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Hong-Li Liu

Publications and source records attributed to Hong-Li Liu.

At least 73 records · Page 4Linked to original sources

The JCMT BISTRO Survey: An 850/450$μ$m Polarization Study of NGC 2071IR in OrionB

We present the results of simultaneous 450 $μ$m and 850 $μ$m polarization observations toward the massive star forming region NGC 2071IR, a target of the BISTRO (B-fields in Star-Forming Region Observations) Survey, using the POL-2 polarimeter and SCUBA-2 camera mounted on the James Clerk Maxwell Telescope. We find a pinched magnetic field morphology in the central dense core region, which could be due to a rotating toroidal disk-like structure and a bipolar outflow originating from the central young stellar object, IRS 3. Using the modified Davis-Chandrasekhar-Fermi method, we obtain a plane-of-sky magnetic field strength of 563$\pm$421 $μ$G in the central $\sim$0.12 pc region from 850 $μ$m polarization data. The corresponding magnetic energy density of 2.04$\times$10$^{-8}$ erg cm$^{-3}$ is comparable to the turbulent and gravitational energy densities in the region. We find that the magnetic field direction is very well aligned with the whole of the IRS 3 bipolar outflow structure. We find that the median value of polarization fractions, 3.0 \%, at 450 $μ$m in the central 3 arcminute region, which is larger than the median value of 1.2 \% at 850 $μ$m. The trend could be due to the better alignment of warmer dust in the strong radiation environment. We also find that polarization fractions decrease with intensity at both wavelengths, with slopes, determined by fitting a Rician noise model, of $0.59 \pm 0.03$ at 450 $μ$m and $0.36 \pm 0.04$ at 850 $μ$m, respectively. We think that the shallow slope at 850 $μ$m is due to grain alignment at the center being assisted by strong radiation from the central young stellar objects.

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An ALMA study of outflow parameters of protoclusters: outflow feedback to maintain the turbulence

With the aim of understanding the role of outflows in star formation, we performed a statistical study of the physical parameters of outflows in eleven massive protoclusters associated with ultra-compact HII regions. A total of 106 outflow lobes are identified in these protoclusters using the ALMA CO (3-2), HCN (4-3) and HCO+ (4-3) line observations. Although the position angles of outflow lobes do not differ in these three tracers, HCN and HCO+ tend to detect lower terminal velocity of the identified outflows compared to CO. The majority of the outflows in our targets are young with typical dynamical time-scales of 10^2-10^4 years, and are mostly composed of low-mass outflows along with at least one high-mass outflow in each target. An anti-correlation of outflow rate with dynamical time-scale indicates that the outflow rate possibly decreases with time. Also, a rising trend of dynamical time-scale with the mass of the associated core hints that the massive cores might have longer accretion histories than the low mass cores. Estimation of different energies in these protoclusters shows that outflows studied here cannot account for the generation of the observed turbulence, but can sustain the turbulence at the current epoch as the energy injection rate from the outflows is similar to the estimated dissipation rate.

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A Low-mass Cold and Quiescent Core Population in a Massive Star Protocluster

Pre-stellar cores represent the initial conditions of star formation. Although these initial conditions in nearby low-mass star-forming regions have been investigated in detail, such initial conditions remain vastly unexplored for massive star-forming regions. We report the detection of a cluster of low-mass starless and pre-stellar core candidates in a massive star protocluster forming cloud, NGC6334S. With the ALMA observations at a $\sim$0.02 pc spatial resolution, we identified 17 low-mass starless core candidates that do not show any evidence of protostellar activity. These candidates present small velocity dispersions, high fractional abundances of NH$_{2}$D, high NH$_{3}$ deuterium fractionations, and are completely dark in the infrared wavelengths from 3.6 up to 70~$μ$m. Turbulence is significantly dissipated and the gas kinematics are dominated by thermal motions toward these candidates. Nine out of the 17 cores are gravitationally bound, and therefore are identified as pre-stellar core candidates. The embedded cores of NGC6334S show a wide diversity in masses and evolutionary stages.

