EDP Sciences
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Issue
A&A
Volume 518, July-August 2010
Herschel: the first science highlights
Article Number A62
Number of page(s) 7
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/200913660
Published online 03 September 2010
A&A 518, A62 (2010)

Extinction AV, R towards emission nebulae derived from common upper level Paschen-Balmer hydrogen lines[*]

A. Greve

IRAM, 300 rue de la Piscine, 38406 Saint-Martin d'Hères, France

Received 13 November 2009 / Accepted 5 April 2010

Abstract
The reddening in and around emission nebulae is characterized by the extinction AV and the ratio R of the absolute-to-selective absorption. Both are usually derived from the photometry of a single star or cluster stars that are associated with an emission nebula. Using the parameterized reddening relation published by Cardelli et al. (1989, ApJ, 345, 245), we show that AV and R can be derived with good precision from the observation of a set of common upper level Paschen-Balmer hydrogen line ratios. The use of common upper level line ratios has the advantage of being nearly independent of the excitation condition of the nebula ($n_{\rm e}$, $T_{\rm e}$). The line ratio method can be applied in regions where no stars are available for photometry.

Key words: dust, extinction

1 Introduction

The reddening in and around emission nebulae is characterized by the extinction AV (magnitude) and the ratio R of the absolute-to-selective absorption, with AV = R E(B-V). In interstellar space is $R \approx 3.1$, while in and around emission nebulae - especially when embedded in a molecular cloud (for the Orion nebula see Goudis 1982; O'Dell & Wen 1992) - the value R can be significantly higher, i.e. $R \approx 4{-}6$. This indicates the presence of dust of a different size and/or composition than in the diffuse interstellar medium (see for instance Whittet 2003; Mathis 1990). The value R is important in studies of both the presence and evolution of dust in/around emission nebulae, while on the practical side the values AVR are important for the abundance analysis of elements with lines that cover the UV, visible, and near-IR wavelength region.

The values AV and R can be derived from the photometry of (cluster) stars, if present and associated with an emission nebula, while the measurement of a few emission line ratios, for instance H$\alpha$/H$\beta $ and H$\alpha$/H$\gamma$, provide only AV. We show that the values AV and R can be derived with good precision when applying the parameterized reddening relation derived by Cardelli et al. (1989, CCM) to a set of common upper level Paschen(P)-Balmer(H) hydrogen emission lines. The use of common PH lines has the advantage (1) of covering the near-IR wavelength region 10 938 Å (P 6)-$\sim$8500 Å ($\sim$P 20) and the blue wavelength region 4102 Å (H 6)-$\sim$3700 Å ($\sim$H 20), which is sensitive to the particular value R (see Fig. 3 in Cardelli et al. 1989; and Fig. 6 below); (2) of their line ratios being nearly independent of the excitation condition ($n_{\rm e}$, $T_{\rm e}$) of the nebula (Osterbrock 1989) so that the ratios can be used as a ``standard candle'' of emission nebulae; and (3) being able to determine AV and R for emission objects where no stars are available for photometry, as in many galactic and extragalactic emission nebulae, and planetary nebulae. Although the PH-method is elegant in the application of the theoretical line ratios (see Osterbrock 1989), its main disadvantage is the weakness of the lines (Table 5). For this reason, the common upper line ratio method has not been exploited widely, but CCD spectroscopy and large aperture telescopes have changed the situation.

To illustrate the PH-method of AV, R determination, we analyse hydrogen emission line observations of M 8 and M 17, made with the BC-spectrograph on the ESO 1.52-m telescope, and observations of M 8, M 16, M 17, M 20, M 42, NGC 3603, and S 311, which were obtained from observations with the UVES-spectrograph on one ESO-VLT 8-m telescope and published by Garcia-Rojas et al. (2005, 2006, 2007) and Esteban et al. (2004, M 42). Where possible, we compare the values AVR derived from the PH-method with values derived from photometry. In addition, we derive AV, R of the planetary nebula NGC 7027 (of higher density and temperature than the emission nebulae) from a combination of emission line data published by Rudy et al. (1992) and Zhang et al. (2005).

