Table 1: Structure and physical conditions in the molecular disk in the Red Rectangle, derived from our model fitting of the CO data. Dependence on the assumed distance is given in the relevant cases. Other parameters of the modeling are also given.
Inner disk ( $r < R_{\rm kep}$ ) Outer disk ( $r > R_{\rm kep}$ )

Parameter Law Values Law Values

Outer radius $R_{\rm kep} = 8.4\times 10^{15}$ ( $\frac{D({\rm pc})}{710}$ ) cm $R_{\rm out} = 2.7 \times 10^{16}$ ( $\frac{D({\rm pc})}{710}$ ) cm

Disk linear $H(R_{\rm kep}) = 1.5\times 10^{16}$ ( $\frac{D({\rm pc})}{710}$ ) cm constant $H = 1.5 \times 10^{16}$ ( $\frac{D({\rm pc})}{710}$ ) cm

thickness $H(0) = 7.5\times 10^{15}$ ( $\frac{D({\rm pc})}{710}$ ) cm

Tangential $V_{\rm t} \propto 1/\sqrt {r}$    $V_{\rm t}(R_{\rm kep})$ = 1.65 km s^-1 $V_{\rm t} \propto 1/r$ $V_{\rm t}(R_{\rm kep}) = 1.65$ km s^-1

velocity (Keplerian) (central mass: 1.7 ( $\frac{D({\rm pc})}{710}$ ) $M_{\odot}$ ) (ang. mom. cons.)

Expansion 0 km s^-1 $V_{\rm exp} \propto \sqrt{a + b/r}$ $V_{\rm exp}(R_{\rm kep}) = 1.6$ km s^-1

velocity $V_{\rm exp}(R_{\rm out}) = 0$ km s^-1

Turbulence constant $\sigma_{\rm turb} = 0.3$ km s^-1 constant $\sigma_{\rm turb}$ = 0.3 km s^-1

velocity

Temperature $T \propto 1/r^{\alpha_{\rm T}}$ $T(R_{\rm kep}) = 60$ K $T \propto 1/r^{\alpha_{\rm T}}$ $T(R_{\rm kep}) = 76$ K

$\alpha_{\rm T} = 0.7$ $\alpha_{\rm T} = 0.7$

Gas density $n \propto 1/r^{\alpha_n}$ $n(R_{\rm kep}) = 4 \times 10^5$ ( $\frac{710}{D({\rm pc})}$ ) cm^-3 $n \propto 1/r^{\alpha_n}$    $n(R_{\rm kep}) = 1.3 \times 10^5$ ( $\frac{710}{D({\rm pc})}$ ) cm^-3

$\alpha_n = 2.2$ $\alpha_n = 2.2$

Other parameters Law Values Comments

Axis inclination from the plane of the sky 5 $^\circ$ from optical and CO data

Axis inclination in the plane of the sky (PA) 11 $^\circ$ from optical and CO data

Distance between 380 and 710 pc various arguments (Sect. 4)

CO relative abundance   constant      $2\times 10^{-4}$    from ¹²CO and ¹³CO data

LSR systemic velocity -0.2 km s^-1 from CO data

**Table 1:** Structure and physical conditions in the molecular disk in the Red Rectangle, derived from our model fitting of the CO data. Dependence on the assumed distance is given in the relevant cases. Other parameters of the modeling are also given.
	Inner disk ( $r < R_{\rm kep}$ )	Outer disk ( $r > R_{\rm kep}$ )
Parameter	Law	Values	Law	Values
Outer radius		$R_{\rm kep} = 8.4\times 10^{15}$ ( $\frac{D({\rm pc})}{710}$ ) cm		$R_{\rm out} = 2.7 \times 10^{16}$ ( $\frac{D({\rm pc})}{710}$ ) cm
Disk	linear	$H(R_{\rm kep}) = 1.5\times 10^{16}$ ( $\frac{D({\rm pc})}{710}$ ) cm	constant	$H = 1.5 \times 10^{16}$ ( $\frac{D({\rm pc})}{710}$ ) cm
thickness		$H(0) = 7.5\times 10^{15}$ ( $\frac{D({\rm pc})}{710}$ ) cm
Tangential	$V_{\rm t} \propto 1/\sqrt {r}$	$V_{\rm t}(R_{\rm kep})$ = 1.65 km s^-1	$V_{\rm t} \propto 1/r$	$V_{\rm t}(R_{\rm kep}) = 1.65$ km s^-1
velocity	(Keplerian)	(central mass: 1.7 ( $\frac{D({\rm pc})}{710}$ ) $M_{\odot}$ )	(ang. mom. cons.)
Expansion		0 km s^-1	$V_{\rm exp} \propto \sqrt{a + b/r}$	$V_{\rm exp}(R_{\rm kep}) = 1.6$ km s^-1
velocity				$V_{\rm exp}(R_{\rm out}) = 0$ km s^-1
Turbulence	constant	$\sigma_{\rm turb} = 0.3$ km s^-1	constant	$\sigma_{\rm turb}$ = 0.3 km s^-1
velocity
Temperature	$T \propto 1/r^{\alpha_{\rm T}}$	$T(R_{\rm kep}) = 60$ K	$T \propto 1/r^{\alpha_{\rm T}}$	$T(R_{\rm kep}) = 76$ K
		$\alpha_{\rm T} = 0.7$		$\alpha_{\rm T} = 0.7$
Gas density	$n \propto 1/r^{\alpha_n}$	$n(R_{\rm kep}) = 4 \times 10^5$ ( $\frac{710}{D({\rm pc})}$ ) cm^-3	$n \propto 1/r^{\alpha_n}$	$n(R_{\rm kep}) = 1.3 \times 10^5$ ( $\frac{710}{D({\rm pc})}$ ) cm^-3
		$\alpha_n = 2.2$		$\alpha_n = 2.2$

Source LaTeX | All tables | In the text

	1 Introduction
	2 Observations
	3 The distribution of the CO emission in the Red Rectangle
	4 CO emission model
	5 Conclusions
	References
	Online Material
	Appendix A: Reliability and uniqueness of the model fitting

Other parameters	Law	Values	Comments
Axis inclination from the plane of the sky		5 $^\circ$	from optical and CO data
Axis inclination in the plane of the sky (PA)		11 $^\circ$	from optical and CO data
Distance		between 380 and 710 pc	various arguments (Sect. 4)
CO relative abundance	constant	$2\times 10^{-4}$	from ¹²CO and ¹³CO data
LSR systemic velocity		-0.2 km s^-1	from CO data