Search

We study the gas inflows towards the Galactic Central Molecular Zone (CMZ) based on the gas morphological and kinematic features from the MWISP in the region of l=1.2 deg--19.0 deg and |b|<3.0 deg. We find that the near dust lane extends to l~15 deg, in which the end of the large-scale gas structure intersects with the 3 kpc-ring at a distance of ~5 kpc. Intriguingly, many filamentary MCs, together with the bow-like/ballistic-like clouds and continuous CO features with notable velocity gradient, are finely outlined along the long structure. These MCs also have relatively large velocity dispersions, indicating the shocked gas generated by local continuous accretion and thus the enhanced turbulence along the entire gas structure. We suggest that the ~3.1--3.6 kpc long CO structure originates from the accretion molecular gas driven by the Galactic bar. The gas near the bar end at the 3 kpc-ring becomes an important reservoir for the large-scale accreting flows inwards to the CMZ through the bar channel. The inclination angle of the bar is estimated to be 20--26 deg, while the pattern speed of the bar is 30--35 km/s. The total mass of the whole gas lane is about (0.9-1.7)x10^7 Msun according to the calculated X_CO=(0.6-1.4)x10^20 cm^-2 (Kkm/s)^-1 from the large-scale CO data and the complementary HI data. The mean gas inflow rate is about 0.8-1.4 Msun/yr, which seems to be comparable to the outflow's rate of the Galactic nuclear winds after applying the updated lower X-factor value above., Comment: 16 pages, 3 figures

The morphology of molecular clouds is crucial for understanding their origin and evolution. In this work, we investigate the morphology of the filamentary molecular clouds (filaments for short) using a portion of the $^{12}\text{CO} (J=1-0)$ data from the Milky Way Imaging Scroll Painting (MWISP) project. The data cover an area spanning $104.75^\circ

Velocity fields of molecular clouds (MCs) can provide crucial information on the merger and split between clouds, as well as their internal kinematics and maintenance, energy injection and redistribution, even star formation within clouds. Using the CO spectral lines data from the Milky Way Imaging Scroll Painting (MWISP) survey, we measure the relative velocities along the line of sight ($\Delta$V$_{\rm LOS}$) between $^{13}$CO structures within $^{12}$CO MCs. Emphasizing MCs with double and triple $^{13}$CO structures, we find that approximately 70$\%$ of $\Delta$V$_{\rm LOS}$ values are less than $\sim$ 1 km s$^{-1}$, and roughly 10$\%$ of values exceed 2 km s$^{-1}$, with a maximum of $\sim$ 5 km s$^{-1}$. Additionally, we compare $\Delta$V$_{\rm LOS}$ with the internal velocity dispersion of $^{13}$CO structures ($\sigma_{\rm ^{13}CO,in}$) and find that about 40$\%$ of samples in either double or triple regime display distinct velocity discontinuities, i.e. the relative velocities between $^{13}$CO structures are larger than the internal linewidths of $^{13}$CO structures. Among these 40$\%$ samples in the triple regime, 33$\%$ exhibit signatures of combinations through the two-body motion, whereas the remaining 7$\%$ show features of configurations through the multiple-body motion. The $\Delta$V$_{\rm LOS}$ distributions for MCs with double and triple $^{13}$CO structures are similar, as well as their $\Delta$V$_{\rm LOS}$/$\sigma_{\rm ^{13}CO,in}$ distributions. This suggests that relative motions of $^{13}$CO structures within MCs are random and independent of cloud complexities and scales., Comment: 16 pages, 11 figures, accepted for publication in AJ

