An inverted infall profile for the collapse of the massive star-forming IRDC SDC335.579-0.292

Abstract: There is increasing evidence for global collapse of clumps over parsec-scales in massive star formation regions. Such collapse may result in characteristic molecular line emission profiles but the spatial variation of such lines has rarely been quantitatively examined. Here we explore the infall properties using the spatially-resolved HCO$^+$ J=1--0 and H$^{13}$CO$^+$ J=1--0 maps of the massive infrared dark cloud (IRDC) SDC335.579-0.292. We compare the observations with the analytical Hill5 model and radiative transfer models. This shows that the best-fit infall velocity towards the cloud centre to be well-constrained to $-0.6$ to $-1.6$ km s$^{-1}$ and the mass infall rate between a few $\times10^{-3}$ and $10^{-2}$ M$_{\odot}$yr$^{-1}$. The comparison also highlights some limitations of the Hill5 method. We demonstrate that the width of optically thin spectral lines, which are usually interpreted as resulting from turbulent motions, are in fact dominated by unresolved, ordered infall motions within the beam. Our results suggest a complex collapse situation where there is a minimum in the infall velocity at $\sim2\times10^{18}$ cm (0.7 pc) with the infall velocity increasing at both smaller and larger radii. The parsec-scale infall with an inverted velocity profile indicates that the accretion in this massive star-forming cloud should have intermediate scales, at which fragmentation or filament formation has to occur before material flows onto the cloud centre.

• The paper reports that SDC335 exhibits an 'inverted' infall profile with a central peak in velocity that declines at intermediate radii before rising again.
• It employs spatially resolved observations of HCO⁺ and H¹³CO⁺ lines alongside Hill5 and radiative transfer models to quantify infall velocities and mass accretion rates.
• The findings challenge turbulence-only interpretations of linewidths, emphasizing the need to account for non-monotonic, infall-dominated accretion in massive star formation.

Inverted Infall Profile in the Massive Star-Forming IRDC SDC335.579-0.292

Overview

The study investigates the infall kinematics of the IRDC SDC335.579-0.292, a paradigmatic massive star-forming region. Using spatially resolved observations of HCO$^+$ J=1–0 and H$^{13}$CO$^+$ J=1–0, quantitative analysis is performed via the semi-analytic Hill5 model as well as comprehensive radiative transfer (RT) modeling with LIME, RADMC-3D, and RATRAN codes. The research uniquely characterizes the radial structure of infall velocities and explores the implications for accretion and fragmentation processes in high-mass star formation.

Observational Framework

SDC335 is a centrally condensed clump of $\sim$5500 $M_\odot$ at 3.25 kpc, with infall signatures previously observed over parsec scales. Mopra 22-m telescope data provides high-resolution spatial and spectral mapping of HCO$^+$ and H$^{13}$CO$^+$ lines, complemented by N$_2$H$^+$ for systemic velocity determination. The blue asymmetric profile of HCO$^{13}$0 J=1–0 is evident over a $^{13}$13 pc region, marking extensive infall.

Figure 1: Spatial distribution of the blue/red peak ratio ($^{13}$2) in SDC335, tracing infall signatures across the clump.

Semi-Analytic Modeling: Hill5 Analysis

The Hill5 model fits the excitation structure and line profiles, yielding robust constraints on infall velocity ($^{13}$3), optical depth, velocity dispersion, and peak excitation temperature. At the clump center, best-fit infall velocities are $^{13}$4 km s$^{13}$5, with velocity dispersions $^{13}$6 km s$^{13}$7.

Figure 2: HCO$^{13}$8 spectrum at the central pixel with Hill5 fit overlay, parameters tightly constrained via MCMC sampling.

Figure 3: MCMC corner plot: distributions and covariances among Hill5 parameters for the central spectrum.

Spatially, Hill5 fits reveal an “inverted” infall profile. The magnitude of infall velocity is maximal at the center ($^{13}$9 km s$^+$0), decreases to a minimum ($^+$1 km s$^+$2) at $^+$3 pc, and increases again at larger radii.

Figure 4: Map of infall velocity magnitude ($^+$4) derived from Hill5 fits across SDC335.

Figure 5: Radial profile of Hill5-fitted infall velocity, highlighting the “inverted” trend: central maximum, intermediate minimum, outer rise.

Annularly averaged spectra confirm the radial velocity reversal, consistent with pixel-based fits.