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ATOMS:ALMA Three-millimeter Observations of Massive Star-forming regions -- III :Catalogues of candidate hot molecular cores and Hyper/Ultra compact HII regions

We have identified 453 compact dense cores in 3 mm continuum emission maps in the ATOMS (ALMA Three-millimeter Observations of Massive Star-forming regions) survey, and compiled three catalogues of high-mass star forming cores. One catalogue, referred to as H/UC-HII catalogue, includes 89 cores that enshroud hyper/ultra compact (H/UC) HII regions as characterized by associated compact H40alpha emission. A second catalogue, referred to as pure s-cHMC, includes 32 candidate Hot Molecular Cores (HMCs) showing rich spectra (N>20lines) of complex organic molecules (COMs) but not associated with H/UC-HII regions. The third catalogue, referred to as pure w-cHMC, includes 58 candidate HMCs with relatively low levels of COM richness and not associated with H/UC-HII regions. These three catalogues of dense cores provide an important foundation for future studies of the early stages of high-mass star formation across the Milky Way. We also find that nearly half of H/UC-HII cores are candidate HMCs. From the number counts of COM-containing and H/UC-HII cores, we suggest that the duration of high-mass protostellar cores showing chemically rich features is at least comparable to the lifetime of H/UC-HII regions. For cores in the H/UC-HII catalogue, the width of the H40alpha line increases as the core size decreases, suggesting that the non-thermal dynamical and/or pressure line-broadening mechanisms dominate on the smaller scales of the H/UC-HII cores.

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The JCMT BISTRO Survey: The Distribution of Magnetic Field Strengths towards the OMC-1 Region

Measurement of magnetic field strengths in a molecular cloud is essential for determining the criticality of magnetic support against gravitational collapse. In this paper, as part of the JCMT BISTRO survey, we suggest a new application of the Davis-Chandrasekhar-Fermi (DCF) method to estimate the distribution of magnetic field strengths in the OMC-1 region. We use observations of dust polarization emission at 450 $μ$m and 850 $μ$m, and C$^{18}$O (3-2) spectral line data obtained with the JCMT. We estimate the volume density, the velocity dispersion and the polarization angle dispersion in a box, 40$''$ $\times$ 40$''$ (5$\times$5 pixels), which moves over the OMC-1 region. By substituting three quantities in each box to the DCF method, we get magnetic field strengths over the OMC-1 region. We note that there are very large uncertainties in inferred field strengths, as discussed in detail in this paper. The field strengths vary from 0.8 to 26.4 mG and their mean value is about 6 mG. Additionally, we obtain maps of the mass-to-flux ratio in units of a critical value and the Alfv$\acute{e}$n mach number. The central parts of the BN-KL and South (S) clumps in the OMC-1 region are magnetically supercritical, so the magnetic field cannot support the clumps against gravitational collapse. However, the outer parts of the region are magnetically subcritical. The mean Alfv$\acute{e}$n mach number is about 0.4 over the region, which implies that the magnetic pressure exceeds the turbulent pressure in the OMC 1 region.

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Revealing the diverse magnetic field morphologies in Taurus dense cores with sensitive sub-millimeter polarimetry

We have obtained sensitive dust continuum polarization observations at 850 $μ$m in the B213 region of Taurus using POL-2 on SCUBA-2 at the James Clerk Maxwell Telescope (JCMT), as part of the BISTRO (B-fields in STar-forming Region Observations) survey. These observations allow us to probe magnetic field (B-field) at high spatial resolution ($\sim$2000 au or $\sim$0.01 pc at 140 pc) in two protostellar cores (K04166 and K04169) and one prestellar core (Miz-8b) that lie within the B213 filament. Using the Davis-Chandrasekhar-Fermi method, we estimate the B-field strengths in K04166, K04169, and Miz-8b to be 38$\pm$14 $μ$G, 44$\pm$16 $μ$G, and 12$\pm$5 $μ$G, respectively. These cores show distinct mean B-field orientations. B-field in K04166 is well ordered and aligned parallel to the orientations of the core minor axis, outflows, core rotation axis, and large-scale uniform B-field, in accordance with magnetically regulated star formation via ambipolar diffusion taking place in K04166. B-field in K04169 is found to be ordered but oriented nearly perpendicular to the core minor axis and large-scale B-field, and not well-correlated with other axes. In contrast, Miz-8b exhibits disordered B-field which show no preferred alignment with the core minor axis or large-scale field. We found that only one core, K04166, retains a memory of the large-scale uniform B-field. The other two cores, K04169 and Miz-8b, are decoupled from the large-scale field. Such a complex B-field configuration could be caused by gas inflow onto the filament, even in the presence of a substantial magnetic flux.

