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Fumitaka Nakamura

Publications and source records attributed to Fumitaka Nakamura.

At least 37 records · Page 2Linked to original sources

Q-band Line Survey Observations toward a Carbon-chain-rich Clump in the Serpens South Region

We have conducted Q-band (30 GHz $-$ 50 GHz) line survey observations toward a carbon-chain emission peak in the Serpens South cluster-forming region with the extended Q-band (eQ) receiver installed on the Nobeyama 45 m radio telescope. Approximately 180 lines have been detected including tentative detection, and these lines are attributed to 52 molecules including isotopologues. It has been found that this position is rich in carbon-chain species as much as Cyanopolyyne Peak in Taurus Molecular Cloud-1 (TMC-1 CP), suggesting chemical youth. Not only carbon-chain species, but several complex organic molecules (CH$_3$OH, CH$_3$CHO, HCCCHO, CH$_3$CN, and tentatively C$_2$H$_3$CN) have also been detected, which is similar to the chemical complexity found in evolved prestellar cores. The HDCS/H$_2$CS ratio has been derived to be $11.3 \pm 0.5$ %, and this value is similar to the prestellar core L1544. The chemically young features that are similar to the less-dense starless core TMC-1 CP ($10^4$ cm$^{-3}$ $-$ $10^5$ cm$^{-3}$) and chemically evolved characters which resemble the dense prestellar core L1544 ($\sim 10^6$ cm$^{-3}$) mean that the clump including the observed position is a pre-cluster clump without any current star formation activity.

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Accretion vs. Core-Filament Collision: Implications for Streamer Formation in Per-emb-2

Recent millimeter and submillimeter observations have unveiled elongated and asymmetric structures around protostars. These structures, referred to as streamers, often exhibit coherent velocity gradients, seemingly indicating a directed gas flow towards the protostars. However, their origin and role in star formation remain uncertain. A protostellar core Per-emb-2, located in Barnard 1, has a relatively large streamer with $10^4$ au, which is more prominent in emission from carbon chain molecules. We aim to unveil the formation mechanism of this streamer. We conducted mapping observations towards Per-emb-2 using the NRO 45-m telescope. We targeted carbon chain molecular lines such as CCS, HC$_3$N, and HC$_5$N. Using astrodendro, we identified one protostellar and four starless cores, including three new detections, on the Herschel map. The starless and protostellar cores are more or less gravitationally bound. We discovered strong CCS and HC$_3$N emissions extending from the north to the south, appearing to bridge the gap between the protostellar core and the starless core north of it. This bridge spans $3\times 10^4$ au with the velocities from 6.5 to 7.0 km s$^{-1}$. The bridge has the velocity gradient opposite to the streamer. Thus, the streamer is unlikely to be connected to this bridge, suggesting that the streamer does not have an accretion origin. We propose that a collision between a spherical core and the filament has shaped the density structure in this region, consequently triggering star formation within the head-tail-shaped core. In this core-filament collision (CFC) scenario, the collision appears to have fragmented the filament into two structures. The streamer is a bow structure, while the bridge is a remnant of the shock-compressed filament. Thus, we conclude that the Per-emb-2 streamer does not significantly contribute to the mass accumulation towards the protostar.

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Magnetic Fields in Massive Star-forming Regions (MagMaR): Unveiling an Hourglass Magnetic Field in G333.46-0.16 using ALMA

The contribution of the magnetic field to the formation of high-mass stars is poorly understood. We report the high-angular resolution ($\sim0.3^{\prime\prime}$, 870 au) map of the magnetic field projected on the plane of the sky (B$_\mathrm{POS}$) towards the high-mass star forming region G333.46$-$0.16 (G333), obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) at 1.2 mm as part of the Magnetic Fields in Massive Star-forming Regions (MagMaR) survey. The B$_\mathrm{POS}$ morphology found in this region is consistent with a canonical ``hourglass'' which suggest a dynamically important field. This region is fragmented into two protostars separated by $\sim1740$ au. Interestingly, by analysing H$^{13}$CO$^{+}$ ($J=3-2$) line emission, we find no velocity gradient over the extend of the continuum which is consistent with a strong field. We model the B$_\mathrm{POS}$, obtaining a marginally supercritical mass-to-flux ratio of 1.43, suggesting an initially strongly magnetized environment. Based on the Davis-Chandrasekhar-Fermi method, the magnetic field strength towards G333 is estimated to be 5.7 mG. The absence of strong rotation and outflows towards the central region of G333 suggests strong magnetic braking, consistent with a highly magnetized environment. Our study shows that despite being a strong regulator, the magnetic energy fails to prevent the process of fragmentation, as revealed by the formation of the two protostars in the central region.

