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Issue
A&A
Volume 711, July 2026
Article Number A105
Number of page(s) 14
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/202658871
Published online 10 July 2026

© The Authors 2026

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1 Introduction

Prestellar cores are gravitationally bound objects with a centrally concentrated density distribution (peak densities >105 cm−3) on the verge of star formation, but do not host any protostar at their center (Ward-Thompson et al. 1999; Keto & Caselli 2008; Pineda et al. 2023). The gravitational collapse of prestellar cores will result in stellar systems. Prestellar cores provide the pristine conditions before the formation of a protostellar seed and the launching of the outflow, altering the chemical and physical conditions at the onset of collapse. Consequently, the study of prestellar core properties is extremely important in revealing the initial physical and chemical conditions needed to understand how stellar systems like our own are assembled. Protostars form from the gravitational collapse of prestellar cores when gravity overcomes opposing forces, i.e., thermal pressure, turbulence, and magnetic pressure and tension. Observations of core velocity dispersions often show narrow linewidth, which are on the order of the thermal velocity dispersions (∼0.2 km/s for a molecular gas at 10 K), suggesting subcritical or transcritical turbulence in prestellar cores (Goodman et al. 1998; Pineda et al. 2010, 2026).

Although inferring the magnetic field (B-field) geometry and strength from observations is challenging, in the past five to ten years significant progress has been made to describe the B-field structure in molecular clouds, filaments, and dense cores (cf. recent reviews by Hull & Zhang 2019; Maury et al. 2022; Pattle et al. 2023). While observationally driven estimates of the mass-to-flux ratio may be hindered by limitations (e.g., Tritsis 2025), estimates of magnetic energies derived from polarization observations toward filaments and cores are often comparable to the gravitational energies (e.g., Pattle et al. 2023), suggesting that B-fields may play an important role in regulating core collapse and star formation (see also the simulations by Nakamura & Li 2008). Recent studies comparing molecular line observations and synthetic maps from magnetohydrodynamic (MHD) simulations also suggest that protostars may form from the collapse of magnetically subcritical or transcritical cores (cf. Yin et al. 2021; Priestley et al. 2022).

To allow for gravitational collapse of the cores, the B-field must diffuse. The decoupling between neutral and charged particles has been proposed to be an efficient diffusion mechanism of the B-field during the prestellar core collapse and the early phases of protostellar evolution. This process, known as ambipolar diffusion (Mestel & Spitzer 1956; Mouschovias 1979, 1987) causes neutral particles to drift through magnetic field lines, allowing the matter to be (quasi-statically) accreted into the core (Mouschovias et al. 2011).

In the classical model of a collapsing magnetized core, an “hourglass” B-field morphology pinched toward the center of mass is expected. This pinched hourglass shape is formed by the material collapsing freely along the field lines, and the flux-frozen field being dragged in by the collapse across the lines (Mestel 1966; Myers et al. 2018). The morphology of the B-field lines is related to the importance of coupling between matter and flux, where weaker flux-freezing leads to stronger ambipolar diffusion and hence less field curvature, i.e., less pinched B-field lines (e.g., Basu et al. 2009; Myers et al. 2018). Observations show a few cases of hourglass magnetic field structures toward massive dense cores (Girart et al. 2009; Beltrán et al. 2019; Saha et al. 2024) and low mass cores (Girart et al. 2006; Frau et al. 2011; Alves et al. 2011; Stephens et al. 2013; Redaelli et al. 2019a). However, in a large number of collapsing cores these pinched magnetic field structures are not observed. While projection effects and line-of-sight (LOS) integration may partly hinder the detection of these hourglass B-field shapes, their nondetection may indicate a partial decoupling of the matter and the field at the core scale, allowing the matter to infall toward the center through ambipolar diffusion without dragging in the B-field lines and consequently increasing the B-field flux.

Despite its importance, detecting the ion-neutral drift in observations is a challenging task: (1) the small predicted drift velocity (a fraction of the sound speed) requiring high-spectral resolution data (Tritsis et al. 2022). (2) The observed charged and neutral molecular species need to be chemically co-evolving to be tracing the same gas; otherwise any difference in the velocity fields could be attributed to different regions and/or densities of the core probed by the two molecules (Tassis et al. 2012). (3) Radiative transfer effects, the geometry of the B-field, and the morphology of the core can all hinder detection (Tritsis et al. 2023).

Two observational signatures of ambipolar diffusion have been proposed: (1) a difference in the systemic velocity between ion and neutral molecules that trace the same gas (e.g., Ciolek & Basu 2000; Tritsis et al. 2023), and (2) a broader linewidth of neutrals, which drift, compared to the ions attached to the field (e.g., Houde et al. 2000). The intensity (Pineda et al. 2024) and velocity (Tang et al. 2018) power spectra of interstellar clouds may also provide insights on interstellar turbulence dissipation and decoupling of ions and neutrals.

Very few observations have reported detections of ionneutral linewidth and/or velocity differences. Three papers from the same team reported broader neutral linewidths compared to the ion linewidths toward the M17 (Li & Houde 2008), DR21(OH) (Hezareh et al. 2010), and NGC 6334 (Tang et al. 2018) high-mass star-forming regions, using the HCN-HCO+(4 –3) and H13CN-H13CO+(4 – 3) neutral-ion pairs. The observed ion-neutral linewidth difference was used to estimate the plane-of-sky (POS) B-field strength toward the star-forming regions. These three works did not find ion-neutral velocity differences. More recently, Pineda et al. (2021) analyzed the Barnard 5 star-forming region using N2H+ and NH3 and found a mean ionneutral velocity difference of ∼0.05 km/s, which they did not discuss as being a signature of ambipolar diffusion. The critical densities of N2H+(1 – 0) and NH3(1,1) at 10K are 6 × 104 cm−3 and 2 × 103 cm−3, respectively (Shirley 2015), so it is likely that these two molecules and transitions do not trace the same gas. Unlike previous observational results, Pineda et al. (2021) detected a larger linewidth in the N2 H+ ion compared to the NH3 neutral molecule, with a difference of about ∼0.015 km/s (for a spectral resolution of ∼0.05 km/s). They proposed this velocity dispersion difference to indicate the penetration of MHD waves within the densest regions of Barnard 5 inducing turbulent oscillations of the ions, which are better coupled to the B-field as opposed to the neutrals. On smaller scales, ALMA observations of H13CO+(3 – 2) and C18O(2 – 1) were used to place an upper limit on the ion-neutral drift velocity of ∼0.35 km/s at 100 au scales toward the Class 0 protostar B335 (Yen et al. 2018).

Detecting the ambipolar diffusion process in prestellar cores, before the onset of protostellar feedback, has an important implication for our understanding of the evolution of the B-field flux during the prestellar core collapse. In addition, magnetic fields are important for transporting angular momentum from the collapsing cores, and play a significant role in the physics of bipolar outflows and jets, and the formation of protoplanetary disks that accompany protostar formation (Machida et al. 2008; Pudritz & Ray 2019). Quantifying observationally the ion-neutral drift velocity and the diffusion of the B-field flux via ambipolar diffusion is, therefore, crucial to study the collapse and evolution of prestellar cores.

In this paper we present new IRAM-30 m telescope observations of deuterated N-bearing ions and neutral molecules toward the L1544 prestellar core. We have selected L1544, which is a well-studied prototypical prestellar core (e.g., Spezzano et al. 2017; Redaelli et al. 2022; Caselli et al. 2022; Jensen et al. 2023, and references therein). We justify the choice of the selected ion-neutral pair in Section 2 and describe the observations in Section 3. The spectral fitting method is described in Section 4. The results are presented in Section 5 and discussed in Section 6. Appendices A−D complement the main text with additional details. Section 7 summarizes and concludes the paper.

2 Selection of the ion-neutral pair

Deuterated N-bearing molecules are late-type species formed in cold (≲15 K) and dense (≳105 cm−3) gas, where their formation is boosted by catastrophic CO freeze-out, which occurs under similar physical conditions (Caselli et al. 1999; Tiné et al. 2000; Öberg & Bergin 2021). N-bearing species, especially NH3 and N2H+ (and their deuterated isotopologues) trace well the central regions of prestellar cores, due to the fact that nitrogen also maintains a significant abundance at densities where the CO is almost completely depleted onto dust grains (e.g., Caselli et al. 2002b; Maret et al. 2006; Hily-Blant et al. 2010; Johnstone et al. 2010). In addition, NH3 and N2H+ are both formed from molecular nitrogen in the dense gas phase (Hily-Blant et al. 2013; Le Gal et al. 2014), implying that they both form above similar density thresholds in the inner parts of the cores with Bonnor-Ebert-like density profiles (Bonnor 1956; Aikawa et al. 2004; Keto & Caselli 2010). Observations of NH3 and N2H+ in a statistical sample of dense cores confirm the tight correlation between both velocity centroids and linewidths of these two N-bearing species, as well as the abundance ratio between NH3 and N2H+ across all cores studied (Johnstone et al. 2010, cf. also Chitsazzadeh et al. 2014). The strong correlations observed between the physical parameters of NH3 and N2H+ suggest that their formation and destruction mechanisms (as well as those of their deuterated isotopologues) are similar, validating them as powerful tracers of the same gas toward dense cores. Single-dish observations have detected a small decrease (a factor of a few) in the abundance of NH3 and N2H+ toward the inner parts of prestellar cores, as opposed to the strong freeze-out (on a few orders of magnitude) detected for C/O-bearing species (e.g., Caselli et al. 1999; Di Francesco et al. 2004; Crapsi et al. 2005; Pagani et al. 2007; Chitsazzadeh et al. 2014; Redaelli et al. 2019b). Recent high-sensitivity observations have detected depletion in deuterated N2D+ and NH2D species at high densities (>>106 cm−3) and small scales (<<0.1 pc) (Redaelli et al. 2019b; Caselli et al. 2022). Despite low freeze-out levels, N2D+ and NH2D have been shown to be ideal probes for studying the velocity and chemical structures of prestellar cores at densities 105−6 cm−3 and ∼0.1 pc scales (e.g., Ceccarelli et al. 2014; Redaelli et al. 2019b, 2025; Spezzano et al. 2025; Caselli et al. 2025). Moreover, these deuterated species (similarly to other molecules probing the dense gas within prestellar cores) show very narrow linewidths with subsonic velocity dispersions (<0.2 km/s), making them ideal tracers for detecting small velocity shifts between ion and neutral molecules expected in the presence of ambipolar diffusion.

