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Nonlinear Axisymmetric Pulsations of Rotating Relativistic Stars


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linkPfeil.gifPulsations of Rotating Relativistic Stars
linkPfeil.gifRelativistic Hydrodynamics
linkPfeil.gifGravitational Waveform Catalog
H. Dimmelmeier
N. Stergioulas (linkPfeilExtern.gifSection of Astrophysics, Astronomy and Mechanics, linkPfeilExtern.gifAristotle University of Thessaloniki, Greece)
J.A. Font (linkPfeilExtern.gifDepartamento de Astronomía y Astrofísica, linkPfeilExtern.gifUniversidad de Valencia, Spain)


Tables of Important Quantities and Pulsation Mode Frequencies:

A is a sequence of differentially rotating models with fixed rest mass M0 = 1.506 Msolar, AU is the corresponding sequence of uniformly rotating models, B is a sequence of differentially rotating models with fixed central rest-mass density rhoc (1 + epsc) = 1.28 x 10-3, and BU is the corresponding sequence of uniformly rotating models. All models are relativistic polytropes with N = 1 (corresponding to gamma = 2) and K = 100.

The following table summarizes the properties of the four investigated sequences A, AU, B, and BU of equilibrium models. rhoc (1 + epsc) is the central energy density M is the gravitational mass, R is the circumferential stellar radius, re is the coordinate stellar radius, rp / re is the axis ratio, Omegac/e are the central/equatorial angular velocity, respectively, and beta is the rotation rate.

Model rhoc (1 + epsc) M R re rp / re Omegac Omegae beta
[10-3] [10-2] [%]
A0 1.444 1.400 9.59 8.13 1.000 0.000 0.000 0.000
A1 1.300 1.405 10.01 8.54 0.930 0.202 0.076 0.018
A2 1.187 1.408 10.40 8.92 0.875 0.258 0.098 0.033
A3 1.074 1.410 10.84 9.35 0.820 0.294 0.113 0.049
A4 0.961 1.413 11.37 9.87 0.762 0.319 0.123 0.066
A5 0.848 1.418 12.01 10.49 0.703 0.334 0.130 0.086
A6 0.735 1.422 12.78 11.25 0.643 0.338 0.134 0.107
A7 0.622 1.427 13.75 12.21 0.579 0.334 0.134 0.131
A8 0.509 1.433 15.01 13.45 0.513 0.320 0.130 0.158
A9 0.396 1.439 16.70 15.13 0.444 0.295 0.122 0.189
A10 0.283 1.447 19.03 17.44 0.370 0.260 0.110 0.223
AU0 1.444 1.400 9.59 8.13 1.000 0.000 0.000 0.000
AU1 1.300 1.404 10.19 8.71 0.919 1.293 1.293 0.020
AU2 1.187 1.407 10.79 9.30 0.852 1.656 1.656 0.037
AU3 1.074 1.411 11.56 10.06 0.780 1.888 1.888 0.055
AU4 0.961 1.415 12.65 11.14 0.698 2.029 2.029 0.076
AU5 0.863 1.420 14.94 13.43 0.575 2.084 2.084 0.095
B0 1.444 1.400 9.59 8.13 1.000 0.000 0.000 0.000
B1 1.444 1.437 9.75 8.24 0.950 0.180 0.067 0.013
B2 1.444 1.478 9.92 8.36 0.900 0.257 0.094 0.026
B3 1.444 1.525 10.11 8.49 0.850 0.319 0.116 0.040
B4 1.444 1.578 10.31 8.63 0.800 0.373 0.134 0.055
B5 1.444 1.640 10.53 8.77 0.750 0.423 0.150 0.071
B6 1.444 1.713 10.76 8.91 0.700 0.471 0.165 0.087
B7 1.444 1.798 11.01 9.05 0.650 0.519 0.179 0.105
B8 1.444 1.899 11.26 9.17 0.600 0.568 0.192 0.124
B9 1.444 2.020 11.50 9.26 0.550 0.623 0.205 0.144
BU0 1.444 1.400 9.59 8.13 1.000 0.000 0.000 0.000
BU1 1.444 1.432 9.83 8.33 0.950 1.075 1.075 0.012
BU2 1.444 1.466 10.11 8.58 0.900 1.509 1.509 0.024
BU3 1.444 1.503 10.42 8.82 0.850 1.829 1.829 0.037
BU4 1.444 1.543 10.78 9.13 0.800 2.084 2.084 0.050
BU5 1.444 1.585 11.20 9.50 0.750 2.290 2.290 0.062
BU6 1.444 1.627 11.69 9.95 0.700 2.452 2.452 0.074
BU7 1.444 1.666 12.30 10.51 0.650 2.569 2.569 0.084
BU8 1.444 1.692 13.07 11.26 0.600 2.633 2.633 0.091
BU9 1.444 1.695 13.44 11.63 0.580 2.642 2.642 0.092

In the following table the frequencies of the fundamental quasi-radial (l = 0) mode, F, its first overtone, H1, the fundamental quadrupole (l = 2 $) mode, 2f, its first overtone, 2p1, and three inertial modes, i-2, i1, and i2 are given for sequences A, AU, B, and BU. All frequencies are given in kHz.