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Filament rotation in the California L1482 cloud

We analyze the gas mass distribution, the gas kinematics, and the young stellar object (YSO) content of the California Molecular Cloud (CMC) L1482 filament. We derive a Gaia DR2 YSO distance of 511$^{+17}_{-16}$ pc. We derive scale-free power-laws for the mean gas line-mass (M/L) profiles; we calculate the gravitational potential and field profiles consistent with these. We present IRAM 30 m C$^{18}$O (1-0) (and other tracers) position-velocity (PV) diagrams that exhibit complex velocity twisting and turning structures. We find a rotational profile in C$^{18}$O perpendicular to the southern filament ridgeline. The profile is regular, confined ($r\lesssim0.4$ pc), anti-symmetric, and to first order linear with a break at $r\sim0.25$ pc. The timescales of the inner (outer) gradients are $\sim$0.7 (6.0) Myr. We show that the centripetal force, compared to gravity, increases toward the break; when the ratio of forces approaches unity, the profile turns over, just before filament breakup is achieved. The timescales and relative roles of gravity to rotation indicate that the structure is stable, long lived ($\sim$ a few times 6 Myr), and undergoing outside-in evolution. Moreover, this filament has practically no star formation, a perpendicular Planck plane-of-the-sky (POS) magnetic field morphology, and POS "zig-zag" morphology, which together with the rotation profile lead to the suggestion that the 3D shape is a corkscrew filament with a helical magnetic field. These results, combined with results in Orion and G035.39-00.33, suggest evolution toward higher densities as rotating filaments shed angular momentum. Thus, magnetic fields may be an essential feature of high-mass (M $\sim10^5$ M$_{\odot}$) cloud filament evolution toward cluster formation.

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Extended HNCO, SiO, and HC$_{3}$N emission in 43 southern star-forming regions

We have selected 43 southern massive star-forming regions to study the spatial distribution of HNCO 4$_{04}$-3$_{03}$, SiO 2-1 and HC$_{3}$N 10-9 line emission and to investigate their spatial association with the dust emission. The morphology of HNCO 4$_{04}$-3$_{03}$ and HC$_{3}$N 10-9 agrees well with the dust emission. HC$_{3}$N 10-9 tends to originate from more compact regions than HNCO 4$_{04}$-3$_{03}$ and SiO 2-1. We divided our sources into three groups: those in the Central Molecular Zone (CMZ), those associated with bubbles (Bubble), and the remaining sources, which are termed 'normal star forming regions' (NMSFR). These three groups, subdivided into three different categories with respect to line widths, integrated intensities, and column densities, hint at the presence of different physical and chemical processes. We find that the dust temperature $T_{\rm d}$, and the abundance ratios of $N_{\rm HNCO}/N_{\rm SiO}$ and $N_{\rm HNCO}/N_{\rm HC3N}$ show a decreasing trend towards the central dense regions of CMZ sources, while $N_{\rm HC3N}/N_{\rm SiO}$ moves into the opposite direction. Moreover, a better agreement is found between $T_{\rm d}$ and $N_{\rm HC3N}/N_{\rm SiO}$ in Bubble and NMSFR category sources. Both outflow and inflow activities have been found in eight of the sixteen bubble and NMSFR sources. The low outflow detection rate indicates that in these sources the SiO 2-1 line wing emission is either below our sensitivity limit or that the bulk of the SiO emission may be produced by the expansion of an H{\sc\,ii} region or supernova remnant, which has pushed molecular gas away forming a shock and yielding SiO.

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The JCMT BISTRO survey: alignment between outflows and magnetic fields in dense cores/clumps

We compare the directions of molecular outflows of 62 low-mass Class 0 and I protostars in nearby (<450 pc) star-forming regions with the mean orientations of the magnetic fields on 0.05-0.5 pc scales in the dense cores/clumps where they are embedded. The magnetic field orientations were measured using the JCMT POL-2 data taken by the BISTRO-1 survey and from the archive. The outflow directions were observed with interferometers in the literature. The observed distribution of the angles between the outflows and the magnetic fields peaks between 15 and 35 degrees. After considering projection effects, our results could suggest that the outflows tend to be misaligned with the magnetic fields by 50+/-15 degrees in three-dimensional space and are less likely (but not ruled out) randomly oriented with respect to the magnetic fields. There is no correlation between the misalignment and the bolometric temperatures in our sample. In several sources, the small-scale (1000-3000 au) magnetic fields is more misaligned with the outflows than their large-scale magnetic fields, suggesting that the small-scale magnetic field has been twisted by the dynamics. In comparison with turbulent MHD simulations of core formation, our observational results are more consistent with models in which the energy densities in the magnetic field and the turbulence of the gas are comparable. Our results also suggest that the misalignment alone cannot sufficiently reduce the efficiency of magnetic braking to enable formation of the observed number of large Keplerian disks with sizes larger than 30-50 au.

