Table 7.

Orbital and astrophysical parameters of BG Ind from the joint photodynamical light curve, RV, ETV, SED, and PARSEC isochrone solution.

Orbital elements
Subsystem
ABA–B
Pa (d)|$1.464\,065_{-0.000\,002}^{+0.000\,002}$||$0.528\,349_{-0.000\,002}^{+0.000\,002}$||$720.9_{-3.1}^{+3.4}$|
a (R)|$7.602_{-0.043}^{+0.038}$||$3.025_{-0.016}^{+0.011}$||$540.4_{-2.2}^{+2.7}$|
e00|$0.209_{-0.048}^{+0.028}$|
ω (°)|$1.6_{-8.8}^{+9.2}$|
i (°)|$73.27_{-0.13}^{+0.06}$||$84.29_{-0.87}^{+0.85}$||$85.5_{-6.3}^{+3.1}$|
|$\mathcal {T}^\mathrm{pri}$| [BJD – 2400 000 ]|$58326.1362_{-0.0012}^{+0.0011}$||$58325.8072_{-0.0022}^{+0.0025}$|
τ [BJD – 24000 00]|$58699_{-21}^{+14}$|
Mass ratio [q = msec/mpri]|$0.919_{-0.006}^{+0.010}$||$0.932_{-0.015}^{+0.014}$||$0.483_{-0.005}^{+0.007}$|
Kpri (km s−1)|$120.47_{-0.75}^{+1.12}$||$138.98_{-1.39}^{+1.23}$||$12.57_{-0.24}^{+0.17}$|
Ksec (km s−1)|$130.99_{-0.50}^{+0.48}$||$149.25_{-1.13}^{+1.09}$||$26.02_{-0.50}^{+0.31}$|
γ (km s−1)|$48.69_{-0.59}^{+0.29}$|
Stellar parameters
AaAbBaBb
Relative quantities and atmospheric properties
Fractional radiusb [R/a]|$0.3084_{-0.0044}^{+0.0016}$||$0.2096_{-0.0019}^{+0.0052}$||$0.2120_{-0.0014}^{+0.0013}$||$0.2019_{-0.0020}^{+0.0018}$|
Fractional flux [in TESS-band]|$0.6294_{-0.0153}^{+0.0064}$||$0.3475_{-0.0060}^{+0.0165}$||$0.0133_{-0.0008}^{+0.0009}$||$0.0092_{-0.0007}^{+0.0008}$|
|$x_\mathrm{bol}^c$||$0.676_{-0.001}^{+0.001}$||$0.671_{-0.001}^{+0.001}$|......
|$y_\mathrm{bol}^c$||$0.174_{-0.003}^{+0.002}$||$0.198_{-0.003}^{+0.002}$|......
|$x_{TESS}^c$||$0.631_{-0.001}^{+0.001}$||$0.618_{-0.001}^{+0.001}$||$0.720_{-0.001}^{+0.001}$||$0.724_{-0.002}^{+0.001}$|
|$y_{TESS}^c$||$0.347_{-0.002}^{+0.002}$||$0.354_{-0.003}^{+0.002}$||$0.281_{-0.005}^{+0.005}$||$0.325_{-0.018}^{+0.019}$|
βd|$0.11_{-0.07}^{+0.10}$||$0.64_{-0.33}^{+0.29}$|0.320.32
Physical quantities
m (M)|$1.432_{-0.024}^{+0.015}$||$1.315_{-0.023}^{+0.026}$||$0.688_{-0.011}^{+0.008}$||$0.640_{-0.011}^{+0.010}$|
Rb (R)|$2.339_{-0.021}^{+0.016}$||$1.592_{-0.019}^{+0.047}$||$0.642_{-0.007}^{+0.005}$||$0.611_{-0.009}^{+0.008}$|
|$T_\mathrm{eff}^b$| (K)|$6442_{-28}^{+29}$||$6816_{-26}^{+26}$||$4609_{-49}^{+48}$||$4327_{-57}^{+62}$|
