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Preliminary Analysis of ULPC Light Curves Using Fourier Preliminary Analysis of ULPC Light Curves Using Fourier Decomposition Technique Chow-Choong Ngeow‡, Scott Lucchini∗, Shashi Kanbur†, Brittany Barrett† and Bin Lin∗ ‡Graduate Institute of Astronomy, National Central University, Jhongli 32001, Taiwan ∗Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA †Department of Physics, SUNY Oswego, Oswego, NY 13126, USA Abstract—Recent work on Ultra Long Period Cepheids For the six stars in the LMC and the SMC, we obtained the (ULPCs) has suggested their usefulness as a distance indicator, V-band data from [1] and the I-band data from [2]. We also but has not commented on their relationship as compared with acquired additional V- and I-band data through the McMaster other types of variable stars. In this work, we use Fourier analysis 1 to quantify the structure of ULPC light curves and compare Cepheid Photometry Archive for four ULPCs in the LMC. them to Classical Cepheids and Mira variables. Our preliminary [3] had some additional data points for HV 883 and HV 2447. results suggest that the low order Fourier parameters (Rk1 and Also, for HV 2883 and HV 5497, we acquired data from [4], φk1) of ULPCs show a continuous trend defined by Classical again through the McMaster Archive. [1] also had V- and I- Cepheids after the resonance around 10 days. However their band data for the five stars in NGC 55, the three stars in NGC Fourier parameters also overlapped with those from Miras, which make the classification of long period variable stars difficult based 300, and the one star in NGC 6822. Again, using the McMaster on the light curves information alone. Archive, additional photometry was acquired for NGC 300-1 Keywords — Cepheids; late-type stars; distance scale (as named by [1]) from [3]. The photometric V- and I-band data for the two stars in I Zw 18 were obtained from [5]. I. INTRODUCTION The periods for these stars were also compiled in [1]. In Cepheid variables are key component in astrophysical re- Table I we have listed all the ULPCs in our data set together search, as they are an indispensable link in the extragalactic with their periods and host galaxies. In this Table, the names distance ladder. However, for the most part, current research of the stars (Column 1) are consistent with those used by focuses on Classical Cepheids with periods less than 60 days. [1]. Column 3 contains the distance modulus (DM) values for There are good reasons for this: in terms of sufficient phase the stars’ host galaxies listed in Column 2. The magnitudes coverage, they take less time to observe, and they have a well (Column 5) are the absolute, reddening corrected, mean V- defined period-luminosity (PL) relation. Also, Cepheids with band magnitudes as calculated by our Fourier analysis with periods greater than 100 days obey a different relation ([1]), orders as shown in Column 6. All the data for these stars was which has not been nearly as well documented. In this work, obtained from [1] and references therein, however for the stars we follow the same conventions as [1], defining these “Ultra where more data was compiled, footnotes have been added. Long Period Cepheids” (ULPCs) to be any fundamental mode Figure 1 presents the ULPC light curves used in this work. Cepheids with a pulsation period greater than 80 days. Even though ULPCs have generally not been studied as in- B. OGLE-III Catalog tensely as shorter period Cepheids, there are many advantages The third installment of the Optical Gravitational Lensing to acquiring data on these ULPCs. As the PL relation indicates, Experiment (OGLE-III) contains photometric data for many the longer the period of a star, the brighter it is. This means that variable stars in the Large and Small Magellanic Clouds. We arXiv:1309.4297v1 [astro-ph.SR] 17 Sep 2013 these