A HINSA view of cosmic-ray ionization in IC 348 and NGC 1333: evidence for a strong low-energy cosmic-ray disparity

Technical Summary: A HINSA view of cosmic-ray ionization in IC 348 and NGC 1333

Problem Statement
The cosmic-ray ionization rate (CRIR, $\zeta_{ion}$) is a fundamental parameter governing the chemical and dynamical evolution of molecular clouds, particularly by regulating the coupling between magnetic fields and gas. While recent observations have revealed elevated CRIR values in massive star-forming regions and near protostars, the physical origins and acceleration mechanisms of low-energy cosmic rays (LECRs, $E < 1$ GeV) remain uncertain. Furthermore, a discrepancy exists in the nearby Perseus molecular cloud complex: while NGC 1333 shows a deficit in diffuse sub-GeV $\gamma$-ray residuals, its neighbor IC 348 exhibits a positive residual and a harder CR energy spectrum, despite NGC 1333 having higher star-formation activity. The extent to which local CR sources overwhelm the Galactic background in these regions, and the nature of the disparity between them, requires clarification.

Methodology
This study presents new estimates of CRIR toward IC 348 and NGC 1333 using the H i narrow self-absorption (HINSA) technique. The methodology involves:

1. Observations: Utilizing H i data from the FAST telescope (NGC 1333) and the GALFA-H i survey (IC 348), combined with archival $^{13}$CO ($J=1-0$ and $3-2$) data from the COMPLETE survey and JCMT, and dust continuum data from the Herschel Gould Belt Survey.
2. HINSA Analysis: Deriving the atomic hydrogen column density $N(\text{HINSA})$ via second-order derivative fitting of H i absorption features against the $^{13}$CO velocity field. The HINSA fraction ($f_{\text{HINSA}} = N(\text{HINSA})/N(\text{H}_2)$) is calculated for regions with $N(\text{H}_2) > 3 \times 10^{21}$ cm$^{-2}$ to minimize photodissociation effects.
3. Density Constraints: Estimating the gas volume density $n(\text{H}_2)$ using non-LTE radiative transfer modeling (RADEX) constrained by $^{13}$CO line intensities and Markov Chain Monte Carlo (MCMC) sampling.
4. CRIR Calculation: Deriving $\zeta_{ion}$ from the steady-state balance between H$_2$ formation on dust grains and destruction by cosmic rays (including ionization, dissociation, and CR-induced UV processes).
5. Spectral Modeling: Modeling the LECR spectrum within a finite slab attenuation framework. The model incorporates constraints from high-energy CR spectra inferred from Fermi $\gamma$-ray observations to fit the observed $\zeta_{ion}$ profiles, varying the low-energy spectral slope ($\alpha$) and the momentum break ($p_0$).

Key Results

• CRIR Disparity: The study finds a pronounced difference in CRIR between the two clouds. In IC 348, the weighted-average $\zeta_{ion}$ ranges from $(5.35 \pm 1.49) \times 10^{-17}$ s$^{-1}$ to $(2.33 \pm 0.55) \times 10^{-16}$ s$^{-1}$. In contrast, NGC 1333 exhibits values roughly an order of magnitude lower, ranging from $(3.94 \pm 2.46) \times 10^{-18}$ s$^{-1}$ to $(1.68 \pm 0.25) \times 10^{-17}$ s$^{-1}$.
• Column Density Trend: In both clouds, $\zeta_{ion}$ decreases with increasing H$_2$ column density, consistent with attenuation models lacking internal acceleration sources.
• Spectral Modeling: The best-fit low-energy CR spectra reproduce the observed profiles. The model indicates that the factor of $\sim$10 difference in ionization rates is driven by a corresponding difference in the low-energy ($\sim$10 MeV) proton flux. The IC 348 spectrum is significantly harder and more intense than that of NGC 1333, which shows a deficit relative to the Galactic background at GeV energies.
• Density and Structure Analysis: The authors investigate potential biases from gas density estimation and cloud structure (via 3D-PDR simulations). While uncertainties in $n(\text{H}_2)$ and fractal cloud structures can bias absolute $\zeta_{ion}$ values (potentially underestimating at low $N(\text{H}_2)$ and overestimating at high $N(\text{H}_2)$), the analysis concludes that these factors cannot account for the order-of-magnitude disparity between the two regions.

Significance and Claims
The paper claims that the observed disparity in CRIR is intrinsic to the physical properties of the clouds rather than an artifact of evolutionary timescales or measurement bias.

• External Acceleration Sources: The high CRIR in IC 348, coupled with its harder $\gamma$-ray spectrum, suggests the presence of local LECR acceleration sources external to the dense cloud cores, likely distinct from the protostellar activity that dominates NGC 1333. The authors propose that stellar-wind termination shocks in the more evolved, less embedded IC 348 cluster (containing more B-type stars) are a plausible source.
• Protostellar Contribution: The results suggest that while protostellar jets may enhance CRIR on small scales (as seen in previous NGC 1333 mapping), they do not drive the large-scale CRIR in these environments, particularly given that NGC 1333 has higher star-formation activity yet lower global CRIR.
• Implications for Star Formation: The globally higher CRIR in IC 348 implies a higher ionization fraction, leading to stronger gas-magnetic field coupling. The authors note this may enhance magnetic braking during core collapse, potentially explaining observational findings that protostellar disks in IC 348 are smaller on average than those in NGC 1333.
• Methodological Validation: The study validates the HINSA technique as a probe for CRIR in low-mass star-forming regions, highlighting the need for future 3D modeling to refine absolute values while confirming the robustness of relative disparities.