Sasaki et al. submitted

投稿版

全体ストーリー

• N14における断片化に沿った階層構造形成、G45、W33、W39におけるHFSを丸ごと覆うような階層構造 ⇒ 自己重力収縮による階層形成

• W49、W51などにおける、PV図におけるブリッジ構造や、N35などにおける、速度勾配に沿った階層構造 ⇒ CCCによる階層形成

• isolatedよりtrunkの方がサイズや質量が大きく、ビリアルパラメータが小さい ⇒ より大規模に成長し重力収縮も強い分子雲が内部に階層を形成し、大質量星を多数形成できる

• isolatedとleafはサイズが同じだが、leafの方が質量が大きく、ビリアルパラメータが小さい ⇒ 強い自己重力により、外側の全体構造からガスを供給したりお互いに衝突・合体など相互作用してガスを供給し成長

• 密度はtrunkよりisolated、isolatedよりleafの方が大きい ⇒ 大質量星を生み出すような分子雲は内部で断片化（階層化）が進んでいる

• isolatedとleafの間でSFR ∝ YSO内包数に有意差はなく、物理量に対するYSO内包数・内包確率も変わらない ⇒ 低質量星を形成できるかどうか、その後の形成個数は階層の有無で変わらない

• isolatedとleafの間で、物理量に対するHi-GAL clump内包確率は変わらない ⇒ 大質量星を形成できるかどうかは階層の有無で変わらない

• isolatedよりもleafの方がHi-GAL clump内包数が有意に大きく、特に高サイズ・高質量・低ビリアルパラメータな範囲では同じ物理量でもleafの方がisolatedより内包数が大きい ⇒ leafはisolatedよりも多くのclumpを保持しているのにもかかわらず、isolatedと同じくらいのガスを残している

• 数10 pcスケールのガス構造の自己重力による収縮や衝突などで、高質量かつ自己重力の強いガス構造が生まれ、それらは断片化することで内部構造を生み出す

• 高密度な内部構造は外部からの継続的なガス降着やお互いの衝突・合体などの相互作用で多数のガスを蓄えることができ、多数の大質量星（クランプ）を生み出せる

• 階層を持たない雲構造は大質量星（クランプ）を小数生み出すことはできてもそれでガスが枯渇してしまう

• 階層があろうかなかろうが、低質量星は同じ個数だけ生み出すことはできる

イントロストーリー

第一段落

大質量星の形成過程が謎
観測的にはフィラメント、HFS、CCCとかいろいろ

第二段落

理論的なGHCモデル
上記の観測的現象を理論的に解釈できる可能性

第三段落

dendrogramを用いれば階層構造を抽出可、実際に観測的検証あり
↓
だがそれらは

• dendrogramで実際に抽出された階層構造と観測的現象との関連の検証には踏み込んでない
• 個別のケーススタディに留まる
  ↓
  より包括的に、観測的現象との関連の検証や物理量の統計的調査が必要

第四段落

• dendrogramで階層的に抽出した階層構造と観測的現象との関連をマッピングにより検証
• 物理量を統計的に評価し、モデル通りのガスの動きをトレースしてるか調べる
• それらを包括的にやります

bibliography memo

Introduction

Andre+14（filament概説レビュー）
Myers 09（様々なHFS領域を概観、レビューみたいなノリ）
Kumar+20（同上）
Fukui+21（CCC概説レビュー）
Vazquez-Semadeni+2019（GHC概説レビュー）
Shen+2024（GHCの観測的検証）
He+2026（同上）

Result

Dewangan+20（N14）
Liu+21（W33）
Fujita+19（W51）
Torii+18（N35）

Discussion

Kirk+13（フィラメントへの降着と内部の断片化）

The multiple molecular emission lines observed in our Mopra survey allow us to infer the possible presence of an accretion flow from the filament onto the central cluster (if the filament is in front of the cluster), and additionally we find that material continues to be accreted onto the filament.

Hacar+13（同上）

Core formation in L1495/B213 has proceeded by hierarchical fragmentation. The cloud fragmented first into several pc-scale regions. Each of these regions later fragmented into velocity-coherent filaments of about 0.5 pc in length.