According to the structures traced by $^{13}$CO spectral lines within the $^{12}$CO molecular clouds (MCs), we investigate the contributions of their internal gas motions and relative motions to the total velocity dispersions of $^{12}$CO MCs. Our samples of 2851 $^{12}$CO MCs harbor a total of 9556 individual $^{13}$CO structures, among which 1848 MCs ($\sim$ 65$\%$) have one individual $^{13}$CO structure and the other 1003 MCs ($\sim$ 35$\%$) have multiple $^{13}$CO structures. We find that the contribution of the relative motion between $^{13}$CO structures ($\sigma_{\rm ^{13}CO, re}$) is larger than that from their internal gas motion ($\sigma_{\rm ^{13}CO, in}$) in $\sim$ 62$\%$ of 1003 MCs in the `multiple' regime. In addition, we find the $\sigma_{\rm ^{13}CO, re}$ tends to increase with the total velocity dispersion($\sigma_{\rm ^{12}CO, tot}$) in our samples, especially for the MCs having multiple $^{13}$CO structures. This result provides a manifestation of the macro-turbulent within MCs, which gradually becomes the dominant way to store the kinetic energy along with the development of MC scales., Comment: 15 pages, 13 figures, accepted for publication in ApJ

We universally search for evidence of kinematic and spatial correlation of supernova remnant (SNR) and molecular cloud (MC) associations for nearly all SNRs in the coverage of the MWISP CO survey, i.e. 149 SNRs, 170 SNR candidates, and 18 pure pulsar wind nebulae (PWNe) in 1 deg < l < 230 deg and -5.5 deg < b < 5.5 deg. Based on high-quality and unbiased 12CO/13CO/C18O (J = 1--0) survey data, we apply automatic algorithms to identify broad lines and spatial correlations for molecular gas in each SNR region. The 91% of SNR-MC associations detected previously are identified in this paper by CO line emission. Overall, there could be as high as 80% of SNRs associated with MCs. The proportion of SNRs associated with MCs is high within the Galactic longitude less than ~50 deg. Kinematic distances of all SNRs that are associated with MCs are estimated based on systemic velocities of associated MCs. The radius of SNRs associated with MCs follows a lognormal distribution, which peaks at ~8.1 pc. The progenitor initial mass of these SNRs follows a power-law distribution with an index of ~-2.3 that is consistent with the Salpeter index of -2.35. We find that SNR-MC associations are mainly distributed in a thin disk along the Galactic plane, while a small amount distributed in a thick disk. With the height of these SNRs from the Galactic plane below ~45 pc, the distribution of the average radius relative to the height of them is roughly flat, and the average radius increases with the height when above ~45 pc., Comment: 77 pages, 20 figures, 4 tables (with machine-readable versions), accepted for publication in ApJS

We report the first high-sensitivity HI observation toward the spiral galaxy M94 with the Five-hundred-meter Aperture Spherical radio Telescope (FAST). From these observations, we discovered that M94 has a very extended HI disk, twice larger than that observed by THINGS, which is accompanied by an HI filament and seven HVCs (high velocity clouds) at different distances. The projected distances of these clouds and filament are less than 50 kpc from the galactic center. We measured a total integrated flux (including all clouds/filament) of 127.3 ($\pm$1) Jy km s$^{-1}$, corresponding to a H I mass of (6.51$\pm$0.06)$\times$10$^{8}$M$_{\odot}$, which is 63.0% more than that observed by THINGS. By comparing numerical simulations with the HI maps and the optical morphology of M94, we suggest that M94 is likely a remnant of a major merger of two galaxies, and the HVCs and HI filament could be the tidal features originated from the first collision of the merger happened about 5 Gyr ago. Furthermore, we found a seemingly isolated HI cloud at a projection distance of 109 kpc without any optical counterpart detected. We discussed the possibilities of the origin of this cloud, such as dark dwarf galaxy and RELHIC (REionization-Limited HI Cloud). Our results demonstrate that high-sensitivity and wide-field HI imaging is important in revealing the diffuse cold gas structures and tidal debris which is crucial to understanding the dynamical evolution of galaxies., Comment: 14 pages, 8 figures

