The thermonuclear explosion of a C/O white dwarf as a Type Ia supernova (SN Ia) generates a kinetic energy comparable to that released by a massive star during a SN II event. Current observations and theoretical models have established that SNe Ia are asymmetric, and therefore--like SNe II--potential sources of gravitational wave (GW) radiation. We perform the first detailed calculations of the GW emission for a SN Ia of any type within the single-degenerate channel. The gravitationally-confined detonation (GCD) mechanism predicts a strongly-polarized GW burst in the frequency band around 1 Hz. Third-generation spaceborne GW observatories currently in planning may be able to detect this predicted signal from SNe Ia at distances up to 1 Mpc. If observable, GWs may offer a direct probe into the first few seconds of the SNe Ia detonation.
Introduction.-The discovery of the Phillips relation [1] enabled the use of Type Ia supernova (SN Ia) as standardizable cosmological candles, and ushered in a new era of astronomy leading to the discovery of the acceleration of the universe [2,3]. Understanding the evolution of SNe Ia may improve the systematics errors associated with the the calibration of the Phillips relation and allow precision studies of dark energy [4].
The single-degenerate (SD) channel of SNe Ia consists of a C/O white dwarf (WD) accreting mass from a nondegenerate main sequence or red giant companion. As the WD approaches the Chandrasekhar limit, carbon burning is initiated in its convective core [5,6]. After a few hundred years of this “simmering” phase, unstable thermonuclear burning is expected to ignite at one or more off-centered points, giving rise to a buoyantlyrising, subsonic deflagration flame bubble.
Both the deflagration-to-detonation transition (DDT) [7] and the gravitationally-confined detonation (GCD) [8,9] models for the SN Ia explosion mechanism begin with this stage of off-centered ignition. The predictions of the two mechanisms depart by the evolution of the bubble as it approaches breakout. The DDT mechanism posits that a transition from deflagration to detonation is made prior to bubble breakout. While the DDT mechanism yields results consistent with observation, it requires that the density at which the transition is made to be set as a free parameter. In contrast, in the GCD model, the flame bubble breaks through the surface of the WD, launching ash into a surface flow; see Figure 1. The initial deflagration phase is relatively inefficient, typically burning only a modest fraction of the mass of the WD. Therefore, in the GCD model, the WD remains gravitationally-bound, leading to a ram-pressure driven detonation at the point opposite of bubble breakout, which subsequently unbinds the WD. Significantly, because both the GCD and the DDT initiate detonations near the edge of the WD, both are intrinsically and strongly asymmetrical. Spectropolarimetry measurements of lines of intermediate mass ions, including Si II and Ca II, yield greater polarizations in the outer layers of SNe Ia [10], strongly suggesting asymmetry in the later phases of burning. Furthermore, Maeda et al. [11] demonstrated that an intrinsic asymmetry in Ia ejecta, viewed from a random direction, can account for their spectral evolution diversity. Taken together, these observations are broadly consistent with the asymmetries predicted by the DDT and the GCD mechanisms of SNe Ia. The combined intrinsic asymmetry and large kinetic energy of the explosion motivates us to consider the nature of gravitational wave (GW) radiation from SNe Ia in this paper. As is the case with SNe II, which are known to be candidate GW sources in the 10 2 -10 3 Hz region of LIGO-like instruments [12][13][14], the asymmetry of SNe Ia naturally leads to the production of GWs.
We may simply estimate the GW signal strength of a SN Ia using the Newtonian-quadrupole approximation to the Einstein field equations: h ≃ G Q/(c 4 D). Here Q is the quadrupole mass moment, D is the distance to the source, and G and c are the universal gravitational constant, and the speed of light, respectively. We can place a robust upper-bound on the SN Ia GW amplitude by assuming that the Ia mechanism is highly aspherical, such that the non-spherical kinetic energy is Q/4 ∼ E ns kin ∼ E kin ∼ 10 51 ergs [15]. With this assumption, we estimate an upper-bound of the dimensionless strain amplitude as 10 -20 at a distance of 10 kpc.
We next estimate the characteristic GW frequency range of a SNe Ia detonation. The detonation speed v det within a WD of radius R is set according to the Chapman-Jouguet detonation condition [16], and yields a characteristic frequency f det ∼ v det /(2R). Esti-mating the radius R ∼ 2000 km as that of a cold, near-Chandrasekhar mass C/O WD, and the Chapman-Jouguet speed as v det ∼ 10 4 km/s, we establish an upper-bound to the frequency of the expected GW signal at < ∼ 2.5 Hz. This simple estimate implicitly assumes no pre-expansion occurs during the initial deflagration phase, and corresponds to an overluminous SNe Ia event which will yield ≃ 1.2M ⊙ of 56 Ni [17]. A lower-bound to the detonation frequency can be estimated using the pre-expansion out to R ∼ 4000 km required to produce the observed nucleosynthetic yield of ≃ 0.7M ⊙ 56 Ni in normal brightness Ia events [18] : f det > ∼ 1 Hz. If the detonation is sufficiently asymmetric, this GW signal may be detectable by proposed third-generation GW instruments. We next develop a more refined estimate by post-processing three-dimensional (3D) simulations of the GCD mechanism [9].
Methodology.-We simulate the evolution of a 3D hydrodynamical GCD SNe Ia in the SD channel [9]. The progenitor WD is evolved from the onset of deflagration through detonation. The simulations employ the Euler equations of inviscid, non-relati
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