Extreme mass loss during common envelope evolution: The origin of the double low-mass white dwarf system J2102–4145

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Table 2.

CE summary for J2102–4145, assuming a residual H mass $M_{H}^{fit} = 10^{- 7} M_{⊙}$ $Mathematical equation: $ M_{\mathrm{H}}^\mathrm{{fit}} = 10^{-7}\,M_\odot $$ that reproduces the observed radius of the secondary WD.

M_ZAMS	M_core	R_phot	a_i	P_i	a_f	ΔE_orb	E_bind	α_CE	E_extra(α_★)
[M_⊙]	[M_⊙]	[R_⊙]	[R_⊙]	[day]	[R_⊙]	[10⁴⁷ erg]	[10⁴⁷ erg]		[10⁴⁷ erg]
1.0	0.315	28.0	60.1	37.0	0.854	2.494	1.44	0.577	{α_★ = 1 : − ; α_★ = 0.5 : 0.192}
1.5	0.315	25.1	50.1	26.6	0.854	2.402	2.41	1.003	{α_★ = 1 : 0.007; α_★ = 0.5 : 1.21}
1.8	0.315	22.1	42.7	20.6	0.854	2.315	3.494	1.510	{α_★ = 1 : 1.18; α_★ = 0.5 : 2.34}

Notes. a_now = 0.80190 R_⊙ (common to all three cases). P_i is the orbital period at CE onset, derived from a_i through Kepler’s third law using M_1, WD = 0.375 M_⊙. E_extra(α_★) denotes the additional energy required to reach the target α_★ while keeping $M_{H}^{fit} = 10^{- 7} M_{⊙}$ $Mathematical equation: $ M_{\mathrm{H}}^{\mathrm{fit}} = 10^{-7}\,M_\odot $$ . The orbital-energy change is computed from a_i to a_f, and the binding energy from m_cut to the stellar surface.

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