Palmeirim+13（同上）

The results presented in this paper reveal the density and temperature structure of the Taurus B211 filament with unprecedented detail. The shape of the column density profile derived for the B211 filament, with a well-defined power-law regime at large radii (see Fig. 5a), and the high column density contrast over the surrounding background (a factor ~10–20, implying a density contrast ~100–400) strongly suggest that the main filament has undergone gravitational contraction. This is also consistent with the supercritical mass per unit length measured for the B211 filament (Mline ≈ 54 M⊙/pc), which suggests that the filament is unstable to both radial contraction and fragmentation into cores (e.g., Inutsuka & Miyama 1997; Pon et al. 2011). Observations confirm that the B211 filament has indeed fragmented, leading to the formation of several prestellar cores (e.g., Onishi et al. 2002) and protostars (e.g., Motte & André 2001; Rebull et al. 2010) along its length.

Myers 09（重力崩壊によるHFS形成とハブへのinfall）

These results suggest that HFS associated with young stellar groups may arise from compression of clumpy gas in molecular clouds.

Peretto+13（同上）

To illustrate some of the expected signatures of globally collapsing clouds we present, in Fig. 8 a snapshot of a published MHD simulation modelling the evolution of a turbulent and magnetized 10 000 M⊙ cloud, that was initially designed to reproduce some of the observational signatures of the DR21 region (Schneider et al. 2010,see Appendix C for more details on the simulation). Overall, this simulation shows some similarities with SDC335, i.e. massive cores in the centre, the formation of filaments converging towards these cores, and a velocity field resembling the one observed in SDC335 (see Fig. 4c).

Gomez & Vazquez-Semadeni 14（同上）

The filaments are not in equilibrium at any time, but instead are long-lived flow features through which the gas flows from the cloud to the clumps. The filaments are long-lived because they accrete from their environment while simultaneously accreting onto the clumps within them; they are essentially the locus where the flow changes from accreting in two dimensions to accreting in one dimension.

Wang+20（同上）

Our findings favor the multiscale gravitational collapse cloud model in Gómez & Vázquez-Semadeni (2014). In this model, a super-Jeans cloud forms from colliding flows and rapidly begins to undergo gravitational collapse. The collapse soon becomes nearly pressureless, proceeding along its shortest dimension, and forms filamentary substructures. The resulting filaments are not in a static equilibrium but are long-lived flow structures that accumulate ambient gas from their environment and direct it toward the major gravitational potential well (hub center).

Takahira+14（CCCによる階層形成とコア合体）

It is therefore likely that cores grow by both accretion and mergers with other neighboring cores, with accretion playing the most dominant role.

Takahira+18（同上）

We show an example of dense core formation by fragmentation in more denser filaments and core merging in the middle and left-hand panels of figure 3.

Sakre+21（同上）

The mass growth of any given dense core is a combination of the accretion of surrounding gas and mergers with other dense cores.

Lada 92（高密度ガスプロパティとYSO形成率の関連）

…star formation does not occur uniformly throughout the dense gas and is strongly favored in a few very massive (M > 200 M☉) dense cores, where efficient conversion of molecular gas into stars has resulted in the production of rich stellar clusters…

Lada+10（同上）

The results of our paper together with previous studies such as those of Lada (1992), Lada et al. (1996), Gao & Solomon (2004), Wu et al. (2005, 2010), etc., strongly indicate that it is primarily the dense gas component (i.e., n(H2) ≳ 104 cm−3) of molecular clouds that actively participates in star formation.

Gao & Solomon 04（同上）

The global star formation efficiency depends on the fraction of the molecular gas in a dense phase.

Wu+05（同上）

Once it is clear that it is the dense gas mass that indicates the star formation rate, it becomes clear why the total surface density of gas may not be a clean star formation indicator.

