arXiv subjects

Guang-Xing Li

Publications and source records attributed to Guang-Xing Li.

At least 55 records · Page 3Linked to original sources

arXiv2024

Massive clumps in W43-main: Structure formation in an extensively shocked molecular cloud

W43-main is a massive molecular complex located at the interaction of the Scutum arm and the Galactic bar undergoing starburst activities. We aim to investigate the gas dynamics, in particular, the prevailing shock signatures from the cloud to clump scale and assess the impact of shocks on the formation of dense gas and early-stage cores. We have carried out NOEMA and IRAM-30m observations at 3 mm with an angular resolution of $\sim$0.1 pc towards five massive clumps in W43 main. We use CH$_{3}$CCH and H$_{2}$CS lines to trace the extended gas temperature and CH$_{3}$OH lines to probe the volume density of the dense gas ($\gtrsim$10$^{5}$ cm$^{-3}$). The emission of SiO (2-1) is extensive across the region ($\sim$4 pc) and is mostly contained within a low-velocity regime, hinting at a large-scale origin of the shocks. The position-velocity maps of multiple tracers show systematic spatio-kinematic offsets supporting the cloud-cloud collision/merging scenario. We identify an additional extended velocity component in CCH emission, which coincides with one of the velocity components of the larger scale $^{13}$CO (2-1) emission, likely representing an outer, less dense gas layer in the cloud merging process. We find that the V-shaped, asymmetric SiO wings are tightly correlated with localised gas density enhancements, which is direct evidence of dense gas formation and accumulation in shocks. We resolve two categories of NH$_{2}$D cores: ones exhibiting only subsonic to transonic velocity dispersion, and the others with an additional supersonic velocity dispersion. The centroid velocities of the latter cores are correlated with the shock front seen by SiO. The kinematics of the $\sim$0.1 pc NH$_{2}$D cores are heavily imprinted by shock activities, and may represent a population of early-stage cores forming around the shock interface.

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arXiv2024

Transport-driven super-Jeans fragmentation in dynamical star-forming regions

The Jeans criterion is one cornerstone in our understanding of gravitational fragmentation. A critical limitation of the Jeans criterion is that the background density is assumed to be a constant, which is often not true in dynamic conditions such as star-forming regions. For example, during the formation phase of the high-density gas filaments in a molecular cloud, a density increase rate $\dot ρ$ implies a mass accumulation time of $t_{\rm acc}= ρ/ \dot ρ= - ρ(\nabla \cdot (ρ\vec{v}))^{-1}$. The system is non-stationary when the mass accumulation time becomes comparable to the free-fall time $t_{\rm ff} = 1 / \sqrt{G ρ}$. We study fragmentation in non-stationary settings, and find that accretion can significantly increase in the characteristic mass of gravitational fragmentation ( $λ_{\rm Jeans,\; aac}= λ_{\rm Jeans} (1 + t_{\rm ff} / t_{\rm acc})^{1/3}$, $m_{\rm Jeans,\, acc} = m_{\rm Jeans} (1 + t_{\rm ff} / t_{\rm acc})$). In massive star-forming regions, this mechanism of transport-driven super-jeans fragmentation can contribute to the formation of massive stars by causing order-of-magnitude increases in the mass of the fragments.

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arXiv2023

Tides in clouds: control of star formation by long-range gravitational force

Gravity drives the collapse of molecular clouds through which stars form, yet the exact role of gravity in cloud collapse remains a complex issue. Studies point to a picture where star formation occurs in clusters. In a typical, pc-sized cluster-forming region, the collapse is hierarchical, and the stars should be born from regions of even smaller sizes ($\approx 0.1\;\rm pc$). The origin of this spatial arrangement remains under investigation. Based on a high-quality surface density map towards the Perseus region, we construct a 3D density structure, compute the gravitational potential, and derive eigenvalues of the tidal tensor ($λ_{\rm min}$, $λ_{\rm mid}$, $λ_{\rm max}$, $λ_{\rm min} < λ_{\rm mid} < λ_{\rm max}$), analyze the behavior of gravity at every location and reveal its multiple roles in cloud evolution. We find that fragmentation is limited to several isolated, high-density ``islands''. Surrounding them, is a vast amount of gas ($75 \%$ of the mass, $95 \%$ of the volume) that stays under the influence of extensive tides where fragmentation is suppressed. This gas will be transported towards these regions to fuel star formation. The spatial arrangement of regions under different tides explains the hierarchical and localized pattern of star formation inferred from the observations. Tides were first recognized by Newton, yet this is the first time its dominance in cloud evolution has been revealed. We expect this link between cloud density structure and role gravity to be strengthened by future studies, resulting in a clear view of the star formation process.

