arXiv subjects

Tie Liu

Publications and source records attributed to Tie Liu.

At least 37 records · Page 2Linked to original sources

arXiv2026

The ALMA-QUARKS survey: Investigating Thermal Feedback of Massive Protostars in Hot Molecular Cores

We identify a sample of 83 spatially resolved hot molecular cores (HMCs) in the QUARKS survey, aiming at investigating thermal feedback from massive stars. Using CH$_3$CN\,(12--11) line emission together with 1.3\,mm continuum data we derive the radial temperature, volume density and \ch3cn{} abundance profiles for the 83 HMCs. Based on the envelope temperature and density profiles, we compute the luminosities of the embedded massive protostars with \radmc{} radiation transfer model. The derived luminosities are comparable (within $\sim1$ dex) to the bolometric luminosities of their natal clumps and show strong correlations with several core-scale properties, including the HMC mass ($Log[ M_\mathrm{env}] = 1.01\,Log [L_\star] - 4.80$), the inner core radius (the flat radius of Plummer-like volume density profile) ($Log[a] = 0.46\,Log[L_\star] + 0.52$) and the central density $ (Log[n_c] = -0.55 Log[L_\star] +10.47) $. These empirical relations provide useful observational constraints for physical models of protostellar objects. Importantly, we find a strong positive correlation between the massive protostellar luminosity and the local thermal Jeans mass. The derived Jeans masses, $M_\mathrm{Jeans}$, exceed the HMC masses $M_\mathrm{env}$, with the average $M_\mathrm{Jeans}$ being two times larger than the average $M_\mathrm{env}$. This provides observational evidence that thermal feedback from massive protostars can effectively suppress further fragmentation of HMCs, thereby promoting massive star formation. In addition, the positive correlation between massive protostellar luminosity and natal clump mass suggests that more massive clumps preferentially host more luminous protostars, leading to stronger thermal feedback.

astro-ph.GA↗

arXiv2026

ALMA-QUARKS view of W49N: Multipolar episodic outflow associated with the most energetic Galactic water maser

We present a detailed investigation of a multipolar episodic molecular outflow in the mini-starburst region W49N, which hosts the most luminous water maser in the Galaxy. Using high-resolution ($\sim$0.3 arcsec) Atacama Large Millimeter/submillimeter Array (ALMA) observations of the $\mathrm{^{12}CO}$ emission as part of the ALMA-QUARKS survey, we analyze the morphology and kinematics of the outflow. Our observations reveal four newly identified outflow lobes in addition to the previously known central bipolar jet. These lobes appear more jet-like rather than exhibiting wide opening angles. Based on the $\mathrm{^{12}CO}$ (2-1) and $\mathrm{^{13}CO}$ (2-1) emission, we provide a more reliable estimate of the outflow's physical parameters, confirming it as one of the most energetic outflows in the Galaxy. Notably, these newly discovered lobes exhibit chains of knots, a characteristic signature of episodic ejection. Furthermore, two of the lobes display prominent S-shaped wiggles, suggestive of a precessing jet. The discovery of these features -- commonly observed in outflows from low-mass protostars -- in such an extreme massive star-forming environment provides compelling evidence that some underlying physical mechanisms for launching outflows are conserved across a wide range of stellar masses.

astro-ph.GA↗

arXiv2026

The Keplerian disk, envelope, and streamers surrounding an early O-type protostar in the Sagittarius C cloud of the Central Molecular Zone

