Astron. Astrophys. 352, 287-296 (1999)

3. Column densities

3.1. Data analysis

We identified numerous interstellar absorption lines of H I , D I , different heavy elements and H₂. In the photospheric spectrum only a few weak, sharp metal lines of C III , C IV , N III , N V , Si III , Si IV , P V , and S V can be identified besides the strong He II lines. The investigations on interstellar metal and deuterium abundances make use of the standard curve of growth technique. Except for the case of the Ly and absorptions, the equivalent widths of the lines were measured either by a trapezium or by a Gaussian fit. The differences between the two methods are well below the typical errors in the equivalent widths. Uncertainties in the measurements occur because of noise and the choice of the continuum. The error due to the latter was estimated by determining the equivalent width for a lower and an upper limit of the continuum level, the photon statistics were taken into consideration by a formula adopted from Jenkins et al. (1973). Both errors added quadratically give the uncertainties in as quoted in Tables 1, 3, and 4.

Table 1. Metal absorption line equivalent widths measured in component A (at  km s^-1) with ORFEUS and IUE .
Notes:
Wavelengths and f-values are from Morton (1991), except for ^* taken from Savage & Sembach (1996)
a) Line blended with FeII at 1260.533 Å. The equivalent width given here has already been corrected for a contribution of  mÅ derived from the determined FeII column density
b) The 1302 OI line is in ORFEUS spectra blended with geocoronal OI emission, in IUE spectra with a reseaux

Some lines of S II , Si II , and N I , which lie between 1190 and 1390 Å, were measured in both the IUE and the ORFEUS spectrum. The line profiles and absorption strengths turn out to be consistent.

3.2. Metals

In order to judge the velocity structure of the absorption it is reasonable to analyze the metal lines at first. We find 2 different absorption components: one at a radial velocity (heliocentric) of  km s^-1 (component A) and one at  km s^-1 (component B). The latter is rather weak, Si II equivalent widths are smaller than 24 mÅ with large uncertainties, so an examination of component B can give only very uncertain results. Even if this component had a very low b-value, the upper limits for the SII and SiII column densities would be roughly cm^-2 and cm^-2 respectively corresponding to a hydrogen column density of cm^-2.

In the following we will concentrate on the cloud at -24 km s^-1. The small LSR velocity of this component suggests a local origin while component B at -75 km s^-1 represents most likely a cloud at larger distance.

Table 1 lists the measured equivalent widths for component A. The lines of Fe II , Si II , and N I were used to determine the b-value of 51 km s^-1 of the curve of growth for metals. Then column densities of other ions were obtained by fitting their equivalent width to the curve. Fig. 2 shows the curve of growth, Table 2 gives the resulting column densities. The errors take the uncertainties in the b-value and in the individual equivalent widths into account. For ions with data points only in the flat part of the curve of growth the column densities have large uncertainties.

Fig. 1. Profiles of metal absorption lines in the IUE LWR, IUE SWP, and the ORFEUS spectrum. The velocity components (heliocentric) at  km s-1 (B) and  km s-1 (A) are labeled

Fig. 2. The curve of growth for absorption by metals on the line of sight to BD +39 3226 (component A) is shown. Plotted are only SiII , FeII , and NI which actually define the curve of growth. Filled symbols represent ORFEUS data, open symbols those from the IUE . The drawn curves represent single cloud absorption with indicated b-value

Table 2. Metal column densities N [cm^-2] and abundances. Solar values are taken from de Boer et al. (1987)

3.3. Neutral hydrogen

We determined the H I column density in two different ways.

First we compared theoretical Voigt profiles convolved with a gaussian instrumental profile to the Ly line in the ORFEUS and the IUE spectrum. This line is always fully damped, therefore the b-value is unimportant and in case of a single velocity component only the column density remains as a parameter. Even small changes in the column density have a clear effect on the profile. We estimate the accuracy in as . Problems arise because of the weaker component B at Å and stellar He II absorption at Å which both are unresolved. Component B should have only a weak influence on the column density, probably dex. The stellar line was calculated from an atmospheric model ( K, , n(He)%, n(H)%) and included in the fit. The uncertainty in N(H I ) due to the stellar model is small, because significant errors in the strength of the calculated stellar line would have made the fit profile asymmetric with regard to the measured profile. An additional background substraction was applied in both spectra of the Lyman line to correct for some residual intensity (% in the ORFEUS spectrum) near the centre. The result is plotted in Fig. 4. It is only possible to give a total column density (for component A and B), which is cm^-2.