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arXiv2023

Magnetic Fields in Giant Filaments Probed by the Velocity Gradient Technique: Regular Magnetic Field interrupted by Magnetization Gaps

We study the magnetic field structures in six giant filaments associated with the spiral arms of the Milky Way by applying the Velocity Gradient technique (VGT) to the 13CO spectroscopic data from GRS, Fugin, and SEDIGSM surveys. Compared to dust polarized emission, the VGT allows us to separate the foreground and background using the velocity information, from which the orientation of the magnetic field can be reliably determined. We find that in most cases, the magnetic fields stay aligned with the filament bodies, which are parallel to the disk midplane. Among these, G29, G47, and G51 exhibit smooth magnetic fields, and G24, G339, and G349 exhibit discontinuities. The fact that most filaments have magnetic fields that stay aligned with the Galactic disk midplane suggests that Galactic shear can be responsible for shaping the filaments. The fact that the magnetic field can stay regular at the resolution of our analysis (<= 10 pc) where the turbulence crossing time is short compared to the shear time suggests that turbulent motion can not effectively disrupt the regular orientation of the magnetic field. The discontinuities found in some filaments can be caused by processes including filament reassembly, gravitational collapse, and stellar feedback.

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arXiv2023

Mapping gravity in stellar nurseries -- establishing the effectiveness of 2D acceleration maps

Gravity is the driving force of star formation. Although gravity is caused by the presence of matter, its role in complex regions is still unsettled. One effective way to study the pattern of gravity is to compute the accretion it exerts on the gas by providing gravitational acceleration maps. A practical way to study acceleration is by computing it using 2D surface density maps, yet whether these maps are accurate remains uncertain. Using numerical simulations, we confirm that the accuracy of the acceleration maps $\mathbf a_{\rm 2D}(x,y)$ computed from 2D surface density are good representations for the mean acceleration weighted by mass. Due to the under-estimations of the distances from projected maps, the magnitudes of accelerations will be over-estimated $|\mathbf a_{\rm 2D}(x,y)| \approx 2.3 \pm 1.8 \; |\mathbf a_{\rm 3D}^{\rm proj}(x,y)|$, where $\mathbf a_{\rm 3D}^{\rm proj}(x,y)$ is mass-weighted projected gravitational acceleration, yet $\mathbf a_{\rm 2D}(x,y)$ and $ \mathbf a_{\rm 3D}^{\rm proj}(x,y)$ stay aligned within 20$^{\circ}$. Significant deviations only occur in regions where multiple structures are present along the line of sight. The acceleration maps estimated from surface density provide good descriptions of the projection of 3D acceleration fields. We expect this technique useful in establishing the link between cloud morphology and star formation, and in understanding the link between gravity and other processes such as the magnetic field. A version of the code for calculating surface density gravitational potential is available at \url{https://github.com/zhenzhen-research/phi_2d}.

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arXiv2023

Effective Shielding of $\lesssim$ 10 GeV Cosmic Rays from Dense Molecular Clumps

The density of cosmic rays inside molecular clouds determines the ionization rate in the dense cores where stars form. It is also one of the drivers of astrochemistry leading to the creation of complex molecules. Through Fermi Large Area Telescope observations of nearby giant molecular clouds, we observed deficits (holes) in the gamma-ray residual map when modelling with the expected gamma-ray diffuse emission from uniform cosmic rays interacting with the molecular content. We propose that the deficit is due to the lack of penetration of the low-energy (sub-GeV to GeV) cosmic rays into denser regions or clumps. This differs from the prevailing view of fast cosmic ray transport in giant molecular clouds where the magnetic turbulence is suppressed by neutral-ion damping, as our results require a slow diffusion inside dense molecular clumps. Through modelling we find that while the shielding is negligible on the cloud scale, it becomes important in the denser, parsec-sized regions where the gravitational collapse is already at play, changing the initial condition of star formation and astrochemistry.

