H₂CO and H_110α observations towards NH₃ sources

Abstract

We observed the H₂CO(1₁₀–1₁₁) absorption lines and H_110α radio recombination lines (RRL) toward 180 NH₃ sources using the Nanshan 25-m radio telescope. In our observation, 138 sources were found to have H₂CO lines and 36 have H_110α RRLs. Among the 138 detected H₂CO sources, 38 sources were first detected. The detection rates of H₂CO have a better correlation with extinction than with background continuum radiation. Line center velocities of H₂CO and NH₃ agree well. The line width ratios of H₂CO and NH₃ are generally larger than unity and are similar to that of ¹³CO. The correlation between column densities of H₂CO and extinction is better than that between NH₃ and extinction. These line width relation and column density relation indicate H₂CO is distributed on a larger scale than that of NH₃, being similar to the regions of ¹³CO. The abundance ratios between NH₃ and H₂CO were found to be different in local clouds and other clouds.

Appendices

Appendix A: Simulation of blended H₂CO HFS

The optical depth of all the HFS is simply assumed to be a superposition of N components,

$$ \tau(v)=\sum_{j=1}^{N} \alpha_j \tau_0 \exp \biggl\{ -4\ln2 \biggl[ \frac{v-(v_j+v_0)}{\Delta v_{\mathrm{int}}} \biggr]^2 \biggr\} , $$

(A.1)

where α_j and v_j are the intensity and velocity of the jth HFS component, and Δv_int is the intrinsic line width. The α_j and v_j data of H₂CO(1₁₀–1₁₁) HFS components were got from (Tucker et al. 1971). Because the optical depth of H₂CO(1₁₀–1₁₁) in most cases is far less than 1, we assume that the intensity is proportional to the opacity. So the spectra line profile is the same as τ(v).

Spectra for Δv_int between 0.43 to 8.69 at intervals of 0.43 km/s (7 KHz to 140 KHz at intervals of 7 KHz) were calculated using Eq. (A.1). Then single Gaussian fittings were made to get the blended line width. The simulated spectra are shown in Fig. 14 and the fitting results are listed in Table 4. The ratios between blended and unblended line widths are plotted in Fig. 9. Because most of our observed line widths are larger than 1 km s⁻¹, this HFS blending effect would not make much difference as regards our sources.

Fig. 9

The ratio of blended line width to intrinsic line width is plotted against the blended line width. The gray box is the region with a ratio between 1.2 and 1

Table 4 HFS simulation result

Appendix B: Non-LTE radiative transfer of H₂CO

To absorb the CMB radiation as observed, the H₂CO 1₁₀–1₁₁ transition must have an excitation temperature lower than CMB. The different cross sections of transitions in collision are considered to be the ones most likely to generate such a low excitation temperature (Townes and Cheung 1969; Garrison et al. 1975; Evans et al. 1975). The excitation of H₂CO should be treated with a non-LTE method, because the LTE approximation would cause an excitation temperature above CMB. We used the Radex Non-LTE molecular radiative transfer code (van der Tak et al. 2007) to calculate the excitation of H₂CO. The predicted line brightness temperature (T_L) and excitation temperature (T_ex) were calculated from the input H₂ number density (n[H₂]), the H₂CO column density (N[H₂CO]), the background brightness temperature (T_bg), and the kinetic temperature (T_kin), where T_bg is the background brightness temperature, which is equal to T_C+T_CMB in Eq. (2).

The result shows that the competition between collision and background radiation dominates the excitation process of H₂CO. Figure 10 shows T_ex vs. T_bg under different T_kin and n[H₂]. Under both low n[H₂] and high n[H₂] conditions, T_ex is less sensitive to T_kin at high T_kin (T_kin>20 K). A similar relation between T_ex and T_kin was obtained by Darling and Zeiger (2012) in high redshift galaxies. At low n[H₂], collisions are insufficient. Then the background radiation dominates the level populations and the excitation temperature of H₂CO almost follows the variation of T_bg, i.e. T_ex≈T_bg−Constant, as is shown in Fig. 10(a). This may contribute to the less clear relation between the detection rate and T_C in Fig. 1(b). At high n[H₂], collisions dominate the level populations and the excitation temperature keeps almost constant over the whole T_bg range.

Fig. 10

Excitation temperature of H₂CO vs. background brightness temperature. The thick black line is for T_ex=T_bg

The possible n[H₂] values of H₂CO 6-cm lines are considered to be 10³<n[H₂]<10⁵ (cm⁻³) (Evans et al. 1975; Henkel et al. 1980). The exact value of n[H₂], which in principle can be derived through the relative intensity of 1₁₀–1₁₁ (6 cm) and 2₁₁–2₁₂ (2 cm) (Henkel et al. 1980; Mangum et al. 2008), is unknown because only the 6-cm lines were observed. But in that n[H₂] interval, the n[H₂] seems not to influence the N[H₂CO] too much, as the contours in that region in Fig. 11(a) are almost parallel to the horizontal axis. To find the potential uncertainty introduced by the unknown n[H₂], we calculated the N[H₂CO] under the assumptions that n[H₂]=10², 10³, 10⁴, and 10⁵ (cm⁻³), respectively. The histogram distributions of the column densities are plotted in Fig. 11(b). The column density distributions of n[H₂]=10³, 10⁴, and 10⁵ (cm⁻³) are almost the same, and that of n[H₂]=10² (cm⁻³) is about one order larger than the others. We also plotted the histogram distribution of column densities under the assumption that T_ex=1.7 K in Sect. 3. The N[H₂CO] distribution of T_ex=1.7 K is about half an order larger than that of 10³<n[H₂]<10⁵ (cm⁻³).

Fig. 11

(a) Contours of T_L in log(n[H₂])−log(N[H₂CO]) space. The figure presents a map of calculated T_L in log(n[H₂])−log(N[H₂CO]) space. For each source, one contour on which T_L is equal to the observed T_MB is drawn. (b) Histogram of N[H₂CO] under different assumptions: n[H₂]=10², 10³, 10⁴, 10⁵ (cm⁻³), and T_ex=1.7 K

Fig. 12

Detected RRL lines (intensity in $T_{\mathrm{A}}^{*}$)

Fig. 13

Sources detected with H₂CO (intensity in $T_{\mathrm{A}}^{*}$)

Fig. 14

Blended HFS simulation of H₂CO. The blended spectra of five HFS components are plotted in a black line and the Gaussian fittings are in a green line