = κM L (1 /D L − /D S ) where κ = 8 . /M (cid:12) . We find the lens system to comprise a star withmass 0 . +0 . − . M (cid:12) with a planet of mass 0 . +1 . − . M Saturn .The projected separation between the host star and the planet is 1 . +0 . − . AU. The distance to the lens system is6 . +1 . − . kpc.The probability density analysis was re-run, this timeleaving out the constraints imposed by our estimate of θ E .The results are essentially the same as those found above.The planet has a mass of 1 . +1 . − . M Saturn and orbits a0 . +0 . − . M (cid:12) star 6 . +1 . − . kpc distant. The projected or-bital radius is now 1 . +0 . − . AU. The planet parameters es-timated from our probability density analyses are essentiallyindependent of our characterisation of the source star.It is important to note that the lens system parametersfound from the Bayesean probability density analysis aresubject to some important assumptions. The first assump-tion is that the probability of the planet system comprisinga planet with the measured mass ratio is independent ofthe mass of the host star and the host star’s distance. Thismay not be the case in reality. We also assume that theorientation of the planetary system is random, and that thedistribution of planetary radii is uniform. This affects our in-terpretation of the planet-star separation. If planets at largeorbit radii are more common than planets with smaller or-bital radii, the separation between host and planet alongthe line-of-sight would be much larger than the projectedseparation.
One peculiar aspect of event MOA-2010-BLG-353 is thecolour of the source star. The very red colour of the sourcemay, in part, be accounted for if the source star was be-hind the Galactic bulge, at distances greater than the usualassumed value of 8 kpc. For this reason, we re-ran the like-lihood analysis, this time requiring the source star to be lo-cated on the far side of the Galactic bulge. We found therange of distances for which a G/K subgiant star wouldhave a colour and magnitude consistent the observed sourcestar, within the quoted errors. In estimating the range ofdistances for the source, we included the dust extinctionprofile in the direction of event MOA-2010-BLG-353 fromthe high resolution 3D dust extinction map of Schultheiset al. (2014). We found that a K5 subgiant at distances8 .
25 kpc < D S < .
75 kpc has a colour and magnitudeconsistent with the source of MOA-2010-BLG-353. Whenwe include this constraint on D S , the lens system parame-ters returned by our probability density analysis – includingconstraints arising from our measurement of θ E – now corre-spond to a 0 . +1 . − . M Saturn planet orbiting a 0 . +0 . − . M (cid:12) star at a projected orbital radius of 1 . +0 . − . AU. The lenssystem is 7 . +0 . − . kpc distant. Microlensing event MOA-2010-BLG-353 has an anomaloussignal consistent with a planetary lens system. The best-fitting binary lens model for this event has a binary massratio of q = (1 . ± . × − and the binary lens elementsare separated by s = 1 . ± . R E . We were not able to finda binary source model which fits the data better than thebest-fitting planetary microlensing model. The variability ofthe source at the baseline is consistent with random noise. c (cid:13) , 000–000 Rattenbury, N. J. et al.
A measurement of microlensing parallax was not possi-ble for this event and so a well-constrained estimate of thebinary lens parameters was not possible.While a parallax signature was not evident in the data,the finite size of the source star could be modelled. However,the nature of the source star is uncertain. The source appearsmuch redder than the majority of field stars for this event.Given the observed source colour and magnitude, we esti-mate the source is a K subgiant star in the Galactic bulge.However, the source may be blended with a nearby red star,leading to an incorrect categorisation of the source star. Adetermination of the source star colour allowed an estima-tion of the angular radius of the angular Einstein ring radius.The errors on this measurement however, are large, and the θ E measurement does not serve to constrain a probabilitydensity analysis of the binary lens system parameters.Subject to some important assumptions, the probabilitydensity analysis for the lens system parameters suggests thatthe binary lens system for MOA-2010-BLG-353 is consis-tent with a 0 . +1 . − . M Saturn planet orbiting a 0 . +0 . − . M (cid:12) M-dwarf, 6 . +1 . − . kpc away. The projected planet-star dis-tance is 1 . +0 . − . AU. One of these assumptions is that thesource star resides in the Galactic bulge, at 8 kpc from ourSun. The very red colour of the source hints at the possi-bility that the source resides on the far side of the bulge.By constraining the position of the source star to be onthe far side of the Galactic bulge, we find that our prob-ability density analysis favours a lens system comprising a0 . +1 . − . M Saturn planet orbiting a 0 . +0 . − . M (cid:12) star at aprojected orbital radius of 1 . +0 . − . AU, with the lens sys-tem 7 . +0 . − . kpc distant.The planetary signal in MOA-2010-BLG-353 was notidentified as such during the microlensing event. It was onlyduring a subsequent systematic analysis of archived lightcurve data that MOA-2010-BLG-353 was found to have ananomalous signal, possibly owing to a planet. Without aplanetary anomaly alert issued in good time, no observa-tions by the follow-up teams were made of this event. OnlyMOA and OGLE survey data were recorded for MOA-2010-BLG-353. This discovery re-emphasises the importance ofconducting a systematic parameter search for all events inarchival data, as pointed out by Suzuki et al. (2014). It alsodemonstrates how planets can be found through high ca-dence microlensing survey operations alone.The Korean Microlensing Telescope Network epitomisesthis new mode of “survey-only” planetary microlensing.However we note that an over-reliance on solitary telescopeobservations, without supporting a system of contempora-neous follow-up observations, may result in missed opportu-nities. In MOA-2010-BLG-353 we see the planetary anomalyessentially only in the MOA data. In the event of telescopefailure, or unfavourable observing conditions, this anomalywould have gone unrecorded. REFERENCES
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