thesis - IRS, The Infrared Spectrograph

34 CHAPTER 3: An ISO and IUE study of Planetary Nebula NGC 2440F (H β ) =S ν2.82 10 9 t 0.53 (1 + He+H ++ 3.7 He++H + )(3.1)the expected H β flux can be found. In Eq. 3.1 S ν =0.411 Jy at 5 GHz (Pottasch 1984), tis the temperature of the nebula in 10 4 K ( in this case T e =15 000 is used) and 2.82 10 9 is aconversion factor if the flux density S ν is in Jy and the F (H β ) in erg cm −2 s −1 . The heliumabundances are taken from Table 3.7 and have been derived using the theoretical predictionsof Benjamin et al. (1999) at a N e =10 000 cm −3 (using N e =100 cm −3 will lead to the samevalues). Eq. 3.1 leads to a predicted H β of 91.0 10 −12 erg cm −2 s −1 . The extinction factor isthus C Hβ = 0.46. This is in good agreement with what Hyung & Aller (1998) (C Hβ = 0.53)found. An average of those two (C Hβ =0.50) has been used in the present paper. The actualcorrection was applied using the Fluks et al. (1994) law.3.3.2 Aperture correctionsNGC 2440 has a measured size (Shields et al. 1981) of 10 ′′ for the main body and a faintenvelope that extends up to 30 ′′ . ISO–SWS uses different size apertures for the differentbands. These sizes range from 14 ′′ x 20 ′′ (the smallest, measuring the 2.38 to 12.0 µmwavelength interval), to larger apertures 14 ′′ x 27 ′′ (12.0–27.5 µm), 20 ′′ x 27 ′′ (27.5–29.0 µm)and 20 ′′ x 33 ′′ (29.0–45.2 µm). The aperture of the IUE is very similar to ISO–SWS smallestaperture, it’s an ellipse of 10 ′′ x 23 ′′ . It is likely that some of the nebula is missing and,because of the similarity in aperture size, the correction factors in the infrared and ultravioletwill be similar. Due to the fact that the nebula is larger than the smallest ISO apertures oneshould expect jumps in the SWS spectrum caused by the different aperture sizes used. Thisis not the case, as can be seen in Fig. 3.1, because the contribution of the continuum at lowerwavelengths (smallest apertures) in this nebula is practically zero. There is a real (see Fig.3.1) contribution of the nebula to the continuum at longer wavelengths, starting at around 21µm. Since no jumps are seen in that part of the spectrum, the total nebular flux has probablybeen measured above 12 µm.In order to correct the infrared lines for aperture effects the SWS measurements have beencompared with those from the Infrared Astronomical Satellite (IRAS), which had an aperturebig enough to contain the whole nebula. This comparison is shown in Table 3.1. The SWSand IRAS fluxes (Pottasch et al. 2000) are shown in Col. 4 and Col. 5. In the last column thescale factor to reproduce the IRAS measurements (basically F iras /F sws ) is given.The advantage of this is that the lines IRAS has measured have been measured by theSWS using different apertures (see above) so that a correction for each one can be applied.As can be seen in Table 3.1 the IRAS fluxes for Ne VI and S IV are bigger than the fluxesmeasured with SWS. This means that some flux is missing in the smaller apertures. That isnot the case for the ions longward of 12 µm which have been measured with a larger aperture.The difference in the fluxes is within the errors expected. Only the S III seems not to agree butthe IRAS flux reported is uncertain. From the Ne II, Ne III and Ne V lines it appears that noflux is missing in these apertures. Therefore, all measurements with the large SWS apertureseem to see almost all the nebular line flux emission. In the smallest apertures some fluxis missing. The aperture correction factor are 1.35 and 1.72 for Ne VI and S IV. Althoughthe Ne VI line from IRAS is noisy, combining these two results lead to an average correction