Wu+10（同上）

In this case, the star formation rate in starburst galaxies depends on the total mass of gas above the threshold density or surface density needed for massive star formation, rather than on a local, nonlinear form of the Schmidt law.

review comment

result: major revision

comments to the author

The manuscript presents an interesting and potentially valuable analysis of hierarchical structure in 13 Galactic star-forming regions using a non-binary dendrogram decomposition of the FUGIN CO data, together with comparisons to Hi-GAL compact clumps and SPICY YSOs. The effort to connect cloud hierarchy with dense structure and star formation is meaningful. However, several methodological definitions, selection effects, and aspects of the statistical interpretation require clarification and robustness checks before the physical conclusions are fully supported. In particular, the distinction between leaves and “isolated structures” is partly analysis-defined rather than a native astrodendro classification and may depend sensitively on the adopted dendrogram thresholds. The cross-region comparability of the dendrogram categories also requires further consideration, since the region-dependent thresholds may cause the same category to correspond to different intensity levels and physical components in different regions. In addition, the YSO association analysis requires clarification because the OFF region is defined using trunk masks and may not represent a genuinely unrelated background population. More generally, care is needed when translating dendrogram topology into specific physical interpretations. These issues should be adequately addressed before the manuscript can be considered for publication.

major comments

1. Clarify the dendrogram terminology and the study-specific definition of “isolated structures”.
     In Section 3.1, please clarify that “isolated structures” are defined specifically for the present analysis rather than being a native astrodendro category. In the standard astrodendro terminology, these single-level structures originate independently at the adopted min_value and are therefore trunks, since they have no parent. At the same time, they are also leaves because they have no children. The manuscript separates these objects from leaves embedded within hierarchical trunks for the subsequent comparison, and this study-specific classification should be stated explicitly. It would also be helpful to note that “isolated” refers to the extracted dendrogram topology under the adopted parameters, rather than necessarily implying physical isolation.

2. Selection of the PPV boundaries and its impact on the dendrogram hierarchy.
     Since the targeted regions are extracted from larger survey cubes, please clarify how the spatial and velocity boundaries of each PPV cube were selected. Do the selected cubes fully encompass the molecular cloud complexes associated with the targeted star-forming regions? Although increasing min_value helps avoid structures truncated by cube boundaries, it may also remove extended low-intensity emission that is physically part of the cloud. Consequently, the identified trunks may represent only bright closed structures above the adopted threshold rather than complete cloud structures. This issue is particularly relevant because the physical interpretation of the manuscript treats trunks as the macroscopic gas reservoirs of the hierarchical systems. If possible, a simple test using somewhat larger extraction boxes for several representative regions would be useful to demonstrate the robustness of the results.

3. Robustness of the dendrogram classification to the adopted parameters.
     This comment is related to the above boundary selection issue. The adaptive selection of min_value is understandable because the targeted regions are extracted from larger Galactic plane survey data and the emission may extend beyond the selected PPV cubes. Avoiding edge-truncated structures is therefore important. However, min_value not only defines the lower intensity boundary of the identified structures, but can also affect the topology of the dendrogram. A structure classified as an isolated structure at a relatively high threshold may become connected to surrounding emission when a lower threshold is adopted, and consequently become part of a larger hierarchy, for example as a leaf embedded within a trunk. Therefore, the distinction between leaves and isolated structures may partly depend on the adopted threshold rather than solely on intrinsic physical differences. It would be useful to test whether the main differences in mass, density, virial state, YSO association, and Hi-GAL clump association remain robust against reasonable variations of min_value.
     A related point concerns the adopted min_delta = 1 sigma. Since min_delta determines the minimum contrast required for a local peak to be identified as an independent dendrogram structure, a 1sigma contrast appears relatively permissive. I do not think that a particular value is necessarily required, especially given the additional min_value and min_npix criteria, but it would be useful to demonstrate that the identified hierarchy is not sensitive to this choice. For example, the authors could compare the resulting structure statistics for min_delta = 1 sigma, 2 sigma, and perhaps 3 sigma, at least for several representative regions, and examine whether the main leaf–isolated-structure comparisons remain unchanged.

4. Distance uncertainties and min_npix (Section 2.1 and Section 3.1).
     The motivation for matching the physical resolution across regions is reasonable, but the adopted smoothing scale and min_npix depend directly on the assumed distances. Since the target angular resolution scales approximately as d^{-1} and min_npix as d^{-2}, distance uncertainties propagate into both the achieved physical resolution and the minimum accepted structure size. This may particularly affect small leaves and isolated structures close to the voxel threshold. Please provide or discuss distance uncertainties and assess whether plausible variations affect the structure catalog and main conclusions.