We report the discovery of a 100 kpc HI tail in the merging galaxy pair NGC 4490/85 detected by the Five-Hundred-meter Aperture Spherical radio Telescope (FAST). The tidal tails extended in both the south and north directions, and they are much longer than that reported previously based on the VLA interferometric maps. The NGC 4490/85 is surrounded by a large gas envelope, and a starburst low metallicity dwarf galaxy MAPS 1231+42 is found to be connected with the gas envelope, indicating that galaxy interaction trigged the intense star formation in it. Based on the fact that the metallicity in MAPS 1231+42 is one order of magnitude lower than that in the two disks of NGC 4490 and NGC 4485, we speculate that the gas near this galaxy should be primordial and could be due to gas inflow from the circum-galactic medium (CGM). We also found a collimated gas component pointing at a nearby dwarf galaxy KK 149, suggesting that this galaxy might also be interacting with the NGC 4490 pair. We discuss the possible origin of the long tidal tails and the extended gas envelope in this merging system based on the new data from FAST., Comment: 10 pages, 8 figures, 1 table.Accepted by MNRAS. The raw data used in the article will be published on the FAST website: https://fast.bao.ac.cn. The PID is N2021_4. Please contact the author (liuyao@nao.cas.cn, mz@nao.cas.cn) for processed data

In this paper, we study the long time behaviour of mean curvature flow in a cylinder with Robin boundary conditions. Such a boundary condition can force the solution to have a singular behaviour at the boundary when $t\to \infty$. The planar version of this problem has been investigated in an existing literature, where the curve shortening flow in $2$-dimensional band with Robin boundary conditions is shown to converge to a translating Grim Reaper with finite speed and fixed profile. By considering a radially symmetric mean curvature flow, denoted by $u(|x|,t)$, in $(N+1)$-dimensional cylinder ($N\geq 2$), we find in the present paper a new feature of the flow: both the interior gradients and the propagating speed of the flow increase to infinity exponentially, $Du/u\sim x$ and $ u\sim C_0 e^{(N-1)t}e^{\frac{|x|^2}{2}}$ as $t\to \infty$ for some $C_0>0$, which is completely different from the 2-dimensional case.

We look into the 2851 $^{12}$CO molecular clouds harboring $^{13}$CO structures to reveal the distribution of the projected angular separations and radial velocity separations between their internal $^{13}$CO structures. The projected angular separations are determined using the minimal spanning tree algorithm. We find that $\sim$ 50$\%$ of the angular separations fall in a narrow range of $\sim$ 3 - 7 arcmin with a median of $\sim$ 5 arcmin, and the corresponding radial velocity separations mainly range from $\sim$ 0.3 km s$^{-1}$ to 2.5 km s$^{-1}$. The mean and standard deviation of the angular separations of the internal $^{13}$CO structures within $^{12}$CO clouds appear to be universal, independent of the $^{12}$CO cloud angular areas and the counts of their internal $^{13}$CO structures. We also reveal a scaling relation between the $^{12}$CO cloud angular area and its harbored $^{13}$CO structure count. These results suggest there is a preferred angular separation between $^{13}$CO structures in these $^{12}$CO clouds, considering the distance effects. According to that, we propose an alternative picture for the assembly and destruction of molecular clouds: there is a fundamental separation for the internal structures of molecular clouds, the build-up and destruction of molecular clouds proceeds under this fundamental unit., Comment: 14 pages, 12 figures, accepted for publication in ApJ