2 The reddening determination AV, R

There are three alternative methods for determining AV and R.

2.1 Photometric method

The photometric determination of AVR uses two-colour diagrams of a group of stars (cluster stars) and usually the assumption/condition that the observed stars are reddened main sequence stars. A systematic deviation of the observed colours from the R = 3.1 reddening line is interpreted to be caused by dust with a higher value R. The colour diagrams of NGC 6611 stars (M 16) and NGC 6618 stars (M 17) used in this way are shown by Chini et al. (1980), Chini & Krügel (1983), and Chini & Wargau (1990).

2.2 Spectro-photometric method

The comparison of (narrow-band) spectro-photometric measurements of a star of known spectral type with its non-reddened energy distribution allows AVR to be determined. The spectral bands can be the colours LKHJIRVBU, as used by Cardelli et al. (1989) for deriving the reddening law.

2.3 Paschen-Balmer common line ratio method

The PH common line ratio method uses the parameterized reddening relation published by Cardelli et al. (1989)

$\displaystyle %
\langle{A}({\lambda})/A(V)\rangle = { a(x) + b(x)/R},$   (1)

which can be written in the form (see Greve et al. 1994)
$\displaystyle %
{A}_{V}~{\Delta}{ a} + ({ A}_{V}/{ R}){\Delta}{ b} =
2.5~\log({ R}_{\rm o}/{ R}_{\rm p}).$   (2)

In relation (2), $R _{\rm p} = I({\rm P}n)/I({\rm H}n)$ is the predicted intensity ratio of the common Paschen-Balmer line pair of quantum level n, while $R_{\rm o}
= F({\rm P}n)/F({\rm H}n)$ is the observed line ratio. The predicted line ratios are taken from Brocklehurst (1971) or Storey $\&$ Hummer (1995). It is found that the ratio $R _{\rm p}$(n) is a constant within $\sim$$\pm$10$\%$ for the range of levels n, densities $n_{\rm e}$, and temperatures $T_{\rm e}$ under consideration (Sect. 3). The values $\Delta a(\lambda$ $_{{\rm P}n}$,$\lambda$ $_{{\rm H}n}$) and $\Delta b(\lambda$ $_{{\rm P}n}$,$\lambda$ $_{{\rm H}n}$) in relation (2) are derived from the relations a(x), b(x) (x = 1/$\lambda$, 0.3 $\mu$m-1 $\leq x \leq 3.3~\mu$m-1) published by Cardelli et al. The values AV and R are obtained from a least-square solution when using $\sim$6 to 10 common line pairs in relation (2).

3 Accuracy of the PH-method

The non-reddened and reddened Paschen and Balmer lines follow a smooth decrement and deviations reveal inconsistencies of the observations and/or data reduction. This is important for blended Paschen and Balmer lines (see Table 5). Inconsistencies can be removed, to some extent, by forcing the observations to follow smooth decrements (see Figs. 2 and 3 below), or in case a large number of line pairs has been observed, by leaving out inconsistent data. For the reduction of the selected, and/or ``cleaned'', set of line ratios we used the least-square method to derive AV and R, and the uncertainties $\sigma$A and $\sigma$R of the parameter AVR (see Bevington $\&$ Robinson 2003). We did not apply a weighting to the observations.

To evaluate the accuracy of the PH-method we took the predicted intensities (Case B) of the 8 line pairs I(Pn), I(Hn) between n = 6 (10 938 Å/4103 Å) and n = 13 (8665 Å/3734 Å)[*] and calculated, using relation (1), for these lines the reddened intensities F(Pn), F(Hn) for selected values AVR. From these intensities we formed the ratios $R_{\rm o}$( $\gamma ) =
\gamma$n F(Pn)/F(Hn) in which the random numbers $0.8 \leq
\gamma _{n} \leq 1.2$ simulate observations of $\la$$\pm$20$\%$ accuracy. The ratios $R_{\rm o}$($\gamma$) were then used in relation (2) to calculate AVR. For a large set of random numbers $\gamma$ nwe find that the values AVR are recovered within 10 to 15$\%$ accuracy of the original values.

