A cataclysmic variable has a white-dwarf accretor of mass and a companion (donor)…

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Celestial mechanics and planetary systems · Celestial mechanics and planetary systems

Stars from the Inside, Ch Binary stars: fitted orbits, modelled eclipses and the Roche geometry

Problem

A cataclysmic variable has a white-dwarf accretor of mass m1=0.90 M⊙m_1 = 0.90\,M_\odot and a companion (donor) star of mass m2=0.27 M⊙m_2 = 0.27\,M_\odot and measured radius R2=0.27 R⊙R_2 = 0.27\,R_\odot, in a circular orbit of period P=0.10 dP = 0.10\,\mathrm{d}. ((a)) Use Kepler's third law to find the orbital separation aa in solar radii. ((b)) Use the Eggleton formula rLa=0.49 q2/30.6 q2/3+ln⁡(1+q1/3),q=m2m1,\frac{r_L}{a} = \frac{0.49\,q^{2/3}}{0.6\,q^{2/3} + \ln(1+q^{1/3})},\qquad q = \frac{m_2}{m_1}, to find the donor's Roche-lobe radius rLr_L in solar radii, and state whether the donor fills its Roche lobe.

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