Model F H1 2f 2p1 i-2 i1 i2
A0 1.458 3.971 1.586 3.726 0.000 0.000 0.000
A1 1.400 3.816 1.577 3.580 0.302 0.460 0.596
A2 1.358 3.733 1.567 3.424 0.399 0.603 0.779
A3 1.307 3.664 1.550 3.237 0.477 0.711 0.917
A4 1.248 3.583 1.535 3.013 0.543 0.794 1.022
A5 1.184 3.494 1.513 2.780 0.603 0.863 1.108
A6 1.105 3.352 1.482 2.557 0.646 0.914 1.163
A7 1.018 3.360 1.432 2.315 0.683 0.946 1.198
A8 0.915 3.114 1.360 2.068 0.711 0.965 1.204
A9 0.809 2.985 1.264 1.827 0.723 0.958 1.180
A10 0.685 2.830 1.098 1.610 0.712 0.911 1.104
AU0 1.458 3.971 1.586 3.726 0.000 0.000 0.000
AU1 1.398 3.785 1.562 3.455 0.280 0.354 0.468
AU2 1.345 3.716 1.554 3.192 0.384 0.478 0.611
AU3 1.283 3.635 1.537 2.885 0.468 0.575 0.736
AU4 1.196 3.552 1.516 2.520 0.545 0.660 0.810
AU5 1.107 3.457 1.459 2.090 0.639 0.747 0.858
B0 1.458 3.971 1.586 3.726 0.000 0.000 0.000
B1 1.407 3.927 1.628 3.713 0.258 0.399 0.518
B2 1.373 3.927 1.670 3.666 0.370 0.567 0.739
B3 1.332 3.964 1.709 3.584 0.463 0.702 0.912
B4 1.287 4.014 1.747 3.490 0.544 0.819 1.061
B5 1.237 4.072 1.789 3.390 0.622 0.921 1.208
B6 1.178 4.118 1.819 3.280 0.681 1.015 1.318
B7 1.077 4.179 1.854 3.187 0.750 1.090 1.439
B8 1.080 4.212 1.900 3.103 0.827 1.213 1.562
B9 0.945 4.469 1.917 3.028 0.890 1.294 1.670
BU0 1.458 3.971 1.586 3.726 0.000 0.000 0.000
BU1 1.413 3.915 1.611 3.634 0.224 0.288 0.385
BU2 1.380 3.907 1.635 3.516 0.326 0.413 0.541
BU3 1.343 3.921 1.669 3.345 0.408 0.511 0.658
BU4 1.304 3.950 1.698 3.200 0.486 0.601 0.762
BU5 1.281 3.964 1.714 3.018 0.552 0.675 0.847
BU6 1.219 4.010 1.729 2.859 0.617 0.743 0.912
BU7 1.207 4.018 1.720 2.677 0.680 0.809 0.969
BU8 1.168 4.030 1.685 2.512 0.723 0.868 1.004
BU9 1.169 4.029 1.679 2.483 0.737 0.878 1.004

The following table gives the frequencies of the fundamental hexadecapole (l = 4) mode, 4f, and its first overtone, 4p1, for the sequence of differentially rotating models A (left) and B (right). All frequencies are given in kHz.

Model 4f 4p1 Model 4f 4p1
A0 2.440 4.896 B0 2.440 4.896
A1 2.370 4.727 B1 2.453 4.877
A2 2.300 4.600 B2 2.468 4.855
A3 2.223 4.372 B3 2.486 4.827
A4 2.130 4.130 B4 2.500 4.781
A5 2.028 3.864 B5 2.504 4.740
A6 1.910 3.617 B6 2.491 4.643
A7 1.780 3.116 B7 2.499 4.556
A8 1.630 2.790 B8 2.501 4.506
A9 1.480 2.430 B9 2.493 4.164
A10 1.330 2.028




topComments to: Harald Dimmelmeier emailharrydee@mpa-garching.mpg.de