bingqiu chen biwei jiang beijing normal university
DESCRIPTION
The data & the method of analysis Variable classification Conclusion Overview Introduction The data & the method of analysis Variable classification Conclusion DiscussionTRANSCRIPT
Department of Astronomy Beijing Normal University
Bingqiu Chen & Biwei JiangBeijing Normal University
2010.4
Frequency analysis of RR Lyrae stars in the LMC
[email protected] normal University
Department of Astronomy
2
Introduction The data & the method of
analysis Variable classification Conclusion Discussion
Overview
[email protected] normal University
Department of Astronomy
RR Lyrae stars: 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 : 0.00001 ~ 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 distanceindicators.( Like the Cepheids)
Types : RRab stars, RRc stars , RRd stars, RRe stars
RR Lyrae Star
[email protected] normal University
Department of AstronomyThe 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).
[email protected] normal University
Department of AstronomyData
24906 light curves from the OGLE-III (Soszynski et al. 2009)
Exclude I <18m & Observed dots’ number <1000
671 stars
0 500 1000 1500 2000 2500 3000 3500 4000 4500 500018.6
18.7
18.8
18.9
19
19.1
19.2
19.3
19.4
19.5
19.6
JD
Mag
nitu
de
light curve
[email protected] normal University
Department of AstronomyMethod
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 [0.5 5.5] 1/d band
Fit the residual with f1 …f2…f3…f4 Visual inspection of lightcurves to check
5
0 1 11
( ) [ cos(2 ) sin(2 )]k kk
I t I A f kt B f kt
[email protected] normal University
Department of AstronomyRR-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 0.611821 1.634466 0.13622 0.0000 0.567 18.850 0.183 5976 0.555120 1.801411 0.07506 0.0000 0.786 18.720 0.253 5990 0.497251 2.011056 0.08135 0.0000 0.746 18.894 0.231 6004 0.581478 1.719756 0.16810 0.0000 0.505 18.740 0.175 6114 0.551528 1.813145 0.09532 0.0000 0.639 18.811 0.203 6125 0.515681 1.939182 0.14685 0.0000 0.410 18.469 0.155 6147 0.545563 1.832968 0.10768 0.0000 0.677 18.813 0.215 6180 0.493846 2.024921 0.08037 0.0000 0.778 18.818 0.253 6300 0.569926 1.754614 0.12083 0.0000 0.503 18.580 0.161
[email protected] normal University
Department of AstronomyPDM & fitting
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
18.8
18.9
19
19.1
19.2
19.3
19.4
19.5
phase
mag
nitu
de
fit figure
phase vs. magnitudefit line
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
18.35
18.4
18.45
18.5
18.55
18.6
18.65
18.7
18.75
18.8
18.85
phase
mag
nitu
de
fit figure
phase vs. magnitudefit line
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
18.2
18.3
18.4
18.5
18.6
18.7
18.8
18.9
19
19.1
X
Y
phase vs. magnitudefit line
[email protected] normal University
Department of AstronomyRR-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 0.345102 2.897696 0.58847 0.0000 0.194 18.828 0.100 0.464248 2.154022 0.60736 0.0000 0.157 0.076
9165 0.344830 2.899981 0.49483 0.0000 0.223 18.779 0.105 0.463814 2.156039 0.55308 0.0000 0.156 0.072
12828
0.345722 2.892498 0.47942 0.0000 0.265 18.906 0.131 0.465272 2.149279 0.56547 0.0000 0.183 0.086
13033
0.367634 2.720098 0.44826 0.0000 0.265 18.797 0.136 0.493743 2.025345 0.56601 0.0000 0.164 0.081