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Digging into the Interior of Hot Cores with ALMA (DIHCA). IV. Fragmentation in High-mass Star-Forming Clumps

Fragmentation contributes to the formation and evolution of stars. Observationally, high-mass stars are known to form multiple-star systems, preferentially in cluster environments. Theoretically, Jeans instability has been suggested to determine characteristic fragmentation scales, and thermal or turbulent motion in the parental gas clump mainly contributes to the instability. To search for such a characteristic fragmentation scale, we have analyzed ALMA 1.33 mm continuum observations toward 30 high-mass star-forming clumps taken by the Digging into the Interior of Hot Cores with ALMA (DIHCA) survey. We have identified 573 cores using the dendrogram algorithm and measured the separation of cores by using the Minimum Spanning Tree (MST) technique. The core separation corrected by projection effects has a distribution peaked around 5800 au. In order to remove biases produced by different distances and sensitivities, we further smooth the images to a common physical scale and perform completeness tests. Our careful analysis finds a characteristic fragmentation scale of $\sim$7000 au, comparable to the thermal Jeans length of the clumps. We conclude that thermal Jeans fragmentation plays a dominant role in determining the clump fragmentation in high-mass star-forming regions, without the need of invoking turbulent Jeans fragmentation.

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An ultra wide-band, high-sensitivity Q-band receiver for single-dish telescopes, eQ: rest frequency determination of CCS ($J_N$ = $4_3$-$3_2$) and SO ($J_N$ = $1_0$-$0_1$), and high-redshift CO ($J$ = 1-0) detection

We report on the development and commissioning of a new Q-band receiver for the Nobeyama 45-m telescope, covering 30--50 GHz with a receiver noise temperature of about 15 K. We name it eQ (extended Q-band) receiver. The system noise temperatures for observations are measured to be $\sim$ 30 K at 33 GHz and $\sim$ 75 K at 45 GHz. The Half-Power-Beam-Width (HPBW) is around 38\arcsec at 43 GHz. To enhance the observation capability, we tested the smoothed bandpass calibration technique and demonstrated the observation time can be significantly reduced compared to the standard position switch technique. The wide-bandwidth capability of this receiver provides precise determination of rest frequencies for molecular transitions with an accuracy of a few kHz through simultaneous observations of multiple transitions. Particularly, we determined the rest frequency of SO ($J_N$ = $1_0$--$0_1$) to be 30.001542 GHz, along with the rest frequency of CCS ($J_N$ = $4_3$--$3_2$) being 45.379033 GHz, adopting CCS ($J_N$ = $3_2$--$2_1$) at 33.751370 GHz as a reference line. The SO profile shows a double peak shape at the Cyanopolyyne Peak (CP) position of the Taurus Molecular Cloud-1 (TMC-1). The SO peaks coincide well with the CCS sub-components located near the outer parts of the TMC-1 filament. We interpret that the gravitational infall of TMC-1 generates shocks which enhance the SO abundance. The TMC-1 map shows that carbon-chain molecules are more abundant in the southern part of the filament, whereas SO is more abundant in the northern part. The eQ's excellent sensitivity allowed us to detect faint CO ($J$ = 1--0) spectra from the high-redshift object at a redshift of 2.442. Our receiver is expected to open new avenues for high-sensitivity molecular line observations in the Q-band.

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INvestigations of massive Filaments ANd sTar formation (INFANT). I. Core Identification and Core Mass Function