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The JCMT BISTRO Survey: Magnetic Fields Associated with a Network of Filaments in NGC 1333

We present new observations of the active star-formation region NGC 1333 in the Perseus molecular cloud complex from the James Clerk Maxwell Telescope B-Fields In Star-forming Region Observations (BISTRO) survey with the POL-2 instrument. The BISTRO data cover the entire NGC 1333 complex (~1.5 pc x 2 pc) at 0.02 pc resolution and spatially resolve the polarized emission from individual filamentary structures for the first time. The inferred magnetic field structure is complex as a whole, with each individual filament aligned at different position angles relative to the local field orientation. We combine the BISTRO data with low- and high- resolution data derived from Planck and interferometers to study the multiscale magnetic field structure in this region. The magnetic field morphology drastically changes below a scale of ~1 pc and remains continuous from the scales of filaments (~0.1 pc) to that of protostellar envelopes (~0.005 pc or ~1000 au). Finally, we construct simple models in which we assume that the magnetic field is always perpendicular to the long axis of the filaments. We demonstrate that the observed variation of the relative orientation between the filament axes and the magnetic field angles are well reproduced by this model, taking into account the projection effects of the magnetic field and filaments relative to the plane of the sky. These projection effects may explain the apparent complexity of the magnetic field structure observed at the resolution of BISTRO data toward the filament network.

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ATOMS: ALMA Three-millimeter Observations of Massive Star-forming regions -- II. Compact objects in ACA observations and star formation scaling relations

We report studies of the relationships between the total bolometric luminosity ($L_{\rm bol}$ or $L_{\rm TIR}$) and the molecular line luminosities of $J=1-0$ transitions of H$^{13}$CN, H$^{13}$CO$^+$, HCN, and HCO$^+$ with data obtained from ACA observations in the "ATOMS" survey of 146 active Galactic star forming regions. The correlations between $L_{\rm bol}$ and molecular line luminosities $L'_{\rm mol}$ of the four transitions all appear to be approximately linear. Line emission of isotopologues shows as large scatters in $L_{\rm bol}$-$L'_{\rm mol}$ relations as their main line emission. The log($L_{\rm bol}$/$L'_{\rm mol}$) for different molecular line tracers have similar distributions. The $L_{\rm bol}$-to-$L'_{\rm mol}$ ratios do not change with galactocentric distances ($R_{\rm GC}$) and clump masses ($M_{\rm clump}$). The molecular line luminosity ratios (HCN-to-HCO$^+$, H$^{13}$CN-to-H$^{13}$CO$^+$, HCN-to-H$^{13}$CN and HCO$^+$-to-H$^{13}$CO$^+$) all appear constant against $L_{\rm bol}$, dust temperature ($T_{\rm d}$), $M_{\rm clump}$ and $R_{\rm GC}$. Our studies suggest that both the main lines and isotopologue lines are good tracers of the total masses of dense gas in Galactic molecular clumps. The large optical depths of main lines do not affect the interpretation of the slopes in star formation relations. We find that the mean star formation efficiency (SFE) of massive Galactic clumps in the "ATOMS" survey is reasonably consistent with other measures of the SFE for dense gas, even those using very different tracers or examining very different spatial scales.

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ATOMS: ALMA Three-millimeter Observations of Massive Star-forming regions -- I. Survey description and a first look at G9.62+0.19

The "ATOMS," standing for {\it ALMA Three-millimeter Observations of Massive Star-forming regions}, survey has observed 146 active star forming regions with ALMA Band 3, aiming to systematically investigate the spatial distribution of various dense gas tracers in a large sample of Galactic massive clumps, to study the roles of stellar feedback in star formation, and to characterize filamentary structures inside massive clumps. In this work, the observations, data analysis, and example science of the "ATOMS" survey are presented, using a case study for the G9.62+0.19 complex. Toward this source, some transitions, commonly assumed to trace dense gas, including CS $J = 2-1$, HCO$^+$ $J = 1-0$ and HCN $J = 1-0$, are found to show extended gas emission in low density regions within the clump; less than 25\% of their emission is from dense cores. SO, CH$_3$OH, H$^{13}$CN and HC$_3$N show similar morphologies in their spatial distributions and reveal well the dense cores. Widespread narrow SiO emission is present (over $\sim$1 pc), which may be caused by slow shocks from large--scale colliding flows or H{\sc ii} regions. Stellar feedback from an expanding H{\sc ii} region has greatly reshaped the natal clump, significantly changed the spatial distribution of gas, and may also account for the sequential high-mass star formation in the G9.62+0.19 complex. The ATOMS survey data can be jointly analyzed with other survey data, e.g., "MALT90", "Orion B", "EMPIRE", "ALMA\_IMF", and "ALMAGAL", to deepen our understandings of "dense gas" star formation scaling relations and massive proto-cluster formation.