Disk-mediated accretion is central to theories of massive star formation, setting the initial conditions for their evolution. Yet observations of Keplerian disks around early O-type protostars remain scarce, as they are often blended into complex surrounding structures. We report ALMA Band 6 observations (300 au resolution) of an accretion disk surrounding a high-mass protostar in the Sagittarius C (Sgr C) cloud in the Central Molecular Zone (CMZ) around the Galactic Center. We identify spectral lines and analyze the spatial distribution of the emission of the complex organic molecules. We use a dynamical model with an inner Keplerian disk and an outer free-fall envelope to fit the three-dimensional position-position-velocity data of the stacked CH$_3$OCHO molecular lines and constrain the mass of the central protostar to be $\sim40^{+2}_{-3} M_{\odot}$. The fitting results additionally show that the disk has a centrifugal radius at about 1300 au. Considering the infall velocity, radius, and mass of the envelope, we estimate the accretion rate from the envelope onto the disk to be $\sim7\times 10^{-3}\ M_{\odot}\,\mathrm{yr^{-1}}$. We also identify spiral-like structures in the disk that can be described by free-falling streamers. Our results highlight the critical role of accretion disks and streamers in the mass accumulation of early O-type stars in the CMZ.

astro-ph.GA↗

arXiv2026

Observations of DNC and DCO$^+$ toward the $\int$-shaped Filament and Starless Cores in the Orion Molecular Clouds

Although the deuterium fraction is known to be a powerful evolutionary tracer, its variation within individual molecular cloud cores is still poorly understood. The northern $\int$-shaped filament and 20 individual starless cores in the Orion A and B clouds were mapped in the deuterated molecules of DNC and DCO$^+$ with the Receiver 7BEE installed on the Nobeyama 45~m radio telescope. In a ~ 5' X 30' map of the northern $\int$-shaped filament in the Orion A cloud, the DNC emission is detected over the filament, whereas the DCO$^+$ emission is localized toward OMC-3, the northernmost region of the filament. The difference in distribution between DNC and DCO$^+$ can be attributed to that between N- and C-bearing molecules as previously suggested by Tatematsu et al. High DNC/HN$^{13}$C column density ratios were observed in OMC-2 and OMC-3, and low ratios in OMC-1. It seems that OMC-2 and OMC-3 still contain molecular gas close to the onset of star formation. In 3' X 3' maps of the individual starless cores in Orion, the column density ratios of DNC/HN$^{13}$C and DCO$^+$/H$^{13}$CO$^+$ are found to be rather constant locally within each core, although the core-to-core variation is not small. Similar timescales of deuterization, depletion, and dynamical evolution might explain the locally constant ratio.

astro-ph.GA↗

arXiv2026

Pairing Regularization for Mitigating Many-to-One Collapse in GANs

Mode collapse remains a fundamental challenge in training generative adversarial networks (GANs). While existing works have primarily focused on inter-mode collapse, such as mode dropping, intra-mode collapse-where many latent variables map to the same or highly similar outputs-has received significantly less attention. In this work, we propose a pairing regularizer jointly optimized with the generator to mitigate the many-to-one collapse by enforcing local consistency between latent variables and generated samples. We show that the effect of pairing regularization depends on the dominant failure mode of training. In collapse-prone regimes with limited exploration, pairing encourages structured local exploration, leading to improved coverage and higher recall. In contrast, under stabilized training with sufficient exploration, pairing refines the generator's induced data density by discouraging redundant mappings, thereby improving precision without sacrificing recall. Extensive experiments on both toy distributions and real-image benchmarks demonstrate that the proposed regularizer effectively complements existing stabilization techniques by directly addressing intra-mode collapse.

cs.LG↗

arXiv2026

Tracking Protostellar Variability in Massive Protoclusters with ALMA: I. Insights from QUARKS and MaMMOtH