Filamentary structures are ubiquitously found in high-mass star-forming clouds. To investigate the relationship between filaments and star formation, we carry out the INFANT (INvestigations of massive Filaments ANd sTar formation) survey, a multi-scale, multi-wavelength survey of massive filamentary clouds with ALMA band 3/band 6 and VLA K band. In this first paper, we present the ALMA band 6 continuum observations toward a sample of 8 high-mass star forming filaments. We covered each target with approximately rectangular mosaic field of view with two 12-m array configurations, achieving an angular resolution of $\sim$0.6" (2700 AU at 4.5 kpc) and a continuum rms of $\sim$0.1 mJy/beam ($\sim$0.06 Msun in gas mass assuming 15 K). We identify cores using the getsf and astrodendro and find the former is more robust in terms of both identification and measuring flux densities. We identify in total 183 dense cores (15--36 cores in each cloud) and classify their star formation states via outflow and warm gas tracers. The protostellar cores are statistically more massive than the prestellar cores, possibly indicating further accretion onto cores after formation of protostars. For the high-mass end ($M_\text{core}$ $>$ 1.5 Msun) of the core mass function (CMF) we derive a power-law index of $-$1.15 $\pm$ 0.12 for the whole sample, and $-$1.70 $\pm$ 0.25 for the prestellar population. We also find a steepening trend in CMF with cloud evolution ($-$0.89 $\pm$ 0.15 for the young group v.s. $-$1.44 $\pm$ 0.25 for the evolved group) and discuss its implication for cluster formation.

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The ALMA Survey of 70 $μ$m Dark High-mass Clumps in Early Stages (ASHES). XI. Statistical Study of Early Fragmentation

Fragmentation during the early stages of high-mass star formation is crucial for understanding the formation of high-mass clusters. We investigated fragmentation within thirty-nine high-mass star-forming clumps as part of the Atacama Large Millimeter/submillimeter Array (ALMA) Survey of 70 $μ$m Dark High-mass Clumps in Early Stages (ASHES). Considering projection effects, we have estimated core separations for 839 cores identified from the continuum emission and found mean values between 0.08 and 0.32 pc within each clump. We find compatibility of the observed core separations and masses with the thermal Jeans length and mass, respectively. We also present sub-clump structures revealed by the 7 m-array continuum emission. Comparison of the Jeans parameters using clump and sub-clump densities with the separation and masses of gravitationally bound cores suggests that they can be explained by clump fragmentation, implying the simultaneous formation of sub-clumps and cores within rather than a step-by-step hierarchical fragmentation. The number of cores in each clump positively correlates with the clump surface density and the number expected from the thermal Jeans fragmentation. We also find that the higher the fraction of protostellar cores, the larger the dynamic range of the core mass, implying that the cores are growing in mass as the clump evolves. The ASHES sample exhibits various fragmentation patterns: aligned, scattered, clustered, and sub-clustered. Using the Q-parameter, which can help to distinguish between centrally condensed and subclustered spatial core distributions, we finally find that in the early evolutionary stages of high-mass star formation, cores tend to follow a subclustered distribution.

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Dense Core Collisions in Molecular Clouds: Formation of Streamers and Binary Stars

Dense core collisions, previously regarded as minor in star formation, are proposed to play a significant role in structure formation around protostellar envelopes and binary formation. Using archival data of nearby star-forming regions, we determine the frequencies of core collisions. Our calculations reveal that a typical core is likely to undergo multiple interactions with other cores throughout its lifetime. To further investigate the core collision process, we employ adaptive mesh refinement hydrodynamic simulations with sink particles. Our simulations demonstrate that following the formation of a protostar within a gravitationally-unstable core, the merging core's accreting gas gives rise to a rotationally-supported circumstellar disk. Meanwhile, the region compressed by the shock between the cores develops into asymmetric arms that connect with the disk. Gas along these arms tends to migrate inward, ultimately falling toward the protostar. One of the arms, a remnant of the shock-compressed region, dominates over the second core gas, potentially exhibiting a distinct chemical composition. This is consistent with recent findings of large-scale streamers around protostars. Additionally, we found that collisions with velocities of $\sim$ 1.5 km s$^{-1}$ result in the formation of a binary system, as evidenced by the emergence of a sink particle within the dense section of the shocked layer. Overall, dense core collisions are highlighted as a critical process in creating $10^3$ au-scale streamers around protostellar systems and binary stars.

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Observations of high-order multiplicity in a high-mass stellar protocluster

The dominant mechanism forming multiple stellar systems in the high-mass regime (M$_\ast \gtrsim $ 8 $M_{\odot}$) remained unknown because direct imaging of multiple protostellar systems at early phases of high-mass star formation is very challenging. High-mass stars are expected to form in clustered environments containing binaries and higher-order multiplicity systems. So far only a few high-mass protobinary systems, and no definitive higher-order multiples, have been detected. Here we report the discovery of one quintuple, one quadruple, one triple and four binary protostellar systems simultaneously forming in a single high-mass protocluster, G333.23--0.06, using Atacama Large Millimeter/submillimeter Array high-resolution observations. We present a new example of a group of gravitationally bound binary and higher-order multiples during their early formation phases in a protocluster. This provides the clearest direct measurement of the initial configuration of primordial high-order multiple systems, with implications for the in situ multiplicity and its origin. We find that the binary and higher-order multiple systems, and their parent cores, show no obvious sign of disk-like kinematic structure. We conclude that the observed fragmentation into binary and higher-order multiple systems can be explained by core fragmentation, indicating its crucial role in establishing the multiplicity during high-mass star cluster formation.