We have obtained column density maps for an unbiased sample of 120 molecular clouds in the third quadrant of the Milky Way mid-plane (b$\le |5|^{\circ}$) within the galactic longitude range from 195$^{\circ}$ to 225$^{\circ}$, using the high sensitivity $^{12}$CO and $^{13}$CO ($J=1-0$) data from the Milky Way Imaging Scroll Painting (MWISP) project. The probability density functions of the molecular hydrogen column density of the clouds, N-PDFs, are fitted with both log-normal (LN) function and log-normal plus power-law (LN+PL) function. The molecular clouds are classified into three categories according to their shapes of N-PDFs, i.e., LN, LN+PL, and UN (unclear), respectively. About 72\% of the molecular clouds fall into the LN category, while 18\% and 10\% into the LN+PL and UN categories, respectively. A power-law scaling relation, $\sigma_s\propto N_{H_2}^{0.44}$, exists between the width of the N-PDF, $\sigma_s$, and the average column density, $N_{H_2}$, of the molecular clouds. However, $\sigma_s$ shows no correlation with the mass of the clouds. A correlation is found between the dispersion of normalized column density, $\sigma_{N/\rm }$, and the sonic Mach number, $\mathcal{M}$, of molecular clouds. Overall, as predicted by numerical simulations, the N-PDFs of the molecular clouds with active star formation activity tend to have N-PDFs with power-law high-density tails.

After the morphological classification of the 18,190 $^{12}$CO molecular clouds, we further investigate the properties of their internal molecular gas structures traced by the $^{13}$CO($J=$ 1$-$0) line emissions. Using three different methods to extract the $^{13}$CO gas structures within each $^{12}$CO cloud, we find that $\sim$ 15$\%$ of $^{12}$CO clouds (2851) have $^{13}$CO gas structures and these $^{12}$CO clouds contribute about 93$\%$ of the total integrated flux of $^{12}$CO emission. In each of 2851 $^{12}$CO clouds with $^{13}$CO gas structures, the $^{13}$CO emission area generally does not exceed 70$\%$ of the $^{12}$CO emission area, and the $^{13}$CO integrated flux does not exceed 20$\%$ of the $^{12}$CO integrated flux. We reveal a strong correlation between the velocity-integrated intensities of $^{12}$CO lines and those of $^{13}$CO lines in both $^{12}$CO and $^{13}$CO emission regions. This indicates the H$_{2}$ column densities of molecular clouds are crucial for the $^{13}$CO lines emission. After linking the $^{13}$CO structure detection rates of the 18,190 $^{12}$CO molecular clouds to their morphologies, i.e. nonfilaments and filaments, we find that the $^{13}$CO gas structures are primarily detected in the $^{12}$CO clouds with filamentary morphologies. Moreover, these filaments tend to harbor more than one $^{13}$CO structure. That demonstrates filaments not only have larger spatial scales, but also have more molecular gas structures traced by $^{13}$CO lines, i.e. the local gas density enhancements. Our results favor the turbulent compression scenario for filament formation, in which dynamical compression of turbulent flows induces the local density enhancements. The nonfilaments tend to be in the low-pressure and quiescent turbulent environments of the diffuse interstellar medium., Comment: 21 pages, 14 Figures; Appendix (17 pages, 19 Figures); Accepted for publication in the journal ApJS

We study a generalized mean curvature flow involving a positive power of the mean curvature and a driving force. In this paper, we first construct all kinds of radially symmetric translating solutions, and then select one of them to satisfy a prescribed boundary angle in a cylinder. We then consider the flow starting at an initial hypersurface: showing the a priori estimates (especially the uniform-in-time bounds for the mean curvature which guarantee the uniform parabolicity of the corresponding fully nonlinear equation), giving the global existence for the solution of the initial boundary value problem, and proving its convergence to the corresponding translating solution. Our study provides a complete exposition on the influence of the dimension, the power of the mean curvature, the driving force and the boundary angles on the existence and stability of radially symmetric translating solutions., Comment: 29 pages

