RR Lyrae Itself and RR Lyraes in Messier 2 in SDSS Filters Qixuan Wu1 & Michael Fitzgerald2 1 Hangzhou No.14 High School, Hangzhou, 310012, China 2 Edith Cowan Institute for Educational Research, School of Education, Perth, 6027, Australia [email protected]

Abstract

Optical Sloan Digital Sky Survey (SDSS) filter using SDSS filter set(u, g, r, i) and Pan- STARRS Z was taken on Messier 2 and RR Lyrae itself. RR Lyraes have been rarely studied in SDSS filters with most research used UBVRI filters. In this research we look at how they behave in SDSS filters. The research suggests the period of RR Lyrae itself is 0.5668 days in all SDSS filters. Using the fact that the distance of M2 to us is 36,200 light (11098 ), the , , Gravity, , Radius and Mass of each RR Lyrae Star in M2 were determined. The observations were taken during the time interval between Modified Julian Date 57459.51 and 57651.24 by 0.4m and 1m class LCOGT. telescope.

Introduction Figure 1: Period Diagram and Relative Position of The same Procedure was used to measure SDSS Photometry on Messier 2. The median magnitude The study on RR Lyrae(Right Ascension: 15h 25m 27.91s : +42◦ 47’ 03.7” J2000.0 and and amplitude of each star were determined through data collection and photometry. The periods of galactic latitude 74.9524◦ longitude +12.3041◦) itself has lasted for more than one century. RR Lyrae stars were determined using software Peranso. was found in 1901 by the America astronomer, Fleming.[1] The star was recorded with a period 0.56 day and magnitude change over 0.75 magnitudes. In contemporary astronomy, the magnitude of this type of star-rr Lyrae-is determined with an amplitude of magnitude between 0.2 - 2 Mag and period Results within one day. Great amounts of traditional photometry have been taken on RR Lyraes during the The research suggests that the period of RR Lyrae is consistent in all filters with a consistent length last decades using the standard UBVRI system. However, few of them focuses on recently developed of 0.5668 days. The amplitude of each band is SDSS g:1.027; SDSS i: 0.748; SDSS r: 1.023; SDSS SDSS photometry system. u: 0.917; Pan-STARRS Z: 0.664. A sample of LL lyr’s period phase diagram is in Figure 2. We investigate the magnitude of all rr Lyrae stars in Messier 2 by processing the images with high Year Observer Period Magnitude Method accuracy photometry. The results revealed that the period-luminosity relation exists in all rr Lyrae 1901 Pickering, E. C., Fleming, W. P.[2] No Data 7.6(Visual) Plate Exposure stars in Messier 2 which is provided in Figure 3. The relations of several color indexes of RR Lyrae 1967 Honey K.R. and Neef J.S. [3] 0.5660 Not taken Film Exposure stars in Messier 2 were also plotted and analyzed. 2002 Ducati, JR [4] 0.5660 7.06(V) CCD  !"#$%#&'()%#

Table 1: Time line of RR Lyrae Photometry /9

/8 h m s ◦ Furthermore, Messier 2(Right Ascension: 21 33 27.02 Declination: -00 49’ 23.7” J2000.0 and /7 ◦ ◦ galactic latitude 53.3709 longitude -35.7698 ) contains more than fifty RR Lyrae variable stars iden- /6 tified by previous observation. The RR Lyrae variable stars in Messier 2 were also examined in our /1 %#*'+(%,-). research regarding their periods and other fundamental parameters. The research indicates that four /5 stars of them are not RR Lyrae variable stars. /4

/3 $/01 $/02 $01 202 01 /02 /01 "#$%#*'+(%,-).

