A Large-field J=1-0 Survey of CO and Its Isotopologues Toward the Cassiopeia A Supernova Remnant

We have conducted a large-field simultaneous survey of $^{12}$CO, $^{13}$CO, and C$^{18}$O $J=1-0$ emission toward the Cassiopeia A (Cas A) supernova remnant (SNR), which covers a sky area of $3.5^{\circ}\times3.1^{\circ}$. The Cas giant molecular cloud (GMC) mainly consists of three individual clouds with masses on the order of $10^4-10^5\ M_{\odot}$. The total mass derived from the $\rm{^{13}CO}$ emission of the GMC is 2.1$\times10^{5}\ M_{\odot}$ and is 9.5$\times10^5\ M_{\odot}$ from the $\rm{^{12}CO}$ emission. Two regions with broadened (6$-$7 km s$^{-1}$) or asymmetric $^{12}$CO line profiles are found in the vicinity (within a 10$'\times10'$ region) of the Cas A SNR, indicating possible interactions between the SNR and the GMC. Using the GAUSSCLUMPS algorithm, 547 $^{13}$CO clumps are identified in the GMC, 54$\%$ of which are supercritical (i.e. $\alpha_{\rm{vir}}<2$). The mass spectrum of the molecular clumps follows a power-law distribution with an exponent of $-2.20$. The pixel-by-pixel column density of the GMC can be fitted with a log-normal probability distribution function (N-PDF). The median column density of molecular hydrogen in the GMC is $1.6\times10^{21}$ cm$^{-2}$ and half the mass of the GMC is contained in regions with H$_2$ column density lower than $3\times10^{21}$ cm$^{-2}$, which is well below the threshold of star formation. The distribution of the YSO candidates in the region shows no agglomeration.Comment: 24 pages, 18 figure

Models of Relative Nearness Incidence Based on Standard Distance Entropy

The model of grey nearness incidence cannot reflect the nearness degree of sequences correctly. Therefore, the model of relative nearness incidence of sequences, curves, and surfaces is suggested based on standard distance entropy to remove the current bottlenecks and its properties are studied. At last, three cases are exemplified to demonstrate the validity and practicability of relative nearness incidence. The proposed models have enriched the theory of grey nearness incidence, filled the defects of grey nearness incidence