13231
0.381419 2.621787 0.38967 0.0000 0.236 18.671 0.111 0.511593 1.954679 0.62089 0.0000 0.125 0.055
15012
0.342056 2.923502 0.58520 0.0000 0.257 18.870 0.118 0.460572 2.171212 0.46108 0.0000 0.240 0.112
16035
0.358375 2.790370 0.57242 0.0000 0.241 18.705 0.125 0.481604 2.076393 0.83545 0.0012 0.121 0.056
16953
0.398631 2.508585 0.25873 0.0000 0.255 18.488 0.128 0.534026 1.872568 0.65147 0.0000 0.093 0.045
17575
0.361737 2.764443 0.48807 0.0000 0.238 18.784 0.114 0.486225 2.056663 0.51665 0.0000 0.173 0.078
18546
0.343408 2.911990 0.55091 0.0000 0.261 18.891 0.125 0.462159 2.163757 0.46099 0.0000 0.219 0.103
17311
0.341071 2.931942 0.49689 0.0000 0.187 18.624 0.100 0.459522 2.176172 0.59474 0.0000 0.221 0.091
17317
0.345953 2.890563 0.46889 0.0000 0.158 18.680 0.066 0.465608 2.147729 0.64579 0.0000 0.146 0.071
[email protected] normal University
Department of AstronomyA1 to A0 ratios
Wide rangeA0,only 1 exceeds A1
[email protected] normal University
Department of AstronomyRR-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 0.647017
1.545554
0.5035
0.0000 0.106 18.05
9 0.044 0.642486
1.556453
0.8118
0.0011 0.042 0.018
6872 0.628018
1.592310
0.1517
0.0000 0.721 18.61
1 0.244 0.620223
1.612323
0.7749
0.0000 0.111 0.053
7970 0.378583
2.641431
0.2523
0.0000 0.254 18.59
7 0.126 0.378540
2.641731
0.8735
0.0202 0.049 0.021
8072 0.534849
1.869686
0.3274
0.0000 0.320 18.95
0 0.122 0.528311
1.892825
0.8861
0.0386 0.053 0.025
8800 0.596506
1.676430
0.2663
0.0000 0.152 17.72
0 0.056 0.593087
1.686092
0.8604
0.0147 0.024 0.011
8809 0.566944
1.763844
0.2794
0.0000 0.556 18.73
8 0.193 0.558472
1.790601
0.8609
0.0147 0.083 0.038
9161 0.471102
2.122681
0.3023
0.0000 0.375 18.62
3 0.147 0.471026
2.123025
0.8272
0.0029 0.084 0.036
9189 0.665077
1.503585
0.1961
0.0000 0.404 18.67
3 0.153 0.673990
1.483701
0.8623
0.0112 0.066 0.023
9239 0.407978
2.451110
0.4478
0.0000 0.245 18.56
4 0.123 0.407934
2.451375
0.7318
0.0000 0.128 0.052
9254 0.640866
1.560389
0.1059
0.0000 0.581 18.59
8 0.196 0.651548
1.534807
0.8975
0.0742 0.044 0.013
9340 0.383829
2.605326
0.3000
0.0000 0.260 18.70
9 0.128 0.383871
2.605040
0.8599
0.0123 0.065 0.024
[email protected] normal University
Department of AstronomyRR-BL1
Frequency difference: RR0: f1>f0 48 stars 72.7% RR1: f1>f0 3 stars 16.7%
[email protected] normal University
Department of AstronomyRR-BL2
RR Lyrae with 2 close symmetric frequencycomponents: 28 4.2% RR1-BL2 : 12~42.8% RR0-BL2 : 16~57.2%
id p0 f0 a0 f1 a1 f2 a2 f1-f0 f2-f05348 0.408541 2.447735 0.258 2.446987 0.036 2.448536 0.035 -0.000748 0.000801 8575 0.379702 2.633646 0.119 2.632782 0.098 1.631312 0.060 -0.000864 -1.002334 9295 0.557803 1.792749 0.508 1.810833 0.106 1.774582 0.090 0.018084 -0.018167 10212 0.334634 2.988337 0.186 2.988668 0.071 2.987979 0.063 0.000331 -0.000358 11476 0.308001 3.246746 0.102 3.173872 0.094 3.246984 0.063 -0.072874 0.000238 11701 0.613466 1.630083 0.311 1.629831 0.179 1.630289 0.129 -0.000252 0.000206 11708 0.313990 3.184819 0.269 3.185052 0.087 3.184604 0.080 0.000233 -0.000215 12991 0.645131 1.550073 0.267 1.541876 0.027 1.558276 0.028 -0.008197 0.008203 13088 0.586977 1.703644 0.405 1.705505 0.073 1.701772 0.045 0.001861 -0.001872 13183 0.274270 3.646038 0.267 3.646744 0.087 3.645336 0.079 0.000706 -0.000702 13235 0.551093 1.814577 0.566 1.810560 0.084 1.818543 0.053 -0.004017 0.003966