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KFPA Examinations of Young STellar Object Natal Environments (KEYSTONE): Hierarchical Ammonia Structures in Galactic Giant Molecular Clouds

We present initial results from the K-band focal plane array Examinations of Young STellar Object Natal Environments (KEYSTONE) survey, a large project on the 100-m Green Bank Telescope mapping ammonia emission across eleven giant molecular clouds at distances of $0.9-3.0$ kpc (Cygnus X North, Cygnus X South, M16, M17, MonR1, MonR2, NGC2264, NGC7538, Rosette, W3, and W48). This data release includes the NH$_3$ (1,1) and (2,2) maps for each cloud, which are modeled to produce maps of kinetic temperature, centroid velocity, velocity dispersion, and ammonia column density. Median cloud kinetic temperatures range from $11.4\pm2.2$ K in the coldest cloud (MonR1) to $23.0\pm6.5$ K in the warmest cloud (M17). Using dendrograms on the NH$_3$ (1,1) integrated intensity maps, we identify 856 dense gas clumps across the eleven clouds. Depending on the cloud observed, $40-100\%$ of the clumps are aligned spatially with filaments identified in H$_2$ column density maps derived from SED-fitting of dust continuum emission. A virial analysis reveals that 523 of the 835 clumps ($\sim63\%$) with mass estimates are bound by gravity alone. We find no significant difference between the virial parameter distributions for clumps aligned with the dust-continuum filaments and those unaligned with filaments. In some clouds, however, hubs or ridges of dense gas with unusually high mass and low virial parameters are located within a single filament or at the intersection of multiple filaments. These hubs and ridges tend to host water maser emission, multiple 70$μ$m-detected protostars, and have masses and radii above an empirical threshold for forming massive stars.

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Large-scale periodic velocity oscillation in the filamentary cloud G350.54+0.69

We use APEX mapping observations of 13CO, and C18O (2-1) to investigate the internal gas kinematics of the filamentary cloud G350.54+0.69, composed of the two distinct filaments G350.5-N and G350.5-S. G350.54+0.69 as a whole is supersonic and gravitationally bound. We find a large-scale periodic velocity oscillation along the entire G350.5-N filament with a wavelength of ~1.3 pc and an amplitude of ~0.12 km/s. Comparing with gravitational-instability induced core formation models, we conjecture that this periodic velocity oscillation could be driven by a combination of longitudinal gravitational instability and a large-scale periodic physical oscillation along the filament. The latter may be an example of an MHD transverse wave. This hypothesis can be tested with Zeeman and dust polarization measurements.

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The JCMT BISTRO Survey: The Magnetic Field of the Barnard 1 Star-Forming Region

We present the POL-2 850 $μ$m linear polarization map of the Barnard 1 clump in the Perseus molecular cloud complex from the B-fields In STar-forming Region Observations (BISTRO) survey at the James Clerk Maxwell Telescope. We find a trend of decreasing polarization fraction as a function of total intensity, which we link to depolarization effects towards higher density regions of the cloud. We then use the polarization data at 850 $μ$m to infer the plane-of-sky orientation of the large-scale magnetic field in Barnard 1. This magnetic field runs North-South across most of the cloud, with the exception of B1-c where it turns more East-West. From the dispersion of polarization angles, we calculate a turbulence correlation length of $5.0 \pm 2.5$ arcsec ($1500$ au), and a turbulent-to-total magnetic energy ratio of $0.5 \pm 0.3$ inside the cloud. We combine this turbulent-to-total magnetic energy ratio with observations of NH$_3$ molecular lines from the Green Bank Ammonia Survey (GAS) to estimate the strength of the plane-of-sky component of the magnetic field through the Davis-Chandrasekhar-Fermi method. With a plane-of-sky amplitude of $120 \pm 60$ $μ$G and a criticality criterion $λ_c = 3.0 \pm 1.5$, we find that Barnard 1 is a supercritical molecular cloud with a magnetic field nearly dominated by its turbulent component.