Based on the MWISP survey, we study high-z CO emission toward the tangent points, in which the distances of the molecular clouds (MCs) are well determined. In the region of l=12-26 deg and |b|<5.1 deg, a total of 321 MCs with |z|> 110 pc are identified, of which nearly 30 extreme high-z MCs (EHMCs at |z|> 260 pc) are concentrated in a narrow region of R_GC=2.6-3.1 kpc. The EHMC concentrations, together with other high-z MCs at R_GC=2.3-2.6 kpc, constitute molecular crater-wall structures surrounding the edges of the HI voids that are physically associated with the Fermi bubbles. Intriguingly, some large high-z MCs, which lie in the crater walls above and below the Galactic plane, show cometary structures with the head toward the plane, favouring the scenario that the entrained molecular gas moves with the multi-phase flows from the plane to the high-z regions. We suggest that the Milky Way nuclear wind has a significant impact on the Galactic gaseous disk. The powerful nuclear wind at ~3-6 Myr ago is likely responsible for the observational features, (1) the enhanced CO gas lying in the edges of the HI voids, (2) the deficiency of atomic and molecular gas within R_GC<3 kpc, (3) the possible connection between the EHMC concentrations and the 3-kpc arm, and (4) the elongated high-z MCs with the tail pointing away from the Galactic plane., Comment: 27 pages, 7 Figures, 1 Table, typo corrected

Using the Five-hundred-meter Aperture Spherical radio Telescope (FAST), we search for HI narrow-line self-absorption (HINSA) features in twelve Planck Galactic cold clumps (PGCCs), one starless core L1521B and four star forming sources. Eight of the 12 PGCCs have emission of J=2-1 of cyanoacetylene (HC3N). With an improved HINSA extraction method more robust for weaker and blended features with high velocity resolution, the detection rates of HINSA in PGCCCs are high, at 92% overall (11/12) and 87% (7/8) among sources with HC3N J=2-1 emissions. Combining the data of molecular spectra and Planck continuum maps, we studied the morphologies, abundances and excitations of HI, CO and HC3N in PGCCs. The distribution of HINSA is similar to that of CO emission. HINSA tends to be not detected in regions associated with warm dust and background ionizing radiation, as well as regions associated with stellar objects. The abundances of HI in PGCCs are approximately 3E-4, and vary within a factor of ~3. The non-thermal velocity dispersions traced by C18O J=1-0 and HINSA are consistent with each other (0.1-0.4 km/s), larger than those of HC3N (~0.1 km/s). Carbon chain molecule abundant PGCCs provide a good sample to study HINSA., Comment: 31 pages, 17 figures, 4 tables

We present the survey of $^{12}$CO/$^{13}$CO/C$^{18}$O (J=1-0) toward the California Molecular Cloud (CMC) within the region of 161.75$^{\circ} \leqslant l \leqslant$ 167.75$^{\circ}$,-9.5$^{\circ} \leqslant b \leqslant $-7.5$^{\circ}$, using the Purple Mountain Observatory (PMO) 13.7 m millimeter telescope. Adopting a distance of 470 pc, the mass of the observed molecular cloud estimated from $^{12}$CO, $^{13}$CO, and C$^{18}$O is about 2.59$\times$10$^{4}$ M$_\odot$, 0.85$\times$10$^{4}$ M$_\odot$, and 0.09$\times$10$^{4}$ M$_\odot$, respectively. A large-scale continuous filament extending about 72 pc is revealed from the $^{13}$CO images. A systematic velocity gradient perpendicular to the major axis appears and is measured to be $\sim$ 0.82 km s$^{-1}$ pc$^{-1}$. The kinematics along the filament shows an oscillation pattern with a fragmentation wavelength of $\sim$ 2.3 pc and velocity amplitude of $\sim$ 0.92 km s$^{-1}$, which may be related with core-forming flows. Furthermore, assuming an inclination angle to the plane of the sky of 45$^{\circ}$, the estimated average accretion rate is $\sim$ 101 M$_\odot$ Myr$^{-1}$ for the cluster LkH$\alpha$ 101 and $\sim$ 21 M$_\odot$ Myr$^{-1}$ for the other regions. In the C$^{18}$O observations, the large-scale filament could be resolved into multiple substructures and their dynamics are consistent with the scenario of filament formation from converging flows. Approximately 225 C$^{18}$O cores are extracted, of which 181 are starless cores. Roughly 37$\%$ (67/181) of the starless cores have $\alpha_{\text{vir}}$ less than 1. Twenty outflow candidates are identified along the filament. Our results indicate active early-phase star formation along the large-scale filament in the CMC region., Comment: 28 pages, 15 figures, accepted by ApJ