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The ALMA Survey of 70 μm Dark High-mass Clumps in Early Stages (ASHES). X: Hot Gas Reveals Deeply Embedded Star Formation

Massive infrared dark clouds (IRDCs) are considered to host the earliest stages of high-mass star formation. In particular, 70 $μ$m dark IRDCs are the colder and more quiescent clouds. At a scale of about 5000 au using formaldehyde (H2CO) emission, we investigate the kinetic temperature of dense cores in 12 IRDCs obtained from the pilot ALMA Survey of 70 $μ$m dark High-mass clumps in Early Stages (ASHES). Compared to 1.3 mm dust continuum and other molecular lines, such as C18O and deuterated species, we find that H2CO is mainly sensitive to low-velocity outflow components rather than to quiescent gas expected in the early phases of star formation. The kinetic temperatures of these components range from 26 to 300 K. The Mach number reaches about 15 with an average value of about 4, suggesting that the velocity distribution of gas traced by H2CO is significantly influenced by a supersonic non-thermal component. In addition, we detect warm line emission from HC3N and OCS in 14 protostellar cores, which requires high excitation temperatures (Eu/k ~ 100 K). These results show that some of the embedded cores in the ASHES fields are in an advanced evolutionary stage, previously unexpected for 70 $μ$m dark IRDCs.

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Digging into the Interior of Hot Cores with ALMA: Spiral Accretion into the High-mass Protostellar Core G336.01-0.82

We observed the high-mass star-forming core G336.01-0.82 at 1.3 mm and 0.05'' (~150 au) angular resolution with the Atacama Large Millimeter/submillimeter Array (ALMA) as part of the Digging into the Interior of Hot Cores with ALMA (DIHCA) survey. These high-resolution observations reveal two spiral streamers feeding a circumstellar disk at opposite sides in great detail. Molecular line emission from CH$_3$OH shows velocity gradients along the streamers consistent with infall. Similarly, a flattened envelope model with rotation and infall implies a mass larger than 10 M$_\odot$ for the central source and a centrifugal barrier of 300 au. The location of the centrifugal barrier is consistent with local peaks in the continuum emission. We argue that gas brought by the spiral streamers is accumulating at the centrifugal barrier, which can result in future accretion burst events. A total high infall rate of ~$4\times10^{-4}$ M$_\odot$ yr$^{-1}$ is derived by matching models to the observed velocity gradient along the streamers. Their contribution account for 20-50% the global infall rate of the core, indicating streamers play an important role in the formation of high-mass stars.

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Unveiling the Dynamics of Dense Cores in Cluster-Forming Clumps: A 3D MHD Simulation Study of Angular Momentum and Magnetic Field Properties

We conducted isothermal MHD simulations with self-gravity to investigate the properties of dense cores in cluster-forming clumps. Two different setups were explored: a single rotating clump and colliding clumps. We focused on determining the extent to which the formed dense cores inherit the rotation and magnetic field of the parental clump. Our statistical analysis revealed that the alignment between the angular momentum of dense cores, $\bf{L}_{\rm core}$, and the rotational axis of the clump is influenced by the strength of turbulence and the simulation setup. In single rotating clumps, we found that $\bf{L}_{\rm core}$ tends to align with the clump's rotational axis if the initial turbulence is weak. However, in colliding clumps, this alignment does not occur, regardless of the initial turbulence strength. This misalignment in colliding clumps is due to the induced turbulence from the collision and the isotropic gas inflow into dense cores. Our analysis of colliding clumps also revealed that the magnetic field globally bends along the shock-compressed layer, and the mean magnetic field of dense cores, $\bf{B}_{\rm core}$, aligns with it. Both in single rotating clumps and colliding clumps, we found that the angle between $\bf{B}_{\rm core}$ and $\bf{L}_{\rm core}$ is generally random, regardless of the clump properties. We also analyzed the dynamical states of the formed cores and found a higher proportion of unbound cores in colliding clumps. In addition, the contribution of rotational energy was only approximately 5% of the gravitational energy, regardless of the model parameters for both single and colliding cases.

