## 2. Neutral hydrogen in the region of the Cepheus BubbleThe HI data were taken from the Leiden/Dwingeloo HI survey
(Hartmann & Burton 1997). The angular and velocity resolution
of the spectra are and
1.03 kms ## 2.1. HI distribution in the channel mapsIn the region to
,
to HI emission is dominated by a
narrow galactic plane layer of at
any radial velocity between -110 kms We focus on the
kms
An inspection of the HI maps of Fig. 1 reveals loop structures
in several velocity regimes. The most prominent ring structure, with
sharp inner edge in the direction of the Cepheus Bubble, appears in
the kms So far we identified the significant cloud complexes related to the Cepheus Bubble by visual inspection of the HI maps. This method, however, is not automatic, can be somewhat subjective, and works less efficiently in regions where the resolution of the kinematic distances, resulting from the differential rotation of the Galaxy, is poor (like in the Cepheus region which is close to the tangent point). Visual inspection may also fail to identify structures which extend over very large radial velocity ranges due to internal and/or peculiar motions. In the next subsection we use a multivariate statistical method for identifying the main structures in the data cube representing the Cepheus Bubble, free from subjective bias. ## 2.2. Multivariate analysis of the HI channel mapsThe positional and velocity data of the neutral hydrogen form a
data cube . We assume that the HI
emission is optically thin, and the observed channel maps are weighted
superpositions of where ,
and
are the measured intensities in the
channel maps, the weighting coefficients, and the contributions of the
components, respectively, and We make the assumption that the correlation between the components is negligible. This assertion enables us to apply the principal components analysis (PCA) for finding the number of significant components (factors) and their numerical values, using standard techniques implemented in statistical software packages. The PCA represents the observed variables ( values in our case) as linear combinations of non-correlated background variables (principal components). We note that although PCA is often used for finding the factors, there are many other techniques for obtaining a factor model. PCA and factor analysis represent two different procedures, strongly related but not identical. PCA obtains the factors by solving the eigenvalue equation of a
matrix built up from the correlations of the observed quantities. The
components of the obtained eigenvectors serve as coefficients of the
factors (the significant principal components in this technique) in
the equation given above. The eigenvalues
give some hint for the `importance'
of the corresponding components. The
and ratios indicate what percentage
of the variance of the observed variables can be explained by the
We analyzed a matrix built up from the mutual correlations between
the HI channel values. We used altogether 43 channels in the
[-38,+6] kms Fig. 3 presents maps of the 6 factor values, and Fig. 4 shows the weighting coefficients for these 6 factors as a function of radial velocity. Fig. 4 reveals that each factor has a well-defined radial velocity interval where it is dominant and where the contributions of the others are almost negligible (these velocity ranges are also given in Table 1).
In the following we compare the results of the PCA with those
derived in the previous subsection. The well defined loop structure in
the [] kms We found that all prominent emission structures, recognized in the HI maps of Fig. 1 (Sect. 2.1), were identified by the PCA as well, and the results of the multivariate analysis could be converted into useful physical information. This approach offers an objective way to get an unbiased estimate of the characteristic radial velocities of the most significant structures, which is not given by the visual inspection. The method also shows how to reduce the size of our data cube without losing too much information, and therefore it could be used for automatic analysis of larger data sets, too. ## 2.3. HI distribution in the position-velocity spaceThe existence of an extended depression in the hydrogen emission at
high negative velocities is also evident from Fig. 5, a
position-velocity diagram taken perpendicularly to the galactic plane
at . The figure shows a large hole
between and
, 37
and -4 kms
We propose to interpret the observed spatial-velocity distribution
as radial expansion of a 3-dimensional shell. According to this
interpretation, the regular ring patterns in the
kms The apparent centre of the shell lies at
kms © European Southern Observatory (ESO) 2000 Online publication: February 9, 2000 |