May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 1 Gravitational Wave Sources near 1 Hz Avetis Abel Sadoyan Mathew Benacquista Montana State Billings Montana State University-Billings D.Sedrakian, M.Hairapetyan, K. Shahabasyan Yerevan State University CRDF/NFSAT Award #ARP YE-04

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 2 Outline White dwarf frequencies Gravitational radiation mechanisms Stochastic background level near 1 hz

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 3 Why White Dwarfs? WD NS

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 4 Why White Dwarfs? White Dwarfs(WD) are stellar configurations with central densities ~ g/ cm 3 -they are on the border between normal stars and relativistic configurations Quadrupole moment of WDs is Q~10 48 g cm 2 - several orders higher then Neutron Star’s Quadrupole moment

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 5 Why White Dwarfs ? White Dwarfs(WD) are the most close potential sources of GWs - there are White Dwarfs at 8 pc distance. WD Population is estimated about ~10 8 in the Galaxy -WDs are the largest population among potential astrophysical sources of GWs

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 6 Strain Amplitudes Oblate shape due to rotation Oscillation is self-similar and is described by: Quadrupole moment Choose z-axis along rotation axis: Q 0 zz =–2Q 0 xx =–2Q 0 yy =–2Q 0

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 7 Polarizations In TT gauge with z-axis along the wave vector: where  is the angle between the wave vector and the white dwarf axis of rotation

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 8 Gravitational Radiation Intensity

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 9 White Dwarf Properties and Resonant Frequencies  c (g/cm 3 ) M 0 (M  ) M (M  ) Ω max Q 0 max (10 48 g cm 2 ) N (57) 

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 10 Frequency Range of WD Oscillations Central density

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 11 M and M o are mass of rotating and non- rotating configurations with same complete number of baryons N Deformation Energy

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 12 White Dwarfs Maximal deformation Energy versus Central density

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 13 GW Amplitudes from WDs rotating with Keplerian angular velocities

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 14 Mechanisms of GW Radiation 1.GWs from Magnetized WDs: -deformation energy is feeding oscillations -magnetodipol radiation torque is breaking rotation 2.GWs from differentially rotating WDs 3.GWs from triaxial WDs

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 15 Types of Models of WDs Model 1.a is calculated by requiring that the largest Doppler broadening of spectral lines due to pulsations be less than thermal Doppler broadening Model 1.m is based on assumption that all non-dissipated part of deformation energy is going to oscillations, it is maximal possible model to that sense.

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 16 GWs from Magnetized WDs 1.a WD Name r (pc) B (MG) hoho F t (Gy ) PG EUVE J PG Feige G KPD PG G

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 17 GWs from Magnetized WDs 1.m WD Name r (pc) B (MG) hoho F t (Gy ) PG    EUVE J    PG    Feige    G    KPD    PG    G     10 -4

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 18 Differentially Rotating WDs model 2.1 Edifrot IEdiss I LifeTime (Gyr) Jo Iho Etta F Flux PG E E+26 2,2 1.26E E E-013.3E-14 EUVE J E E+28 0,1 8.52E E E-012.2E-11 PG E E+26 0,5 9.87E E E-012.6E-13 Feige E E+25 11,8 9.33E E E-012.4E-14 G E E+26 11,8 4.51E E E-021.2E-13 KPD E E+26 2,2 1.01E E E-012.6E-14 PG E E+25 2,2 4.93E E E+001.3E-14 G E E+26 2,2 3.63E E E-019.4E-14 Average 1.9E-26

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 19 Differentially Rotating WDs model 2.2 Edifrot IIEdiss II LifeTime (Gyr) Jo IIhoEttaFlux PG E E+25 1,4 8.44E E E-012.2E-14 EUVE J E E+28 0,1 5.53E E E-011.4E-11 PG E E+26 0,2 6.49E E E-011.7E-13 Feige E E+25 9,3 6.38E E E-011.7E-14 G E E+26 9,3 3.09E E E-028.0E-14 KPD E E+25 1,4 6.80E E E-011.8E-14 PG E E+25 1,4 3.31E E E-018.6E-15 G E E+26 1,4 2.44E E E-016.3E-14

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 20 Triaxsial WDs model 3.r Rotating triaxsial ellipsoid  с  10 6, g/сm 3 M/MM/M Re108Re108 I 3  g.сm 2  max H, km  J 0  erg/sec h0h0  0  10 2 Gyear ,

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 21 Triaxsial WDs model 3.n Non Rotating, oscillating triaxsial ellipsoid  c  10 6 g/см 3 M0/MM0/M R  10 8 cm I 0  g.см 2 , s -1 H, km  hoho  10 3 Gyear

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 22 Stochastic background level Background is not isotropic: Assuming a galactic distribution of white dwarfs to follow the disk population, we assign a density distribution of WDs: in galacto-centric cylindrical coordinates, with R 0 =2.5kpc and h=200pc

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 23 Conclusions Gravitational radiation spectrum near 1 hz is inhabited by Isolated White dwarfs Model 1.a h av+ = Model 1.m h av+ = Model 2.1 h av+ = Model 2.2 h av+ = Standard inflation gives h~ – in this frequency range.

May 30, 2006 LIGO-G Z Gravitational Wave Advanced Detectors Workshop 24 Equation of State for White Dwarfs where