For this work, we have thus chosen to compare the velocities of N2D+(2 – 1) and para-NH2D(111 – 101), which have similar critical densities within a factor of 3, with 4 × 105 cm−3 and 1.4 × 105 cm−3 (computed at 10K), respectively, making them highly likely to be tracing similar densities and regions within the ∼0.1 pc scale of prestellar cores. This is supported by the integrated intensity of these two molecules showing their similar spatial distribution within the ∼0.1 pc scale of the L1544 prestellar core (cf. the integrated intensity maps in Appendix A).

3 Observations

The observations were carried out with the IRAM-30m telescope at Pico Veleta, Spain. The EMIR multiband mm receiver (Carter et al. 2012) was used with the VESPA1 autocorrelator as backend. We observed with high-spectral resolutions corresponding to velocity resolutions of 0.0379 km/s for N2D+ and 0.0266 km/s for pNH2D at the rest (unsplit) frequencies of 154 217.0112MHz for N2D+(J = 2 – 1) and 110153.5940MHz for para-NH2D(JKa,Kc = 111 - 101) (cf. e.g., Dore et al. 2004; Daniel et al. 2016). The Vlsr for both cubes was set to 7.2 km/s.

For the rest of the paper we will refer to N2 D+ (2 – 1) and para-NH2D(111 – 101), as N2D+ and pNH2D, respectively.

The on-the-fly mapping mode was used to observe maps centered toward the dust peak of the L1544 core. The central coordinates of our maps are RAJ2000.0 = 05h04m16.539s and DecJ2000.0 = 25° 10′47″54. The position-switching mode was used with a reference position offset of ∼ 10′ from the target position. The calibration was achieved by measuring the emission from the sky, an ambient load, and a cold load every ∼15 min. The telescope pointing was corrected every ∼2 h. We reduce the data with the GILDAS/CLASS software package (the Grenoble Image and Line Data Analysis System, a software developed by IRAM2). The position-position-velocity (PPV) cubes of the observed molecules are reprojected onto the same spatial pixel grid at a half power beam width (HPBW) resolution of 23.′5, or 0.019 pc at the 170 pc distance of L1544 (cf. Galli et al. 2019), and pixel size of 8″. The typical rms of the spectra (on the Ta* scale) are 0.02 and 0.05 K, for N2D+ and pNH2D respectively.

4 Spectral fitting

We used the p y speckit analysis toolkit (Ginsburg & Mirocha 2011; Ginsburg et al. 2022) to fit the hyperfine structure of the N2D+ and pNH2 D spectra, with 26 and 35 hyperfines, respectively. p y speckit3 has the most recent libraries of hyperfine frequencies for these two molecules. The fitting results from p y speckit include the excitation temperature Tex, the optical depth τ, the velocity in the local standard of rest (lsr) Vlsr, the velocity dispersion σv,obs, and the associated uncertainties for all four parameters derived from the chi-square minimization approach (Ginsburg et al. 2022). We have validated the fitting results using the hyperfine module (HFS mode) ofGildas/CLASS2.

The accuracy of the spectroscopy of the N2D+ (Dore et al. 2004; Pagani et al. 2009) and pNH2D (Daniel et al. 2016; Melosso et al. 2021) lines reported in the catalogs, on the order of 0.005–0.008 km/s, is smaller by a factor of 3–7 compared to the velocity resolution of our data. Consequently, the observed differences between the centroid velocities of the lines (cf. Section 5) are unlikely to originate from the rest frequencies considered here and derived from spectroscopic measurements. We also note that the velocity accuracy is homogeneous for all hyperfine transitions (cf. Ginsburg et al. 2022).

Spectra with a peak signal-to-noise ratio less than five have been excluded from the analysis. In Appendix A, we show representative N2D+ and pNH2 D spectra and the best fit model toward the peak intensity of the core, i.e., the central pixel of the maps. We also present the derived fitting uncertainties on the velocities.

To compare the velocity dispersions of the two molecules of interest N2D+ and pNH2D, we estimate the total velocity dispersion of the mean free particle. We also derive the nonthermal velocity dispersion of the gas by subtracting the thermal velocity dispersion from the observed linewidth adopting a gas temperature of 10 K, which is the mean gas temperature of L1544 at the observed ∼0.05–0.1 pc scales and ∼105−6 cm−3 densities (Crapsi et al. 2007; Spezzano et al. 2017). We derive maps of σv,tot and σv,NT for both N2D+ and pNH2D. The details and results of the calculations are given in Appendix B.

Thumbnail: Fig. 1 Refer to the following caption and surrounding text. Fig. 1

Centroid velocity maps derived from pixel-per-pixel fitting of the N2 D+ ( top left) and pNH2D (top right) spectra with pyspeckit (cf. Section 4). The white contours at 0.8, 1.7, and 2.5 × 1022 cm−2 trace the gas column density as derived from Herschel data (from Spezzano et al. 2017) and are the same on both panels. The white filled circles show the 23″.5 beam size (0.019 pc at the 170pc distance of L1544) and the white vertical lines indicate the 0.05 pc scale. The excitation temperature maps are shown in Appendix A. The bottom plots show the distribution of the velocity for N2D+ in red and pNH2D in blue (bottom left) and a scatter plot (bottom right). The median values of the distributions indicated by the vertical dashed lines are 7.16 km/s for N2D+ and 7.21 km/s for pNH2D. The oblique solid and dashed blue lines indicate the 1:1 and the −0.05 km/s relations, respectively. The gray error bars on the scatter plot are the ±1σ uncertainties on the centroid velocities derived from the pyspeckit fit. The mean values of these uncertainties are 0.003 and 0.006 km/s for the N2D+ and pNH2D data points, respectively (the histograms of the uncertainties are presented in Appendix A).

5 Results: Ion-neutral velocity difference

The integrated intensity and excitation temperature Tex maps of N2D+ and pNH2D show the highly centrally concentrated emission within the ∼0.05 pc diameter of the core (cf. Appendix A). The integrated intensity radial profiles of N2D+ and pNH2D are very similar, with only a ∼20% larger value for pNH2D within the central part of the core. On the Tex maps, N2D+ shows a slightly (∼25%) more extended emission compared to that of pNH2D4, which is highly concentrated for gas column densities >1.7 × 1022 cm−2 as derived from Herschel/SPIRE data (Spezzano et al. 2016). This latter column density corresponds to a volume density of ∼105 cm−3 assuming a spherical density structure (with a diameter of 0.05 pc). The mean and standard deviation of the Texneutral/TexionMathematical equation: $T_{\rm ex}^{\rm neutral}/T_{\rm ex}^{\rm ion}$ ratio and the τneutral/τion are 1.03 ± 0.44 and 0.99 ± 0.18 (cf. histograms in Appendix A) suggesting that these two molecules are tracing similar optical depth and densities, making them strong candidates for chemically coevolving molecules within the core, further supporting our choice of ion-neutral pairs to investigate signatures of ambipolar diffusion toward L1544.

Figure 1 presents the velocity structure of L1544 as mapped with N2D+ and pNH2D. The spectra with a peak signal-to-noise ratio less than than five excluded from the analysis are shown with uniform gray colors.

The velocity maps for both N2D+ and pNH2D show the presence of velocity gradients along and across L1544. Such velocity gradients are usually attributed to rotation and infall (e.g., Tafalla et al. 1998; Ohashi et al. 1999; Caselli et al. 2002a; Williams et al. 2006). The mean and standard deviation of the centroid velocity distributions are 7.199 and 0.054 km/s for N2D+ and 7.151 and 0.050 km/s for pNH2D. The velocity scatter plot in Figure 1 highlights the systematic velocity shift between N2D+ and pNH2D. The spatial distribution of the velocity difference is given in the left panel of Figure 2 where higher values are found in the northwest part of the core decreasing values from the southeast to the northwest. The right panel of Figure 2 shows the velocity difference δVshift histogram with a mean value of 0.05 km/s and a standard deviation of 0.02 km/s. The detected ion-neutral mean value δVshift is spectrally resolved by a factor of 1.7 and the standard deviation of the distribution is smaller than the (∼0.03 km/s) velocity resolution of our current data.

The observed N2D+ and pNH2D spectral lines are narrow and characterized by velocity dispersions dominated by thermal motions, with σv,tot ∼ 0.2 and σv,NT ∼ 0.1 km/s (cf. Appendix B). On average, a difference of –0.004 km/s is detected in the total velocity dispersion of both species with a standard deviation of 0.006 km/s (cf. Appendix B). This measured difference in the ion-neutral velocity dispersion is an order of magnitude smaller than the velocity resolution of our data (~0.03 km/s).

Figure 3 presents a scatter plot of the ion-neutral velocity difference as a function of the column density derived from Herschel data. For column densities >2.4 × 1022 cm−2, toward the center of the core, δVshlft – 0.05 km/s. For these data points δσv,tot – 0.005 km/s, which indicates σv,totneutral>σv,totionMathematical equation: $ \sigma_{\rm v,tot}^{\rm neutral}>\sigma_{\rm v,tot}^{\rm ion}$. For column densities <2.4 × 1022 cm−2 the scatter of both δV and δσv,tot is greater.

The spatial resolution of our data (–0.019 pc) and the narrow column density range (only a factor of 1.8) probed by our observations are a limitation to further discuss the spatial variations in the ion-neutral velocity difference and velocity dispersion. Higher spatial resolution observations spanning a broader dynamic range of column density are needed to resolve the core and study the spatial velocity variations.

