Astronomy & Astrophysics

Table 4: Parameters of $\pi ^{1}$ Gruis deduced from the fit of the analytical visibility model to the data sets DATA_SPECTRO_CAL.
Parameter Value

Effective temperature (K): $T_{\rm eff}$ 3000

Luminosity ( $L_{\odot}$ ): $L_{\rm\star}$ 9300 $\pm$ 2700

Central star diameter (mas): 2 $\varepsilon_{\rm\star}$ 21.6 $\pm$ 0.3

Shell inner radius (mas): $\varepsilon_{\rm in}$ 159 $\pm$ 10

Inner boundary temperature (K): $T_{\rm in}$ 776 $\pm$ 25

Dust bump wavelength ( $\mu$ m): $\lambda_{\rm c}$ 11^*

Bump amplitude ( $\times$ 10^-4): A 8.3 $\pm$ 0.6

Bump width ( $\mu$ m): $\Delta\lambda$ 2.8 $\pm$ 0.3

Bump optical depth ( $\times$ 10^-3): $\tau_{\rm 11 ~\mu m}$ 1.5 $\pm$ 0.2

Density power law coefficient: p 1.7

Spectral index: $\beta$ 1

$\chi^{2}_{\rm red}$ 0.55

$\textstyle \parbox{7cm}{ $*$\space Fixed at pre-determined value.}$

**Table 4:** Parameters of $\pi ^{1}$ Gruis deduced from the fit of the analytical visibility model to the data sets *DATA_SPECTRO_CAL*.
Parameter	Value
Effective temperature (K): $T_{\rm eff}$	3000
Luminosity ( $L_{\odot}$ ): $L_{\rm\star}$	9300 $\pm$ 2700
Central star diameter (mas): 2 $\varepsilon_{\rm\star}$	21.6 $\pm$ 0.3
Shell inner radius (mas): $\varepsilon_{\rm in}$	159 $\pm$ 10
Inner boundary temperature (K): $T_{\rm in}$	776 $\pm$ 25
Dust bump wavelength ( $\mu$ m): $\lambda_{\rm c}$	11^*
Bump amplitude ( $\times$ 10^-4): A	8.3 $\pm$ 0.6
Bump width ( $\mu$ m): $\Delta\lambda$	2.8 $\pm$ 0.3
Bump optical depth ( $\times$ 10^-3): $\tau_{\rm 11 ~\mu m}$	1.5 $\pm$ 0.2
Density power law coefficient: p	1.7
Spectral index: $\beta$	1
$\chi^{2}_{\rm red}$	0.55

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