1. Bingqiu Chen & Biwei Jiang Beijing Normal University
Frequency analysis of RR Lyrae stars in the LMC
Bingqiu Chen & Biwei Jiang
Beijing Normal University
2010.4
Department of Astronomy Beijing Normal University

2. The data & the method of analysis Variable classification Conclusion
Overview
Introduction
The data & the method of analysis
Variable classification
Conclusion
Discussion

3. RR Lyrae Star RR Lyrae stars: Types : Period : 0.1 to 1 day
Amplitude in V : up to 1.5 magnitudes
Spectral type : A5 to F5
Absolute visual magnitude : about +0.5
Mass : about half a solar mass
Low metal abundance Z : ~ 0.01
Evolutionary stage: Away from the main sequence & burning Helium in their core. Useful tracer of galactic evolution.
Obey a period-luminosity-color relation & used as distance indicators.( Like the Cepheids)
Types :
RRab stars, RRc stars , RRd stars, RRe stars

4. The Blazhko effect
A long-term modulation of the amplitude, shape, and phase of the light and radial velocity curve.
Blazhko effect period : 11 to 533 days
Occurs in 1/3 RRab stars, & a few RRc stars . (The incidence is lower in LMC).
A century of study:
Nonradial modes triggered by resonance effects
Magnetic field
e.g. : Dziembowski and Mizerski (2004).

5. Data 24906 light curves from the OGLE-III Exclude 671 stars
(Soszynski et al. 2009)
Exclude
I <18m & Observed dots’ number <1000
671 stars

6. Method Frequency analysis based on a PDM method : f0
In the [1 5] 1/d band
Fit the light curve with five harmonics of f0:
Frequency analysis with the residual: f1
In the [ ] 1/d band
Fit the residual with f1
…f2…f3…f4
Visual inspection of lightcurves to check

7. RR-S Singly-periodic RR Lyrae : 495 stars 73.7%
RR0: (fundamental mode): 369~74.5%
RR1: (1st overtone mode) : 124~25.1%
RR2: (2nd overtone mode) : 2~0.4% ID P f Θ s
amp
mag A
762
0.0000
0.567
18.850
0.183
5976
0.786
18.720
0.253
5990
0.746
18.894
0.231
6004
0.505
18.740
0.175
6114
0.639
18.811
0.203
6125
0.410
18.469
0.155
6147
0.677
18.813
0.215
6180
0.778
18.818
6300
0.503
18.580
0.161

8. PDM & fitting

9. Period distribution

10. Period–amplitude diagram

11. RR-01 Double modes RR Lyrae : 12 ~1.8%
There main pulsation modes are all 1st overtone (RR1-01) ID p1 f1 Θ1 s1 a1 m c1 p0 f0 Θ0 s0 a0 c0
5901
0.0000
0.194
18.828
0.100
0.157
0.076
9165
0.223
18.779
0.105
0.156
0.072
12828
0.265
18.906
0.131
0.183
0.086
13033
18.797
0.136
0.164
0.081
13231
0.236
18.671
0.111
0.125
0.055
15012
0.257
18.870
0.118
0.240
0.112
16035
0.241
18.705
0.0012
0.121
0.056
16953
0.255
18.488
0.128
0.093
0.045
17575
0.238
18.784
0.114
0.173
0.078
18546
0.261
18.891
0.219
0.103
17311
0.187
18.624
0.221
0.091
17317
0.158
18.680
0.066
0.146
0.071

12. Phased lightcurves

13. A1 to A0 ratios
Wide range
A0,only 1 exceeds A1

14. Petersen diagram

15. RR-BL1 RR Lyrae with 1 close frequency component:
Number : 84 stars 12.5%
RR1-BL1: 18 ~ 21.4%
RR0-BL1: 66 ~ 78.6% id p0 f0 Θ0 s0 a0
mag c0 p1 f1 Θ1 s1 a1 c1
6033
0.5035
0.0000
0.106
18.059
0.044
0.8118
0.0011
0.042
0.018
6872
0.1517
0.721
18.611
0.244
0.7749
0.111
0.053
7970
0.2523
0.254
18.597
0.126
0.8735
0.0202
0.049
0.021
8072
0.3274
0.320
18.950
0.122
0.8861
0.0386
0.025
8800
0.2663
0.152
17.720
0.056
0.8604
0.0147
0.024
0.011
8809
0.2794
0.556
18.738
0.193
0.8609
0.083
0.038
9161
0.3023
0.375
18.623
0.147
0.8272
0.0029
0.084
0.036
9189
0.1961
0.404
18.673
0.153
0.8623
0.0112
0.066
0.023
9239
0.4478
0.245
18.564
0.123
0.7318
0.128
0.052
9254
0.1059
0.581
18.598
0.196
0.8975
0.0742
0.013
9340
0.3000
0.260
18.709
0.8599
0.0123
0.065