From the line ratios $R _{\rm p} = I$(Pn)/I(Hn) ( $8 \leq n \leq 20$; Case B) published by Osterbrock (1989), Brocklehurst (1971), and Storey $\&$ Hummer (1995) it follows that $R _{\rm p}$ varies by $\sim$$\pm$5$\%$ for electron densities between 10 2 $\la$ $n_{\rm e}$[cm-3] $\la$104and electron temperatures between 5000 $\la$ $T_{\rm e}$ [K] $\la$15 000. When using the observed line ratios of M 16 (Garcia-Rojas et al. 2006) and the predicted ratios $R _{\rm p} = 0.345~ \pm ~0.017$ ($\pm$5$\%$) in relation (2), it is found that the calculated values AV and R also vary by $\pm$5$\%$. Generally, the accuracy of the PH-method is set by the accuracy of the observations rather than the emission nebula parameter $n_{\rm e}$, $T_{\rm e}$. For the higher temperature and higher electron density of planetary nebulae the predicted ratio is $R_{\rm p} \approx 0.31$, i.e approximately 10$\%$ lower than for emission nebulae (see Osterbrock 1989; Storey $\&$Hummer 1995), however the same accuracy estimates hold.

4 Observations

4.1 New observations

Our observations of M 8 and M 17 were made with the ESO 1.52-m telescope and the BC-spectrograph in 1st and 2nd order, at a resolution of $\lambda$/$\Delta$ $\lambda = 4500$. The spectra were flat-fielded and calibrated against the standard star LTT 7379 (Stone & Baldwin 1983; Baldwin & Stone 1984). The line intensities were extracted from Gaussian profile fits, and the intensities are normalized to F(H $\beta) = 100$. The accuracy of the observations is $\sim$15$\%$. Our data of M 8 and M 17 are listed in Tables 1 and 2. The M 8 data cover an area of $10^{\prime \prime }\times 2^{\prime \prime }$ in the Hour-Glass region close to the position HG, where the observations by Sanchez & Peimbert (1991) and Garcia-Rojas et al. (2007) were made. The position of the slit (2 $^{\prime \prime }$width) across M 17 is shown in Fig. 1.

\begin{figure}
\par\includegraphics[width=8cm,clip]{13660fig1.ps}
\end{figure} Figure 1:

Part of M 17 and slit sections A, B (3*-1*) and C (Table 2). The stars 1, 2 and 3 observed by Chini et al. (1980) are indicated. The distance between star 1 and 3 is 83 $^{\prime \prime }$.

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\begin{figure}
\par\includegraphics[width=7.6cm,clip]{13660fig2.ps}
\end{figure} Figure 2:

M 17. Illustration of the smoothness of the Paschen (P) and Balmer (H) decrement. Solid dots: observations (region A, Table 2), open circles: predictions ( $n_{\rm e} = 1000$ cm-3, $T_{\rm e} = 10~000$ K).

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\begin{figure}
\par\includegraphics[width=7.6cm,clip]{13660fig3.ps}
\end{figure} Figure 3:

Observed Paschen decrement of M 8 and M 20 (data from Garcia-Rojas et al. 2006, 2007). Open circles: inconsistent data that were corrected to follow a smooth decrement (dashed line). The lines P8, P13 are not blended by sky emission lines (Table 5).

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Figure 2 illustrates the smoothness of the predicted and observed Paschen and Balmer decrement for region A of M 17 (Table 2). The observed Paschen lines P 11, P 12, and P 14 and the observed Balmer lines H 8 and H 11 show some deviation from a smooth decrement, attributed mainly to contamination by sky emission lines in the Paschen line region (for the sky emission lines see Osterbrock & Martel 1992; Hanuschik 2003; Table 5) and to the He I 3889 Å blend of the Balmer H 8 line (Table 5). All observations used in this investigation were checked graphically in this way, and if necessary, corrections were made so that the intensities follow smooth decrements. In Table 2, the data in brackets are corrected in this way, and the corrected values (region A) are used in relation (2).