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arXiv2023

ATOMS: ALMA Three-millimeter Observations of Massive Star-forming regions -- XV. Steady Accretion from Global Collapse to Core Feeding in Massive Hub-filament System SDC335

We present ALMA Band-3/7 observations towards "the Heart" of a massive hub-filament system (HFS) SDC335, to investigate its fragmentation and accretion. At a resolution of $\sim0.03$ pc, 3 mm continuum emission resolves two massive dense cores MM1 and MM2, with $383(^{+234}_{-120})$ $M_\odot$ (10-24% mass of "the Heart") and $74(^{+47}_{-24})$ $M_\odot$, respectively. With a resolution down to 0.01 pc, 0.87 mm continuum emission shows MM1 further fragments into six condensations and multi-transition lines of H$_2$CS provide temperature estimation. The relation between separation and mass of condensations at a scale of 0.01 pc favors turbulent Jeans fragmentation where the turbulence seems to be scale-free rather than scale-dependent. We use the H$^{13}$CO$^+$ (1-0) emission line to resolve the complex gas motion inside "the Heart" in position-position-velocity space. We identify four major gas streams connected to large-scale filaments, inheriting the anti-clockwise spiral pattern. Along these streams, gas feeds the central massive core MM1. Assuming an inclination angle of $45(\pm15)^{\circ}$ and a H$^{13}$CO$^+$ abundance of $5(\pm3)\times10^{-11}$, the total mass infall rate is estimated to be $2.40(\pm0.78)\times10^{-3}$ $M_\odot$ yr$^{-1}$, numerically consistent with the accretion rates derived from the clump-scale spherical infall model and the core-scale outflows. The consistency suggests a continuous, near steady-state, and efficient accretion from global collapse, therefore ensuring core feeding. Our comprehensive study of SDC335 showcases the detailed gas kinematics in a prototypical massive infalling clump and calls for further systematic and statistical analyses in a large sample.

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arXiv2022

WISDOM Project XII. Clump properties and turbulence regulated by clump-clump collisions in the dwarf galaxy NGC404

We present a study of molecular structures (clumps and clouds) in the dwarf galaxy NGC 404 using high-resolution (0.86x0.51 pc^2) Atacama Large Millimeter/sub-millimeter Array ^{12}CO(2-1) observations. We find two distinct regions in NGC 404: a gravitationally-stable central region (Toomre parameter Q=3-30) and a gravitationally-unstable molecular ring (Q<=1). The molecular structures in the central region have a steeper size -- linewidth relation and larger virial parameters than those in the molecular ring, suggesting gas is more turbulent in the former. In the molecular ring, clumps exhibit a shallower mass -- size relation and larger virial parameters than clouds, implying density structures and dynamics are regulated by different physical mechanisms at different spatial scales. We construct an analytical model of clump-clump collisions to explain the results in the molecular ring. We propose that clump-clump collisions are driven by gravitational instabilities coupled with galactic shear, that lead to a population of clumps whose accumulation lengths (i.e. average separations) are approximately equal to their tidal radii. Our model-predicted clump masses and sizes (and mass -- size relation) and turbulence energy injection rates (and size -- linewidth relation) match the observations in the molecular ring very well, suggesting clump-clump collisions is the main mechanism regulating clump properties and gas turbulence in that region. As expected, our collision model does not apply to the central region, where turbulence is likely driven by clump migration.

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arXiv2022

Weather Forecast of the Milky Way: Shear and Stellar feedback determine the lives of Galactic-scale filaments

The interstellar medium (ISM) is an inseparable part of the Milky Way ecosystem whose evolutionary history remains a challenging question. We trace the evolution of the molecular ISM using a sample of Young Stellar Objects (YSO) association --molecular cloud complex (YSO-MC complex). We derive their three-dimensional (3D) velocities by combining the Gaia astrometric measurements of the YSO associations and the CO observations of the associated molecular clouds. Based on the 3D velocities, we simulate the motions of the YSO-MC complexes in the Galactic potential and forecast the ISM evolution by tracing the motions of the individual complexes, and reveal the roles of shear and stellar feedback in determining ISM evolution: Galactic shear stretches Galactic-scale molecular cloud complexes, such as the G120 Complex, into Galactic-scale filaments, and it also contributes to the destruction of the filaments; while stellar feedback creates interconnected superbubbles whose expansion injects peculiar velocities into the ISM. The Galactic-scale molecular gas clumps are often precursors of the filaments and the Galactic-scale filaments are transient structures under a constant stretch by shear. This evolutionary sequence sets a foundation to interpret other gas structures. Animations are available at https://gxli.github.io/ISM-6D/movie.html.