6 Discussion

6.1 Interpretation of the observed velocity difference

To fully characterize the initial condition of star formation and the onset of collapse of magnetized prestellar cores, it is essential to describe the physical processes and the timescales governing the diffusion of the magnetic field. The magnetic flux is reduced within the core due to the partial decoupling of the charged and neutral particles, allowing the neutrals to slip through the B-field lines, while the charged particles feeling the Lorentz force remain attached to the B-field. These decoupled infall motions result in a drift velocity vdrift = |Vneutral – Vion|, where vdrift∼ηADl,Mathematical equation: v_{\rm drift}\sim\frac{\eta_{\rm AD}}{l},(1)

with ηAD the ambipolar resistivity and l the characteristic scale of B-field fluctuations.

On microscopic level the ambipolar resistivity is a function of the total density (ρ), the magnetic field strength (B), and the ionization degree (x(e)) of the core. When the adsorption of charged particles onto dust grains is negligible, the ambipolar resistivity is expressed as ηAD(ρ,B,x(e))∝B2ρ2x(e).Mathematical equation: \eta_{\rm AD}(\rho,B,x(e))\propto \frac{B^2}{\rho^{2}x(e)}.\label{eq:etaAD}(2)

The ionization degree within dense cores x(e), without an internal protostellar source, is controlled by the interstellar cosmic-ray ionization rate, the gas-phase recombination, and the dust grain size distribution (McKee 1989; Caselli et al. 1998; Ivlev et al. 2015). The cosmic-ray ionization rate in prestellar cores, including L1544, is observationally estimated to be ζH2 ~ 10−17 s−1 (Redaelli et al. 2021, 2025). Equation (2) considers only gas-phase recombination. When dust grains are present, the adsorption of charged particles onto the dust grains could also play a role, in which case the expression of ηAD differs from that of Equation (2).

Several dynamical models ranging from early studies (e.g., Basu & Mouschovias 1995; Tassis & Mouschovias 2007) to more recent 3D simulations (e.g., Tritsis et al. 2022; Tritsis 2025) have explored the impact of ambipolar diffusion on core collapse. While these latter studies investigated ion-neutral drift velocities without invoking the evolution of the dust size distribution, the strong dependence of ηAD (and hence vdrift) on the abundance of small grains in the core centers has been discussed in a number of recent works (e.g., Zhao et al. 2021; Tsukamoto & Okuzumi 2022). Silsbee et al. (2020) have investigated the differential grain drift due to ambipolar diffusion affecting the dust coupling to the magnetic field and to the neutral gas. They showed that small grains (mostly negatively charged), which stay coupled to the magnetic field are efficiently depleted within the core center due to a rapid coagulation with larger grains, drifting through the magnetic field toward the core center due to infall motions. They calculated an ion-neutral velocity drift of ~0.05 km/s for L1544.

In a dedicated recent study, Fukihara et al. (2026) calculated the time evolution of ηAD at dense core densities of 106 cm−3 as grains grow via accretion and coagulation5. They demonstrate that within several free-fall times, dust grains grow sufficiently contributing to the increase of ηAD, resulting in a more efficient decoupling between charged and neutral particles. They demonstrate that vdrift – 0.05–0.10km/s due to ambipolar diffusion are expected at core densities of 106 cm−3 with magnetic field fluctuations on the order of the Jeans length (corresponding to the characteristic scale of density fluctuations in self-gravitating cores in frozen-in conditions) when the following three conditions are satisfied: 1) magnetic field strengths are 100–300 μG, 2) ζH2 ~ 10−17 s−1, and 3) the very small < 0.02 μm grains (VSG) are depleted due to dust growth. They show that when the above conditions are not satisfied, the resulting vdrift are smaller (~0.001 km/s). The VSG are found to be efficiently depleted through accretion within one free-fall time –104 yr for densities of 106 cm−3 followed by the growth of grains via coagulation reaching maximum sizes of –10 μm within –10 free-fall times (Fukihara et al. 2026, see also Ormel et al. 2009).

While dust grain growth from observations has not yet been well constrained and is still debated, multiple observational results based on different methods strongly indicate the growth of dust grains from the diffuse interstellar medium (ISM) to the dense prestellar cores (see, e.g., a recent review by Maury et al. 2022): (1) the observed mid-IR scattered light toward starless cores (coreshine, e.g., Pagani et al. 2010); (2) the change of the dust emissivity index derived from submillimeter dust continuum observations (e.g., Bracco et al. 2017; Galametz et al. 2019; Chacón-Tanarro et al. 2019); (3) the observed 2–5% polarization fractions in the submillimeter (e.g., Valdivia et al. 2019; Le Gouellec et al. 2020) all require micron-sized grains to account for the observation; (4) recent spectroscopic observations of interstellar icy grains with the James Webb Space Telescope (JWST) reveal that the grains reach micrometer sizes before the protostellar phase (e.g., Dartois et al. 2024).

As presented in Section 5, we detect a 0.05 km/s velocity shift between N2D+ and pNH2D toward the inner –0.05 pc scale of L1544 (Figure 1). We propose that the theoretically predicted ion-neutral drift velocities at dense core densities including dust grain growth on the order of 0.05–0.1 km/s suggest that the observed 0.05 km/s velocity difference between N2 D+ and pNH2 D toward L1544 may be tracing the decoupling between ions and neutrals due to ambipolar diffusion. We detect the 0.05 km/s velocity shift toward the inner –0.05 pc of the core. This –0.05 pc scale is on the order of the Jeans length –0.06 pc (at the density of 105 cm−3 and temperature of 10 K, cf. Section 5), suggesting that the characteristic scale of B-field fluctuations and/or bending due to gravity within the core may be on the order of the Jeans length as suggested by Fukihara et al. (2026) under the specific conditions of a spherically collapsing self-gravitating gas. Observational studies of the ion and neutral velocity power spectra have found ambipolar diffusion length scales within the range of –2 mpc (Li & Houde 2008) and ~20–30 mpc (Pineda et al. 2024; Houde et al. 2009, 2016). These latter length scales estimated from the analysis of cloud scale data are smaller than the Jeans length mentioned above for L1544 at the density of 105 cm−3. High-angular resolution observations of the velocity and magnetic field structures are required to describe the characteristic scale of magnetic field fluctuations and its origin within L1544.

An important implication in confirming the origin of the observed velocity difference resulting from ambipolar diffusion helps us constrain the total 3D magnetic field strength toward the ~0.05 pc of L1544 to be on the order of 100–300 μG. This predicted range of magnetic field strength is compatible with the 140 μG strength estimated from dust polarized emission observations at 850 μm with the James Clerk Maxwell Telescope (JCMT)/SCUPOL (Crutcher et al. 2004, see also Clemens et al. 2016).

Thumbnail: Fig. 2 Refer to the following caption and surrounding text. Fig. 2

Left : map of the difference between the neutral pNH2D and the ion N2D+ centroid velocity (δVshift = Vneutral – Vion). The filled white circle shows the 23″.5 beam size (0.019 pc at the 170 pc distance of L1544) and the white vertical line indicates the 0.05 pc scale. Right : histogram of δ Vshift. The mean and standard deviation of the δVshift distribution are 0.05 and 0.02 km/s, respectively, where the mean uncertainty on δVshift is 0.006 km/s (cf. Appendix A).
Thumbnail: Fig. 3 Refer to the following caption and surrounding text. Fig. 3

Scatter plot of the difference between the neutral pNH2D and the ion N2D+ centroid velocity (δVshift = Vneutral – Vion) versus the NH2 column density derived from Herschel and reprojected to the same spatial grid as that of the molecular line data. The scatter in δVshift is larger for smaller NH2 values. The color of the data points and the color bar indicate the difference of the ion-neutral total velocity dispersion (δσv,tot).

6.2 Projection effects

The theoretical studies (Silsbee et al. 2020; Fukihara et al. 2026) discussed in Section 6.1 obtained 3D velocity drifts υdrift on the order of 0.05 km/s for reasonable assumptions for dense core physical parameters (density, magnetic field, ionization), assuming a simplified magnetic field geometry, and also do not consider asymmetries in the core properties.

Because the observations trace the LOS velocity of the gas, both the physical geometry of the core and the spatial structure of the infall and/or contraction6 motions strongly influence the observed velocity pattern of Vlsr. In the absence of turbulence, (1) when the core has a uniform spherical density structure undergoing a symmetric infall, with or without ion-neutral drift velocities, no LOS velocity gradients or drift velocities can be detected. In the presence of (anisotropic) turbulence, however, the symmetry of the velocity field is broken and both velocity gradients and velocity drifts can be detected; (2) when the core has a flattened ellipsoidal density structure, velocity gradients tracing the infall are observable and the presence of the LOS ionneutral velocity drift is characterized by a sign inversion between the redshifted and blueshifted velocity gradients of the infalling core; (3) when the core is a titled and bent ellipsoid, velocity gradients are observed, and the LOS ion-neutral velocity drift has the same sign. Our observations of L1544 show a velocity gradient with a drift velocity that does not change sign, suggesting that L1544 may be well described by a bent ellipsoid with asymmetric velocities tracing infall, contraction and/or accretion. The description of a bent ellipsoid is compatible with the observed maps of L1544 and with multiple studies that found asymmetric accretion flows suggested by the observed velocity fields and shock signatures (Kim et al. 2022; Lin et al. 2022; Giers et al. 2025).

For increasing densities toward the core center, vdrift is expected to decrease (see Equation (2) and cf. also Mouschovias 1991). Our observations probe a column density range of a factor of 1.8 (between –1.6 to 2.8 ×1022 cm−2). The velocity drift on such a small range is expected to change on the order of 40% (assuming B ∝ p1/2)7, which is on the order of the observed υdrift scatter (Figure 3). The observed scatter, which may result from a more complex velocity field and is affected by projection effects, may hide the expected decrease of υdrift with increasing column density. In particular, in their non-ideal MHD simulations, Tritsis (2025) found that at an evolved stage of a turbulent core collapse, the twisting of the B-field lines near the core midplane induces a fraction of the υdrift vectors to point outward. Such a complex velocity structure would manifest as positive and negative υdrift gradients on either side of the core midplane. To better constrain the origin of the observed υdrift and its scatter, higher angular (and spectral) resolution data are required to resolve the velocity distribution and probe a broader range of column density within the core.