16. Phased lightcurves

17. RR-BL1 Frequency difference: RR0: f1>f0  48 stars 72.7%

18. RR-BL2 RR Lyrae with 2 close symmetric frequency components: 28 4.2%id p0 f0 a0 f1 a1 f2 a2
f1-f0
f2-f0
5348
0.258
0.036
0.035
8575
0.119
0.098
0.060
9295
0.508
0.106
0.090
10212
0.186
0.071
0.063
11476
0.102
0.094
11701
0.311
0.179
0.129
11708
0.269
0.087
0.080
12991
0.267
0.027
0.028
13088
0.405
0.073
0.045
13183
0.079
13235
0.566
0.084
0.053

19. Phased lightcurves

20. Relation of Δf & f0

21. RR-BL3+ RR Lyrae with several close components : 29 4.2%id p0 a0 a1 a2 a3
f1-f0
f2-f0
f3-f0
7634
0.1540
0.1216
0.1065
0.0983
10248
0.4282
0.1563
0.1049
0.1053
11434
0.3987
0.1441
0.1525
0.1118
12620
0.2287
0.1071
0.0887
0.0780
12972
0.2400
0.1152
0.0934
0.1056
12994
0.5543
0.1632
0.1181
0.1091
13023
0.5032
0.1112
0.0739
0.0798
13039
0.1514
0.1000
0.0928
0.1025
13078
0.5608
0.1553
0.1208
0.0814
13095
0.1982
0.0901
0.0548
0.0493

22. RR-BL3+

23. Relation of Δf & f0

24. RR-D & RR-unknown id p0 f0 Θ0 a0 m0 p1 f1 Θ1 s1 a1
7071
0.3352
0.474
19.043
0.7996
0.0004
0.147
16756
0.4502
0.432
18.506
0.6978
0.0000
0.276
16779
0.1346
0.654
18.695
0.8967
0.0826
0.061
17512
0.2898
0.287
18.447
0.8827
0.0462
0.050
13184
0.4371
0.254
18.617
0.6163
0.137
17331
0.3886
0.257
18.669
0.7573
0.098
6 RR-D & 17 unknown type double period RR Lyrae stars id p0 f0 Θ0 a0
mag p1 f1 Θ1 s1 a1
13070
0.2849
0.371
18.598
0.8473
0.0035
0.079
13230
0.2014
0.421
18.813
0.8116
0.0003
0.070
13254
0.0933
0.269
17.491
0.8807
0.0315
0.019
15056
0.3674
0.278
18.855
0.7799
0.0000
0.097
16035
0.5724
0.241
18.705
0.8355
0.0012
0.121
16818
0.0924
0.634
18.522
0.8951
0.0539
0.046
16953
0.2587
0.255
18.488
0.6515
0.093
17317
0.6458
0.146
18.680
0.4689
0.158

25. Main pulsation modes are all 1st overtone
Conclusion
Type
Number
Percent
Notes
RR-S
RR0-S
369
55.0%
fundamental mode
RR1-S
124
18.5%
1st overtone mode
RR2-S 2
0.3%
2nd overtone mode
RR-01 12
1.8%
Main pulsation modes are all 1st overtone
RR-BL1
RR0-BL1 66
9.8%
RR1-BL1 18
2.7%
RR-BL2
RR0-BL2
RR1-BL2 16
2.4%
RR-BL3+
RR0-BL3+ 14
2.1%
RR1-BL3+ 15
2.2%
RR-D 6
0.9%
P1=1,2 c/d
RR-unknown 17
2.5%

26. Discussion Blazhko effect occurs more frequently in RR0 than RR1.
The Blazhko period is short in RR1, while sometimes long in RR0 than in RR1.
With the number of oscillating components, the numbers of the RR0-BLn and RR1-BLn stars have a trend to be the same, so the Blazhko effect depends on the mode of pulsation and the number of oscillating components.
For the RR-BL1,RR-BL2, & RR-BL3+, it seems the Blazhko can lead the period to split for any number (1-4) of components, so nonradial mode of oscillation seems better explain for Blazhko effect.

27. Thank You!