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arXiv2022

A massive Keplerian protostellar disk with flyby-induced spirals in the Central Molecular Zone

Accretion disks are an essential component in the paradigm of the formation of low-mass stars. Recent observations further identify disks surrounding low-mass pre-main-sequence stars perturbed by flybys. Whether disks around more massive stars evolve in a similar manner becomes an urgent question. We report the discovery of a Keplerian disk of a few solar masses surrounding a 32 solar-mass protostar in the Sagittarius C cloud around the Galactic Center. The disk is gravitationally stable with two embedded spirals. A combined analysis of analytical solutions and numerical simulations demonstrates that the most likely scenario to form the spirals is through external perturbations induced by a close flyby, and one such perturber with the expected parameters is identified. The massive, early O-type star embedded in this disk forms in a similar manner with respect to low-mass stars, in the sense of not only disk-mediated accretion, but also flyby-impacted disk evolution.

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arXiv2022

Density Exponent Analysis: Gravity-driven steepening of the density profiles of star-forming regions

The evolution of molecular interstellar clouds is a complex, multi-scale process. The power-law density exponent describes the steepness of density profiles, and it has been used to characterize the density structures of the clouds yet its usage is usually limited to spherically symmetric systems. Importing the Level-Set Method, we develop a new formalism that generates robust maps of a generalized density exponent $k_ρ$ at every location for complex density distributions. By applying it to high fidelity, high dynamical range map of the Perseus molecular cloud constructed using data from the Herschel and Planck satellites, we find that the density exponent exhibits a surprisingly wide range of variation ($-3.5 \lesssim k_ρ \lesssim -0.5$). Regions at later stages of gravitational collapse are associated with steeper density profiles. Inside a region, gas located in the vicinities of dense structures has very steep density profiles with $k_ρ \approx -3$, which forms because of depletion. This density exponent analysis reveals diverse density structures, forming a coherent picture that gravitational collapse leads to a continued steepening of the density profile. We expect our method to be effective in studying other power-law-like density structures, including granular materials and the Large-Scale Structure of the Universe.

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arXiv2022

Discovery of a coherent, wave-like velocity pattern for the Radcliffe Wave

Recently studies discovered that part of the Gould Belt belongs to a 2.7 kpc-long {coherent, thin} wave consisting of a chain of clouds, where a damped undulation pattern has been identified from the spatial arrangement of the clouds. We use the proper motions of Young Stellar Objects (YSOs) anchored inside the clouds to study the kinematic structure of the Radcliffe Wave in terms of $v_z$, and identify a damped, wave-like pattern from the $v_z$ space, which we call "velocity undulation". We propose a new formalism based on the Ensemble Empirical Mode Decomposition (EEMD) to determine the amplitude, period, and phase of the undulation pattern, and find that the spatial and the velocity undulation share an almost identical spatial frequency of about 1.5 kpc, and both are damped when measured from one side to the other. Measured for the first cycle, they exhibit a phase difference of around $2π/3$. The structure is oscillating around the midplane of the Milky Way disk with an amplitude of $\sim\,130\,\pm\,20\,\rm pc$. The vertical extent of the Radcliffe Wave exceeds the thickness of the molecular disk, suggesting that the undulation of the undulation signature might originate from a perturbation, e.g. the passage of a dwarf galaxy.

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arXiv2022

Multi-scale decomposition of astronomical maps -- a constrained diffusion method

We propose a new, efficient multi-scale method to decompose a map (or signal in general) into components maps that contain structures of different sizes. In the widely-used wave transform, artifacts containing negative values arise around regions with sharp transitions due to the application of band-limited filters. In our approach, the decomposition is achieved by solving a modified, non-linear version of the diffusion equation. This is inspired by the anisotropic diffusion methods, which establish the link between image filtering and partial differential equations. In our case, the artifact issue is addressed where the positivity of the decomposed images is guaranteed. Our new method is particularly suitable for signals which contain localized, non-linear features, as typical of astronomical observations. It can be used to study the multi-scale structures of astronomical maps quantitatively and should be useful in observation-related tasks such as background removal. We thus propose a new measure called the "scale spectrum", which describes how the image values distribute among different components in the scale space, to describe maps. The method allows for input arrays of an arbitrary number of dimensions, and a python3 implementation of the algorithms is included in the Appendix and available at https://gxli.github.io/Constrained-Diffusion-Decomposition/.