4.2 Observations by Garcia-Rojas et al. and Esteban et al.

Table 1:   Observations of M 8, $10^{\prime \prime }\times 2^{\prime \prime }$ area of the Hour Glass region HG (see Sanchez & Peimbert 1991).

Paschen and Balmer line observations of M 8, M 16, M 17, M 20, NGC 3603, and S 311 are taken from Garcia-Rojas et al. (2005, 2006, 2007). Their observations are based on echelle spectra (3200-10 350 Å), but the lines P 14, P 15, H 8, and H 14 were not observed since they fall in the order separation of the spectra. The accuracy of the observations is 5 to 15$\%$. When applying relation (2) to the observations of M 20, an inconsistent result AVR (100$\%$ < $\sigma$A, $\sigma$R) is obtained that can be attributed to some peculiarities of the observed Paschen decrement, as shown in Fig. 3. The inconsistent data were forced to a smooth decrement, and the corrected data are used in relation (2).

Table 2:   Observation of M17 (Fig. 1).

The observations of M 42 are taken from Esteban et al. (2004). The 9 line pairs used in the PH-method are between n = 7 and n = 19, while the line pairs n = 8, 10, 14, and 15 were not observed (order separation). Again, the accuracy of the observations is 5 to 15$\%$.

4.3 NGC 7027: observations by Rudy et al. and Zhang et al.

From Rudy et al. (1992) we take the observed emission line ratios P n/P 6 for $6 \leq n \leq 14$, and from Zhang et al. (2005) we take the observed emission line ratios P n/H$\beta $ for $10 \leq n \leq
22$ and H n/H$\beta $ for $6 \leq n \leq 22$. The Paschen line intensities ( $10 \leq n \leq 14$) of both observations were compared to arrive at a common intensity scale. The Paschen line P 8 (9545 Å) (Rudy et al. 1992) is not used since it is blended with [SIII] (9532 Å), the corresponding Balmer line H 8 (3889 Å) is blended with He I 3889 Å. The published intensity of H 14 (3721 Å) is blended with [OII] (3727 Å), and the H 16 line may be blended by the line He I 3705 Å. The intensities of H 14 and H 16 were corrected to follow a smooth decrement (correction H 14 from 1.753 to 0.73, H 16 from 0.853 to 0.55). The Paschen and Balmer line intensities obtained in this way are shown in Fig. 4. The accuracy of the combined observations is probably of the order of 25$\%$.

5 Results and notes on individual objects

The values AV and R derived from the PH-method are compared in Table 3 with determinations from the photometric method (2.1) and (2.2). The uncertainties $\sigma$A, $\sigma$R of the AVR determinations are summarized in Table 4. The value R agrees when derived either from the photometric method or the PH-method. Some notes follow on the individual objects.

Table 3:   Determination of AV, R from common upper level PH lines, and R derived from stellar photometry.

\begin{figure}
\par\includegraphics[width=7.6cm,clip]{13660fig4.ps}
\end{figure} Figure 4:

Paschen (P) and Balmer (H) decrement of NGC 7027, based on observations of Rudy et al. (1992) and Zhang et al. (2005). The published intensities of the Balmer lines n = 14 and n = 16 (open circles) are corrected to follow a smooth decrement.

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M 8 . For the exciting star Herschel 36 (HD 164740), in the Hour-Glass region of M 8, the value R = 4.6-5.6 was derived by Hecht et al. (1982) and R = 5.3 by Cardelli et al. (1989), while Sanchez $\&$ Peimbert (1991) use R = 5.0. The PH-method applied to our observation (Table 1, 7 line pairs) of the emission region close to Her 36 gives AV = 2.3 mag and R = 4.35. The PH-method applied to the observation of Garcia-Rojas et al. (2007) of the same region gives the values AV = 2.2 mag and R = 6.1for the 11 line pairs between $7 \leq n \leq 20$. It is necessary to consider the value R = 6.1 with some caution because of inconsistencies between the Garcia-Rojas et al. (2007) Balmer line measurements (for $\lambda$ < 4100 Å) compared to those of Esteban et al. (1999), while the observation by Esteban et al. does not provide a solution AVR, probably because of the stated difficulties of the P8 to P11 line calibration as explained in both publications. Finally, the measurements by McCall et al. (1990) cover stars in an area of several 10', so that their value R = 4.6 is the average over a large area (method 2.1).