We attempt to visually classify the morphologies of 18190 molecular clouds, which are identified in the $^{12}$CO(1-0) spectral line data over $\sim$ 450 deg$^{2}$ of the second Galactic quadrant from the Milky Way Imaging Scroll Painting project (MWISP). Using the velocity-integrated intensity maps of the $^{12}$CO(1-0) emission, molecular clouds are first divided into unresolved and resolved ones. The resolved clouds are further classified as non-filaments or filaments. Among the 18190 molecular clouds, $\sim$ 25 $\%$ are unresolved, $\sim$ 64$\%$ are non-filaments, and $\sim$ 11$\%$ are filaments. In the terms of the integrated flux of $^{12}$CO(1-0) spectra of the whole 18190 molecular clouds, $\sim$ 90$\%$ are from filaments, $\sim$ 9$\%$ are from non-filaments, and the rest $\sim$ 1$\%$ are from unresolved sources. Although non-filaments are dominant in the number of the discrete molecular clouds, filaments are the main contributor of $^{12}$CO emission flux. We also present the number distributions of physical parameters of the molecular clouds in our catalog, including their angular sizes, velocity spans, peak intensities of $^{12}$CO(1-0) emission, and $^{12}$CO(1-0) total fluxes. We find that there is a systematic difference between the angular sizes of the non-filaments and filaments, with the filaments tending to have larger angular scales. The H$_{2}$ column densities of them are not significantly different. We also discuss the observational effects, such as those induced by the finite spatial resolution, beam dilution and line-of-sight projection, on the morphological classification of molecular clouds in our sample., Comment: 17 pages, 8 figures, 3 tables, appendix: 7 figures, accepted for publication in ApJS

Sixty five Planck Galactic cold clumps (PGCCs) from the first quadrant (IQuad) and thirty nine of PGCCs from the Anti-Center direction region (ACent) were observed in $^{12}$CO, $^{13}$CO and C$^{18}$O J=1-0 lines using the PMO 13.7-m telescope. All the targets were detected with all the three lines, except for 12 IQuad and 8 ACent PGCCs without C$^{18}$O detection. Seventy six and 49 velocity components were obtained in IQuad and ACent respectively. One-hundred and forty-six cores were extracted from 76 IQuad clumps and 100 cores from 49 ACent clumps. The average T$_{\mathrm{ex}}$ of IQuad cores and ACent cores are 12.4 K and 12.1 K, respectively. The average line width of $^{13}$CO of IQuad cores and ACent cores are 1.55 km s$^{-1}$ and 1.77 km s$^{-1}$, respectively. Among the detected cores, 24 in IQuad and 13 in ACent have asymmetric line profiles. The small blue excesses, $\sim$0.03 in IQuad and 0.01 in ACent, indicate that the star formation is not active in these PGCC cores. Power-law fittings of core mass function to the high mass end give indexes of -0.57 in IQuad and -1.02 in ACent which are flatter than the slope of initial mass function given by \citeauthor{1955ApJ...121..161S}. The large turnover masses with value of 28 M$_{\odot}$ for IQuad cores and 77 M$_{\odot}$ for ACent cores suggest low star formation efficiencies in PGCCs. The correlation between virial mass and gas mass indicates that most of PGCC cores in both regions are not likely pressure-confined.