As vectors of the ion-neutral drift velocity are perpendicular to the local B-field, observations of the B-field structure derived from dust polarized emission toward L1544 would provide invaluable hints on the pinching of the B-field lines and thus on the ongoing ambipolar diffusion process. Ciolek & Basu (2000) suggested a model for the mean B-field in L1544 close to the POS, while recent polarization observations (Kim et al. 2025) favor a more inclined configuration of the B-field. In the absence of turbulence, for an axisymmetric B-field configuration, a more inclined B-field with respect to the POS will decrease the measured υdrift along the LOS. On the other hand, an inclined B-field configuration coupled with the presence of asymmetries in both the density and velocity structures will break the symmetry of the integrated emission allowing the detection of υdrift (cf. Section 6.4). The presence of asymmetries in the density, B-field, and velocity structures combined with dust growth (cf. Section 6.1) is jointly needed to interpret the observed velocity difference between N2D+ and pNH2D toward L1544 as a drift due to ambipolar diffusion.

The broadening of the linewidth of neutrals compared to the linewidth of ions has been suggested as a signature of ongoing ambipolar diffusion (e.g., Li & Houde 2008, see also Section 1). However, these latter studies have been targeting (optically thick) molecular lines (e.g., HCO+, CO) with supersonic linewidths tracing lower density gas in the turbulent environments surrounding star-forming cores (in high-mass star-forming regions). Disentangling the various physical mechanisms (interstellar turbulence, impact of stellar feedback, ambipolar diffusion, radiative transfer effects, opacity effects) that may contribute to the observed differences between the linewidths of these different molecules may be challenging. In contrast to previous studies in supersonic environments, in our observations toward the central part of L1544, the (nonthermal) velocity dispersions of N2D+ and pNH2D are subsonic (cf. Appendix B) and the contraction motions within the ∼0.05 pc L1544 core are also subsonic. Consequently, the subsonic inward motion of the neutrals decoupled from the B-field and the ions may not have a strong impact on broadening the linewidth of pNH2D, hence the similar linewidth observed for N2D+ and pNH2D. In addition, the LOS integration and projection effects may also impact the observed linewidth (Priestley et al. 2022), making the linewidth difference between ions and neutrals not a reliable diagnostic when the magnetized object has some inclination. In particular, for L1544, the detection of the velocity difference between N2D+ and pNH2D combined with the absence of significant difference in linewidth would be compatible with an inclined configuration of the system.

To better constrain the geometric limitations of the observations (velocity centroid and linewidth maps) and understand the origin of the observed velocity and linewidth difference between N2D+ and pNH2D toward L1544, a quantitative comparison with synthetic maps for various projection angles derived from nonideal MHD simulations including ambipolar diffusion and grain growth is required. This study will be presented in a future publication (Misugi et al., in prep.).

6.3 Assessing the co-spatiality of the N2D+ and pNH2D emission

We chose N-bearing deuterated molecules N2D+ and pNH2D to investigate the ion-neutral velocity difference because of their similar critical densities within a factor of three. The observed ratio of fitted Tex and τ values close to one (see Appendix A) suggests that these molecules may be tracing the same densities, supporting our choice of selecting them for the analysis aimed at studying the ion-neutral velocity drift due to ambipolar diffusion. The spatial distributions are also very similar (see Fig. A.3), although higher-angular-resolution observations are needed to better resolve the core structure. Interestingly, N2D+, which has a critical density of 4 × 105 cm−3,2.8 times higher than the critical density of pNH2D, shows a slightly more extended emission (see Fig. A.3), which may contribute to broadening the linewidth of the N2D+ and masking the possible detection of a larger neutral linewidth compared to the ion linewidth proposed by Li & Houde (2008). Radiative transfer effects, LOS integration, projection effects, and density and/or velocity asymmetries may also hinder any possible detection of linewidth differences.

To better understand the origin of the observed velocity difference, we also compare, in Appendix C, the Vlsr of N2D+(2 –1) and pNH2D with that of N2D+(1 – 0) obtained with the IRAM-30 m telescope. This latter ion has a critical density of 8 × 104 cm−3 at 10 K, a factor of 1.7 and 5 lower than pNH2D and N2D+(2-1), respectively. For this comparison, we smooth the three data cubes to the coarser 34" angular resolution of N2D+(1-0). The spectral resolution of N2D+(1-0) is 0.076 km/s. We do not resample the three data cubes spectrally, but correct for the channel response (see Appendix C). We confirm that spectrally smoothing the data to a two and three times coarser resolution does not change the fitted value of Vlsr and minimally broadens the linewidth (∼4%). We find a mean velocity difference between pNH2D and N2D+(1 – 0) of 0.013 km/s, which is smaller than the spectral resolution of the data (cf. Appendix C). The distributions of the Tex and τ ratios between the ion and the neutral are broader when the ion is N2D+(1 – 0) compared to those when the ion is N2D+(2 – 1), suggesting that the N2D+(2 – 1) emission is more closely correlated with that of pNH2D.

6.4 Analytical model of an infalling and/or contracting core with drift velocity

The observed velocity difference may be a combination of ionneutral velocity drifts and different infall motions of slightly different gas density regimes probed by the chosen ion-neutral pair. To test whether the observations could be reproduced with a model of an infalling-rotating core with a drift velocity between ions and neutrals, we designed an analytical model of an ellipsoidal core with parametrized geometry and parametrized density and velocity profiles. The 3D core models are then integrated along the lines of sight to derive synthetic spectral maps (i.e., PPV cubes). Thanks to a JAX-based architecture (Bradbury et al. 2018), the model is completely differentiable with respect to the input parameters. With this approach, the derived synthetic PPV cubes are used to optimize the parameters and minimize the difference with the observed PPV cubes. Further details of the model are described in Appendix D. We modeled a set of parameter configurations to determine which scenario is the most plausible for interpreting our observations. Although this is an idealized experiment, where radiative transfer is simplified and chemistry is parametrized, it provides a useful framework for understanding our observations. It suggests that to explain the observed velocity difference between N2D+(2-1) and pNH2D, the interpretation based on the drift velocity in the presence of asymmetric infall and/or contraction cannot be excluded, as well as the interpretation in which the observations are produced by a combined effect of the drift velocity and different abundance distributions of the two molecules. The detailed models, analyzes, and results of this experiment are presented in Grassi et al. (2026).

7 Summary and conclusions

The analyzes of the velocity structure on the ∼0.1 pc scale toward the L1544 prestellar core of the deuterated N2D+(2-1) ion and pNH2D(111 – 101) neutral molecules show a mean difference of 0.05 km/s with a standard deviation of 0.02 km/s (Figure 2). This observed velocity difference may be tracing the decoupling between ions and neutrals within the core, hinting at the ongoing ambipolar diffusion and the onset of the core collapse. The observed velocity difference is supported by theoretical calculations of evolution of the ambipolar diffusion coefficient in dense core environments including dust grain growth (cf. Section 6.1). In addition to the difference of the centroid velocity, the difference between the linewidths of ions and neutrals is an observational signature of the presence of ion-neutral drift and ongoing ambipolar diffusion. In our observations, we do not detect a significant difference between the linewidths for N2D+ and pNH2D. This may be attributed to the subsonic infall motions of the gas in L1544, which would mask the expected broadening of the linewidth of the neutrals, infalling faster compared to the ions better coupled with the B-field. The absence of linewidth differences may also be due to geometric effects in the presence of inclination of the system with respect to the POS.

Although recent calculations from Fukihara et al. (2026) support the interpretation of our observational results as tracing ambipolar diffusion, we cannot completely exclude the possibility that the two species we have studied may be tracing slightly different regions and densities and thus the dynamical properties of different regions within the core. To better describe the physical and chemical properties of L1544, high-angularresolution data with interferometers (ALMA/NOEMA) and the next generation large single-dish telescopes (AtLAST) equipped with high-spectral resolution (10 kHz) spectrometers are needed. Future observations of ion-neutral pairs toward a large sample of prestellar cores at different evolutionary stages and in different environments, compared to simulations with ambipolar diffusion, will help to better constrain the origin of the observational results. Such statistical studies will also provide the data needed to assess the impact of the magnetic field geometry and density structure, as well as the effect of projections and/or inclinations on the observed velocities and linewidths derived from LOS integration.

Finally, we propose that measurements of ion-neutral drift velocities within dense filaments and cores may provide new constraints on the 3D magnetic field strength and the evolution of dust size distribution within prestellar cores on their way to star formation.

Acknowledgements

S.S., T.G., P.C., J.P., S.J., and A.I. gratefully acknowledge the support of the Max Planck Society. This work was supported by the NINS-DAAD International Personal Exchange Program (2023-2025). This program is a joint funding initiative of the National Institutes of Natural Sciences (NINS) in Japan and the German Academic Exchange Service (DAAD).