astro-ph.IM↗

arXiv2022

Network of Star Formation: Fragmentation controlled by scale-dependent turbulent pressure and accretion onto the massive cores revealed in the Cygnus-X GMC complex

Molecular clouds have complex density structures produced by processes including turbulence and gravity. We propose a triangulation-based method to dissect the density structure of a molecular cloud and study the interactions between dense cores and their environments. In our {approach}, a Delaunay triangulation is constructed, which consists of edges connecting these cores. Starting from this construction, we study the physical connections between neighboring dense cores and the ambient environment in a systematic fashion. We apply our method to the Cygnus-X massive GMC complex and find that the core separation is related to the mean surface density by $Σ_{\rm edge} \propto l_{\rm core }^{-0.28 }$, which can be explained by {fragmentation controlled by a scale-dependent turbulent pressure (where the pressure is a function of scale, e.g. $p\sim l^{2/3}$)}. We also find that the masses of low-mass cores ($M_{\rm core} < 10\, M_{\odot}$) are determined by fragmentation, whereas massive cores ($M_{\rm core} > 10\, M_{\odot}$) grow mostly through accretion. The transition from fragmentation to accretion coincides with the transition from a log-normal core mass function (CMF) to a power-law CMF. By constructing surface density profiles measured along edges that connect neighboring cores, we find evidence that the massive cores have accreted a significant fraction of gas from their surroundings and thus depleted the gas reservoir. Our analysis reveals a picture where cores form through fragmentation controlled by scale-dependent turbulent pressure support, followed by accretion onto the massive cores, {and the method can be applied to different regions to achieve deeper understandings in the future.

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arXiv2022

Kinematics of the molecular interstellar medium probed by Gaia: steep velocity dispersion-size relation, isotropic turbulence, and location-dependent energy dissipation

The evolution of the molecular interstellar medium is controlled by processes such as turbulence, gravity, stellar feedback, and Galactic shear. AL a part of the ISM-6D https://gxli.github.io/ISM-6D/ project, using Gaia astrometric measurements towards a sample of young stellar objects (YSOs), we study morphology and kinematic structure of the associated molecular gas. We identify 150 YSO associations with distance $d \lesssim 3 \;\rm kpc$. The YSO associations are elongated, with a median aspect ratio of 1.97, and are oriented parallel to the disk midplane, with a median angle of 30$^{\circ}$. The turbulence in the molecular clouds as probed by the YSOs is isotropic, and the velocity dispersions are related to the sizes by $σ_{v,{\rm 2D}} = 0.74\;(r/{\rm pc})^{0.67} \;({\rm km/s})\;$. The slope is on the steeper side, yet consistent with previous measurements. The energy dissipation rate of turbulence $\dotε = σ_{v,{\rm 3D}}^3 /L$ decreases with the Galactocentric distance, with a gradient of 0.2 $\rm dex \; kpc^{-1}$, which can be explained if turbulence is driven by cloud collisions. In this scenario, the clouds located in the inner Galaxy have higher chances to accrete smaller clouds and are more turbulent. Although the density structures of the complexes are anisotropic, the turbulence is consistent with being isotropic. If the alignment between density structures and the Galactic-disk mid-plane is due to shear, we expect $t_{\rm cloud} \gtrsim t_{\rm shear}\approx 30\; \rm Myr$. This cloud lifetime is longer than the turbulence crossing time, and a continuous energy injection is required to maintain the turbulence.