[email protected] normal University
Department of AstronomyRR-BL3+
RR Lyrae with several close components :29 4.2% RR1-BL3+ : 14~48.3% RR0-BL3+ : 15~51.7%id p0 a0 a1 a2 a3 f1-f0 f2-f0 f3-f0
7634 0.335445
0.1540
0.1216
0.1065
0.0983
-0.000213
-0.000516
-0.002413
10248
0.558091
0.4282
0.1563
0.1049
0.1053
-0.001243
0.001263
-0.000623
11434
0.550632
0.3987
0.1441
0.1525
0.1118 0.009155 0.00028
8 0.00017
7
12620
0.377995
0.2287
0.1071
0.0887
0.0780 0.000353
-0.000964
-0.001810
12972
0.352589
0.2400
0.1152
0.0934
0.1056
-0.001872
-0.000501
-0.001518
12994
0.465035
0.5543
0.1632
0.1181
0.1091 0.022866 0.01142
6
-0.022867
13023
0.477521
0.5032
0.1112
0.0739
0.0798
-0.000122
0.000209
-0.000258
13039
0.364503
0.1514
0.1000
0.0928
0.1025
-0.000926
-0.000240
-0.000652
13078
0.465452
0.5608
0.1553
0.1208
0.0814 0.005300 0.00266
2
-0.005297
13095
0.319488
0.1982
0.0901
0.0548
0.0493 0.000336 0.00120
0 0.00069
8
[email protected] normal University
Department of AstronomyRR-D & RR-unknown
id p0 f0 Θ0 a0 mag p1 f1 Θ1 s1 a1
13070 0.569207
1.756831 0.2849 0.371 18.59
8 0.36231
6 2.76001
8 0.8473 0.0035 0.079
13230 0.599241
1.668779 0.2014 0.421 18.81
3 0.46490
2 2.15099
2 0.8116 0.0003 0.070
13254 0.520395
1.921617 0.0933 0.269 17.49
1 0.61143
0 1.63551
0 0.8807 0.0315 0.019
15056 0.347967
2.873839 0.3674 0.278 18.85
5 0.88281
4 1.13274
1 0.7799 0.0000 0.097
16035 0.358375
2.790370 0.5724 0.241 18.70
5 0.48160
4 2.07639
3 0.8355 0.0012 0.121
16818 0.602977
1.658437 0.0924 0.634 18.52
2 0.27035
9 3.69879
0 0.8951 0.0539 0.046
16953 0.398631
2.508585 0.2587 0.255 18.48
8 0.53402
6 1.87256
8 0.6515 0.0000 0.093
17317 0.465608
2.147729 0.6458 0.146 18.68
0 0.34595
3 2.89056
3 0.4689 0.0000 0.158
6 RR-D & 17 unknown type double period RR Lyrae stars
id p0 f0 Θ0 a0 m0 p1 f1 Θ1 s1 a1
7071 0.601141
1.663504 0.3352 0.474 19.04
3 0.99770
9 1.00229
6 0.799
6 0.000
4 0.147
16756
0.529150
1.889822 0.4502 0.432 18.50
6 0.99963
2 1.00036
8 0.697
8 0.000
0 0.276
16779
0.588831
1.698279 0.1346 0.654 18.69
5 0.99661
2 1.00340
0 0.896
7 0.082
6 0.061
17512
0.625897
1.597707 0.2898 0.287 18.44
7 0.99741
2 1.00259
5 0.882
7 0.046
2 0.050
13184
0.304925
3.279495 0.4371 0.254 18.61
7 0.49939
1 2.00243
7 0.616
3 0.000
0 0.137
17331
0.298121
3.354348 0.3886 0.257 18.66
9 0.49942
4 2.00230
6 0.757
3 0.000
0 0.098
[email protected] normal University
Department of AstronomyConclusion
Type Number Percent Notes
RR-S RR0-S 369 55.0% fundamental modeRR1-S 124 18.5% 1st overtone modeRR2-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% fundamental modeRR1-BL1 18 2.7% 1st overtone mode
RR-BL2 RR0-BL2 12 1.8% fundamental modeRR1-BL2 16 2.4% 1st overtone mode
RR-BL3+ RR0-BL3+ 14 2.1% fundamental mode
RR1-BL3+ 15 2.2% 1st overtone mode
RR-D 6 0.9% P1=1,2 c/dRR-
unknown 17 2.5%
[email protected] normal University
Department of AstronomyDiscussion
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, sothe Blazhko effect depends on the mode of pulsation and thenumber 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.
Thank You!