M 17 . The values AVR do not change when leaving out in the least-square fit the line pair P8/H8, instead of using the corrected ratio from a smooth decrement (Fig. 2).

Figure 1 shows that Star 1 observed by Chini et al. (1980) is covered by the slit. Figure 5 is the spectral distribution of Star 1 measured by us at the wavelengths listed for the standard star LTT 7379 (Stone & Baldwin 1983; Baldwin & Stone 1984). Star 1 is assumed to have the spectral type O 4 V (Chini et al. 1980), and the catalogued spectral distribution (Pickles 1998) of a very similar O 5 V star is inserted in Fig. 5. The O 5 V star was taken since the catalogued spectral distribution extends to 10 400 Å. Using the value R = 4.2, obtained from the two-colour diagram of the cluster NGC 6618, for Star 1, Chini et al. (1980) derived the extinction AV = 9.2 mag towards this star. Applying method (2.2) to all data points of the observation shown in Fig. 5 a, we obtain the values AV = 10.4 mag ($\sigma$A = 3 $\%$) and R = 4.5 ($\sigma$R = 5 $\%$) for Star 1. The value R = 4.5 agrees well with the value R = 4.1 derived from the PH-method applied to the lines of the nearby emission region (Fig. 1). Figure 5 b shows that the CCM reddening curve can be applied in this region of M 17.

\begin{figure}
\par\includegraphics[width=8cm,clip]{13660fig5.ps}
\end{figure} Figure 5:

a) Observation (dots) of Star 1 in M 17 (Fig. 1), classified by Chini et al. (1980) to be of spectral type O4 V. Continuous line: spectral distribution of a non-reddened O5 V star, taken from Pickles (1998). The data are normalized at 8000 Å. b) Magnitude difference between the O5 V star, reddened by AV = 10.4 mag, R = 4.5, and the observation of Star 1.

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Star 3 is located at the edge of region A of strong emission (Fig. 1), which did not allow the derivation of a clean spectral distibution of the reddened star. From the ratios P 9/H 9 and P 10/H 10 measured in the nebular region N 3 near Star 3 (Table 2), together with the value R = 4.2, we obtain AV = 4.0 mag, which compares well with the value AV = 3.7 mag derived by Chini et al. (1980) for this star.

The emission line intensities of M 17 (position 14) published by Garcia-Rojas et al. (2006), and used here, are for a region $\sim$4' to the east of the cluster NGC 6618 and $\sim$2' to the east of Star 3 in Fig. 1. The value R seems to be constant over a large area of the nebula.

M 20 . There is contradictory information for the value R in the direction of the central star HD 164492 in M 20. Anderson (1970) and Lynds et al. (1985) use R = 5, while Kohoutek et al. (1999) use R = 3.1, although they did not make a new determination of R. Garcia-Rojas et al. (2007) use R = 3.1. The data of Fig. 3 show deviations of the P 8, P 13, and P 16 intensities from a smooth Paschen decrement, while the observations of the Balmer lines (not shown) follow a smooth decrement. When correcting the observation of Garcia-Rojas et al. (2007), i.e. P 8 from 4.274 to 6.73, P 13 from 2.131 to 1.41 and P 16 from 0.84 to 0.77, and using in relation (2) the 14 line pairs between $7 \leq n \leq 22$, the result is AV = 1.0 mag and R = 5.5.

Again, when leaving out in the least-square fit the line pairs P8/H8 and P13/H13 instead of using the corrected values (Fig. 3), the solution is AV = 1.2 mag ($\sigma$A = 19 $\%$), R = 6.7 ($\sigma$R = 33$\%$, Table 4). However, the range R $\pm$ $\sigma$R is wide for both cases, and contains both values R.

