Hydrogen-burning white-dwarf envelope

A hydrogen-burning white-dwarf envelope is a thin nondegenerate surface layer in which accreted or residual hydrogen can undergo nuclear fusion above a degenerate core.

In a thin nondegenerate hydrogen-burning white-dwarf envelope, fix gravity $g$ and use $P=g\Sigma$, $\rho =B\Sigma /T$. With opacity $\kappa ={\kappa }_0\rho T^{-2}$ and specific heating $ϵ={ϵ}_0\rho T^{15}$, set $y=T^7$, $x={\Sigma }^2/2$. Then $y^{\prime }=AF$ and $F^{\prime }=-{ϵ}_{0}B{y}^2$, where $A=21{\kappa }_{0}B/(4ac)$ and ${\omega }^2=A{ϵ}_{0}B$. Radiative-zero surface and zero core-flux base conditions give $(y^{\prime }{)}^2=(2{\omega }^2/3)(y_b^3-y^3)$. Thus $T_b\propto F_s^{2/21}$ and $F_s=12I^3/(A{\omega }^2{\Sigma }_b^6)$, with $I={\int }_0^1(1-t^3{)}^{-1/2}dt$. At fixed column the specific heating varies as $T^{14}$ while radiative cooling varies as $T^7$, giving thin-shell instability in this approximation.

Thin-shell instability is a thermal runaway of nuclear burning in a geometrically thin layer whose pressure is constrained by overlying weight, weakening expansion-driven cooling.

A classical nova is a thermonuclear runaway in hydrogen-rich material accreted onto a white dwarf, producing a sudden luminous outburst and ejecting part of the envelope.

An idealized classical nova that slowly ejects mass $\delta m$ isotropically from the accretor, compared with the orbital period, but quickly compared with the mass-transfer timescale, expands a circular binary star's Roche lobe. The ejecta carry accretor specific angular momentum $j_1/J=M_2/(M_{1}M)=q/M$. Taking $\delta J/J=-q\delta m/M$, $\delta M_1=-\delta m$ and $\delta M_2=0$ in $J=M_1{M}_2\sqrt{Ga/M}$ proves $\delta a/a=\delta m/M$. The lobe law $R_L\propto a(M_2/M{)}^{1/3}$ then gives $\delta R_L/R_L=4\delta m/(3M)$. A donor whose radius is unchanged moves inside its lobe.

For constant external loss $\Gamma =-\dot{J}>0$ and a donor sequence $R_2\propto M_2^{\zeta }$, the fractional gap closes at rate $2\Gamma /J$, giving $t_d=2J\delta m/(3M\Gamma )$. The binary mass-transfer contact equation gives accumulation time $t_s=J\delta m(\zeta +5/3-2q)/(2M_2\Gamma )$. ThereforeThis first-order result requires $\delta m/M\ll 1$, a positive contact denominator and a fixed donor radius during the eruption. At $\zeta =1$ it reduces to $2q/[(1+q)(4-3q)]$.