Digging with care. Martin Dominik University of St Andrews Scotland. Martin Dominik. ystematic analysis of subtle microlensing features

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1 Digging with care ystematic analysis of subtle microlensing features Martin Dominik University of St Andrews Scotland with support from RoboNet'team MiNDSTEp'team 'team Martin Dominik

2 Obvious detections vs subtle features obvious MOA$2009$BLG$266 but: P(χ ) = (e.g. 5 points at 2σ) low detection threshold false positives get high number statistics be sensitive to low-mass companions avoid wasting telescope resources high detection threshold no insurance against false positives correlated noise can produce pseudo-detections at large χ 2 on just high enough cadence cannot hang detection on to points that show similar deviations as other points considered noise we need to understand our error bars consistent interpretation of data (Penny D. Sackett, 1995) establish noise model and estimate noise statistics

3 Low-mass planets and satellites signals may be subtle, but are well localised brightening [mag] 5 Mw 1 Mw days since 31.0 July 2005 UT model parameters describing anomaly vast majority of photometric data other parameters can be well determined from photometric data outside anomaly / parameter hierarchy / disentaglement of subspaces D = D N D A D N D A = P ~ P N P A avoid misestimation / check consistency: (no) effect of anomaly region on P N estimate of noise statistics that does not depend on putative anomaly (assuming everything else is regular)

4 Obtain noise statistics M data sets with N [m] data points (F n [m ],σ n [m ],t n [m ] ) F [m ] [m ] [m ] (t) = F base A(t) F B A(t) 1!σ n [m ] ( [m σ ] n,κ [m ] [m ],s ) 0 = ( κ [m ] [m ] σ ) 2 n + ( [m s ] [m ] 0 F ) 2 κ [m ] n simple effective error bar model s 0 [m ] scaling factor systematic uncertainty r n [m ] ( F [m ] [m (t),f ] [m ] n,!σ ) n = F [m ] F [m ] (t) n [m ]!σ n 2 [m w ] n = 1 r 2 [m ] n [m for r ] K!r [m ] n < K!r [m ] [m 0 for r ] n K!r [m ] robust fitting, bi-square weight function (accounting for outliers and non-gaussian tail) pseudo-gaussian, alternatives: more elaborate models such as Student s t etc.!χ 2 M N [m ] [m ] = [m ] w ( n r ) 2 N [m ] n + 2 [m ] ln!σ n m=1 n=1 n=1 modified χ 2, counting data points with weight 0 w n [m ] 1

5 -2014-BLG-1186: a event RTmodel 7 March light curve substantially affected by parallax model does not work well with data? and RoboNet data telling different stories? reported uncertainties very small What is signal, what is systematic uncertainty? noise statistics

6 -2014-BLG-1186 residuals weighted CDF weight distribution P = 0.17 (Anderson-Darling) P = 0.98 (Anderson-Darling) LSC'B P = 0.60 (Anderson-Darling) without putative anomaly ( t )

7 -2014-BLG-1186 without putative anomaly /I LSC'B LSC'C CPT'A CPT'B COJ'A COJ'B FTS t_ / t_e 290 +/- 17 days u_ / pie_n / pie_e / very robust measurement of parallax time-scale uncertainty related to blend uncertainty similar estimates for only, but uncertainties larger

8 -2014-BLG-1186 without putative anomaly /I LSC'B LSC'C CPT'A CPT'B COJ'A COJ'B FTS t_ / t_e 290 +/- 17 days u_ / pie_n / pie_e / very robust measurement of parallax time-scale uncertainty related to blend uncertainty similar estimates for only, but uncertainties larger

9 no anomaly in BLG-1186? 'w/o/anomaly/region 'anomaly/region only /I

10 Reviewing the putative anomaly CPT'A CPT'B COJ'A COJ'B /I

11 Reviewing the putative anomaly CPT'A CPT'B COJ'A COJ'B /I various data sets appear to give consistent picture

12 Reviewing the putative anomaly CPT'A CPT'B COJ'A COJ'B /I various data sets appear to give consistent picture anomaly apparent

13 Reviewing the putative anomaly LSC'B LSC'C CPT'A CPT'B COJ'A COJ'B FTS /I various data sets appear to give consistent picture anomaly apparent baseline/blending less well defined for some data sets

14 Modelling the BLG-1186 anomaly LSC'B LSC'C CPT'A CPT'B COJ'A COJ'B FTS /I data points point source χ 2 =

15 Modelling the BLG-1186 anomaly LSC'B LSC'C CPT'A CPT'B COJ'A COJ'B FTS ρ = 0 ρ = ρ = ρ = /I data points point source χ 2 =

16 Modelling the BLG-1186 anomaly LSC'B LSC'C CPT'A CPT'B COJ'A COJ'B FTS t_ t_e 294 days u_ pie_n pie_e /I data points point source χ 2 = 2017 finite source χ 2 = binarity not affecting parallax measurement

17 Which model? lg q lg d lg q α α lg d

18 Which model? planetary vs non-planetary solutions χ 2 (p i ) / probability for true parameters p 0 being in vicinity of p i Δχ 2 (p 1, p 2 ) χ 2 (p 1 ) χ 2 (p 2 ) / probability for p 1 being preferred over p 2 can use χ 2 test: P[χ N 2 χ 2 (p i )] applicable regardless of model being linear in p or not normally-distributed uncertainties: χ 2 follows χ 2 -distribution PDF( 2χ 2 N ) ~ N ( 2N 1,1) otherwise: evaluate distribution of χ 2 based on non-normal σ does not work without consistent model for measurement uncertainties!

19 special thanks to... Valerio Valerio/Bozza Markus/Hundertmark EHenne/Bachelet Rachel/Street Andrzej/Udalski