Fig. 3. The curve of growth for H I and D I towards BD +39 3226. In the damping part the curves split, the lower curve is for Ly , the upper one is for Ly . Note that the D I points lie essentially on the Doppler part of the curve of growth

Fig. 4. Theoretical fits to the Lyman line in the IUE and the ORFEUS spectrum. In both spectra the residual intensity near the centre of the absorption has been set to zero. The contribution of the stellar He II line located Å towards shorter wavelengths as calculated from an atmospheric model is included in the fits and plotted separately. The two shown fits represent (H I ) and 20.1. Near the centre the geocoronal emission peak is visible

To confirm this value, we also applied the curve-of-growth analysis to the Lyman series from Ly to Ly , except for Ly and Ly which seem distorted. The Ly and Ly lines have strong damping wings which, together with the further structure of the spectrum, do not allow the determination of reliable equivalent widths. Higher Lyman lines are also visible but may be blended with stellar He II , because the distance between these lines is smaller than the stellar radial velocity. Besides, near the Lyman edge it is not possible to set the continuum properly. We measured the equivalent width of Ly by comparing the line with computed two-component-profiles (Voigt profiles convolved with the instrumental Gauss profile), one component for the H I and one for the D I line. For the other lines the damping wings are negligible and we used two-component Gauss fits.

We note that for the higher Lyman series lines (-) the instrumental profile degrades the true absorption such that residual light is expected near the bottom of the profiles (see Fig. 6 and 7). A calculation shows this to be at the level of up to 10%. In addition, also in these lines geocoronal emission is present but not readily recognizable in the profiles considered (in Lyman and it is clearly present). Since the absolute level of the contamination is not reliably known we have refrained from corrections.

Fig. 5. Curve of growth for HI in detail. The data points and the corresponding theoretical curves are labeled

Fig. 6. The Lyman lines used in our curve of growth analysis in the ORFEUS spectrum. The positions of D and H absorption by component A () are marked

Fig. 7. For two of the Lyman lines a 500 km s-1 wide section of the spectrum is displayed. Top : Deuterium and hydrogen Lyman line in the ORFEUS spectrum (data points) with a two-component fit (Voigt profile convolved with instrumental Gauss). Bottom : Deuterium and hydrogen Lyman line (data points) with a two-component Gauss profile. In both plots the positions of the velocity components A and B found in the metal lines are marked for the HI lines. Component B has only negligible effect on the absorption profile

In case of Ly the FeII line situated between the HI and the DI line at 937.652 Å was modeled and used as a third, fixed component in the fit. An analogous procedure was necessary for the H₂ Werner Q(1), 4-0 line lying at Å between the HI and DI Lyman lines. Attempts to include velocity component B by additional fit components showed that it has negligible influence on the line shape. Examples for the fits are shown in Fig. 7. Though the velocity structure is not resolved in the Lyman series, a single-cloud curve of growth should be sufficient since there is one clearly dominant cloud. As expected the H I curve of growth has a significantly higher Doppler-velocity than the metals' curve due to the much smaller atomic mass of hydrogen. For a given b each measured equivalent width and its error correspond to a column density with an error depending on the slope of the curve of growth. We calculated for different b-values from the weighted mean of the 5 column densities resulting from the 5 measured equivalent widths. The least mean square deviation is found for  km s^-1, leading to cm^-2. Fig. 3 and 5 show the curve for H I .

The Lyman fit and the curve of growth analysis give consistent results, so a mean value of cm^-2 can be derived.

3.4. Deuterium

The absorption of deuterium was investigated in 5 lines (see Table 3). The DI Lyman and lines are shown in Fig. 7. Along with the H I data, the D I equivalent widths are plotted in Fig. 3. For DI Ly only an upper limit can be given which is rather high due to the continuum uncertainty. The Doppler parameter is only of minor importance for the determination of the D I column density because the data points lie mainly on the linear part of the curve of growth. The deuterium data points seem to suggest a somewhat higher b-value than 10.5 km s^-1 but we used the same curve as for hydrogen since we expect . The weighted mean of the column densities derived for  km s^-1 from the four measured values is cm^-2.

Table 3. Hydrogen and deuterium equivalent widths. Wavelengths and oscillator strengths are taken from Morton (1991). HI and DI Ly have been corrected for the influence of FeII absorption at 937.652 Å, HI and DI Ly for the influence of the H₂ We Q(1), 4-0 line at 930.574 Å.
Notes:
 Wavelength calculated from HI Ly .