|$L_\mathrm{bol}^b$| (L)|$8.433_{-0.169}^{+0.199}$||$4.934_{-0.179}^{+0.279}$||$0.167_{-0.009}^{+0.009}$||$0.118_{-0.009}^{+0.009}$|
|$M_\mathrm{bol}^b$||$2.45_{-0.03}^{+0.02}$||$3.04_{-0.06}^{+0.04}$||$6.72_{-0.06}^{+0.06}$||$7.09_{-0.08}^{+0.08}$|
|$M_V^b$||$2.45_{-0.03}^{+0.03}$||$3.02_{-0.06}^{+0.04}$||$7.23_{-0.09}^{+0.10}$||$7.83_{-0.13}^{+0.13}$|
log gb (dex)|$3.852_{-0.005}^{+0.011}$||$4.150_{-0.016}^{+0.007}$||$4.660_{-0.002}^{+0.003}$||$4.672_{-0.004}^{+0.004}$|
Global quantities
log (age)b, e (dex)|$9.40_{-0.01}^{+0.02}$||$9.32_{-0.01}^{+0.03}$|
[M/H]b (dex)|$-0.189_{-0.037}^{+0.038}$|
E(BV) (mag)|$0.018_{-0.013}^{+0.015}$|
|$(M_V)_\mathrm{tot}^b$||$1.93_{-0.03}^{+0.03}$|
Distance (pc)|$69.7_{-0.9}^{+0.7}$|
Orbital elements
Subsystem
ABA–B
Pa (d)|$1.464\,065_{-0.000\,002}^{+0.000\,002}$||$0.528\,349_{-0.000\,002}^{+0.000\,002}$||$720.9_{-3.1}^{+3.4}$|
a (R)|$7.602_{-0.043}^{+0.038}$||$3.025_{-0.016}^{+0.011}$||$540.4_{-2.2}^{+2.7}$|
e00|$0.209_{-0.048}^{+0.028}$|
ω (°)|$1.6_{-8.8}^{+9.2}$|
i (°)|$73.27_{-0.13}^{+0.06}$||$84.29_{-0.87}^{+0.85}$||$85.5_{-6.3}^{+3.1}$|
|$\mathcal {T}^\mathrm{pri}$| [BJD – 2400 000 ]|$58326.1362_{-0.0012}^{+0.0011}$||$58325.8072_{-0.0022}^{+0.0025}$|
τ [BJD – 24000 00]|$58699_{-21}^{+14}$|
Mass ratio [q = msec/mpri]|$0.919_{-0.006}^{+0.010}$||$0.932_{-0.015}^{+0.014}$||$0.483_{-0.005}^{+0.007}$|
Kpri (km s−1)|$120.47_{-0.75}^{+1.12}$||$138.98_{-1.39}^{+1.23}$||$12.57_{-0.24}^{+0.17}$|
Ksec (km s−1)|$130.99_{-0.50}^{+0.48}$||$149.25_{-1.13}^{+1.09}$||$26.02_{-0.50}^{+0.31}$|
γ (km s−1)|$48.69_{-0.59}^{+0.29}$|
Stellar parameters
AaAbBaBb
Relative quantities and atmospheric properties
Fractional radiusb [R/a]|$0.3084_{-0.0044}^{+0.0016}$||$0.2096_{-0.0019}^{+0.0052}$||$0.2120_{-0.0014}^{+0.0013}$||$0.2019_{-0.0020}^{+0.0018}$|
Fractional flux [in TESS-band]|$0.6294_{-0.0153}^{+0.0064}$||$0.3475_{-0.0060}^{+0.0165}$||$0.0133_{-0.0008}^{+0.0009}$||$0.0092_{-0.0007}^{+0.0008}$|
|$x_\mathrm{bol}^c$||$0.676_{-0.001}^{+0.001}$||$0.671_{-0.001}^{+0.001}$|......
|$y_\mathrm{bol}^c$||$0.174_{-0.003}^{+0.002}$||$0.198_{-0.003}^{+0.002}$|......