Millimeter/submillimeter variability is often attributed to dynamical disk-mediated accretion, yet detection is limited to low-mass protostars in nearby clouds. Recent observations have also revealed significant (sub)millimeter variability in high-mass protostars, but the confirmed cases are scarce and lack systematic monitoring. In this work, we analyzed multi-epoch Atacama Large Millimeter/submillimeter Array (ALMA) Band 6 (1.3 mm) continuum observations of 22 massive protoclusters, with epoch separations ranging from a few hours to more than two years, while achieving a consistent angular resolution of approximately 0.3 arcsec. These data allow us to track variability of protostars across a broader mass range and in an environment markedly different from nearby clouds. Using a custom processing pipeline for data reduction, image alignment, and relative flux calibration, we achieve high-precision flux measurements and, for the first time, investigate millimeter variability in massive protoclusters based on interferometric data in a statistical manner. Applying the astrodendro algorithm, we identified 383 condensations and tracked their variations in peak intensities. Standard deviation analysis and difference maps reveal five variable sources, corresponding to a lower limit of 1.3% on the variable fraction. Among these, I13111-6228 stands out as it hosts a hypercompact H II region that exhibits a 68% increase in continuum peak intensity over one year, with an uncertainty of 2%.

astro-ph.GA↗

arXiv2026

Q/W-band Observations toward Starless Cores in Orion (QWOSCO) I. Overview, Isotopologues, Isomers, and Complex Organics

Molecular inventories in starless cores are powerful tools for probing the physical and chemical structures at the earliest stages of star formation. Wide-band spectral scans are invaluable for obtaining a comprehensive view of the chemical composition. In this paper, we present the first results from the project Q/W-band Observations toward Starless Cores in Orion (QWOSCO), which uses the Yebes 40-m telescope to survey 23 starless cores in the Orion cloud at the Q (31.0--50.5 GHz) and W (71.1--91.4 GHz) bands with a total bandwidth of 40 GHz. We detect approximately 40 molecular species and derive their column densities, with each species exhibiting a characteristic spread of roughly one order of magnitude. The derived isomer and isotopologue column density ratios, including A/E, ortho/para, cyclic/linear, HNC/HCN, 12C/13C, 14N/15N, 16O/18O, 32S/34S, and D/H, are consistent with expectations for starless environments. Our results together with the literature suggest that the complex organic molecules (COMs) CH3OH and CH3CHO are both likely ubiquitous in starless cores. The column density ratio of CH3CHO with respect to CH3OH in starless cores are comparable or lower by a factor of around 25 than those in hot corinos at the protostellar stages if the CH3OH column density is directly derived or rescaled from that of 13CH3OH, respectively. Accordingly, we discuss the possible roles of methanol opacity and chemical mechanisms across the starless and protostellar stages.

astro-ph.GA↗

arXiv2026

The ALMA-QUARKS Survey: Evidence of an Explosive Molecular Outflow in IRAS 15520--5234

We present a study of the massive protocluster IRAS 15520$-$5234, which displays evidence of an explosive molecular outflow that unleashed a kinetic energy of at least 10$^{48}$ erg. The protocluster contains 16 dense cores detected in the ALMA band 6 continuum emission maps, having masses in the range from 0.2 to 11.0 M$_{\odot}$. Our analysis of CO $(2-1)$ emission reveals 28 well collimated outflow fingers, the majority of which follow a Hubble-Lemaître velocity law. The outflow fingers show no preferred orientation in the plane of sky and emerge from a common center of origin. We estimate the total mass, momentum, and kinetic energy of the outflow fingers and find that the values are at least one order of magnitude higher than the typical bipolar outflows associated with massive protostars. The morphology and kinematics of the outflow fingers suggest that the outflow associated with IRAS 15520$-$5234 is explosive in nature. We calculate the dynamical age of the explosive event to be approximately 6550 years. Additionally, we estimate the frequency of such explosive outflows in the Galaxy, which is one event every 83 years. Finally, we speculate that the rearrangement of masses within the massive protocluster and the dynamical interaction among the massive cores may result in the formation of such an energetic event.

astro-ph.GA↗

arXiv2026

B-fields And dust in interstelLar fiLAments using Dust POLarization (BALLAD-POL): VI. Grain alignment mechanisms in the massive quiescent filament G16.96+0.27 using dust polarization observations from JCMT/POL-2

