tokens: 10 and 15 per cent, respectively. Figure 2. Distribution of the resultant distance uncertainties of the catalogued PGCCs. In Fig. 3 , we compare our newly derived extinction distances with the kinematic values deduced by Zhang et al. ( 2018 ). In general, the newly estimated extinction distances differ significantly from the kinematic ones. Amongst the sample objects, 10 clumps have similar kinematic distances ( d Z18 ∼ 0.46 kpc), as they all have similar radial velocities (8.0 or 3.0 km s −1 ). However, their directly measured extinction distances range from 0.21 to 0.51 kpc. It is quite possible that the peculiar and non-circular motions of the clumps may have significantly affected the calculation of their kinematic distances (Liszt Burton 1981 ; Gómez 2006 ; Reid et al. 2009 ). For some PGCCs, such as G176.17-02.10 and G177.14-01.21, the differences between the two sets of distances are very large. The kinematic distance probabilities of those clumps derived with the Bayesian Distance Calculator (see table 1 of Zhang et al. 2018 ) are very small (less than 0.5), indicating that those kinematic distances are poorly constrained. Figure 3. Comparison of our extinction distances with their kinematic values from Zhang et al. ( 2018 ). In the left-hand panel, the black dash line denoting complete equality is used to guide the eyes. 5 DISCUSSION The improved distance estimates allow us to revise some of the distance-dependent physical properties of the cores of the PGCCs, such as their radii, masses, and the virial parameters. We update those physical parameters by simply rescaling the results of Zhang et al. ( 2018 ). For example, effective radius R eff of a Planck core is proportional to distance d , R eff ∝ d . Thus the revised radius is evaluated as Similarly, the revised mass M ′ is given by We note that these updates also lead to changes of other parameters, such as the virial parameter, which is given by Fig. 4 plots the space distribution of these 61 PGCCs in the X – Y space with both the original kinematic distances and our updated distances, where the distance changes are indicated. According to the formula (3) and (4), we present the changes of these physical quantities in Fig. 5 . From the histograms in the left-hand panel of Fig. 5 , we find that on the whole the radii and masses calculated with the new extinction distances tend to be smaller than those of Zhang et al. ( 2018 ), by respectively ∼ 17.9 and 32.6 per cent. This leads us to conclude that to understand the local molecular structures, accurate distances are necessary. We use an MCMC algorithm to fit the mass–radius relation for both sets of distances. The new distances yield a slope of 1.95 ± 0.09, comparable to 1.93 ± 0.09 obtained with the kinematic distances. In spite of the significant changes, the slope is largely unaffected. The result is understandable, considering that a change in the distance measurement leads to changes in both mass and size estimates. Since the
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O B-Software I-Software I-Software O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O