|$x_{TESS}^c$||$0.631_{-0.001}^{+0.001}$||$0.618_{-0.001}^{+0.001}$||$0.720_{-0.001}^{+0.001}$||$0.724_{-0.002}^{+0.001}$|
|$y_{TESS}^c$||$0.347_{-0.002}^{+0.002}$||$0.354_{-0.003}^{+0.002}$||$0.281_{-0.005}^{+0.005}$||$0.325_{-0.018}^{+0.019}$|
βd|$0.11_{-0.07}^{+0.10}$||$0.64_{-0.33}^{+0.29}$|0.320.32
Physical quantities
m (M)|$1.432_{-0.024}^{+0.015}$||$1.315_{-0.023}^{+0.026}$||$0.688_{-0.011}^{+0.008}$||$0.640_{-0.011}^{+0.010}$|
Rb (R)|$2.339_{-0.021}^{+0.016}$||$1.592_{-0.019}^{+0.047}$||$0.642_{-0.007}^{+0.005}$||$0.611_{-0.009}^{+0.008}$|
|$T_\mathrm{eff}^b$| (K)|$6442_{-28}^{+29}$||$6816_{-26}^{+26}$||$4609_{-49}^{+48}$||$4327_{-57}^{+62}$|
|$L_\mathrm{bol}^b$| (L)|$8.433_{-0.169}^{+0.199}$||$4.934_{-0.179}^{+0.279}$||$0.167_{-0.009}^{+0.009}$||$0.118_{-0.009}^{+0.009}$|
|$M_\mathrm{bol}^b$||$2.45_{-0.03}^{+0.02}$||$3.04_{-0.06}^{+0.04}$||$6.72_{-0.06}^{+0.06}$||$7.09_{-0.08}^{+0.08}$|
|$M_V^b$||$2.45_{-0.03}^{+0.03}$||$3.02_{-0.06}^{+0.04}$||$7.23_{-0.09}^{+0.10}$||$7.83_{-0.13}^{+0.13}$|
log gb (dex)|$3.852_{-0.005}^{+0.011}$||$4.150_{-0.016}^{+0.007}$||$4.660_{-0.002}^{+0.003}$||$4.672_{-0.004}^{+0.004}$|
Global quantities
log (age)b, e (dex)|$9.40_{-0.01}^{+0.02}$||$9.32_{-0.01}^{+0.03}$|
[M/H]b (dex)|$-0.189_{-0.037}^{+0.038}$|
E(BV) (mag)|$0.018_{-0.013}^{+0.015}$|
|$(M_V)_\mathrm{tot}^b$||$1.93_{-0.03}^{+0.03}$|
Distance (pc)|$69.7_{-0.9}^{+0.7}$|

aTime of the inferior conjunction of the secondary component (i.e. mid-time of a primary eclipse). bInterpolated (or derived) from the PARSEC isochrones. cinterpolated linear (x) and logarithmic (y) limb-darkening coefficients. Note that bolometric coefficients used only during the calculation of the reflection effect; therefore, they were not set for binary B. dGravity darkening coefficients. eThe age of the evolved primary component of binary A was allowed to vary independently of the other three stars – see the text for details.

Table 7.

Orbital and astrophysical parameters of BG Ind from the joint photodynamical light curve, RV, ETV, SED, and PARSEC isochrone solution.

Orbital elements
Subsystem
ABA–B
Pa (d)|$1.464\,065_{-0.000\,002}^{+0.000\,002}$||$0.528\,349_{-0.000\,002}^{+0.000\,002}$||$720.9_{-3.1}^{+3.4}$|
a (R)|$7.602_{-0.043}^{+0.038}$||$3.025_{-0.016}^{+0.011}$||$540.4_{-2.2}^{+2.7}$|
e00|$0.209_{-0.048}^{+0.028}$|
ω (°)|$1.6_{-8.8}^{+9.2}$|
i (°)|$73.27_{-0.13}^{+0.06}$||$84.29_{-0.87}^{+0.85}$||$85.5_{-6.3}^{+3.1}$|
|$\mathcal {T}^\mathrm{pri}$| [BJD – 2400 000 ]|$58326.1362_{-0.0012}^{+0.0011}$||$58325.8072_{-0.0022}^{+0.0025}$|
τ [BJD – 24000 00]|$58699_{-21}^{+14}$|
Mass ratio [q = msec/mpri]|$0.919_{-0.006}^{+0.010}$||$0.932_{-0.015}^{+0.014}$||$0.483_{-0.005}^{+0.007}$|
Kpri (km s−1)|$120.47_{-0.75}^{+1.12}$||$138.98_{-1.39}^{+1.23}$||$12.57_{-0.24}^{+0.17}$|
Ksec (km s−1)|$130.99_{-0.50}^{+0.48}$||$149.25_{-1.13}^{+1.09}$||$26.02_{-0.50}^{+0.31}$|
γ (km s−1)|$48.69_{-0.59}^{+0.29}$|
Stellar parameters
AaAbBaBb
Relative quantities and atmospheric properties
Fractional radiusb [R/a]|$0.3084_{-0.0044}^{+0.0016}$||$0.2096_{-0.0019}^{+0.0052}$||$0.2120_{-0.0014}^{+0.0013}$||$0.2019_{-0.0020}^{+0.0018}$|
Fractional flux [in TESS-band]|$0.6294_{-0.0153}^{+0.0064}$||$0.3475_{-0.0060}^{+0.0165}$||$0.0133_{-0.0008}^{+0.0009}$||$0.0092_{-0.0007}^{+0.0008}$|
|$x_\mathrm{bol}^c$||$0.676_{-0.001}^{+0.001}$||$0.671_{-0.001}^{+0.001}$|......
