Noise model and accurate fitting of high magnification

PSPL events

Pascal Fouqué

Alerts from OGLE-III and MOA-II in 2008

• 912 alerts (647 OGLE, 475 MOA)• OGLE: Feb. 23 - Nov. 3• MOA: Feb. 9 - Oct. 21• 176 possible anomalies (including HME)• 97 followed by microFUN• 78 RoboNet-II / LCOGT• 78 PLANET• 74 MindStep

29 announced as possible HME• KB08022• OB08013 = KB08032• KB08044 = OB08054• KB08054• KB08087• KB08096• OB08140 = KB08115• KB08105• OB08199 = KB08144• OB08209 = KB08155• OB08210 = KB08177• OB08215 = KB08161• KB08149• KB08151• KB08159• KB08198• OB08279 = KB08225• OB08303 = KB08267• OB08426• KB08310• KB08311• KB08349 = OB08509• KB08383• KB08384• KB08402• KB08415• OB08580• KB08428• KB08453

First impressions• More MOA than OGLE announcements• Not all of them were HME• Some present further anomalies• Not all announced:

– OB08155 = KB08137– OB08290 = KB08241– OB08307 = KB08215– OB08349 = KB08261– OB08358 = KB08264– OB08367 = KB08269– KB08307 = OB08448– KB08325– KB08352– KB08356– OB08506– OB08513 = KB08401

A posteriori

• Difficult to predict Amax from few points• Include priors as in BAP (M. Albrow)• Even when finished, accurate

parameters are difficult to measure:– Combining several telescopes– MOA only events– Blending– Noise model

Analysis

• plens fitting program: K. Horne, used by RoboNet/LCOGT

• Noise model: 3 components:– Bright or HM events: errors down to 1 mmag: add

percent systematic error: 2 to 5 mmag– Baseline: add flux accuracy due to faint

background stars; larger for fainter stars: 0 to 0.1 mag

– Rescale error bars: for OGLE, 0.8 - 2.0

Modelling parameters

• Fit: 4 (t0, tE, u0, m0): no blending

• 5: blending grid: parameters vs b = fb/fs

• 6: 0 (baseline flux accuracy in mag)

• 7: f (error bar scaling factor)

• Grid 0 vs. f

Example of OB08279: blend ratio grid

Example of OB08279: noise model grid

Real HME events• Definition: Amax > 40 (4 mag)

• About 16: 2% of all events• Retained (11 MOA, 5 OGLE):

– KB08087 (60)– KB08096 (300)– KB08149 (600)– KB08151 (300)– KB08198 (40)– KB08310 (ext src)– KB08311 (200)– KB08383 (ext src)– KB08415 (130)– KB08428 (100)– KB08453 (100)– OB08013 (44)– OB08199 (44)– OB08279 (4000)– OB08290 (ext src)– OB08303 (55)

• Extended source effects in some: O279?

OB08279 = KB08225

• Highly blended event: b = 40• tE = 130 days, u0 = 2 10-4 (OGLE only)• OGLE, MOA, FUN, Canopus,

RoboNet-II/LCOGT• Marginal extended source effect: = u0

• Extended source: 2= 60• Fix LLD for 5000 K dwarf• Andy’s sfit program, Yoo approx.:• u0 = 4.3 10-4 -> 5.7 10-4 and = 5.9 10-4

PSPL ESPL

OB08290 = KB08241

• Clear extended source effect: ~ 60 |u0|• tE = 16.5 days• 12 telescopes: OGLE, MOA, FUN (4),

LCOGT/RoboNet (3), PLANET (3)• Negligible blending• V, R, I, clear: fit LLD• Andy’s sfit program, Yoo approx. = 0.0220

OB08290 = KB08241

V=0.72, =0.45 ≈ EROS 2000-BLG-5 -> K3 III• Target in 2MASS but blended: IRSF separates

components• Estimate of extinction: isochrones fit• Bonatto et al. (2004) isochrones for 2MASS

photometric system• IRSF images (S. Nishiyama)• Aks=0.44, Aj=2.5 Aks, Ah=1.7 Aks, =14.4• J0=13.85, H0=13.17, Ks0=13.01: K4 III• CTIO V - I CMD: V0=16.10, I0=14.73: K3 III• Martin’s galactic model: disk lens (2/3-1/3), M=0.3

Msun at 5.8 kpc

Reddening law and extinction corrections

• Sumi (2004) gives E(V-I) for each OGLE-II field• Ai = 0.964 E(V-I), Av = 1.964 E(V-I)• What to do when OGLE-III event not in OGLE-II field?• Once OGLE-III calibrated, use RGC: clump measured color gives

E(V-I) (assume source and clump equally extincted)• Ai: three routes: use Sumi’s Ri (or other value), use clump

measured magnitude and assumed distance (depends on bar geometry)

• Third route: use near-infrared extinction maps, but which ratio E(V-I)/Aks ?

• Near-infrared ( > 0.8 m): power-law:• E(-Ks)/E(J-Ks) = a - + b• Cardelli et al. (1989): = 1.61• He et al. (1995): = 1.73• Nishiyama et al. (2006): = 1.99• I adopt Av/Aks=10, E(V-I)/Aks=4.4

New IRSF work

• Nishiyama et al. (2008): compare OGLE-II and IRSF for Udalski’s A region (l = 0, b = -2)

• Aj/Av = 0.187 +- 0.009• Similarly, Aj/Ai = 0.392 +- 0.004• Gives Ri = Ai/E(V-I) = 0.91 +- 0.13• Nice confirmation of Sumi’s result 0.930 +- 0.006• Extrapolating to E(V-I)/Aks ? Not same region• If correct: Av/Aks=16.2 +- 0.8, E(V-I)/Aks = 8.5 +- 0.8

Isochrone fits

• 2MASS images not deep enough• Needs IRSF images• Nishiyama uses (H-Ks)0 = 0.07 + his reddening law:• Aj=3.0 Aks, Ah=1.73 Aks• Example of OB08290: gives Aks=0.48 but bad fit• I get 0.42 with Aj=2.6 Aks and same Ah/Aks• Proves that reddening law depends on direction