We have performed the first set of 2D Newtonian multi-group flux-limited diffusion radiation-hydro-dynamics calculations of accretion induced collapse using initial rotational equilibrium configurations [Yoon & Langer 2005] set up with accreting-white-dwarf rotation laws [Yoon & Langer 2004]. The general results of the simulations are discussed in [Dessart et al. 2006] Here we have focussed on the gravitational wave emissions of two progenitor white dwarf models that differ in initial central angular velocity and total white dwarf mass (1.46-M_Sun model with Omega_c = 0, 1.92-M_Sun model with Omega_c = 17.62 rad/s). For the first time we present gravitational waveform estimates for AIC.

We find that due to the high initial white dwarf central densities of 5 x 10¹⁰ g/cm³, electron capture sets in quickly and in a very efficient fashion. This results in fast collapse and small inner core masses. At the time of core bounce the small inner core of the 1.46-M_Sun model is only slightly rotationally deformed. This leads to a weak peak matter gravitational wave signal (see Table 1) that qualitatively resembles what has been suggested as a type-III ``fast collapse'' waveform in previous studies [e.g., Zwerger & Müller 1997, Dimmelmeier et al. 2002]. The 1.92-M_Sun model exhibits greater centrifugal flattening, but experiences strong rotational support only during the plunge phase of collapse, leading to a matter gravitational waveform whose morphology still resembles the above mentioned type-III, but clearly shows the imprint of fast rotation. Therefore we classify it as type-III/II transitional --- a type of waveform morphology not published before.

Both AIC models show strong anisotropies in their neutrino radiation fields throughout their postbounce evolution. Our analysis of the gravitational wave emission from anisotropic neutrino radiation fields (using the formalism introduced by [Epstein 1978]) indicates that the neutrino waveform dominates the amplitudes at postbounce times greater than ~50 ms, but not the total gravitational wave energy emission. The neutrino waveform has an inherent memory effect, leaving behind a constant offset in h once the anisotropic emission subsides (on the timescale of ~10 s). It is not entirely clear how such ``DC''-like offsets would be detectable by current and future gravitational wave antennas (but see [Braginskii & Thorne 1987] and [Buonanno et al. 2005]).

(Click for PDF version of this table)

Table 1 summarizes the quantitative aspects of the AIC models' gravitational wave signature. Please note that the numbers for the total radiated energy and the related maximum characteristic gravitational wave strains [ Flanagan & Hughes 1998] are different from what we stated in [Dessart et al. 2006] since we have found and corrected an error in our analysis routines.

The characteristic strain spectrum of the 1.46-M_Sun model's mass-quadrupole emission peaks at ~430 Hz with a maximum h_char ~1.45 x 10^-21 while the more centrifugally supported 1.92-M_Sun model has a maximum h_char2.8 x 10^-21 at f ~166 Hz. The gravitational wave emission in both models is dominated in amplitude by the component that is due to anisotropic neutrino emission, reaching h_char,max of 4.59 and 19.88 x 10^-21 in the 1.46-M_Sun and 1.92-M_Sun models, respectively. However, owing to the low-frequency nature of this emission, the emitted energy is minuscle and current and future LIGOs are unlikely to be able to detect this gravitational wave component.

Based on a comparison with LIGO sensitivity we surmise that for optimal source--detector orientation, the mass-quadrupole emission of the 1.92-M_Sun model should be detectable by current and future LIGO-class observatories throughout the Milky Way. The 1.46-M_Sun model may be marginally detectable by the currently operative LIGO I detectors, but should certainly be visible to advanced LIGO throughout the Milky Way, provided favorable source/detector orientation. Note that we find final ratios of rotational kinetic to gravitational potential energy, beta = T/W, of ~0.06 and ~0.26 in the 1.46-M_Sun and 1.92-M_Sun models, respectively. Both betas may be large enough for the models to undergo nonaxisymmetric rotational instabilities which could lead to the prolonged and strong emission of gravitational waves in a narrow frequency band. This deserves further investigation in 3D.

[Fryer et al. 2002] estimated the gravitational wave emission from aspherical accelerated mass motions in the single rotating AIC model of [Fryer et al. 1999]. This model employed a simple, solid-body rotation law and had a final beta of ~0.06. They did not consider anisotropic neutrino emission. Our more realistic models yield maximum (matter) gravitational wave amplitudes that are 1.5--2 orders of magnitude smaller than those predicted by [Fryer et al. 2002]. The total energy emission matches to within a factor of a few since our models emit at higher frequencies.

We point out that the results and conclusions presented here on the gravitational wave signature of accretion-induced collapse should be considered as preliminary in a variety of aspects. Our calculations are performed in axisymmetry, rely on Newtonian gravity, do not include magnetic field effects, and treat neutrino radiation transport in the MGFLD approximation. We have considered only two initial white dwarf models and for both assumed unusually high initial central densities. A large parameter study in initial rotational configuration and central density will be required to fully understand the systematics of AIC collapse and postbounce evolution, and the corresponding gravitational waveforms. Nevertheless, we believe that our work marks an important step towards realistic models of AICs and reliable predictions of their gravitational wave signature.