Table 3: Input and derived parameters obtained from a $\chi ^2$ minimization procedure applied to several data sets: all data (BMAD), near-IR V² and closure phases (BMIRCP), closure phases alone (BMCP), and near-IR V²alone (BMIR). There is no uncertainty associated to $\beta$ and $T_{\rm p}$ because they define two test models based on theoretical limits for the gravity darkening (see text for details). Selected dependent parameters for the best models are also listed.
Fixed input parameters BMAD BMIRCP BMCP BMIR

$v_{\rm eq} \sin i$ ( $\!~{\rm km~s^{-1}}$ ) 227 227 227 227

M ( $\!~{M}_{\odot}$ ) 1.8 1.8 1.8 1.8

i (deg) - - - $50\hbox{$^\circ$ }$

( $\beta,T_{\rm p}$ (K)) - - - (0.25, 8500)

Results of the $\chi ^2$ analyses BMAD BMIRCP BMCP BMIR

$\chi^2_{\rm min}/{\rm d.o.f.}$ 7.3 3.2 1.5 0.50

( $\beta,T_{\rm p}$ (K))^a (0.25, 8500) (0.25, 8500) (0.25, 8500) -

i (deg) $55\hbox{$^\circ$ }\pm 8\hbox{$^\circ$ }$ $55\hbox{$^\circ$ }\pm 14\hbox{$^\circ$ }$ $50\hbox{$^\circ$ }\pm 12\hbox{$^\circ$ }$ -

$2a=\oslash_{\rm eq}$ (mas) $3.83 \pm 0.06$ $3.88 \pm 0.08$ $3.88 \pm 0.03$ $3.44 \pm 0.05$

$R_{\rm eq}\ {}^b$ ( $~{R}_{\odot}$ ) $2.117\pm0.035$ $2.145\pm0.045$ $2.145\pm0.020$ $1.902\pm0.029$

$\eta$ (deg) $92\hbox{$^\circ$ }\pm 6 \hbox{$^\circ$ }$ $62\hbox{$^\circ$ }\pm 17\hbox{$^\circ$ }$ $95\hbox{$^\circ$ }\pm 23 \hbox{$^\circ$ }$ $113\hbox{$^\circ$ }\pm 12 \hbox{$^\circ$ }$

Dependent parameters BMAD BMIRCP BMCP BMIR

$T_{\rm eq}$ (K) 6509 6483 6171 6453

$v_{\rm eq}$ ( $~{\rm km~s^{-1}}$ ) 277 277 296 296

$v_{\rm eq}/v_{\rm crit}(\%)$ 76% 76% 80% 77%

$f_{\rm rot}$ (cycles/day) 2.585 2.552 2.729 3.077

$2b=\oslash_{\rm p}^{\rm max}$ (mas) 3.29 3.33 3.32 2.99

$a/b=\oslash_{\rm eq}/\oslash_{\rm p}^{\rm max}$ 1.164 1.165 1.169 1.149

$R_{\rm eq}/R_{\rm p}$ 1.237 1.240 1.275 1.243

Theoretical limit preferred compared to ( $\beta,T_{\rm p}$ (K)) = (0.08, 8000).
From $\oslash _{\rm eq}$ and Hipparcos distance ( $d=5.143\pm0.025$ pc).

**Table 3:** Input and derived parameters obtained from a $\chi ^2$ minimization procedure applied to several data sets: all data (BMAD), near-IR V² and closure phases (BMIRCP), closure phases alone (BMCP), and near-IR V²alone (BMIR). There is no uncertainty associated to $\beta$ and $T_{\rm p}$ because they define two test models based on theoretical limits for the gravity darkening (see text for details). Selected dependent parameters for the best models are also listed.
Fixed input parameters	BMAD	BMIRCP	BMCP	BMIR
$v_{\rm eq} \sin i$ ( $\!~{\rm km~s^{-1}}$ )	227	227	227	227
M ( $\!~{M}_{\odot}$ )	1.8	1.8	1.8	1.8
i (deg)	-	-	-	$50\hbox{$^\circ$ }$
( $\beta,T_{\rm p}$ (K))	-	-	-	(0.25, 8500)
Results of the $\chi ^2$ analyses	BMAD	BMIRCP	BMCP	BMIR
$\chi^2_{\rm min}/{\rm d.o.f.}$	7.3	3.2	1.5	0.50
( $\beta,T_{\rm p}$ (K))^a	(0.25, 8500)	(0.25, 8500)	(0.25, 8500)	-
i (deg)	$55\hbox{$^\circ$ }\pm 8\hbox{$^\circ$ }$	$55\hbox{$^\circ$ }\pm 14\hbox{$^\circ$ }$	$50\hbox{$^\circ$ }\pm 12\hbox{$^\circ$ }$	-
$2a=\oslash_{\rm eq}$ (mas)	$3.83 \pm 0.06$	$3.88 \pm 0.08$	$3.88 \pm 0.03$	$3.44 \pm 0.05$
$R_{\rm eq}\ {}^b$ ( $~{R}_{\odot}$ )	$2.117\pm0.035$	$2.145\pm0.045$	$2.145\pm0.020$	$1.902\pm0.029$
$\eta$ (deg)	$92\hbox{$^\circ$ }\pm 6 \hbox{$^\circ$ }$	$62\hbox{$^\circ$ }\pm 17\hbox{$^\circ$ }$	$95\hbox{$^\circ$ }\pm 23 \hbox{$^\circ$ }$	$113\hbox{$^\circ$ }\pm 12 \hbox{$^\circ$ }$
Dependent parameters	BMAD	BMIRCP	BMCP	BMIR
$T_{\rm eq}$ (K)	6509	6483	6171	6453
$v_{\rm eq}$ ( $~{\rm km~s^{-1}}$ )	277	277	296	296
$v_{\rm eq}/v_{\rm crit}(\%)$	76%	76%	80%	77%
$f_{\rm rot}$ (cycles/day)	2.585	2.552	2.729	3.077
$2b=\oslash_{\rm p}^{\rm max}$ (mas)	3.29	3.33	3.32	2.99
$a/b=\oslash_{\rm eq}/\oslash_{\rm p}^{\rm max}$	1.164	1.165	1.169	1.149
$R_{\rm eq}/R_{\rm p}$	1.237	1.240	1.275	1.243

Source LaTeX | All tables | In the text

	1 Introduction
	2 Interferometric observations
	3 Modeling Altair
	4 Results from the $\chi ^2$ analysis
	5 Discussion
	6 Summary and conclusions
	References