5. Statistical model in Section 4.2 and the Appendix.
     The additive model (Eqs. 7-8) itself is reasonable, but its physical interpretation appears to assume that the dendrogram structure categories are comparable across regions. This assumption may not be trivial because the adopted min_value varies substantially from region to region. In regions with a high threshold, a trunk may correspond only to the bright inner part of a molecular cloud, whereas at a lower threshold it may include a much more extended envelope. In that case, the same dendrogram label may not represent the same physical component across the sample. A region-dependent offset alone may not fully account for this if the effect of structure type itself changes from region to region. I suggest discussing this assumption explicitly and assessing whether the inferred differences between structure types remain meaningful when the same dendrogram category may correspond to different intensity levels and physical components in different regions.

6. YSO association analysis (Section 3.3)
     The ON/OFF background subtraction method is reasonable in principle, especially for inner-Galactic regions where unrelated foreground/background YSOs along the line of sight may be significant. However, the implementation requires clarification.
     - Since OFF regions are defined using trunk boundaries, please clarify whether isolated structures are excluded from the OFF regions. If isolated structures remain in the OFF regions, YSOs physically associated with them may contribute to the estimated background and be partially subtracted, producing an asymmetric comparison between leaves and isolated structures.
     - In addition, because trunk boundaries depend on the adopted min_value, physically associated molecular emission may exist outside the trunks, particularly when min_value is relatively high. In that case, YSOs associated with the same molecular cloud complex could also be included in the OFF region and treated as background. Please clarify how this possibility is handled and whether it affects the YSO comparison.

7. Section 4.1: The case studies provide useful illustrations of how the dendrogram decomposition maps onto the observed PPV morphology. However, I suggest being cautious in assigning specific physical interpretations to the dendrogram categories themselves. Dendrograms primarily describe the topology of emission in PPV space, and similar hierarchical configurations may arise from different physical processes. The examples in this section therefore seem most appropriately presented as qualitative consistency checks or illustrations.

8. Interpretation of super-Jeans fragmentation / Li (2024).
   The discussion invoking Li (2024) should be made more cautious. Li (2024) presents a proposed accretion-modified Jeans framework in which the effective Jeans scale can increase in a dynamically accumulating medium. However, the present manuscript does not measure the accretion timescale or the relevant ratio t_ff/t_acc, nor does it directly test the modified Jeans criterion.
   Therefore, the observed tendency for leaves to host more massive Hi-GAL clumps may be qualitatively consistent with such a scenario, but it should not be presented as a direct demonstration of super-Jeans fragmentation or as a unique signature of that model. In addition, the physical scales probed by the present CO dendrogram structures and the fragmentation scales discussed in Li (2024) should be distinguished.

minor comments

1. Section 1, lines 99-103.
   The motivation of moving beyond individual case studies toward a uniform sample analysis is well justified. However, the scope of the sample may deserve clearer qualification. The 13 targets are selected massive/active star-forming regions rather than a representative sample of the broader Galactic molecular-cloud population. I therefore suggest moderating statements that may imply general applicability to Galactic molecular clouds and framing the study more explicitly as a uniform analysis of multiple massive star-forming regions.

2. Section 2.1: explicitly state the main-beam temperature conversion
   The manuscript lists the main-beam efficiencies but does not write the conversion explicitly. For clarity, please state the adopted relation, T_mb = T_A* / eta_mb. This is a minor point, but it makes the calibration and subsequent physical calculations easier to follow.

3. Section 2.1: The 8.5 arcsec pixel size currently appears only later in Section 3.1 when min_npix is defined. It would be clearer to introduce it in Section 2.1 together with the other basic data properties.

4. Table 1: rms values.
   It would be helpful to state explicitly in the caption of Table 1 that the listed rms values are measured after the smoothing procedure. This small clarification would make the table easier to read.

5. Section 2.3: Hi-GAL clump distances.
   The manuscript states that the Hi-GAL clumps have kinematically derived distances provided in the catalog, but this description is rather brief. It would be helpful to provide a specific reference for the distance determinations, or to point explicitly to the relevant table or catalog documentation where the adopted distances or their derivation are described.

6. In Section 3.1, the effective angular resolution \theta is defined only when min_npix is introduced. Since this quantity is already central to the distance-dependent smoothing described earlier, I suggest defining \theta at its first appearance in the data-smoothing section and then using the same notation consistently throughout the manuscript.