Dust polarization induced by aligned non-spherical grains acts as an important tool to trace the magnetic field (B-field) morphologies and strengths in molecular clouds and constrain grain properties and their alignment mechanisms. The widely accepted grain alignment theory is the alignment induced by RAdiative Torques (RATs). In this work, we investigate grain alignment mechanisms in a massive, quiescent and filamentary Infrared Dark Cloud G16.96+0.27 using thermal dust polarization observation with JCMT/POL-2 at 850 $μ$m. We observe the so-called phenomenon of polarization hole attributed to the decrease in polarization fraction in denser regions of higher total intensity and gas density. Our study finds that B-field tangling effect is minimal to cause the polarization hole, and the dominant factor is the reduction in grain alignment efficiency in denser regions, consistent with RAT mechanism. To test RAT theory, we calculate various quantities describing grain alignment, including minimum size of aligned grains, magnetic and magnetic relaxation parameter, and show that RAT mechanism can explain observational data. Our study also reveals evidence for magnetically-enhanced RAT (M-RAT) mechanism required to explain the observed high polarization fractions of above 10 % in the outer regions of the filament. Finally, we perform detailed modeling of thermal dust polarization using $\mathrm{DustPOL\_py}$ based on M-RAT theory and find that the modeling could successfully reproduce the observational data when maximum grain size is around 0.45 $μ$m accompanied by an increase in grain axial ratio, along with the consideration of variations in the magnetic field's inclination angle with the line of sight.

astro-ph.GA↗

arXiv2026

KCFRC: Kinematic Collision-Aware Foothold Reachability Criteria for Legged Locomotion

Legged robots face significant challenges in navigating complex environments, as they require precise real-time decisions for foothold selection and contact planning. While existing research has explored methods to select footholds based on terrain geometry or kinematics, a critical gap remains: few existing methods efficiently validate the existence of a non-collision swing trajectory. This paper addresses this gap by introducing KCFRC, a novel approach for efficient foothold reachability analysis. We first formally define the foothold reachability problem and establish a sufficient condition for foothold reachability. Based on this condition, we develop the KCFRC algorithm, which enables robots to validate foothold reachability in real time. Our experimental results demonstrate that KCFRC achieves remarkable time efficiency, completing foothold reachability checks for a single leg across 900 potential footholds in an average of 2 ms. Furthermore, we show that KCFRC can accelerate trajectory optimization and is particularly beneficial for contact planning in confined spaces, enhancing the adaptability and robustness of legged robots in challenging environments.

cs.RO↗

arXiv2026

Digging into the Interior of Hot Cores with ALMA (DIHCA). VI. The Formation of Low-mass Multiple Systems in High-mass Cluster-forming Regions

Most stars form in multiple systems, with profound implications in numerous astronomical phenomena intrinsically linked to multiplicity. However, our knowledge about the process on how multiple stellar systems form is incomplete and biased toward nearby molecular clouds forming only low-mass stars, which are unrepresentative of the stellar population in the Galaxy. Most stars form within dense cores in clusters alongside high-mass stars (>8 M$_{\odot}$), as likely the Sun did. Here we report deep ALMA 1.33 mm dust continuum observations at ~160 au spatial resolution, revealing 72 low-mass multiple systems embedded in 23 high-mass cluster-forming regions, as part of the Digging into the Interior of Hot Cores with ALMA (DIHCA) survey. We find that the companion separation distribution presents a distinct peak at ~1200 au, in contrast to the one at ~4000 au observed in nearby low-mass regions. The shorter fragmentation scale can be explained by considering the higher pressure exerted by the surrounding medium, which is higher than the one in low-mass regions, due to the larger turbulence and densities involved. Because the peak of the companion separation distribution occurs at much larger scales than the expected disk sizes, we argue that the observed fragmentation is produced by turbulent core fragmentation. Contrary as predicted, the multiplicity fraction remains constant as the stellar density increases. We propose that in the extremely dense environments where high-mass stars form, dynamical interactions play an important role in disrupting weakly bound systems.