References

  1. Aikawa, Y., Herbst, E., Caselli, P., Roberts, H., & Ohashi, N. 2004, in The Dense Interstellar Medium in Galaxies, eds. S. Pfalzner, C. Kramer, C. Staubmeier, & A. Heithausen (Berlin: Springer), 91, 461 [Google Scholar]
  2. Alves, F. O., Girart, J. M., Lai, S.-P., Rao, R., & Zhang, Q. 2011, ApJ, 726, 63 [NASA ADS] [CrossRef] [Google Scholar]
  3. Basu, S., & Mouschovias, T. C. 1995, ApJ, 453, 271 [Google Scholar]
  4. Basu, S., Ciolek, G. E., Dapp, W. B., & Wurster, J. 2009, New A, 14, 483 [NASA ADS] [CrossRef] [Google Scholar]
  5. Beltrán, M. T., Padovani, M., Girart, J. M., et al. 2019, A&A, 630, A54 [Google Scholar]
  6. Bonnor, W. B. 1956, MNRAS, 116, 351 [NASA ADS] [CrossRef] [Google Scholar]
  7. Bracco, A., Palmeirim, P., André, P., et al. 2017, A&A, 604, A52 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  8. Bradbury, J., Frostig, R., Hawkins, P., et al. 2018, JAX: composable transformations of Python+NumPy programs, http://github.com/jax-ml/jax [Google Scholar]
  9. Carter, M., Lazareff, B., Maier, D., et al. 2012, A&A, 538, A89 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  10. Caselli, P., Walmsley, C. M., Terzieva, R., & Herbst, E. 1998, ApJ, 499, 234 [Google Scholar]
  11. Caselli, P., Walmsley, C. M., Tafalla, M., Dore, L., & Myers, P. C. 1999, ApJ, 523, L165 [Google Scholar]
  12. Caselli, P., Walmsley, C. M., Zucconi, A., et al. 2002a, ApJ, 565, 331 [NASA ADS] [CrossRef] [Google Scholar]
  13. Caselli, P., Walmsley, C. M., Zucconi, A., et al. 2002b, ApJ, 565, 344 [Google Scholar]
  14. Caselli, P., Pineda, J. E., Sipilä, O., et al. 2022, ApJ, 929, 13 [NASA ADS] [CrossRef] [Google Scholar]
  15. Caselli, P., Spezzano, S., Redaelli, E., et al. 2025, A&A, 703, A77 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  16. Ceccarelli, C., Caselli, P., Bockelée-Morvan, D., et al. 2014, in Protostars and Planets VI, eds. H. Beuther, R. S. Klessen, C. P. Dullemond, & T. Henning (Tucson: University of Arizona Press), 859 [Google Scholar]
  17. Chacón-Tanarro, A., Pineda, J. E., Caselli, P., et al. 2019, A&A, 623, A118 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  18. Chitsazzadeh, S., Di Francesco, J., Schnee, S., et al. 2014, ApJ, 790, 129 [NASA ADS] [CrossRef] [Google Scholar]
  19. Ciolek, G. E., & Basu, S. 2000, ApJ, 529, 925 [Google Scholar]
  20. Clemens, D. P., Tassis, K., & Goldsmith, P. F. 2016, ApJ, 833, 176 [Google Scholar]
  21. Crapsi, A., Caselli, P., Walmsley, C. M., et al. 2005, ApJ, 619, 379 [Google Scholar]
  22. Crapsi, A., Caselli, P., Walmsley, M. C., & Tafalla, M. 2007, A&A, 470, 221 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  23. Crutcher, R. M., Nutter, D. J., Ward-Thompson, D., & Kirk, J. M. 2004, ApJ, 600, 279 [Google Scholar]
  24. Daniel, F., Coudert, L. H., Punanova, A., et al. 2016, A&A, 586, L4 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  25. Dartois, E., Noble, J. A., Caselli, P., et al. 2024, Nat. Astron., 8, 359 [NASA ADS] [CrossRef] [Google Scholar]
  26. DeepMind, Babuschkin, I., Baumli, K., et al. 2020, The DeepMind JAX Ecosystem, http://github.com/google-deepmind [Google Scholar]
  27. Di Francesco, J., André, P., & Myers, P. C. 2004, ApJ, 617, 425 [NASA ADS] [CrossRef] [Google Scholar]
  28. Dore, L., Caselli, P., Beninati, S., et al. 2004, A&A, 413, 1177 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  29. Frau, P., Galli, D., & Girart, J. M. 2011, A&A, 535, A44 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  30. Fukihara, H., Tsukamoto, Y., Hirashita, H., Arzoumanian, D., & Misugi, Y. 2026, ApJ, 999, 79 [Google Scholar]
  31. Galametz, M., Maury, A. J., Valdivia, V., et al. 2019, A&A, 632, A5 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  32. Galli, P. A. B., Loinard, L., Bouy, H., et al. 2019, A&A, 630, A137 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  33. Giers, K., Spezzano, S., Lin, Y., et al. 2025, A&A, 699, A103 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  34. Ginsburg, A. & Mirocha, J. 2011, PySpecKit: Python Spectroscopic Toolkit, Astrophysics Source Code Library [record ascl:1109.001] [Google Scholar]
  35. Ginsburg, A., Sokolov, V., de Val-Borro, M., et al. 2022, AJ, 163, 291 [NASA ADS] [CrossRef] [Google Scholar]
  36. Girart, J. M., Rao, R., & Marrone, D. P. 2006, Science, 313, 812 [Google Scholar]
  37. Girart, J. M., Beltrán, M. T., Zhang, Q., Rao, R., & Estalella, R. 2009, Science, 324, 1408 [NASA ADS] [CrossRef] [Google Scholar]
  38. Goodman, A. A., Barranco, J. A., Wilner, D. J., & Heyer, M. H. 1998, ApJ, 504, 223 [Google Scholar]
  39. Grassi, T., Pineda, J. E., Spezzano, S., et al. 2026, A&A, accepted [arXiv:2603.06791] [Google Scholar]
  40. Hezareh, T., Houde, M., McCoey, C., & Li, H.-b. 2010, ApJ, 720, 603 [Google Scholar]
  41. Hily-Blant, P., Walmsley, M., Pineau Des Forêts, G., & Flower, D. 2010, A&A, 513, A41 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  42. Hily-Blant, P., Pineau des Forêts, G., Faure, A., Le Gal, R., & Padovani, M. 2013, A&A, 557, A65 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  43. Houde, M., Peng, R., Phillips, T. G., Bastien, P., & Yoshida, H. 2000, ApJ, 537, 245 [Google Scholar]
  44. Houde, M., Vaillancourt, J. E., Hildebrand, R. H., Chitsazzadeh, S., & Kirby, L. 2009, ApJ, 706, 1504 [Google Scholar]
  45. Houde, M., Hull, C. L. H., Plambeck, R. L., Vaillancourt, J. E., & Hildebrand, R. H. 2016, ApJ, 820, 38 [NASA ADS] [CrossRef] [Google Scholar]
  46. Hull, C. L. H., & Zhang, Q. 2019, Front. Astron. Space Sci., 6, 3 [Google Scholar]
  47. Hwang, J., Kim, J., Pattle, K., et al. 2021, ApJ, 913, 85 [NASA ADS] [CrossRef] [Google Scholar]
  48. Ivlev, A. V., Padovani, M., Galli, D., & Caselli, P. 2015, ApJ, 812, 135 [Google Scholar]
  49. Jensen, S. S., Spezzano, S., Caselli, P., Grassi, T., & Haugbolle, T. 2023, A&A, 675, A34 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  50. Johnstone, D., Rosolowsky, E., Tafalla, M., & Kirk, H. 2010, ApJ, 711, 655 [NASA ADS] [CrossRef] [Google Scholar]
  51. Kandori, R., Tomisaka, K., Tamura, M., et al. 2018, ApJ, 865, 121 [Google Scholar]
  52. Kauffmann, J., Bertoldi, F., Bourke, T. L., Evans, II, N. J., & Lee, C. W. 2008, A&A, 487, 993 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  53. Kawasaki, Y., Koga, S., & Machida, M. N. 2022, MNRAS, 515, 2072 [NASA ADS] [CrossRef] [Google Scholar]
  54. Keto, E., & Caselli, P. 2008, ApJ, 683, 238 [Google Scholar]
  55. Keto, E., & Caselli, P. 2010, MNRAS, 402, 1625 [Google Scholar]
  56. Kim, S., Lee, C. W., Tafalla, M., et al. 2022, ApJ, 940, 112 [NASA ADS] [CrossRef] [Google Scholar]
  57. Kim, S., Lee, C. W., Pattle, K., et al. 2025, Nat. Astron., submitted, https://doi.org/10.21203/rs.3.rs-7429059/v1 [Google Scholar]
  58. Kingma, D. P., & Ba, J. 2015, in 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings, eds. Y. Bengio, & Y. LeCun [Google Scholar]
  59. Lê, N., Tram, L. N., Karska, A., et al. 2024, A&A, 690, A191 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  60. Le Gal, R., Hily-Blant, P., Faure, A., et al. 2014, A&A, 562, A83 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  61. Le Gouellec, V. J. M., Maury, A. J., Guillet, V., et al. 2020, A&A, 644, A11 [EDP Sciences] [Google Scholar]
  62. Lebreuilly, U., Vallucci-Goy, V., Guillet, V., Lombart, M., & Marchand, P. 2023, MNRAS, 518, 3326 [Google Scholar]
  63. Li, H.-b., & Houde, M. 2008, ApJ, 677, 1151 [NASA ADS] [CrossRef] [Google Scholar]
  64. Lin, Y., Spezzano, S., Sipilä, O., Vasyunin, A., & Caselli, P. 2022, A&A, 665, A131 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  65. Machida, M. N., Inutsuka, S.-i., & Matsumoto, T. 2008, ApJ, 676, 1088 [CrossRef] [Google Scholar]
  66. Maret, S., Bergin, E. A., & Lada, C. J. 2006, Nature, 442, 425 [Google Scholar]
  67. Maury, A., Hennebelle, P., & Girart, J. M. 2022, Front. Astron. Space Sci., 9, 949223 [NASA ADS] [CrossRef] [Google Scholar]
  68. McKee, C. F. 1989, ApJ, 345, 782 [NASA ADS] [CrossRef] [Google Scholar]
  69. Melosso, M., Bizzocchi, L., Dore, L., et al. 2021, J. Mol. Spectr., 377, 111431 [Google Scholar]
  70. Mestel, L. 1966, MNRAS, 133, 265 [NASA ADS] [CrossRef] [Google Scholar]
  71. Mestel, L., & Spitzer, Jr., L. 1956, MNRAS, 116, 503 [NASA ADS] [CrossRef] [Google Scholar]
  72. Mouschovias, T. C. 1979, ApJ, 228, 475 [Google Scholar]
  73. Mouschovias, T. C. 1987, ASI Ser., 210, 491 [Google Scholar]
  74. Mouschovias, T. C. 1991, ApJ, 373, 169 [NASA ADS] [CrossRef] [Google Scholar]
  75. Mouschovias, T. C., Ciolek, G. E., & Morton, S. A. 2011, MNRAS, 415, 1751 [NASA ADS] [CrossRef] [Google Scholar]
  76. Myers, P. C. 1983, ApJ, 270, 105 [Google Scholar]
  77. Myers, P. C., Basu, S., & Auddy, S. 2018, ApJ, 868, 51 [Google Scholar]
  78. Nakamura, F., & Li, Z. 2008, ApJ, 687, 354 [NASA ADS] [CrossRef] [Google Scholar]
  79. Öberg, K. I., & Bergin, E. A. 2021, Phys. Rep., 893, 1 [Google Scholar]
  80. Ohashi, N., Lee, S. W., Wilner, D. J., & Hayashi, M. 1999, ApJ, 518, L41 [Google Scholar]
  81. Ormel, C. W., Paszun, D., Dominik, C., & Tielens, A. G. G. M. 2009, A&A, 502, 845 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  82. Pagani, L., Bacmann, A., Cabrit, S., & Vastel, C. 2007, A&A, 467, 179 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  83. Pagani, L., Daniel, F., & Dubernet, M.-L. 2009, A&A, 494, 719 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  84. Pagani, L., Steinacker, J., Bacmann, A., Stutz, A., & Henning, T. 2010, Science, 329, 1622 [Google Scholar]
  85. Pattle, K., Fissel, L., Tahani, M., Liu, T., & Ntormousi, E. 2023, ASP Conf. Ser., 534, 193 [NASA ADS] [Google Scholar]
  86. Pineda, J. E., Goodman, A. A., Arce, H. G., et al. 2010, ApJ, 712, L116 [Google Scholar]
  87. Pineda, J. E., Schmiedeke, A., Caselli, P., et al. 2021, ApJ, 912, 7 [NASA ADS] [CrossRef] [Google Scholar]
  88. Pineda, J. E., Arzoumanian, D., Andre, P., et al. 2023, ASP Conf. Ser., 534, 233 [NASA ADS] [Google Scholar]
  89. Pineda, J. E., Soler, J. D., Offner, S., et al. 2024, A&A, 690, L5 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  90. Pineda, J. E., Friesen, R. K., (co-PIs), et al. 2026, ApJS, 282, 18 [Google Scholar]
  91. Priestley, F. D., Yin, C., & Wurster, J. 2022, MNRAS, 515, 5689 [NASA ADS] [CrossRef] [Google Scholar]
  92. Pudritz, R. E., & Ray, T. P. 2019, Front. Astron. Space Sci., 6, 54 [Google Scholar]
  93. Redaelli, E., Alves, F. O., Santos, F. P., & Caselli, P. 2019a, A&A, 631, A154 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  94. Redaelli, E., Bizzocchi, L., Caselli, P., et al. 2019b, A&A, 629, A15 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  95. Redaelli, E., Sipilä, O., Padovani, M., et al. 2021, A&A, 656, A109 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  96. Redaelli, E., Chacón-Tanarro, A., Caselli, P., et al. 2022, ApJ, 941, 168 [NASA ADS] [CrossRef] [Google Scholar]
  97. Redaelli, E., Spezzano, S., Caselli, P., et al. 2025, A&A, 696, A171 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  98. Saha, P., Sanhueza, P., Padovani, M., et al. 2024, ApJ, 972, L6 [Google Scholar]
  99. Shirley, Y. L. 2015, PASP, 127, 299 [Google Scholar]
  100. Silsbee, K., Ivlev, A. V., Sipilä, O., Caselli, P., & Zhao, B. 2020, A&A, 641, A39 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  101. Spezzano, S., Bizzocchi, L., Caselli, P., Harju, J., & Brünken, S. 2016, A&A, 592, L11 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  102. Spezzano, S., Caselli, P., Bizzocchi, L., Giuliano, B. M., & Lattanzi, V. 2017, A&A, 606, A82 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  103. Spezzano, S., Redaelli, E., Caselli, P., et al. 2025, A&A, 694, A27 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  104. Stephens, I. W., Looney, L. W., Kwon, W., et al. 2013, ApJ, 769, L15 [Google Scholar]
  105. Tafalla, M., Mardones, D., Myers, P. C., et al. 1998, ApJ, 504, 900 [NASA ADS] [CrossRef] [Google Scholar]
  106. Tafalla, M., Myers, P. C., Caselli, P., Walmsley, C. M., & Comito, C. 2002, ApJ, 569, 815 [Google Scholar]
  107. Tang, K. S., Li, H.-B., & Lee, W.-K. 2018, ApJ, 862, 42 [Google Scholar]
  108. Tassis, K., & Mouschovias, T. C. 2007, ApJ, 660, 370 [Google Scholar]
  109. Tassis, K., Hezareh, T., & Willacy, K. 2012, ApJ, 760, 57 [Google Scholar]
  110. Tiné, S., Roueff, E., Falgarone, E., Gerin, M., & Pineau des Forêts, G. 2000, A&A, 356, 1039 [NASA ADS] [Google Scholar]
  111. Tritsis, A. 2025, A&A, 700, A152 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  112. Tritsis, A., Federrath, C., Willacy, K., & Tassis, K. 2022, MNRAS, 510, 4420 [NASA ADS] [CrossRef] [Google Scholar]
  113. Tritsis, A., Basu, S., & Federrath, C. 2023, MNRAS, 521, 5087 [NASA ADS] [CrossRef] [Google Scholar]
  114. Tsukamoto, Y., & Okuzumi, S. 2022, ApJ, 934, 88 [NASA ADS] [CrossRef] [Google Scholar]
  115. Valdivia, V., Maury, A., Brauer, R., et al. 2019, MNRAS, 488, 4897 [NASA ADS] [CrossRef] [Google Scholar]
  116. Ward-Thompson, D., Motte, F., & Andre, P. 1999, MNRAS, 305, 143 [Google Scholar]
  117. Williams, J. P., Lee, C. W., & Myers, P. C. 2006, ApJ, 636, 952 [NASA ADS] [CrossRef] [Google Scholar]
  118. Yen, H.-W., Zhao, B., Koch, P. M., et al. 2018, A&A, 615, A58 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  119. Yin, C., Priestley, F. D., & Wurster, J. 2021, MNRAS, 504, 2381 [NASA ADS] [CrossRef] [Google Scholar]
  120. Zhao, B., Caselli, P., Li, Z.-Y., et al. 2021, MNRAS, 505, 5142 [NASA ADS] [CrossRef] [Google Scholar]
4