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Chemical Differentiation around Five Massive Protostars Revealed by ALMA -Carbon-Chain Species, Oxygen-/Nitrogen-Bearing Complex Organic Molecules-

We present Atacama Large Millimeter/submillimeter Array Band 3 data toward five massive young stellar objects (MYSOs), and investigate relationships between unsaturated carbon-chain species and saturated complex organic molecules (COMs). An HC$_{5}$N ($J=35-34$) line has been detected from three MYSOs, where nitrogen(N)-bearing COMs (CH$_{2}$CHCN and CH$_{3}$CH$_{2}$CN) have been detected. The HC$_{5}$N spatial distributions show compact features and match with a methanol (CH$_{3}$OH) line with an upper-state energy around 300 K, which should trace hot cores. The hot regions are more extended around the MYSOs where N-bearing COMs and HC$_{5}$N have been detected compared to two MYSOs without these molecular lines, while there are no clear differences in the bolometric luminosity and temperature. We run chemical simulations of hot-core models with a warm-up stage, and compare with the observational results. The observed abundances of HC$_{5}$N and COMs show good agreements with the model at the hot-core stage with temperatures above 160 K. These results indicate that carbon-chain chemistry around the MYSOs cannot be reproduced by warm carbon-chain chemistry, and a new type of carbon-chain chemistry occurs in hot regions around MYSOs.

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The ALMA Survey of 70 μm Dark High-mass Clumps in Early Stages (ASHES). VIII. Dynamics of Embedded Dense Cores

We present the dynamical properties of 294 cores embedded in twelve IRDCs observed as part of the ASHES Survey. Protostellar cores have higher gas masses, surface densities, column densities, and volume densities than prestellar cores, indicating core mass growth from the prestellar to the protostellar phase. We find that ~80% of cores with virial parameter ($α$) measurements are gravitationally bound ($α$< 2). We also find an anti-correlation between the mass and the virial parameter of cores, with massive cores having on average lower virial parameters. Protostellar cores are more gravitationally bound than prestellar cores, with an average virial parameter of 1.2 and 1.5, respectively. The observed non-thermal velocity dispersion (from N$_{2}$D$^{+}$ or DCO$^{+}$) is consistent with simulations in which turbulence is continuously injected, whereas the core-to-core velocity dispersion is neither in agreement with driven nor decaying turbulence simulations. We find no significant increment in the line velocity dispersion from prestellar to protostellar cores, suggesting that dense gas within the core traced by these deuterated molecules is not yet severely affected by turbulence injected from outflow activity at the early evolutionary stages traced in ASHES. The most massive cores are strongly self-gravitating and have greater surface density, Mach number, and velocity dispersion than cores with lower masses. Dense cores have not significant velocity shifts relative to their low-density envelopes, suggesting that dense cores are co-moving with their envelopes. We conclude that the observed core properties are more in line with predictions of ``clump-fed" scenarios rather than with ``core-fed" scenarios.

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The ALMA Survey of 70 $μ$m Dark High-mass Clumps in Early Stages (ASHES). IX. Physical Properties and Spatial Distribution of Cores in IRDCs

The initial conditions found in infrared dark clouds (IRDCs) provide insights on how high-mass stars and stellar clusters form. We have conducted high-angular resolution and high-sensitivity observations toward thirty-nine massive IRDC clumps, which have been mosaicked using the 12m and 7m arrays from the Atacama Large Millimeter/submillimeter Array (ALMA). The targets are 70 $μ$m dark massive (220-4900 $M_\odot$), dense ($>$10$^4$ cm$^{-3}$), and cold ($\sim$10-20K) clumps located at distances between 2 and 6 kpc. We identify an unprecedented number of 839 cores, with masses between 0.05 and 81 $M_\odot$ using 1.3 mm dust continuum emission. About 55% of the cores are low-mass ($<$1 $M_\odot$), whereas $\lesssim$1% (7/839) are high-mass ($\gtrsim$27 $M_\odot$). We detect no high-mass prestellar cores. The most massive cores (MMC) identified within individual clumps lack sufficient mass to form high-mass stars without additional mass feeding. We find that the mass of the MMCs is correlated with the clump surface density, implying denser clumps produce more massive cores and a larger number of cores. There is no significant mass segregation except for a few tentative detections. In contrast, most clumps show segregation once the clump density is considered instead of mass. Although the dust continuum emission resolves clumps in a network of filaments, some of which consist of hub-filament systems, the majority of the MMCs are not found in the hubs. Our analysis shows that high-mass cores and MMCs have no preferred location with respect to low-mass cores at the earliest stages of high-mass star formation.