3.5. Molecular hydrogen

The ORFEUS spectra also contain a large number of absorption lines from molecular hydrogen. Only one component is visible here. The average radial velocity of 18 lines measured in the echelle orders 50-59 is  km s^-1, slightly different from the velocity found for the metal absorption lines. The metal radial velocity of  km s^-1, was measured as the average value of 20 lines in the echelle orders 42-60. Since we have not found any obvious systematic velocity shift between different orders, a possible explanation may be the presence of an additional weak unresolved absorption component in the metal lines.

We have determined equivalent widths using trapezium fits. No better quality of the results would be achievable from fitting gaussian profiles since most of the lines are only weak and do not show clear profiles. The equivalent width for rotational states are similar to the strength of noise peaks, so only upper limits are determined. Results are presented in Table 4.

Table 4. H₂ equivalent widths and column densities [cm^-2].
Notes:
a) f values from Morton & Dinerstein (1976)
b) b: line is possibly blended; n: spectrum has locally small S/N

Column densities for the different rotational excitation levels are derived from these equivalent widths by fitting to a theoretical curve of growth (Fig. 9). The b-value is restricted by the lower J levels to 2.5 to 3 km s^-1. The column densities for and 1 lie in the flat part of the curve of growth and therefore are sensitive to variations of the b-value, enlarging the errors for their column densities. The higher rotational levels are located on the doppler part of the curve which in principle allows a good definition of column densities. However, most of these lines are weak and have larger errors in the equivalent widths which again leads to larger errors in the column densities. For only upper limits can be given. The resulting column densities are listed in Table 4.

Fig. 8. Overview of the spectra for some H2 transitions. The spectra shown are filtered by a wavelet algorithm. The H2 absorption at  km s-1 is clearly visible for the transitions with . At higher rotational states the equivalent widths are similar to the strength of noise peaks. Additional absorption lines marked are: a) Ly R(1), 2-0; b) Ly R(0), 4-0; c) Ly P(1), 4-0; s) features of probably stellar origin, which could not be unambiguously identified

Fig. 9. Curve of growth for the different excitation levels of H2. Downward arrows denote upper limits for the equivalent width. The b-value is based on the absorption in levels to 2

The population of the lower rotational states of molecular hydrogen is determined by collisional excitation, following a Boltzmann distribution. The excitation temperature can therefore be derived as

where the statistical weight is equal to , multiplied by a factor of 3 for J odd in regard to the triplet nature of ortho-H₂. For the upper levels UV photons have to be considered as the primary source of excitation (Spitzer & Zweibel 1974; Spitzer et al. 1974). An equivalent excitation temperature can be derived here, but this has by no means the physical implications of an actual kinetic temperature.

We have determined excitation temperatures by using an error weighted least square fit. A temperature of  K is derived for the lower levels to 2, for the upper levels we find an upper limit in the equivalent excitation temperature of  K.

Looking at Fig. 10, where the column density , weighted by the statistical weight , is plotted against the excitation energy of the rotational state J, a clear distinction is visible between the collisionally Boltzmann excited levels and the UV photon excited levels . Although the upper levels scatter around the fit, a much smaller slope is obvious, compared with the lower levels.

Fig. 10. Excitation plot for the H2 column densities. Plotted is the statistically weighted column density vs. excitation energy of the rotational states. A clear separation of collisionally excited levels () and of UV photon excited levels () is visible. The lines denote least square fits to an assumed Boltzmann distribution for levels m to n with the appropriate temperature . The error given for the Boltzmann excitation temperature is the standard deviation of the fit. For only an upper limit can be given

The H₂ ortho-to-para ratio (OPR) derived from the by far most prominent rotational states and 1 is . The excitation temperature calculated using the lowest para-states and 2 is  K. This value essentially coincides with the temperature determined from the OPR of  K. We therefore can assume that we see thermalized, purely collisionally excited gas in the excitation levels up to , following the Boltzmann distribution (see Dalgarno et al. 1973).

For the higher excitation levels information is less clear due to the scatter in the data points. Fitting the ortho- and para-states separately we get  K and  K, so the excitation temperature for the upper states probably can be restricted to  K rather than  K as stated above.

© European Southern Observatory (ESO) 1999

Online publication: November 23, 1999
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