The spatial distribution of N2H+ toward prestellar cores also shows a slightly more extended emission compared to that of NH3 (see, e.g., Tafalla et al. 2002), indicating the possible inheritance of the spatial distributions of their deuterated species.

5

Fukihara et al. (2026) did not consider fragmentation due to graingrain collisions because the relative grain velocity in their calculation is below (<100 m/s) the fragmentation limit (as shown in Kawasaki et al. 2022). See also Lebreuilly et al. (2023) for a discussion on the impact of fragmentation on dust growth.

6

The dedicated model of Keto & Caselli (2010) reproducing the observed molecular line profiles of the L1544 prestellar core demonstrated that L1544 is quasi-statically contracting and is not undergoing a free-fall infall (probably due to the magnetic pressure opposing gravitational free-fall). In this section, we use “infall” to describe the kinematics of cores, where the infall motions correspond to quasi-static contraction for L1544.

7

This relation is compatible with observational results estimating the spatial distribution of the B-field strength toward individual filaments and cores at a given evolutionary stage (Kandori et al. 2018; Hwang et al. 2021; Lê et al. 2024).

Appendix A Fitting results

Figure A.1 shows the N2D+(2 – 1) and pNH2D spectra toward the central pixel of the maps (RAJ2000.0 = 05h04m16.539s and DecJ2000.0 = 25°10′47″54). The red profile shows the best fit model. The velocity resolutions are 0.0379 km/s for N2D+(2 – 1) and 0.0266 km/s for pNH2D. The rest (unsplit) frequencies are 154217.0112MHz for N2D+ and 110153.5940MHz for pNH2D. The Vlsr for both cubes was set to 7.2km/s. All the spectra show a single velocity component.

Thumbnail: Fig. A.1 Refer to the following caption and surrounding text. Fig. A.1

Observed N2D+(2 – 1) (left) and pNH2D (right) spectra in black toward the central position of the map. The best fit obtained with p y speckit is shown in red. The blue profiles are the best fits for all the hyperfines. The results of the fit are indicated in the top right corner of each plot, with Tex the excitation temperature in K, τ the optical depth, V the velocity in km/s, and σv,obs the velocity dispersion in km/s.

Figure A.2 shows the distributions of the 1σ uncertainty on the centroid velocities and on the uncertainty on the velocity difference derived from the p y speckit fit (cf. Section 4). The main uncertainties on the order of ∼ 0.006 km/s are an order of magnitude smaller than the observed velocity difference (cf. Section 5).

Thumbnail: Fig. A.2 Refer to the following caption and surrounding text. Fig. A.2

Left: Distribution of the 1σ uncertainty on the centroid velocity N2D+ and pNH2D derived from the pyspeckit fit. The mean values of these uncertainties, indicated with the vertical lines, are 0.0033 and 0.0056km/s for the N2D+ and pNH2D data points, respectively. Right: Distribution of uncertainty on Vneutral – Vion derived from error propagation. The mean value of the distribution is 0.006 km/s.