|$y_\mathrm{bol}^c$||$0.174_{-0.003}^{+0.002}$||$0.198_{-0.003}^{+0.002}$|......
|$x_{TESS}^c$||$0.631_{-0.001}^{+0.001}$||$0.618_{-0.001}^{+0.001}$||$0.720_{-0.001}^{+0.001}$||$0.724_{-0.002}^{+0.001}$|
|$y_{TESS}^c$||$0.347_{-0.002}^{+0.002}$||$0.354_{-0.003}^{+0.002}$||$0.281_{-0.005}^{+0.005}$||$0.325_{-0.018}^{+0.019}$|
βd|$0.11_{-0.07}^{+0.10}$||$0.64_{-0.33}^{+0.29}$|0.320.32
Physical quantities
m (M)|$1.432_{-0.024}^{+0.015}$||$1.315_{-0.023}^{+0.026}$||$0.688_{-0.011}^{+0.008}$||$0.640_{-0.011}^{+0.010}$|
Rb (R)|$2.339_{-0.021}^{+0.016}$||$1.592_{-0.019}^{+0.047}$||$0.642_{-0.007}^{+0.005}$||$0.611_{-0.009}^{+0.008}$|
|$T_\mathrm{eff}^b$| (K)|$6442_{-28}^{+29}$||$6816_{-26}^{+26}$||$4609_{-49}^{+48}$||$4327_{-57}^{+62}$|
|$L_\mathrm{bol}^b$| (L)|$8.433_{-0.169}^{+0.199}$||$4.934_{-0.179}^{+0.279}$||$0.167_{-0.009}^{+0.009}$||$0.118_{-0.009}^{+0.009}$|
|$M_\mathrm{bol}^b$||$2.45_{-0.03}^{+0.02}$||$3.04_{-0.06}^{+0.04}$||$6.72_{-0.06}^{+0.06}$||$7.09_{-0.08}^{+0.08}$|
|$M_V^b$||$2.45_{-0.03}^{+0.03}$||$3.02_{-0.06}^{+0.04}$||$7.23_{-0.09}^{+0.10}$||$7.83_{-0.13}^{+0.13}$|
log gb (dex)|$3.852_{-0.005}^{+0.011}$||$4.150_{-0.016}^{+0.007}$||$4.660_{-0.002}^{+0.003}$||$4.672_{-0.004}^{+0.004}$|
Global quantities
log (age)b, e (dex)|$9.40_{-0.01}^{+0.02}$||$9.32_{-0.01}^{+0.03}$|
[M/H]b (dex)|$-0.189_{-0.037}^{+0.038}$|
E(BV) (mag)|$0.018_{-0.013}^{+0.015}$|
|$(M_V)_\mathrm{tot}^b$||$1.93_{-0.03}^{+0.03}$|
Distance (pc)|$69.7_{-0.9}^{+0.7}$|
Orbital elements
Subsystem
ABA–B
Pa (d)|$1.464\,065_{-0.000\,002}^{+0.000\,002}$||$0.528\,349_{-0.000\,002}^{+0.000\,002}$||$720.9_{-3.1}^{+3.4}$|
a (R)|$7.602_{-0.043}^{+0.038}$||$3.025_{-0.016}^{+0.011}$||$540.4_{-2.2}^{+2.7}$|
e00|$0.209_{-0.048}^{+0.028}$|
ω (°)|$1.6_{-8.8}^{+9.2}$|
i (°)|$73.27_{-0.13}^{+0.06}$||$84.29_{-0.87}^{+0.85}$||$85.5_{-6.3}^{+3.1}$|
|$\mathcal {T}^\mathrm{pri}$| [BJD – 2400 000 ]|$58326.1362_{-0.0012}^{+0.0011}$||$58325.8072_{-0.0022}^{+0.0025}$|
τ [BJD – 24000 00]|$58699_{-21}^{+14}$|
Mass ratio [q = msec/mpri]|$0.919_{-0.006}^{+0.010}$||$0.932_{-0.015}^{+0.014}$||$0.483_{-0.005}^{+0.007}$|
Kpri (km s−1)|$120.47_{-0.75}^{+1.12}$||$138.98_{-1.39}^{+1.23}$||$12.57_{-0.24}^{+0.17}$|
Ksec (km s−1)|$130.99_{-0.50}^{+0.48}$||$149.25_{-1.13}^{+1.09}$||$26.02_{-0.50}^{+0.31}$|
γ (km s−1)|$48.69_{-0.59}^{+0.29}$|
Stellar parameters
AaAbBaBb
Relative quantities and atmospheric properties
Fractional radiusb [R/a]|$0.3084_{-0.0044}^{+0.0016}$||$0.2096_{-0.0019}^{+0.0052}$||$0.2120_{-0.0014}^{+0.0013}$||$0.2019_{-0.0020}^{+0.0018}$|
Fractional flux [in TESS-band]|$0.6294_{-0.0153}^{+0.0064}$||$0.3475_{-0.0060}^{+0.0165}$||$0.0133_{-0.0008}^{+0.0009}$||$0.0092_{-0.0007}^{+0.0008}$|
|$x_\mathrm{bol}^c$||$0.676_{-0.001}^{+0.001}$||$0.671_{-0.001}^{+0.001}$|......