M 42. The emission line spectrum published by Esteban et al. (2004) is taken at 27 $^{\prime \prime }$from the Trapezium star $\theta$1 Ori C. Cardelli $\&$ Clayton (1988) derived R = 5.50 and E(B-V) = 0.34 in the direction of this star. This gives $A_{V} = 0.34~ \times ~5.50 =
1.9$ mag. For an earlier determination of R between 4.4 and 7.7 for the Orion nebula region see Costero $\&$ Peimbert (1970).

NGC 3603. Pandey et al. (2000) published $R = 4.3~ \pm ~0.2$ as best value, mainly based on UBV photometry of cluster stars. Their paper illustrates the sensitivity of the value R on the photometric data set and the method of analysis.

S 311. The H II region S 311 is excited by the star HD 64315 of type O 6 Vnne (Gamen et al. 2006). HD 64315 belongs to the cluster NGC 2467, which, however, seems to be a superposition of early-type stars rather than a true physical cluster (Feinstein $\&$ Vazquez 1989). Grubissich (1969) suggests that the value of R lies between 1.8 and 3.9 for NGC 2467. The colour excess of HD 64315 is E(V-B) = 0.54, which gives the extinction AV = 1.7 mag for R = 3.1, and the value AV = 3.0 mag for R = 5.5 derived from the PH-method (Table 3).

NGC 7027. The planetary nebula NGC 7027 is associated with dust (see for instance Seaton 1979; Middlemass 1990; Sanchez Contreras et al. 1998); however, to derive the extinction AV, the standard value R = 3.1 is generally used. Application of the PH-method with the predicted ratio $R _{\rm p} = 0.31$ (Sect. 3) to the data shown in Fig. 4 gives AV = 3.9 mag and R = 4.4 if using the 16 line pairs between $6 \leq n \leq 22$. The same values AVR are obtained when leaving out the inconsistent line pairs P14/H14 and P16/H16 instead of using the corrected measurements (Fig. 4). If the low-density/low-temperature ratio $R _{\rm p} = 0.345$ (Sect. 3) were used, the values would be AV = 3.7, R = 4.5, illustrating the small dependence of the PH-method on $n_{\rm e}$, $T_{\rm e}$, i.e. $R _{\rm p}$, of the nebula.

Table 4:   Accuracy of AVR determination.

Table 5:   Line strengths, sky line blends, emission line blends (H$\beta $ = 100).

\begin{figure}
\par\includegraphics[width=8cm,clip]{13660fig6.ps}
\vspace{2.5mm}
\end{figure} Figure 6:

Position of the Paschen and Balmer lines ( $6 \leq n \leq 20$) with respect to the linear near-IR part of the reddening curve and the blue part that is sensitive to R (values R = 3.1, 4, 5, 6). The reddening curve is the parametrized form of relation (1) (Cardelli et al. 1989).

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6 Observational and astrophysical aspects of the PH-method

6.1 Sky lines, line blends, instrumental sensitivity

The common upper level PH lines are weak so that elimination of sky lines and nebular line blends is important. Table 5 indicates that the intensity of the Pn and Hn lines (for $6 \la n \la 20$) are between $\sim$30$\%$ and 1$\%$ of H$\beta $ (=100). The table also indicates that the weaker Pn lines are located in the region of many OH sky emission lines (Osterbrock $\&$ Martel 1992; Hanuschik 2003), often of equal strength as the nebular emission lines, while there are hardly any nebular emission line blends in the red wavelength region. The Hn lines of the blue wavelength region are relatively strong, while the sky lines in this wavelength region are very weak (Osterbrock et al. 1996; Hanuschik 2003, his Fig. 5). The lines H8, H10, H14, and H16 (see Table 5) coincide with strong nebular emission lines. A high spectral resolution and off-source sky background exposures are required. The atmospheric extinction is measured on a nearby standard star.

The common upper level Pn-Hn lines are outside the maximum response of commonly used CCD detectors; however, the sensitivity of any observation of the Pn-Hn lines also depends on the aperture of the telescope and the resolution of the spectrograph. Typical values of CCD efficiencies are $\sim$80-90$\%$ for the H$\alpha$-H$\beta $ region, $\sim$35-60$\%$ for the 3500-4000 Å region and $\sim$60-10$\%$ for the 8500-11 000 Å region. It is difficult to obtain good measurements of the P6 10 938 Å line, though the data of Tables 1 and 2 contain reliable values (accuracy <25 $\%$).

