On superChandrasekharmass progenitors

Whatever the evolutionary channel for SNe Ia progenitors may be, the accreting white dwarf is supposed to gain large amounts of angular momentum until it explodes (Langer et al. 2000; Piersanti et al. 2003; Saio & Nomoto 2004; Yoon & Langer 2004a). Owing to the effect of the centrifugal force on the white dwarf structure, the critical mass limit for thermonuclear explosion or collapse can significantly increase beyond the canonical Chandrasekhar limit of ~1.4M0. In particular, differentially rotating white dwarfs can be dynamically stable up to 4.0M0, as shown by Ostriker & Bodenheimer (1968). The mass of rigidly rotating white dwarfs cannot exceed 1.48MQ since the amount of angular momentum that a rigidly rotating white dwarf can retain is severely limited (e.g. James 1964).

Interestingly, Yoon & Langer (2004a) showed that non-magnetic white dwarfs should rotate differentially, for the following reason. In a rotating flow, the linear condition for the dynamical shear instability (DSI) is given by

where N2 denotes the Brunt-Vaisala frequency, a the shear factor (:= drn/dlnr), and Ric the critical Richardson number. In other words, shear with a > ac := ^N2/Ri c is susceptible to the DSI (see Figure 38.4). Although the DSI can reduce the degree of differential rotation on a dynamical time until the rotation profile becomes stable against the DSI (a —> ac), further redistribution of angular momentum by the secular shear instability or by Eddington-Sweet circulations can occur only on a thermal timescale (~108 yr in the core of white dwarfs), which is much longer than the accretion time (105-106 yr). Consequently, the white dwarf rotates differentially with a shear rate close to the critical value for the onset of the DSI throughout the mass-accretion phase, as shown in Yoon & Langer (2004a).

A thermonuclear explosion may occur when the central density of accreting white dwarfs exceeds about 2 x 109 g cm-3 (e.g. Yoon & Langer 2003). The mass needed for a differentially rotating white dwarf to reach this density depends on the total amount of angular momentum retained in the white dwarf, as shown in Figure 38.5. Therefore, white dwarfs exploding as Type-Ia SNe may have masses in the range from 1.38MQ to 2.0MQ for the SD scenario, or up to 2.4MQ in the DD scenario. The upper limit for the critical mass is determined by the available amount of mass in each scenario (Yoon & Langer 2005; Langer et al. 2000). This theoretical prediction may have been confirmed by the recent analysis of SNLS-30D3bb (SN 2003fg), which is the most luminous SN Ia ever observed (Howell et al. 2006). The nickel mass produced in this supernova appears to be about double (MNi « 1.3Mq) that in usual SNe Ia (MNi « 0.6M0), while the velocity of the

Figure 38.4. The threshold shear factor a := drn/dln r for the dynamical (solid line) and the secular (dashed line) shear instability, as a function of the local density. Constant gravity and temperature, i.e. g = 109 cm s-2, T = 5 x 107 are assumed. The chemical composition is also assumed to be constant, with XC = 0.43 and XO = 0.54. For the critical Richardson number, Ri>c = 0.25 is used; Re,c = 2,500 is used for the critical Reynolds number. See Yoon & Langer (2004a) for a detailed discussion.

Figure 38.4. The threshold shear factor a := drn/dln r for the dynamical (solid line) and the secular (dashed line) shear instability, as a function of the local density. Constant gravity and temperature, i.e. g = 109 cm s-2, T = 5 x 107 are assumed. The chemical composition is also assumed to be constant, with XC = 0.43 and XO = 0.54. For the critical Richardson number, Ri>c = 0.25 is used; Re,c = 2,500 is used for the critical Reynolds number. See Yoon & Langer (2004a) for a detailed discussion.

