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Large Magellanic Cloud Distance from Cepheid Variables using Least Square Solutions
Choong Ngeow (UIUC) & Shashi Kanbur (SUNY Oswego)
ABSTRACT: We determine the LMC distance using Cepheid variables in the LMC. We combine the individual LMC Cepheid distances obtained from the infrared surface brightness method and a dataset with a large number of LMC Cepheids. Using the standard least squares method, the LMC distance can be found from the ZP offsets of these two samples. We have adopted both a linear P-L relation and a ``broken'' P-L relation in our calculations. The resulted LMC distance moduli are 18.478±0.034 mag and 18.486±0.036 mag (the quoted errors are random error only), respectively, which are consistent to the adopted 18.50 mag.

I . I n t r o d u c t io n
· Gieren et al (2005, hereafter G05): determined the distance to 13 LMC Cepheids (including 6 short-period Cepheids in LMC cluster NGC 1866) and derive the Cepheid period-luminosity (P-L) relation. · LMC hosts >600 Cepheids available from the Optical Gravitational Lensing Experiment (OGLE) database. · By combining these two datasets, it is possible to determine both of the LMC distance modulus and P-L relation simultaneously (see Figure 1).
Figure 1: Illustration of the least squares method. Introducing an offset of the ZP, µ, between the calibrated Cepheids from infrated surface brightness method and a large number of OGLE Cepheids will allow the LMC distance and the P-L relation to be solved simultaneously .

I I I . R e s u lt s
· For linear P-L relation: V-band: µ= 18.468±0.059; a = -1.363±0.068; b = -2.761±0.036 I-band: µ= 18.483±0.041; a = -1.863±0.046; b = -2.981±0.024 · For non-linear P-L relation: V-band: µ= 18.485±0.063 Long period (P>10days): aV aI Short period (P<10days): aV aI & = = = = I-band: µ= 18.486±0.043 -1.228±0.208; bV = -2.838±0.155 -1.688±0.143; bI = -3.093±0.106 -1.278±0.072; bV = -2.939±0.061 -1.801±0.049; bI = -3.092±0.041

II. D a ta & M eth o d s
· Data used: (1) G05 (2) OGLE data from Kanbur & Ngeow (2006). · The least squares take the form: #0, if G05 m = % $µ + a + b log( P ), % = " !1, if OGLE · Recent studies have suggested the LMC Cepheid P-L relation is nonlinear (Kanbur & Ngeow 2004,2006; Sandage et al 2004). · We also adopt a "broken" P-L relation with a break period at 10 days.

· V and I band averaged distance modulus is given in the ABSTRACT. · F-test (Kanbur & Ngeow 2004) results for non-linear P-L relation: FV = 7.32; FI = 6.87 (null hypothesis [linear P-L relation] can be rejected with >95% CL if F > 3).
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