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JCMT BISTRO survey: Magnetic Fields within the Hub-Filament Structure in IC 5146

We present the 850 $μ$m polarization observations toward the IC5146 filamentary cloud taken using the Submillimetre Common-User Bolometer Array 2 (SCUBA-2) and its associated polarimeter (POL-2), mounted on the James Clerk Maxwell Telescope (JCMT), as part of the B-fields In STar forming Regions Observations (BISTRO). This work is aimed at revealing the magnetic field morphology within a core-scale ($\lesssim 1.0$ pc) hub-filament structure (HFS) located at the end of a parsec-scale filament. To investigate whether or not the observed polarization traces the magnetic field in the HFS, we analyze the dependence between the observed polarization fraction and total intensity using a Bayesian approach with the polarization fraction described by the Rice likelihood function, which can correctly describe the probability density function (PDF) of the observed polarization fraction for low signal-to-noise ratio (SNR) data. We find a power-law dependence between the polarization fraction and total intensity with an index of 0.56 in $A_V\sim$ 20--300 mag regions, suggesting that the dust grains in these dense regions can still be aligned with magnetic fields in the IC5146 regions. Our polarization maps reveal a curved magnetic field, possibly dragged by the contraction along the parsec-scale filament. We further obtain a magnetic field strength of 0.5$\pm$0.2 mG toward the central hub using the Davis-Chandrasekhar-Fermi method, corresponding to a mass-to-flux criticality of $\sim$ $1.3\pm0.4$ and an Alfvénic Mach number of $<$0.6. These results suggest that gravity and magnetic field is currently of comparable importance in the HFS, and turbulence is less important.

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Raman sideband cooling of $^{25}$Mg$^+$ -$^{27}$Al$^+$ ions pair and observation of quantum logic spectra

We perform quantum logic spectroscopy (QLS) on $^{27}$Al$^+$ ion $^1$S$_0$ - $^3$P$_1$ transition, which is an important step toward the QLS based $^{27}$Al$^+$ ion optical clock. As a precondition of QLS, both the stretch (STR) mode and the common (COM) mode of the $^{27}$Al$^+$ and $^{25}$Mg$^+$ ions pair are cooled to the vibrational ground state by Raman sideband cooling. The mean phonon number is measured to be 0.10(1) for the STR mode and 0.01(1) for the COM mode, respectively. The heating rate is evaluated to be 13(3) phonons/s for the STR mode and 5.5(1) phonons/s for the COM mode.

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The JCMT BISTRO Survey: The Magnetic Field In The Starless Core $ρ$ Ophiuchus C

We report 850~$μ$m dust polarization observations of a low-mass ($\sim$12 $M_{\odot}$) starless core in the $ρ$ Ophiuchus cloud, Ophiuchus C, made with the POL-2 instrument on the James Clerk Maxwell Telescope (JCMT) as part of the JCMT B-fields In STar-forming Region Observations (BISTRO) survey. We detect an ordered magnetic field projected on the plane of sky in the starless core. The magnetic field across the $\sim$0.1~pc core shows a predominant northeast-southwest orientation centering between $\sim$40$^\circ$ to $\sim$100$^\circ$, indicating that the field in the core is well aligned with the magnetic field in lower-density regions of the cloud probed by near-infrared observations and also the cloud-scale magnetic field traced by Planck observations. The polarization percentage ($P$) decreases with an increasing total intensity ($I$) with a power-law index of $-$1.03 $\pm$ 0.05. We estimate the plane-of-sky field strength ($B_{\mathrm{pos}}$) using modified Davis-Chandrasekhar-Fermi (DCF) methods based on structure function (SF), auto-correlation (ACF), and unsharp masking (UM) analyses. We find that the estimates from the SF, ACF, and UM methods yield strengths of 103 $\pm$ 46 $μ$G, 136 $\pm$ 69 $μ$G, and 213 $\pm$ 115 $μ$G, respectively. Our calculations suggest that the Ophiuchus C core is near magnetically critical or slightly magnetically supercritical (i.e. unstable to collapse). The total magnetic energy calculated from the SF method is comparable to the turbulent energy in Ophiuchus C, while the ACF method and the UM method only set upper limits for the total magnetic energy because of large uncertainties.

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