6.2 Photometric method versus PH-method

There are two differences between any line ratio method (for instance H$\alpha$/H$\beta $ ratio or PH-method (2.3)) and the photometric methods ((2.2), (2.2)):

(a)
the photometric methods are not affected by light scattered in the nebula (see Osterbrock 1989; Krügel #Kr&), so that the photometric methods can be summarized as the slab-screen extinction method;

(b)
the line ratio method uses observed emission line intensities (or fluxes) that are affected by (1) internal extinction and scattering in the emission nebula itself, (2) possible back scattering on the rear surface of the emission nebula, and (3) external extinction and scattering in a slab-screen in front of the nebula. These effects apply to all line ratio methods, and are not a particularity of the PH-method. There are many studies that calculate (estimate) these effects; for instance, for (1) see Mathis (1970, 1972, 1983), for (2) see O'Dell et al. (1992), for (3) see Natta $\&$ Panagia (1984), Osterbrock (1989), and others. A general conclusion of these studies is, that from measured line ratios and their spatial variation, it is difficult to decide in which proportion the effects (1)-(3) do occur, unless one has recourse to radio and emission line flux meaurements (see for instance Mathis 1983; Caplan & Deharveng 1986). From radiative transfer calculations of several models of emission nebulae, scattering functions and albedos of the dust grains, and especially applied to the common upper level line ratio P6/H6, Mathis (1970) concludes that ``the assumption that all dust is external to a nebula is very good for determining relative line strengths for wavelengths between those for which the extinction correction was determined. As [his] Table 3 shows, the errors are not worse if the [extinction] correction is determined from H$\alpha$/H$\beta $ instead of P6/H6''.


Throughout this paper we have used the CCM parameterized extinction law. This may not necessarily be the most appropriate extinction law for a particular emission nebula, as suggested for the Orion nebula (M 42) by Bautista et al. (1995), although their conclusion needs to be confirmed. We have also assumed, as is usually done, that Case B applies to the emission nebulae discussed here.

7 Summary

The position of the Paschen lines Pn and Balmer lines Hn, for $6 \leq n \leq 20$, with respect to the reddening curve is illustrated in Fig. 6. The Paschen lines cover the linear part of the reddening curve, and the Balmer lines cover the blue section that is sensitive to the actual value R.

The PH-method of extinction determination AVR exploits the favourable fact that the predicted intensity ratios R$_{\rm p}$(n) of common Paschen-Balmer lines are nearly insensitive to the excitation condition $n_{\rm e}$, $T_{\rm e}$ of the emission nebula. The ratios R$_{\rm p}$(n) are constant within $\sim$5$\%$ for different levels n at given $n_{\rm e}$, $T_{\rm e}$, and constant within $\sim$10$\%$ for the range from low-density/low-temperature emission nebulae (R$_{\rm p}$ (n) = 0.34) to high-density/high-temperature planetary nebulae (R$_{\rm p}$ (n) = 0.31). The accuracy of the PH-method depends therefore primarily on the accuracy of the observations. The consistency of the observation/data reduction can be checked because the observed lines must show a smooth Paschen and Balmer decrement.

We have shown for 6 emission nebulae (Table 3) that the extinction AV and the total-to-selective absorption R are easily derived from the common Paschen-Balmer line method (2.3), and that the values agree with those derived from the photometric methods (2.1) and (2.2) of associated stars and/or stellar clusters, keeping in mind that the value R derived from the photometric method (2.1) is the average over the extended star cluster region.

The PH-method can be used for emission nebulae and planetary nebulae where no stars are available for photometry. It is worth noting that for the emission nebulae and the planetary nebula of Table 3 the values R are higher than $\sim$4, thus higher than the value R = 3.1 of the diffuse interstellar medium that is often used because of lack of exact knowledge. The PH-method opens the possibility of investigating emission nebulae in a more systematic and extended way for their actual values R. The PH-method can be used for mapping of the value R across nebulae and - when using large telescopes - investigation of extra-galactic emission nebulae in near-by galaxies, such as the LMC, SMC, M 31, and M 51.