|$y_\mathrm{bol}^c$||$0.174_{-0.003}^{+0.002}$||$0.198_{-0.003}^{+0.002}$|......
|$x_{TESS}^c$||$0.631_{-0.001}^{+0.001}$||$0.618_{-0.001}^{+0.001}$||$0.720_{-0.001}^{+0.001}$||$0.724_{-0.002}^{+0.001}$|
|$y_{TESS}^c$||$0.347_{-0.002}^{+0.002}$||$0.354_{-0.003}^{+0.002}$||$0.281_{-0.005}^{+0.005}$||$0.325_{-0.018}^{+0.019}$|
βd|$0.11_{-0.07}^{+0.10}$||$0.64_{-0.33}^{+0.29}$|0.320.32
Physical quantities
m (M)|$1.432_{-0.024}^{+0.015}$||$1.315_{-0.023}^{+0.026}$||$0.688_{-0.011}^{+0.008}$||$0.640_{-0.011}^{+0.010}$|
Rb (R)|$2.339_{-0.021}^{+0.016}$||$1.592_{-0.019}^{+0.047}$||$0.642_{-0.007}^{+0.005}$||$0.611_{-0.009}^{+0.008}$|
|$T_\mathrm{eff}^b$| (K)|$6442_{-28}^{+29}$||$6816_{-26}^{+26}$||$4609_{-49}^{+48}$||$4327_{-57}^{+62}$|
|$L_\mathrm{bol}^b$| (L)|$8.433_{-0.169}^{+0.199}$||$4.934_{-0.179}^{+0.279}$||$0.167_{-0.009}^{+0.009}$||$0.118_{-0.009}^{+0.009}$|
|$M_\mathrm{bol}^b$||$2.45_{-0.03}^{+0.02}$||$3.04_{-0.06}^{+0.04}$||$6.72_{-0.06}^{+0.06}$||$7.09_{-0.08}^{+0.08}$|
|$M_V^b$||$2.45_{-0.03}^{+0.03}$||$3.02_{-0.06}^{+0.04}$||$7.23_{-0.09}^{+0.10}$||$7.83_{-0.13}^{+0.13}$|
log gb (dex)|$3.852_{-0.005}^{+0.011}$||$4.150_{-0.016}^{+0.007}$||$4.660_{-0.002}^{+0.003}$||$4.672_{-0.004}^{+0.004}$|
Global quantities
log (age)b, e (dex)|$9.40_{-0.01}^{+0.02}$||$9.32_{-0.01}^{+0.03}$|
[M/H]b (dex)|$-0.189_{-0.037}^{+0.038}$|
E(BV) (mag)|$0.018_{-0.013}^{+0.015}$|
|$(M_V)_\mathrm{tot}^b$||$1.93_{-0.03}^{+0.03}$|
Distance (pc)|$69.7_{-0.9}^{+0.7}$|

aTime of the inferior conjunction of the secondary component (i.e. mid-time of a primary eclipse). bInterpolated (or derived) from the PARSEC isochrones. cinterpolated linear (x) and logarithmic (y) limb-darkening coefficients. Note that bolometric coefficients used only during the calculation of the reflection effect; therefore, they were not set for binary B. dGravity darkening coefficients. eThe age of the evolved primary component of binary A was allowed to vary independently of the other three stars – see the text for details.

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