Figure A.3 shows the integrated intensity maps and the excitation temperature Tex maps of N2D+ and pNH2D, displaying the highly centrally concentrated emission of the ion-neutral pair. The integrated intensity radial profiles of N2D+ and pNH2D (Figure A.4) are very similar, with only a ∼ 20% larger value for pNH2D within the central part of the core (radii < 0.01 pc). On the Tex maps, N2D+ appears slightly (∼ 25%) more extended compared to that of pNH2D. The mean and standard deviation of the Texneutral/TexionMathematical equation: $T_{\rm ex}^{\rm neutral}/T_{\rm ex}^{\rm ion}$ ratio and the τneutral/τion are 1.03 ± 0.44 and 0.99 ± 0.18 (Figure A.5) further supporting that these two molecules are tracing similar optical depth and densities.

Appendix B Total velocity dispersion

To compare the velocity dispersions of the two molecules of interest N2D+ and pNH2D, we estimate the total velocity dispersion of the mean free particle with a molecular weight of μp = 2.33 in molecular clouds (Kauffmann et al. 2008). We derive the non-thermal velocity dispersion of the gas by subtracting the thermal velocity dispersion from the linewidth measured for each species, assuming that the two contributions are independent of each other and could be added in quadrature (Myers 1983). The thermal velocity dispersion of each species is given by σT(μobs)=kBT/μobsmH,Mathematical equation: $ \sigma_\mathrm{T}(\upmu_{\rm obs})=\sqrt{k_{\rm B}T/\upmu_{\rm obs}m_{\rm H}}, $, where kB is the Boltzmann constant, mH is the hydrogen mass, μobs is the atomic weight of the observed molecule with μobs = 30 for N2D+ and μobs = 18 for pNH2D. We adopted a gas temperature of 10 K which is the mean gas temperature of L1544 at the observed scales and densities (Crapsi et al. 2007; Spezzano et al. 2017).

Thumbnail: Fig. A.3 Refer to the following caption and surrounding text. Fig. A.3

Top: Integrated intensity maps for N2D+ (left) and pNH2D (right). Bottom: Excitation temperature (Tex) maps derived from pixel-per-pixel fitting of the N2D+ (left) and pNH2D ( right) spectra with p y speckit (cf. Section 4). The white contours at 0.8, 1.7, and 2.5 × 1022 cm−2 trace the gas column density as derived from Herschel data (from Spezzano et al. 2017) and are the same on all panels. The white filled circles show the 23″.5 beam size (0.019 pc at the 170 pc distance of L1544) and the white vertical lines indicate the 0.05 pc scale.
Thumbnail: Fig. A.4 Refer to the following caption and surrounding text. Fig. A.4

Integrated intensity radial profile of N2D+ (red) and pNH2D (blue). The profiles are obtained by circularly averaging the radial profiles about the central pixel of the integrated intensity maps (cf. Figure A.3). The vertical bars indicate the standard deviation on the azimuthal average at each radial distance.

The non-thermal velocity dispersion is calculated as σv,NT=σv,obs2−σT2(μobs)Mathematical equation: $\sigma_{\rm v,NT}=\sqrt{\sigma^2_{\rm v,obs}-\sigma^2_\mathrm{T}(\upmu_{\rm obs})}$, where στ is the thermal velocity dispersion of the observed species with στ ∼ 0.053 and 0.068 km/s for N2D+ and pNH2D, respectively and σobs is the observed velocity dispersion for each molecule derived from the fit (Section 4). The total velocity dispersion of the mean free particle (μp = 2.33) and thermal velocity dispersion σT=kBT/μpmH∼0.19±0.02Mathematical equation: $\sigma_\mathrm{T}=\sqrt{k_{\rm B}T/\upmu_{\rm p} m_{\rm H}}\sim0.19\pm0.02$ km/s for T = 10 ± 2 K is given by σv,tot=σv,NT2+σT2Mathematical equation: $\sigma_{\rm v,tot}=\sqrt{\sigma^2_{\rm v,NT}+\sigma^2_\mathrm{T}}$. We derive maps of σv,tot and σv,NT for both N2D+ and pNH2D. Figure B.1 shows the distributions of σv,tot and σv,NT. Figure B.2 shows the map of the difference of the ion-neutral total velocity dispersion (δσv,tot=σv,totneutral−σv,totionMathematical equation: $\delta \sigma_{\rm v,tot}=\sigma_{\rm v,tot}^{\rm neutral}-\sigma_{\rm v,tot}^{\rm ion}$) and the histograms of δσv,tot and δσv,NT.

Appendix C Comparing with N2D+ (1 – 0)

We here compare the results of the pyspeckit fits of the pNH2D, N2 D+ (2 – 1), and N2 D+(1 – 0) PPV cubes. The rest frequency of N2D+(1 – 0) is 77.1096162 MHz and the spectral resolution of the cube is 0.076 km/s. All the cubes have been smoothed to the coarser 34" angular resolution of N2D+(1 – 0). We do not resample the data spectrally and correct for the channel response to derive σv=σv,obs2−(Δchannel/2.355)2Mathematical equation: $\sigma_{\rm v}=\sqrt{\sigma_{\rm v,obs}^2-(\Delta_{\rm channel}/2.355)^2}$, where σv,obs is the velocity dispersion derived from the fit and Δchannel the velocity resolution of the PPV cube. The critical densities computed for 10 K are 0.8 × 105, 1.4 × 105, and 4 × 105, for N2D+ (1 – 0), pNH2D, and N2D+ (2 – 1), respectively.

Thumbnail: Fig. A.5 Refer to the following caption and surrounding text. Fig. A.5

left: Histogram of the Tex ratio of pNH2D and N2D+(2-1). The mean, median, and standard deviation of the distribution are 0.99, 0.97, and 0.18 K, respectively. The inset shows the scatter plot of the Tex values and their uncertainties. The oblique line indicates the 1:1 relation. Right: Similar to the left panel for the τ(0) values. The mean, median, and standard deviation of the distribution are 1.03, 0.98, 0.44, respectively.
Thumbnail: Fig. B.1 Refer to the following caption and surrounding text. Fig. B.1

Left: Histograms of σv,tot for N2D+ in red and pNH2D in blue. The median and standard deviation of the distributions are 0.215 km/s and 0.005 km/s for N2D+ and 0.210km/s and 0.007km/s for pNH2D. Right: Histograms of σv,NT for N2D+ in red and pNH2D in blue. The median and standard deviation of the distributions are 0.103 km/s and 0.012 km/s for N2D+ and 0.091 km/s and 0.016km/s for pNH2 D.
Thumbnail: Fig. B.2 Refer to the following caption and surrounding text. Fig. B.2

Left: Map of the difference between the neutral (pNH2D) and the ion (N2D+) total velocity dispersion (δσv,tot=σv,totneutral−σv,totionMathematical equation: $\delta \sigma_{\rm v,tot}=\sigma_{\rm v,tot}^{\rm neutral}-\sigma_{\rm v,tot}^{\rm ion}$). Right: Histogram of δσv,tot in black and of δσv,NT in gray. The vertical dashed black and gray lines indicate the mean values for the δσv,tot and δσv,NT distributions, respectively. The mean and standard deviation for δσv,tot are –0.004 km/s and 0.006 km/s, and for δσv,NT are –0.007 km/s and 0.014 km/s, respectively.

Figure C.1 and Table C.1 compare the observed properties of pNH2D, N2D+(2 – 1), and N2D+(1 – 0). The standard deviation of the distributions of Texneutral/TexionMathematical equation: $T_{\rm ex}^{\rm neutral}/T_{\rm ex}^{\rm ion}$ and the τneutral/τion ratios when the ion is N2D+ (1 – 0) are broader compared to those when the ion is N2D+(2 – 1), suggesting that the N2D+(2 – 1) emission is more closely correlated to that of pNH2D. The total velocity dispersion of N2D+ (1 – 0) is broader (by 0.013 km/s) than that of pNH2D, which may hint at the more turbulent gas and slightly lower density gas envelop that N2D+(1 – 0) may be tracing as opposed to that traced by N2D+(2 – 1) and pNH2D.

Thumbnail: Fig. C.1 Refer to the following caption and surrounding text. Fig. C.1

Top-left: Histrograms of the Texn/TexiMathematical equation: $T_{\rm ex}^n/T_{\rm ex}^i$ ratio values, where the ion is N2D+(2 – 1) in black and N2D+(1-0) in blue. The velocity data cubes are all smoothed to the spatial resolution of N2D+(1 – 0) with HPBW of 34″. The mean and standard deviation of the distributions are given in Table C.1. The inset shows the scatter plot of the Tex values and their uncertainties. The oblique line indicates the 1:1 relation. Top-right: Similar as the top-left panel for the τ values. Bottom-left: Scatter plot of the velocity dispersion. The oblique solid and dashed blue lines indicate the 1:1 and the 0.012 km/s relations, respectively. Bottom-right: Scatter plot of the centroid velocity of N2D+(2 – 1) in red, pNH2D in blue, and N2D+(1 – 0) in purple versus the NH2Mathematical equation: $N_{\rm H_2}$ column density derived from Herschel for data points with NH2 > 1.7 × 1022 cm−2. The vertical gray lines show the fitting uncertainties of Vlsr.
Table C.1

Table summarizing the mean and standard deviation of the distributions shown in Fig. C.1.