Filament S242 is 25 pc long with massive clumps and YSO clusters concentrated in its end regions; it is considered a good example of edge collapse. We mapped this filament in the $^{12}$CO(1-0) and $^{13}$CO(1-0) lines. A large-scale velocity gradient along filament S242 has been detected; the relative velocity between the two end-clumps is $\sim$ 3 km s$^{-1}$, indicating an approaching motion between them. These signatures are consistent with the filament S242 being formed through the collapse of a single elongated entity, where an effect known as "gravitational focusing" drives the ends of the filament to collapse (edge collapse). Based on this picture, we estimate a collapse timescale of $\sim$ 4.2 Myr, which is the time needed for a finite and elongated entity evolving to the observed filament S242. For the whole filament, we find that increases in surface densities lead to increases in velocity dispersion, which can be consistently explained as the result of self-gravity. We also calculated the contribution of longitudinal collapse to the observed velocity dispersion and found it to be the dominant effect in driving the gas motion near the end-clumps. We propose that our filament S242 is formed through a two-stage collapse model, where the edge collapse of a truncated filament is followed by a stage of longitudinal accretion toward the dense end-clumps., Comment: 14 pages, 11 figures; Accepted for publication in A&A

We consider an anisotropic curvature flow $V= A(\mathbf{n})H + B(\mathbf{n})$ in a band domain $\Omega :=[-1,1]\times R$, where $\mathbf{n}$, $V$ and $H$ denote the unit normal vector, normal velocity and curvature, respectively, of a graphic curve $\Gamma_t$. We consider the case when $A>0>B$ and the curve $\Gamma_t$ contacts $\partial_\pm \Omega$ with slopes equaling to $\pm 1$ times of its height (which are unbounded when the solution moves to infinity). First, we present the global well-posedness and then, under some symmetric assumptions on $A$ and $B$, we show the uniform interior gradient estimates for the solution. Based on these estimates, we prove that $\Gamma_t$ converges as $t\to \infty$ in $C^{2,1}_{\text{loc}} ((-1,1)\times R)$ topology to a cup-like traveling wave with {\it infinite} derivatives on the boundaries.

N131 is a typical infrared dust bubble showing an expanding ringlike shell. We study what kinds of CO line ratios can be used to trace the interaction in the expanding bubble. We carry out new $\rm CO\,(3-2)$ observations towards bubble N131 using the JCMT 15-m telescope, and derive line ratios by combining with our previous $\rm CO\,(2-1)$ and $\rm CO\,(1-0)$ data from the IRAM 30-m telescope observations. To trace the interaction between the molecular gas and the ionized gas in the HII region, we use RADEX to model the dependence of CO line ratios on kinetic temperature and H$_2$ volume density, and examine the abnormal line ratios based on other simulations. We present $\rm CO\,(3-2)$, $\rm CO\,(2-1)$, and $\rm CO\,(1-0)$ integrated intensity maps convolved to the same angular resolution (22.5$"$). The three different CO transition maps show apparently similar morphology. The line ratios of $W_{\rm CO\,(3-2)}$/$W_{\rm CO\,(2-1)}$ mostly range from 0.2 to 1.2 with a median of $0.54\pm0.12$, while the line ratios of $W_{\rm CO\,(2-1)}$/$W_{\rm CO\,(1-0)}$ range from 0.5 to 1.6 with a median of $0.84\pm0.15$. The high CO line ratios $W_{\rm CO\,(3-2)}$/$W_{\rm CO\,(2-1)}\gtrsim 0.8 $ and $W_{\rm CO\,(2-1)}$/$W_{\rm CO\,(1-0)}\gtrsim 1.2$ are beyond the threshold predicted by numerical simulations based on the assumed density-temperature structure for the inner rims of ringlike shell, where are the compressed areas in bubble N131. These high CO integrated intensity ratios, such as $W_{\rm CO\,(3-2)}$/$W_{\rm CO\,(2-1)}\gtrsim0.8$ and $W_{\rm CO\,(2-1)}$/$W_{\rm CO\,(1-0)}\gtrsim1.2$, can be used as a tracer of gas compressed regions with a relatively high temperature and density. This further suggests that the non-Gaussian part of the line-ratio distribution can be used to trace the interaction between the molecular gas and the hot gas in the bubble., Comment: 6 pages, 9 figures, Accepted for publication in A&A