7. Clarify the input data used for the dendrogram extraction.
     Section 3.1 refers generally to 3D PPV data cubes, while Section 2.1 introduces 12CO, 13CO, and C18O data. Please state explicitly which molecular-line cube was used for the dendrogram decomposition. If the structures were identified from the smoothed 13CO(J=1–0) cube, this should be stated directly.

8. The min_npix values in Table 2 cannot be reproduced from the stated formula for several regions. Please verify the min_npix values listed in Table 2. Using the formula given in the manuscript, min_npix = (1.5 theta / 8.5 arcsec)^2 x 2, and the effective angular resolutions in Table 1, several tabulated values are not reproducible. For example, for M16, Table 1 gives theta = 123 arcsec. This yields (1.5 x 123 / 8.5)^2 x 2 = 942, whereas Table 2 lists 1058. Using the unrounded angular resolution derived from 20 arcsec x (11.11 / 1.8) still gives only about 949, so the discrepancy cannot be explained by simple rounding. Similar, though smaller, discrepancies appear for several other regions.

9. Section 4.1.2, lines 505–506: broad velocity bridge in Figure 5(b).
   The manuscript mentions a broad velocity bridge in Figure 5(b), but its location is not explicitly indicated. For clarity and ease of reading, it would be helpful to provide the approximate position of this feature in the l–v diagram (e.g., its Galactic longitude and velocity range), or to mark it directly in the figure.

10. Figures 2–6: The molecular-line tracer used for the integrated-intensity maps and PV diagrams is not explicitly stated either in the figure captions or in the corresponding discussion in Section 4.1. Please specify the transition used for these maps (presumably 13CO J=1-0), preferably in the Figure 2 caption so that Figures 2–6 are self-contained.

11. Lines 525–529: The sentence is somewhat difficult to read, particularly the phrase “the dendrogram hierarchy encloses within continuous hierarchies the gas …”. I suggest rephrasing it.

12. Section 4.2: The discussion of the physical-property distributions is largely qualitative. It would be helpful to provide representative summary statistics, such as the median values (and, if appropriate, interquartile ranges) for the main structure categories. In particular, reporting characteristic values for leaves and isolated structures would allow the reader to more readily assess the magnitude of the differences discussed in the text.

13. Section 4.2.1, lines 574–576: It may be useful to note that the larger effective radii and masses of trunks are partly expected from their dendrogram definition, since trunks correspond to the root-level structures that encompass the largest connected regions. A brief clarification of this point would help distinguish trends that are partly inherent to the hierarchical construction from those carrying additional physical significance.

14. Lines 580–582: The statement that large-scale, massive environments are “physically required” to harbor internal hierarchical structures appears stronger than warranted by the present analysis. Given that the larger size and mass of trunks are partly related to their dendrogram definition, I suggest rephrasing this as an observed association within the present sample rather than a physical requirement.

15. Section 4.3 and Figures 11, 12, 14, 15, and 16: The quantities plotted on the vertical axes would benefit from a more explicit definition. In particular, please clarify how the association probability is calculated, how the data points are binned, how the “mean number” of associated YSOs/clumps is defined within each bin, and how the uncertainties are estimated. These details are not described in the main text, figure captions, or Appendix, and providing them would improve reproducibility and interpretation of the trends.

16. Lines 702–705: The term “gas depletion” may be somewhat ambiguous here, since the Hi-GAL clumps themselves still consist predominantly of gas. If the intended meaning is depletion of the more diffuse surrounding gas reservoir as material is concentrated into dense clumps, please state this more explicitly.

17. Lines 746–754: This sentence is rather long and difficult to follow because several causal and qualifying statements are embedded within a single sentence. I suggest splitting it into two or more sentences to clarify the proposed connection between the converging velocity components, the embedded leaves, and the inferred interactions.

18. Line 829: The phrase “invariant low-mass population” appears somewhat too strong, since the analysis only shows no significant difference in the observed SPICY YSO counts. I suggest using a more specific and cautious wording, such as “comparable observed low-mass YSO counts.”

19. Section 5.3, lines 921–924: This statement appears somewhat repetitive of the discussion in lines 910–914. I suggest condensing these passages or revising the latter to emphasize a distinct implication rather than restating the same conclusion.

参考

PASJ：投稿の手引き

observation analysis paper d1 project