D. Magnitude System in ISOPHOT

The zero magnitude of a given ISOPHOT filter is defined as the signal of the `ideal' (i.e. model) Vega which would have been measured in that filter with an infinitely large aperture.

The ideal spectrum of Vega was derived from a Kurucz model with $T_{eff}$ = 9400 K , log($g$) = 3.900, metal poor, $V_{turb}=$ 0.0 kms$^{-1}$ and no infrared excess due to circumstellar dust, extended to 300 $\mu$m and absolutely calibrated as described by Cohen et al. 1992, [6], and Walker & Cohen 1992, [55].

The magnitude $m_{filter}$ can be obtained from the PHT auto analysis data product by applying the relation:

$$m_{filter} = -2.5~{\rm log}\, \lbrack \frac{F_{\nu}(measured)}{F_{\nu,0}}\rbrack~~,$$ (D.1)

where $F_{\nu}(measured)$ is the AAR flux density. The values for $F_{\nu,0}$ with filter identifier and reference wavelength ${\lambda}_{ref}$ are listed in Table D.1.

For completeness, we have included in Table D.1 the corresponding powers on the detector $P_0({\lambda}_{ref})$, the ideal Vega flux density at the reference wavelength $F_{\nu}({\lambda}_{ref})$, and the colour correction $k$.

$P_0({\lambda}_{ref})$ can be applied to the SPD products, thereby taking into account the point spread function correction, see Equations 5.8 and 5.9. The values of $k$ are very close to the ones which have been derived for a 10000 K blackbody, see Table C.2.

Table D.1: Zero magnitude flux densities of ISOPHOT filter bands.

filter	${\lambda}_{ref}$	$P_0({\lambda}_{ref})$	$F_{\nu,0}({\lambda}_{ref})$	$F_{\nu}({\lambda}_{ref})$	$k$
ID	[$\mu$m]	[W]	[Jy]	[Jy]	[  ]
P_3.29	3.3	4.60E$-$13	312.0	318.2	0.981
P_3.6	3.6	2.15E$-$12	284.7	270.9	1.051
P_4.85	4.8	1.24E$-$12	163.2	152.1	1.072
P_7.3	7.3	1.01E$-$12	79.96	71.09	1.125
P_7.7	7.7	1.61E$-$13	65.14	64.23	1.014
P_10	10	1.77E$-$13	39.40	38.60	1.021
P_11.3	11.3	3.94E$-$14	29.96	30.40	0.985
P_12.8	12.8	5.71E$-$13	35.47	26.97	1.315
P_16	15	1.26E$-$13	24.21	23.79	1.018
P_11.5	12	5.46E$-$14	17.25	17.40	0.991
P_20	20	5.17E$-$14	9.940	9.840	1.010
P_25	25	3.47E$-$14	8.109	6.307	1.286
P_60	60	7.29E$-$16	1.233	1.087	1.135
P_100	100	3.55E$-$16	0.4068	0.3866	1.052
C_50	65	5.76E$-$16	1.197	0.9245	1.295
C_60	60	7.60E$-$16	1.153	1.087	1.061
C_70	80	5.22E$-$16	0.7489	0.6075	1.233
C_90	90	8.45E$-$16	0.5597	0.4787	1.169
C_100	100	4.03E$-$16	0.4261	0.3866	1.102
C_105	105	2.25E$-$16	0.3683	0.3503	1.052
C_120	120	1.15E$-$16	0.3253	0.2672	1.217
C_135	150	1.32E$-$16	0.1862	0.1698	1.096
C_160	170	1.60E$-$16	0.1587	0.1316	1.205
C_180	180	6.92E$-$17	0.1288	0.1172	1.099
C_200	200	2.27E$-$17	0.0972	0.0945	1.028