Appendix D 3D differentiable analytical model of collapsing core

We have developed a 3D analytical model of a prestellar core controlled by a set of parameters. The versors u of the velocity vector field at each position x = (x,y, z) are determined by the 3 × 3 matrix M (i.e., 9 parameters) as u = Mx. For example, a symmetric free-fall is described by M = −I, where I is the identity matrix. The velocity of the neutral molecule v is scaled from the versors u assuming a Gaussian radial profile controlled by three parameters, v=ua0exp⁡[−(r−a1)2/a2]Mathematical equation: $\mathbf{v}=\mathbf{u}\,a_0 \exp\left[-(r - a_1)^2 / a_2\right]$, where r = ||x||2. In other words, M determines the direction of the global vector field, while the Gaussian radial profile determines its magnitude. For the ion velocity, we have four configurations: (i) same velocity, i.e., vi = v, (ii) drifted velocity, vi = (1 + δ) v, (iii) different Gaussian profile but same M, and (iv) completely independent velocity (i.e., different Gaussian profile and different M). Analogously, we describe the profile abundances of the two molecules with two Gaussian functions, controlled by 3 parameters n = b0exp [-(r′ − b1)2/b2], where r′=x2+y2+εz2Mathematical equation: $r'=\sqrt{x^2 + y^2 + \varepsilon\,z^2}$ is the radius of an ellipsoid with the prolateness/oblateness controlled by an additional parameter ε. We have (i) a configuration with the same density profiles for both molecules, only scaled by a relative parameterized factor, and (ii) completely independent density profiles. Finally, the rotation of the object with respect to the observer is determined by two additional parameters, representing the intrinsic rotation angles (one of the three angles is degenerate due to the ellipsoid symmetry). All these parameters determine the velocity vector and the density at each position x.

To mimic the line emission of the given molecule, we use the available line velocity differences and relative intensities from p y speckit. The lines are added using a Gaussian profile and a broadening parameter to form the spectra at the given position. The obtained intensity is scaled by the molecule abundance at the given position. The final observed spectrum is computed by summing the intensity in a uniform grid of velocity channels, an approach that mimics an optically thin radiative transfer. The result is a spectrum for each desired projected map point, i.e., a PPV cube.

The code obtained from the previous analytical model is written in JAX, a differentiable, GPU-based, and just-in-time compiled Python library. This allows us to produce a PPV cube with minimal computational impact (100-1000 models per second depending on the configurations on an NVIDIA A100 80GB), but, more importantly, to obtain the gradients of each PPV element with respect to each input parameter, thereby enabling us to optimize the parameters to minimize the difference between the observed PPV and the predicted PPV. To this aim, we use Optax (DeepMind et al. 2020) with an Adam optimizer (Kingma & Ba 2015). The code is capable of optimizing both the neutral and ion PPV cubes simultaneously.

Although the model is capable of reproducing the observations with a high degree of accuracy, it is important to note that the model is an idealized representation of L1544 and, therefore, cannot reproduce some of the observed features, which are, for example, determined by the asymmetries of the actual core. The detailed model and results are presented in Grassi et al. (2026).

All Tables

Table C.1

Table summarizing the mean and standard deviation of the distributions shown in Fig. C.1.

In the text

All Figures

Thumbnail: Fig. 1 Refer to the following caption and surrounding text. Fig. 1

Centroid velocity maps derived from pixel-per-pixel fitting of the N2 D+ ( top left) and pNH2D (top right) spectra with pyspeckit (cf. Section 4). The white contours at 0.8, 1.7, and 2.5 × 1022 cm−2 trace the gas column density as derived from Herschel data (from Spezzano et al. 2017) and are the same on both panels. The white filled circles show the 23″.5 beam size (0.019 pc at the 170pc distance of L1544) and the white vertical lines indicate the 0.05 pc scale. The excitation temperature maps are shown in Appendix A. The bottom plots show the distribution of the velocity for N2D+ in red and pNH2D in blue (bottom left) and a scatter plot (bottom right). The median values of the distributions indicated by the vertical dashed lines are 7.16 km/s for N2D+ and 7.21 km/s for pNH2D. The oblique solid and dashed blue lines indicate the 1:1 and the −0.05 km/s relations, respectively. The gray error bars on the scatter plot are the ±1σ uncertainties on the centroid velocities derived from the pyspeckit fit. The mean values of these uncertainties are 0.003 and 0.006 km/s for the N2D+ and pNH2D data points, respectively (the histograms of the uncertainties are presented in Appendix A).
In the text
Thumbnail: Fig. 2 Refer to the following caption and surrounding text. Fig. 2

Left : map of the difference between the neutral pNH2D and the ion N2D+ centroid velocity (δVshift = Vneutral – Vion). The filled white circle shows the 23″.5 beam size (0.019 pc at the 170 pc distance of L1544) and the white vertical line indicates the 0.05 pc scale. Right : histogram of δ Vshift. The mean and standard deviation of the δVshift distribution are 0.05 and 0.02 km/s, respectively, where the mean uncertainty on δVshift is 0.006 km/s (cf. Appendix A).
In the text
Thumbnail: Fig. 3 Refer to the following caption and surrounding text. Fig. 3

Scatter plot of the difference between the neutral pNH2D and the ion N2D+ centroid velocity (δVshift = Vneutral – Vion) versus the NH2 column density derived from Herschel and reprojected to the same spatial grid as that of the molecular line data. The scatter in δVshift is larger for smaller NH2 values. The color of the data points and the color bar indicate the difference of the ion-neutral total velocity dispersion (δσv,tot).
In the text
Thumbnail: Fig. A.1 Refer to the following caption and surrounding text. Fig. A.1

Observed N2D+(2 – 1) (left) and pNH2D (right) spectra in black toward the central position of the map. The best fit obtained with p y speckit is shown in red. The blue profiles are the best fits for all the hyperfines. The results of the fit are indicated in the top right corner of each plot, with Tex the excitation temperature in K, τ the optical depth, V the velocity in km/s, and σv,obs the velocity dispersion in km/s.
In the text
Thumbnail: Fig. A.2 Refer to the following caption and surrounding text. Fig. A.2

Left: Distribution of the 1σ uncertainty on the centroid velocity N2D+ and pNH2D derived from the pyspeckit fit. The mean values of these uncertainties, indicated with the vertical lines, are 0.0033 and 0.0056km/s for the N2D+ and pNH2D data points, respectively. Right: Distribution of uncertainty on Vneutral – Vion derived from error propagation. The mean value of the distribution is 0.006 km/s.
In the text
Thumbnail: Fig. A.3 Refer to the following caption and surrounding text. Fig. A.3

Top: Integrated intensity maps for N2D+ (left) and pNH2D (right). Bottom: Excitation temperature (Tex) maps derived from pixel-per-pixel fitting of the N2D+ (left) and pNH2D ( right) spectra with p y speckit (cf. Section 4). The white contours at 0.8, 1.7, and 2.5 × 1022 cm−2 trace the gas column density as derived from Herschel data (from Spezzano et al. 2017) and are the same on all panels. The white filled circles show the 23″.5 beam size (0.019 pc at the 170 pc distance of L1544) and the white vertical lines indicate the 0.05 pc scale.
In the text
Thumbnail: Fig. A.4 Refer to the following caption and surrounding text. Fig. A.4

Integrated intensity radial profile of N2D+ (red) and pNH2D (blue). The profiles are obtained by circularly averaging the radial profiles about the central pixel of the integrated intensity maps (cf. Figure A.3). The vertical bars indicate the standard deviation on the azimuthal average at each radial distance.
In the text
Thumbnail: Fig. A.5 Refer to the following caption and surrounding text. Fig. A.5

left: Histogram of the Tex ratio of pNH2D and N2D+(2-1). The mean, median, and standard deviation of the distribution are 0.99, 0.97, and 0.18 K, respectively. The inset shows the scatter plot of the Tex values and their uncertainties. The oblique line indicates the 1:1 relation. Right: Similar to the left panel for the τ(0) values. The mean, median, and standard deviation of the distribution are 1.03, 0.98, 0.44, respectively.
In the text
Thumbnail: Fig. B.1 Refer to the following caption and surrounding text. Fig. B.1

Left: Histograms of σv,tot for N2D+ in red and pNH2D in blue. The median and standard deviation of the distributions are 0.215 km/s and 0.005 km/s for N2D+ and 0.210km/s and 0.007km/s for pNH2D. Right: Histograms of σv,NT for N2D+ in red and pNH2D in blue. The median and standard deviation of the distributions are 0.103 km/s and 0.012 km/s for N2D+ and 0.091 km/s and 0.016km/s for pNH2 D.
In the text
Thumbnail: Fig. B.2 Refer to the following caption and surrounding text. Fig. B.2

Left: Map of the difference between the neutral (pNH2D) and the ion (N2D+) total velocity dispersion (δσv,tot=σv,totneutral−σv,totionMathematical equation: $\delta \sigma_{\rm v,tot}=\sigma_{\rm v,tot}^{\rm neutral}-\sigma_{\rm v,tot}^{\rm ion}$). Right: Histogram of δσv,tot in black and of δσv,NT in gray. The vertical dashed black and gray lines indicate the mean values for the δσv,tot and δσv,NT distributions, respectively. The mean and standard deviation for δσv,tot are –0.004 km/s and 0.006 km/s, and for δσv,NT are –0.007 km/s and 0.014 km/s, respectively.
In the text
Thumbnail: Fig. C.1 Refer to the following caption and surrounding text. Fig. C.1

Top-left: Histrograms of the Texn/TexiMathematical equation: $T_{\rm ex}^n/T_{\rm ex}^i$ ratio values, where the ion is N2D+(2 – 1) in black and N2D+(1-0) in blue. The velocity data cubes are all smoothed to the spatial resolution of N2D+(1 – 0) with HPBW of 34″. The mean and standard deviation of the distributions are given in Table C.1. The inset shows the scatter plot of the Tex values and their uncertainties. The oblique line indicates the 1:1 relation. Top-right: Similar as the top-left panel for the τ values. Bottom-left: Scatter plot of the velocity dispersion. The oblique solid and dashed blue lines indicate the 1:1 and the 0.012 km/s relations, respectively. Bottom-right: Scatter plot of the centroid velocity of N2D+(2 – 1) in red, pNH2D in blue, and N2D+(1 – 0) in purple versus the NH2Mathematical equation: $N_{\rm H_2}$ column density derived from Herschel for data points with NH2 > 1.7 × 1022 cm−2. The vertical gray lines show the fitting uncertainties of Vlsr.
In the text

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