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Digging into the Interior of Hot Cores with ALMA (DIHCA). III: The Chemical Link between NH$_{2}$CHO, HNCO, and H$_{2}$CO

We have analyzed the NH$_{2}$CHO, HNCO, H$_{2}$CO, and CH$_{3}$CN ($^{13}$CH$_{3}$CN) molecular lines at an angular resolution of $\sim 0.3''$ obtained by the Atacama Large Millimeter/submillimeter Array (ALMA) Band 6 toward 30 high-mass star-forming regions. The NH$_{2}$CHO emission has been detected in 23 regions, while the other species have been detected toward 29 regions. A total of 44 hot molecular cores (HMCs) have been identified using the moment 0 maps of the CH$_{3}$CN line. The fractional abundances of the four species have been derived at each HMC. In order to investigate pure chemical relationships, we have conducted a partial correlation test to exclude the effect of temperature. Strong positive correlations between NH$_{2}$CHO and HNCO ($ρ=0.89$) and between NH$_{2}$CHO and H$_{2}$CO (0.84) have been found. These strong correlations indicate their direct chemical links; dual-cyclic hydrogen addition and abstraction reactions between HNCO and NH$_{2}$CHO and gas-phase formation of NH$_{2}$CHO from H$_{2}$CO. Chemical models including these reactions can reproduce the observed abundances in our target sources.

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CARMA-NRO Orion Survey: unbiased survey of dense cores and core mass functions in Orion A

The mass distribution of dense cores is a potential key to understand the process of star formation. Applying dendrogram analysis to the CARMA-NRO Orion C$^{18}$O ($J$=1--0) data, we identify 2342 dense cores, about 22 \% of which have virial ratios smaller than 2, and can be classified as gravitationally bound cores. The derived core mass function (CMF) for bound starless cores which are not associate with protostars has a slope similar to Salpeter's initial mass function (IMF) for the mass range above 1 $M_\odot$, with a peak at $\sim$ 0.1 $M_\odot$. We divide the cloud into four parts based on the declination, OMC-1/2/3, OMC-4/5, L1641N/V380 Ori, and L1641C, and derive the CMFs in these regions. We find that starless cores with masses greater than 10 $M_\odot$ exist only in OMC-1/2/3, whereas the CMFs in OMC-4/5, L1641N, and L1641C are truncated at around 5--10 $M_\odot$. From the number ratio of bound starless cores and Class II objects in each subregion, the lifetime of bound starless cores is estimated to be 5--30 free-fall times, consistent with previous studies for other regions. In addition, we discuss core growth by mass accretion from the surrounding cloud material to explain the coincidence of peak masses between IMFs and CMFs. The mass accretion rate required for doubling the core mass within a core lifetime is larger than that of Bondi-Hoyle accretion by a factor of order 2. This implies that more dynamical accretion processes are required to grow cores.

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MHD simulations of dense core collision

We investigated the effect of magnetic fields on the collision process between dense molecular cores. We performed three-dimensional magnetohydrodynamic simulations of collisions between two self-gravitating cores using the Enzo adaptive mesh refinement code. The core was modeled as a stable isothermal Bonnor-Ebert (BE) sphere immersed in uniform magnetic fields. Collisions were characterized by the offset parameter $b$, Mach number of the initial core $\mathcal{M}$, magnetic field strength $B_{0}$, and angle $θ$ between the initial magnetic field and collision axis. For head-on ($b = 0$) collisions, one protostar was formed in the compressed layer. The higher the magnetic field strength, the lower the accretion rate. For models with $b = 0$ and $θ= 90^{\circ}$, the accretion rate was more dependent on the initial magnetic field strength compared with $b = 0$ and $θ= 0^{\circ}$ models. For off-center ($b = 1$) collisions, the higher specific angular momentum increased; therefore, the gas motion was complicated. In models with $b = 1$ and $\mathcal{M} = 1$, the number of protostars and gas motion highly depended on $B_{0}$ and $θ$. For models with $b = 1$ and $\mathcal{M} = 3$, no significant shock-compressed layer was formed and star formation was not triggered.

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