variables can be observed at much greater distances than were interested in the V- and I-band photometric light curves are currently possible. This added brightness would allow us to data for fundamental mode Cepheids and longer period Mira- use Cepheids to measure distances out to 100 Mpc and beyond like variables. We also obtained the periods for all the stars [1]. In this work, our goal is to study the structural properties we used from the catalog. From OGLE-III LMC Cepheid of ULPC light curves. We are interested in comparing the light catalog ([6]), we chose 1,804 (out of 1,849) Cepheids based curves of ULPCs to shorter period Classical Cepheids as well on what data was available for these stars. We then obtained as to longer period Mira-like variables (Miras). the V- and I-band photometric light curve data for these II. DATA Cepheids. Similarly, of the 2,626 available fundamental mode Cepheids in the SMC ([7]), we selected 2,596. The OGLE-III A. ULPCs catalog also contains photometric and period data for ”long There is very limited data for ULPCs available right now, period variables” (LPVs). These LPVs are classified into three but we were able to compile data for 17 ULPCs in 6 different different types: Miras, OSARGs, and SRVs ([8]). We chose galaxies, including the Large and Small Magellanic Clouds (LMC/SMC), NGC 6822, NGC 55, NGC 300, and I Zw 18. 1http://crocus.physics.mcmaster.ca/Cepheid/ HV 883 HV 2447 HV 2883 HV 5497 -8 -8 -7.6 -8 -7.6 -7.2 -7.6 -7.6 -7.2 -6.8 -7.2 -6.8 -6.4 -7.2 -6.8 -6.4 -6 -6.8 -6.4 -6 -5.6 -6.4 -5.6 -6 -5.2 -5.2 -5.6 -4.8 -6 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 HV 821 HV 829 NGC 6822 - 1 NGC 55 - 1 -8.4 -8.4 -7.2 -8.4 -8 -8 -6.8 -8 -6.4 -7.6 -7.6 -6 -7.6 -7.2 -7.2 -5.6 -7.2 -6.8 -6.8 -5.2 -6.4 -6.4 -4.8 -6.8 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 NGC 55 - 2 NGC 55 - 3 NGC 55 - 4 NGC 55 - 5 -8 -7.6 -7.6 -7.2 -7.2 -7.2 -6.8 -7.6 -6.8 -6.8 -6.4 -7.2 -6.4 -6.4 -6 -6 -6.8 -6 -5.6 -5.6 -6.4 -5.6 -5.2 -5.2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 NGC 300 - 1 NGC 300 - 2 NGC 300 - 3 V1 V15 -7.6 -8.4 -8 -8.8 -9.2 -7.2 -8 -8.4 -8.8 -6.8 -7.6 -7.6 -8 -8.4 -6.4 -7.2 -7.6 -8 -6 -6.8 -7.2 -5.6 -6.4 -7.2 -7.6 -5.2 -6 -6.8 -6.8 -7.2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 Fig. 1. ULPC light curves with their respective Fourier fits. The absolute V (open squares) and I (filled squares) magnitudes are represented along the y-axis, and the phase of pulsation is along the x-axis. 1,407 of the listed 1,663 Mira variables and again used both their V- and I-band photometric data. TABLE I DATA ON THE ULPCS THAT WE USED. C. NGC 300 Cepheid Data Name Galaxy DM Period [days] MV N [9] acquired V- and I-band photometric data for 64 Cepheids HV 883a LMC 133.6 -6.30 4 from NGC 300 with periods ranging from 11 to 115 days. HV 2447a LMC 118.7 -6.47 4 However, three of the Cepheids have periods greater than 80 b 18.50 HV 2883 LMC 109.2 -5.98 3 days, so they are included as ULPCs, not as regular Cepheids HV 5497b LMC 98.6 -6.62 4 HV 821 SMC 127.5 -6.99 4 of NGC 300. The remaining 61 stars and their light curve data 18.93 HV 829 SMC 84.4 -7.00 4 were added to our Classical Cepheid data set. NGC 6822 - 1 NGC 6822 23.31 123.9 -5.41 3 NGC55-1 NGC55 175.9 -7.17 4 III. FOURIER ANALYSIS NGC 55 - 2 NGC 55 152.1 -6.87 3 NGC 55 - 3 NGC 5526.43 112.7 -6.21 3 We characterized the structure of all the observed light NGC 55 - 4 NGC 55 97.7 -5.89 4 curves in our data set using the technique of Fourier decompo- NGC 55 - 5 NGC 55 85.1 -5.58 3 NGC 300 - 1a NGC 300 115.8 -6.15 3 sition. That is, the following function was fit to the observed NGC 300 - 2 NGC 30026.37 89.1 -6.66 3 data for a given star: NGC 300 - 3 NGC 300 83.0 -7.11 2 V1 IZw18 129.8 -7.30 2 N 31.30 V15 I Zw 18 125.0 -7.62 2 mag(t)= A0 + X Ak sin(kωt + φk) (1) k=1 a Additional data from [3].
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