Figure 38.5. The critical angular momentum for thermonuclear explosion of CO white dwarfs (JSN Ia; solid line), and for electron-capture (EC)-induced collapse of CO white dwarfs (JEC, CO; dash-dotted line) and ONeMg white dwarfs (JEC, ONM; dashed line), as a function of the white dwarf mass. A SN Ia explosion is expected when /ECjCO < J < JSN Ia (shown as the hatched region). Electron-capture-induced collapse is supposed to occur when J < Jec,co for CO white dwarfs, and when J < JEC,ONeMg for ONeMg white dwarfs.

M/M0

Figure 38.5. The critical angular momentum for thermonuclear explosion of CO white dwarfs (JSN Ia; solid line), and for electron-capture (EC)-induced collapse of CO white dwarfs (JEC, CO; dash-dotted line) and ONeMg white dwarfs (JEC, ONM; dashed line), as a function of the white dwarf mass. A SN Ia explosion is expected when /ECjCO < J < JSN Ia (shown as the hatched region). Electron-capture-induced collapse is supposed to occur when J < Jec,co for CO white dwarfs, and when J < JEC,ONeMg for ONeMg white dwarfs.

Figure 38.6. A schematic representation of supernova-progenitor evolution for various scenarios in the M-J plane. Thick lines starting at a white dwarf mass of ~ M0 with J = 0 indicate various possible evolutionary paths of accreting white dwarfs: with accretion and simultaneous loss of angular momentum (A), without angular-momentum loss during the accretion phase (B), with inefficient accretion of angular momentum (C), and with maximum efficiency of internal angular-momentum transport (D) (see the text for details). The region where SN Ia explosion is expected is hatched, and the region where electron-capture-induced collapse is likely is shaded. For M ~ (10-7-10-6)M yr-1, a supernova explosion is expected at the upper borderline of the hatched area. The thin dashed line gives the M-J relation of rigidly rotating white dwarfs at critical rotation. Dotted lines denote lines of constant growth time of the r-mode instability (rr). See Yoon & Langer (2005) for more details.

M/Ma

Figure 38.6. A schematic representation of supernova-progenitor evolution for various scenarios in the M-J plane. Thick lines starting at a white dwarf mass of ~ M0 with J = 0 indicate various possible evolutionary paths of accreting white dwarfs: with accretion and simultaneous loss of angular momentum (A), without angular-momentum loss during the accretion phase (B), with inefficient accretion of angular momentum (C), and with maximum efficiency of internal angular-momentum transport (D) (see the text for details). The region where SN Ia explosion is expected is hatched, and the region where electron-capture-induced collapse is likely is shaded. For M ~ (10-7-10-6)M yr-1, a supernova explosion is expected at the upper borderline of the hatched area. The thin dashed line gives the M-J relation of rigidly rotating white dwarfs at critical rotation. Dotted lines denote lines of constant growth time of the r-mode instability (rr). See Yoon & Langer (2005) for more details.

ejecta is unusually low, which could be explained only by invoking a super-Chandrasekhar-mass progenitor of mass about 2.0MQ (Howell et al. 2006; Jeffrey et al. 2007).

Such an unusually massive white dwarf can exist only due to differential rotation. It should be noted that the merger of a double CO white dwarf per se cannot produce a super-Chandrasekhar white dwarf with a mass above 1.5 MQ - as is often misunderstood in the literature - unless differential rotation is involved (see Figure 38.6): if the central object is kept rotating rigidly, e.g. by magnetic torques, coalescence of double CO white dwarfs would produce a SN Ia progenitor whose mass is limited to about 1.48M©, surrounded by a carbon-oxygen Keplerian disk consisting of a fraction of the disrupted matter of the secondary.

On the other hand, the light curve of SN 2003fg deviates significantly from the standard relation between the maximum brightness and width. Since differentially rotating progenitors of SNe Ia may follow complicated evolutionary paths as illustrated in Figure 38.6 (Yoon & Langer 2005), it should thus be carefully investigated why most SNe Ia in nearby galaxies have a fairly homogeneous nature while some do not, a question that may have important implications for the use of SNe Ia for cosmological probes.

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