Eccentric binaries: Periastron events and tidal heating

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Table 5.

Input parameters and results MACHO 80.7443.1718.

Parameter	Value	Notes
Data from observations and input parameters

P_orb	32.83627 d	^(a)
e	0.507	^(a)
m₁	34.5 M_⊙	^(b)
m₂	15.7 M_⊙	^(b)
R₁	23.7 R_⊙	^(b)
V_rot	250 km s⁻¹	^(c)
L_*	1.57 × 10³⁹ ergs s⁻¹	^(b)
ΔF_peri/F	∼23%	^(d)
β₀	1.95
λ	1
N_cy	100
N_r	5
a	159 R_⊙
r_per	78.5 R_⊙

Output values and results

${\dot{E}}_{peri}$ $\dot{E}_{\mathrm{peri}}$	3.7 × 10³⁸ ergs s⁻¹	^(e)
${\dot{E}}_{apo}$ $\dot{E}_{\mathrm{apo}}$	6.6 × 10³⁶ ergs s⁻¹	^(e)
$⟨ {\dot{E}}_{tot} ⟩$ $\langle\dot{E}_{\mathrm{tot}}\rangle$	6.5 × 10³⁷ ergs s⁻¹	^(e)
$Δ {\dot{E}}_{peri}$ $\Delta\dot{E}_{\mathrm{peri}}$ /L_*	23.5%	^(f)
R_{max − peri}	23.83 R_⊙	^(g)
R_{min − per}	23.63 R_⊙	^(g)
R_{max − ap}	23.76 R_⊙	^(g)
R_{min − ap}	23.66 R_⊙	^(g)
⟨R_per⟩	23.71 R_⊙	^(h)
⟨R_ap⟩	23.70 R_⊙	^(h)

Notes.

^(a)

Jayasinghe et al. (2019);

^(b)

Jayasinghe et al. (2021);

^(c)

adopting an orbital inclination i = 44° and vsin(i) = 174 km s⁻¹ from Jayasinghe et al. (2021);

^(d)

estimated from Fig. 9 of Jayasinghe et al. (2021) which shows maximum light at levels of ∼1.2 to ∼1.26 (depending on the TESS sector) above the average value ∼1 between subsequent periastron passages;

^(e)

output from TIDES-nvv;

^(f)

( ${\dot{E}}_{tot}^{peri} - {\dot{E}}_{tot}^{apo}$ $\dot{E}_{\mathrm{tot}}^{\mathrm{peri}}{-}\dot{E}_{\mathrm{tot}}^{\mathrm{apo}}$ )/L_*;

^(g)

maximum and minimum equatorial radius at periastron and apastron, including high frequency oscillations, from the TIDES-1 version of the code with ν = 0.028 $R_{⊙}^{2}$ $R^2_\odot$ d⁻¹. The corresponding values from the TIDES1-vv model with λ = 0.01 are 23.76 and 23.67 R_⊙;

^(h)

average polar radius at periastron and apastron from the TIDES-1 version of the code.

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