We consider a curvature flow $V=H$ in the band domain $\Omega :=[-1,1]\times \R$, where, for a graphic curve $\Gamma_t$, $V$ denotes its normal velocity and $H$ denotes its curvature. If $\Gamma_t$ contacts the two boundaries $\partial_\pm \Omega$ of $\Omega$ with constant slopes, in 1993, Altschular and Wu \cite{AW1} proved that $\Gamma_t$ converges to a {\it grim reaper} contacting $\partial_\pm \Omega$ with the same prescribed slopes. In this paper we consider the case where $\Gamma_t$ contacts $\partial_\pm \Omega$ with slopes equaling to $\pm 1$ times of its height. When the curve moves to infinity, the global gradient estimate is impossible due to the unbounded boundary slopes. We first consider a special symmetric curve and derive its uniform interior gradient estimates by using the zero number argument, and then use these estimates to present uniform interior gradient estimates for general non-symmetric curves, which lead to the convergence of the curve in $C^{2,1}_{loc} ((-1,1)\times \R)$ topology to the {\it grim reaper} with span $(-1,1)$.

In this paper we investigate the spectral problem in Finsler geometry. Due to the nonlinearity of the Finsler-Laplacian operator, we introduce \textit{faithful dimension pairs} by means of which the spectrum of a compact reversible Finsler metric measure manifold is defined. Various upper and lower bounds of such eigenvalues are provided in the spirit of Cheng, Buser and Gromov, which extend in several aspects the results of Hassannezhad, Kokarev and Polterovich. Moreover, we construct several faithful dimension pairs based on Lusternik-Schnirelmann category, Krasnoselskii genus and essential dimension, respectively; however, we also show that the Lebesgue covering dimension pair is not faithful. As an application, we show that the Bakry-\'Emery spectrum of a closed weighted Riemannian manifold can be characterized by the faithful Lusternik-Schnirelmann dimension pair.

We present a multi-wavelength study of the Planck cold clump G181.84+0.31, which is located at the northern end of the extended filamentary structure S242. We have extracted 9 compact dense cores from the SCUBA-2 850 um map, and we have identified 18 young stellar objects (YSOs, 4 Class I and 14 Class II) based on their Spitzer, Wide-field Infrared Survey Explorer (WISE) and Two-Micron All-Sky Survey (2MASS) near- and mid-infrared colours. The dense cores and YSOs are mainly distributed along the filamentary structures of G181.84 and are well traced by HCO$^{+}$(1-0) and N$_{2}$H$^{+}$(1-0) spectral-line emission. We find signatures of sequential star formation activities in G181.84: dense cores and YSOs located in the northern and southern sub-structures are younger than those in the central region. We also detect global velocity gradients of about 0.8$\pm$0.05 km s$^{-1}$pc$^{-1}$ and 1.0$\pm$0.05 km s$^{-1}$pc$^{-1}$ along the northern and southern sub-structures, respectively, and local velocity gradients of 1.2$\pm$0.1 km s$^{-1}$pc$^{-1}$ in the central substructure. These results may be due to the fact that the global collapse of the extended filamentary structure S242 is driven by an edge effect, for which the filament edges collapse first and then further trigger star formation activities inward. We identify three substructures in G181.84 and estimate their critical masses per unit length, which are $\sim$ 101$\pm$15 M$_{\odot}$ pc$^{-1}$, 56$\pm$8 M$_{\odot}$ pc$^{-1}$ and 28$\pm$4 M$_{\odot}$ pc$^{-1}$, respectively. These values are all lower than the observed values ($\sim$ 200 M$_{\odot}$ pc$^{-1}$), suggesting that these sub-structures are gravitationally unstable., Comment: 20 pages, 17 figures, article, accepted