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arXiv2022

Widespread subsonic turbulence in Ophiuchus North 1

Supersonic motions are common in molecular clouds. (Sub)sonic turbulence is usually detected toward dense cores and filaments. However, it remains unknown whether (sub)sonic motions at larger scales ($\gtrsim$1~pc) can be present in different environments or not. Located at a distance of about 110 pc, Ophiuchus North 1 (Oph N1) is one of the nearest molecular clouds that allows in-depth investigation of its turbulence properties by large-scale mapping observations of single-dish telescopes. We carried out the $^{12}$CO ($J=1-0$) and C$^{18}$O ($J=1-0$) imaging observations toward Oph N1 with the Purple Mountain Observatory 13.7 m telescope. The observations have an angular resolution of $\sim$55\arcsec (i.e., 0.03~pc). Most of the whole C$^{18}$O emitting regions have Mach numbers of $\lesssim$1, demonstrating the large-scale (sub)sonic turbulence across Oph N1. Based on the polarization measurements, we estimate the magnetic field strength of the plane-of-sky component to be $\gtrsim$9~$μ$G. We infer that Oph N1 is globally sub-Alfv{é}nic, and is supported against gravity mainly by the magnetic field. The steep velocity structure function can be caused by the expansion of the Sh~2-27 H{\scriptsize II} region or the dissipative range of incompressible turbulence. Our observations reveal a surprising case of clouds characterised by widespread subsonic turbulence and steep size-linewidth relationship. This cloud is magnetized where ion-neutral friction should play an important role.

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arXiv2021

The DR21(OH) Trident -- Resolving the Massive Ridge into Three Entangled Fibers As the Initial Condition of Cluster Formation

DR21(OH) ridge, the central part of a high-mass star and cluster forming hub-filament system, is resolved spatially and kinematically into three nearly parallel fibers (f1, f2, and f3) with a roughly north-south orientation, using the observations of molecular transitions of H$^{13}$CO$^+$ (1-0), N$_2$H$^+$ (1-0), and NH$_2$D (1$_{1,1}$-1$_{0,1}$) with the Combined Array for Research in Millimeter Astronomy. These fibers are all mildly supersonic ($σ_{\rm V}$ about 2 times the sound speed), having lengths around 2 pc and widths about 0.1 pc, and they entangle and conjoin in the south where the most active high-mass star formation takes place. They all have line masses 1 - 2 orders of magnitude higher than their low-mass counterparts and are gravitationally unstable both radially and axially. However, only f1 exhibits high-mass star formation all the way along the fiber, yet f2 and f3 show no signs of significant star formation in their northern parts. A large velocity gradient increasing from north to south is seen in f3, and can be well reproduced with a model of free-fall motion toward the most massive and active dense core in the region, which corroborates the global collapse of the ridge and suggests that the disruptive effects of the tidal forces may explain the inefficiency of star formation in f2 and f3. On larger scales, some of the lower-density, peripheral filaments are likely to be the outer extensions of the fibers, and provide hints on the origin of the ridge.

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arXiv2021

Evolutions of CH$_3$CN abundance in molecular clumps

To investigate the effects of massive star evolution on surrounding molecules, we select 9 massive clumps previously observed with the Atacama Pathfinder Experiment (APEX) telescope and the Submillimeter Array (SMA) telescope. Based on the observations of APEX, we obtain luminosity to mass ratio L$_{\rm clump}$/M$_{\rm clump}$ that range from 10 to 154 L$_{\sun}$/M$_{\sun}$, where some of them embedded Ultra Compact (UC) H\,{\footnotesize II} region. Using the SMA, CH$_3$CN (12$_{\rm K}$--11$_{\rm K}$) transitions were observed toward 9 massive star-forming regions. We derive the CH$_3$CN rotational temperature and column density using XCLASS program, and calculate its fractional abundance. We find that CH$_3$CN temperature seems to increase with the increase of L$_{\rm clump}$/M$_{\rm clump}$ when the ratio is between 10 to 40 L$_{\sun}$/M$_{\sun}$, then decrease when L$_{\rm clump}$/M$_{\rm clump}$ $\ge$ 40 L$_{\sun}$/M$_{\sun}$. Assuming the CH$_3$CN gas is heated by radiation from the central star, the effective distance of CH$_3$CN relative to the central star is estimated. The distance range from $\sim$ 0.003 to $\sim$ 0.083 pc, which accounts for $\sim$ 1/100 to $\sim$ 1/1000 of clump size. The effective distance increases slightly as L$_{\rm clump}$/M$_{\rm clump}$ increases (R$_{\rm eff}$ $\sim$ (L$_{\rm clump}$/M$_{\rm clump}$)$^{0.5\pm0.2}$). Overall, the CH$_3$CN abundance is found to decrease as the clumps evolve, e.g., X$_{\rm CH_3CN}$ $\sim$ (L$_{\rm clump}$/M$_{\rm clump}$)$^{-1.0\pm0.7}$. The steady decline of CH$_3$CN abundance as the clumps evolution can be interpreted as a result of photodissociation.

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