The PH-method gives the value R for the entire wavelength region between $\sim$3700 Å and 10 400 Å. The PH-method does not allow any investigation of a different value R of, for instance, the blue wavelength region and the red wavelength region as applied by Garcia-Rojas et al. (2006, 2007) to M 8 and M 16. The PH-method relies on precise measurements of the Balmer lines (5 to 10$\%$ accuracy) since the lines of the blue wavelength region are sensitive to the actual value of R (see Fig. 6).

Acknowledgements
For the line ratios we used Storey & Hummer's programme inrat.f, retrieved from the CDS. We thank the referee (G. C. Clayton) for his comments, and in particular for the remarks that resulted in adding Sect. 6 summarizing the observational and astrophysical aspects of the PH-method.

References

Footnotes

... lines[*]
Partially based on observations made at ESO, La Silla.
...Å)[*]
With intensities of I(10938)/I (4103) = 9.03/ 25.95 = 0.348 and I(8665)/I (3734) = 0.83/ 2.41 = 0.344 for $n_{\rm e} = 1000$ cm-3, $T_{\rm e} = 10~000$ K; H $\beta = 100$ (Storey $\&$ Hummer 1995).

All Tables

Table 1:   Observations of M 8, $10^{\prime \prime }\times 2^{\prime \prime }$ area of the Hour Glass region HG (see Sanchez & Peimbert 1991).

Table 2:   Observation of M17 (Fig. 1).

Table 3:   Determination of AV, R from common upper level PH lines, and R derived from stellar photometry.

Table 4:   Accuracy of AVR determination.

Table 5:   Line strengths, sky line blends, emission line blends (H$\beta $ = 100).

All Figures

  \begin{figure}
\par\includegraphics[width=8cm,clip]{13660fig1.ps}
\end{figure} Figure 1:

Part of M 17 and slit sections A, B (3*-1*) and C (Table 2). The stars 1, 2 and 3 observed by Chini et al. (1980) are indicated. The distance between star 1 and 3 is 83 $^{\prime \prime }$.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=7.6cm,clip]{13660fig2.ps}
\end{figure} Figure 2:

M 17. Illustration of the smoothness of the Paschen (P) and Balmer (H) decrement. Solid dots: observations (region A, Table 2), open circles: predictions ( $n_{\rm e} = 1000$ cm-3, $T_{\rm e} = 10~000$ K).

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=7.6cm,clip]{13660fig3.ps}
\end{figure} Figure 3:

Observed Paschen decrement of M 8 and M 20 (data from Garcia-Rojas et al. 2006, 2007). Open circles: inconsistent data that were corrected to follow a smooth decrement (dashed line). The lines P8, P13 are not blended by sky emission lines (Table 5).

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=7.6cm,clip]{13660fig4.ps}
\end{figure} Figure 4:

Paschen (P) and Balmer (H) decrement of NGC 7027, based on observations of Rudy et al. (1992) and Zhang et al. (2005). The published intensities of the Balmer lines n = 14 and n = 16 (open circles) are corrected to follow a smooth decrement.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8cm,clip]{13660fig5.ps}
\end{figure} Figure 5:

a) Observation (dots) of Star 1 in M 17 (Fig. 1), classified by Chini et al. (1980) to be of spectral type O4 V. Continuous line: spectral distribution of a non-reddened O5 V star, taken from Pickles (1998). The data are normalized at 8000 Å. b) Magnitude difference between the O5 V star, reddened by AV = 10.4 mag, R = 4.5, and the observation of Star 1.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8cm,clip]{13660fig6.ps}
\vspace{2.5mm}
\end{figure} Figure 6:

Position of the Paschen and Balmer lines ( $6 \leq n \leq 20$) with respect to the linear near-IR part of the reddening curve and the blue part that is sensitive to R (values R = 3.1, 4, 5, 6). The reddening curve is the parametrized form of relation (1) (Cardelli et al. 1989).

Open with DEXTER
In the text


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