3.3 Parameter variations

Our approach to parameterizing the variations of velocity, emissivity and field ordering along the jets is to specify values at four standard locations: inner jet, inner boundary (just inside the flaring region), outer boundary and an arbitrary fiducial point in the outer region. There is insufficient information to constrain any variations along the inner region, so constant values are assumed there. We allow discontinuities in most variables at the inner boundary, as there is unambiguous evidence for an abrupt change in the emissivity, at least, at this position. By contrast, all quantities vary continuously through the flaring and outer regions. We specify their values at the three locations, together with any parameters required to specify the functional form of the variation. Table 4 summarizes the details, as follows:

Column 1: 

Symbol (as defined in the text),

Columns 2 - 5:

the values of the quantity at the four standard locations (blank if not used),

Column 6:

Any other parameters needed to quantify the variation.

Columns 7 - 9:

The functional forms of the variation in the three regions.

Similarly, the functional forms used to describe transverse variations in the shear layer are listed in Table 5. There are no variations across the spine in SSL models.

Table 4: Summary of the functional variations of velocity, emissivity and field ordering parameters along the model jets.

Quantity	Free parameters					Functional dependences
	0 - $r_1$	$r_1$	$r_0$	$r_{\rm f}$	Other	Inner	Flaring	Outer
	Velocities
$\beta_\rho(\rho)$	$\beta_{\rm i}$	$\beta_1$	$\beta_0$	$\beta_{\rm f}$	$H$	$\beta_{\rm i}$	$b_0 + b_1 \rho^{H-1} + b_2 \rho^H$	$c_0 \exp(-c_1 \rho)$
$\bar{v}(\rho)$	$v_{\rm i}$	$v_1$	$v_0$			$v_{\rm i}$	$v_1 + \frac{(r-r_1)(v_0-v_1)}{r_0-r_1}$	$v_0$
	Emissivity (for each of spine and shear layer)
$\epsilon_\rho(\rho)$					$g$, $E_{\rm i}$,$E_{\rm f}$, $E_{\rm o}$	$g(\rho/r_1)^{-E_{\rm i}}$	$(\rho/r_1)^{-E_{\rm f}}$	$(r_0/r_1)^{-E_{\rm f}}(\rho/r_0)^{-E_{\rm o}}$
$\bar{e}(\rho)$		$e_1$	$e_0$			1	$e_1 + \frac{(r-r_1)(e_0-e_1)}{r_0-r_1}$	$e_0$
	Field component ratios (for each of spine and shear layer)
$j_\rho(\rho)$	$j_{\rm i}$	$j_1$	$j_0$	$j_{\rm f}$		$j_{\rm i}$	$j_1 + \frac{(r-r_1)(j_0-j_1)}{r_0-r_1}$	$j_0 + \frac{(r-r_0)(j_{\rm f}-j_0)}{r_{\rm f}-r_0}$
$k_\rho(\rho)$	$k_{\rm i}$	$k_1$	$k_0$	$k_{\rm f}$		$k_{\rm i}$	$k_1 + \frac{(r-r_1)(k_0-k_1)}{r_0-r_1}$	$k_0 + \frac{(r-r_0)(k_{\rm f}-k_0)}{r_{\rm f}-r_0}$

2002-06-13