:.+;.<<%=(>%(. Methods "#$%#?%#

(a) RR Lyrae Period (b) Color Index Example

Observation Figure 2: Phase Diagram and Color Index Plot

The observations were taken during Modified Ju-  !"#$##%&  !"#$##"% Telescope Filters Exposure Time lian Date 57459.51 and 57651.24 with 1101 im- 0:+1 09+8

0.4m SDSS g 3.89s ages. In the images taken, 319 images are in SDSS 0.+9 09+1

0.4m SDSS r 2.41s g, 252 in SDSS i, 249 in SDSS r, 36 in SDSS 0.+1 0.+8 0.4m SDSS i 4.09s u, 245 in Pan-STARRS Z. The SDSS g, r, i and 09+9 0.+1 5%67*( 5(67*' Pan-STARRS Z images were taken using the 0.4m- 09+1 08+8 234 0.4m Pan-STARRS Z 14.45s 234 1.0m SDSS u 12.5s class telescope. SDSS u images were taken using 0-+9 08+1 1.0m-class telescope due to SDSS u filter’s rela- 0-+1 0-+8

Table 2: Exposure Setting tively low exposure efficiency. The duration of the 08+9 0-+1 +, +- +. +/ 0+1 0+, +, +- +. +/ 0+1 0+, image is listed: '("%)* &'"()* 2345%67*(;'("%)* '4"'::()5 (5' The telescope in the research is provided by LCOGT. global telescope. The research uses 0.4m and (4"(<<%)5 %5( 2345(67*';&'"()* 1.0m telescopes, the telescope and CCD specifications are listed: (a) SDSS i (b) SDSS r

Class Aperture CCD Pixel Bin Field of View Figure 3: Linear Regression Line Deduced form Messier 2 RR Lyrae Stars 0.4m Class Telescope 0.4m SBIG STX6303 2Kx2K 2x2 19’x29’ 1.0m Class Telescope 1m SBIG 16803 4Kx4K 1x1 27’x27’ Conclusion

Table 3: Time line of RR Lyrae Photometry We undertook the research report in this paper of rr Lyrae itself and rr Lyrae stars in Messier 2 using data provided by LCOGT. telescope. We conclude that rr Lyrae itself has a period of 0.5668 days and further analyze the star in different SDSS filter set. We also found and determined the period- Photometry luminosity relation and other fundamental properties of rr Lyrae stars in Messier 2 globular cluster using SDSS filters. PSF DAOPhot photometry is automatically undertaken using the Our Solar Siblings photometric pipeline for each of the images. PSF photometry provides us with a higher signal to noise and sensi- tivity than aperture photometry. This also allows us to measure stars closer to the center of globular Acknowledgements clusters such as M2. Four stars were used as comparison star in RR Lyr itself research, their informa- tion is shown in the table: I(Qixuan) personally acknowledge the great help from Dr. Michael Fitzgerald from Edith Cowan University for nearly two of support. We thank LCO network for providing telescope times to us. This work makes use of observations Star Right Ascension Declination from the LCO network 0.4-meter telescope and 1.0-meter telescope. This research has made use of ”Aladin sky atlas” developed at CDS, Strasbourg Observatory, France BD+42 3334 19h 25m 04.77s +42◦ 41’ 31.27” BD+42 3339 19h 25m 59.33s +42◦ 43’ 42.50” BD+42 3337 19h 25m 25.91s +42◦ 57’ 09.29” References h m s ◦ KIC 7280725 19 25 31.84 +42 51’ 12.83” [1] C Martin and HC Plummer. Rr lyræ, on the short-period variable. Monthly Notices of the Royal Astronomical Society, 75:566, 1915. [2] Edward C Pickering, HR Colson, WP Fleming, and LD Wells. Sixty-four new variable stars. The Astrophysical Journal, 13, 1901. [3] KR Honey and JS Neff. A photometric comparison of , su draconis, and . The Astronomical Journal, 72:804, 1967. Table 4: Comparison Star [4] JR Ducati. Vizier online data catalog: Catalogue of stellar photometry in johnson’s 11-color system. VizieR Online Data Catalog, 2237, 2002.