Figure 6: Annular averages of HCO$^+$5 spectra and Hill5 fits for radii 0, 28, 47 arcsec: each exhibits decreasing infall velocity with radius.

Radiative Transfer Modeling and Comparison

RT models utilize spherical symmetry with power-law density profiles ($^+$6, $^+$7), temperature gradients (minimum 20 K, central source $^+$8 K, $^+$9 $\sim$0), and fixed HCO$\sim$1 abundances. Infall velocity profiles are parameterized for various radial dependencies, including uniform, increasing, and decreasing cases.

Figure 7: RADMC-3D computed temperature profiles for $\sim$2 and $\sim$3 density laws, matching IRDC thermal structure.

RT fits at the central pixel, using LIME, RADMC-3D, and RATRAN, show best-fit infall velocities between $\sim$4 and $\sim$5 km s$\sim$6, with mass inflow rates of a few $\sim$7 to $\sim$8 $\sim$9 yr$M_\odot$0, largely insensitive to density power-law but sensitive to infall structure.

Figure 8: LIME model grid comparison to central pixel data, with velocity and turbulence parameters assessed by $M_\odot$1 fit statistics.

Figure 9: RT central pixel line profile fits for $M_\odot$2 and $M_\odot$3 models; $M_\odot$4 statistics indicate robust agreement.

The degeneracy in infall radial structure is highlighted: both increasing and decreasing infall velocity profiles can match global line shapes, but only higher-J transitions or optically thin tracers (H$M_\odot$5CO$M_\odot$6) distinguish the physical scenarios.

Figure 10: Comparison of J=1–0 and J=3–2 synthetic spectra: higher-J transitions accentuate differences between infall models.

Figure 11: Velocity profiles for best-fit models: “inverted” (outside-in), uniform, and inside-out collapse structures contrasted.

Linewidths and Evidence for Ordered Motion

The spatially constant line width of H$M_\odot$7CO$M_\odot$8 J=1–0 across the clump is incompatible with purely turbulent broadening. RT modeling shows unresolved infall dominates the linewidth, contrary to standard turbulence interpretations.

Figure 12: Synthetic spectra for LIME models with varying infall profiles: J=1–0 and J=3–2 responses to infall structure.

Figure 13: Line profile characterization schematic; observed profiles show blue asymmetry quantified by $M_\odot$9 and dip ratios.

This result challenges the prevailing assumption that optically thin molecular line widths exclusively probe turbulent velocities in dense clumps.

Mass Accretion Rates and Structural Implications

Derived accretion rates are substantial ($^+$0–$^+$1 $^+$2 yr$^+$3), with spatial variation dictated by infall velocity profile and density law. The “inverted” profile physically implies mass flux is higher at larger radii. This necessitates intermediate-scale fragmentation or filament formation to channel material to the clump core.

Figure 14: Radial mass accretion rate profiles: dashed/solid lines for $^+$4, $^+$5 parameterizes the velocity structure.

Model Degeneracy and Hill5 Limitations

Hill5 estimates align closely with RT outputs for uniform velocity but increasingly deviate as radial structure becomes complex. Systematic under-/over-estimation of true velocity occurs; results must be interpreted with caution, and Hill5 fitting is best understood as a lower limit for infall velocities.

Figure 15: Hill5 fits to RATRAN, LIME, and RADMC-3D synthetic spectra; model line shapes matched, but input velocities misestimated.

Implications and Future Directions

The study robustly establishes that large-scale infall in SDC335 deviates from free-fall or uniform velocity paradigms; an “inverted” profile is observed with central minima in infall velocity. This has profound significance for theories of massive star formation, indicating non-monotonic accretion and requiring intermediate fragmentation processes. The mass inflow rates and spatially constant line widths observed mandate reconsideration of clump stability analyses and virial parameter estimates, as infall motions can masquerade as turbulence.

Future work is suggested to resolve degeneracies via multi-transition, high-angular resolution observations, and extended RT analyses on larger samples. The impact of infall-dominated linewidths for the interpretation of star-forming region dynamics warrants systematic survey.

Conclusion

This comprehensive, quantitative study of SDC335 highlights the necessity of spatially resolved infall analyses and advanced RT modeling in massive star-forming regions. The identification of an “inverted” infall profile, significant mass inflow rates, and infall-dominated linewidths fundamentally inform models of accretion, fragmentation, and feedback in high-mass IRDCs. The methodology sets new standards for kinematic inference and challenges established turbulence-centric paradigms in the dense ISM.