astro-ph.GA↗

arXiv2026

ATOMS-QUARKS survey: Inflow and infall in massive protocluster G318.049+00.086: Evidence of competitive accretion

We present a gas kinematic study of the massive protocluster G318.049+00.086. The protocluster is reported to contain 12 prestellar core candidates and 4 protostellar cores. Filamentary structures are identified using the 1.3 mm dust continuum map, with four of them converge into a dense central region, forming a hub-filament system (HFS). High velocity gradients (10 - 20 km s$^{-1}$ pc$^{-1}$) derived from PV analysis of H$^{13}$CO$^{+}$ emission along three of those filaments are suggestive of mass inflow onto the central hub. A mass inflow rate higher than $10^{3}$ M$_{\odot}$ Myr$^{-1}$ along the filaments is indicating that the central hub is capable of forming massive star(s). Investigation of H$^{13}$CO$^{+}$ and CCH spectral profiles revealed the majority of the cores having the characteristic blue asymmetric line profiles, typical signature of gravitational collapse. The remaining few cores showed red asymmetric profiles, indicative of gas expansion. Also, the derived mass infall rates for the protostellar cores in hub-region is significantly higher in comparison to those located along the filaments. The mass-radius relationship of the cores revealed that the cores with red profiles reside in the massive star formation regime. However, the global velocity gradient along the filaments suggests that these particular cores are losing material to the hub. Our results are supporting a competitive accretion scenario of massive star formation where gas is expected to be funnelled from less gravitationally dominant cores to the cores located at the gravitationally favorable position.

astro-ph.GA↗

arXiv2026

Probing Star-Forming Properties via ALMA Observations of Massive Protocluster IRAS 15596-5301

To deepen our understanding of star-forming properties, we studied a massive protocluster IRAS 15596-5301 using ALMA 870 um and 3 mm data. High-resolution 870 um data reveal 34 dense cores, including 3 hot molecular cores, with subsequent line surveys detecting 22 molecular species toward them. Two velocity components (I15596-red/I15596-blue) were found in the averaged H13CO+(1-0) spectrum, and two filaments were identified from velocity-resolved integrated intensity maps. A spatial overlap between the two filaments was observed, and this overlapping region exhibits a distinct bridge-shaped feature in the position-velocity diagram constructed along the entire filamentary structures. Combined with the reduced H13CO+/HCO+ ratio in the overlapping region and the three-dimensional position-position-velocity cube data, we conclude that a non-head-on collision occurs between the edges of the two filamentary structures in IRAS 15596-5301. Cluster analysis demonstrates that clusters located in the collision region host more evolved chemical rich dense cores than their counterparts in other regions. Our results thus indicate that star formation in I15596 is triggered or accelerated by a mild non-head-on collision between two filaments.

astro-ph.GA↗

arXiv2026

CH3CCH as a thermometer in warm molecular gas

Kinetic temperature is a fundamental parameter in molecular clouds. Symmetric top molecules, such as NH$_3$ and CH$_3$CCH, are often used as thermometers. However, at high temperatures, NH$_3$(2,2) can be collisionally excited to NH$_3$(2,1) and rapidly decay to NH$_3$(1,1), which can lead to an underestimation of the kinetic temperature when using rotation temperatures derived from NH$_3$(1,1) and NH$_3$(2,2). In contrast, CH$_3$CCH is a symmetric top molecule with lower critical densities of its rotational levels than those of NH$_3$, which can be thermalized close to the kinetic temperature at relatively low densities of about 10$^{4}$ cm$^{-3}$. To compare the rotation temperatures derived from NH$_3$(1,1)$\&$(2,2) and CH$_3$CCH rotational levels in warm molecular gas, we used observational data toward 55 massive star-forming regions obtained with Yebes 40m and TMRT 65m. Our results show that rotation temperatures derived from NH$_3$(1,1)$\&$(2,2) are systematically lower than those from CH$_3$CCH 5-4. This suggests that CH$_3$CCH rotational lines with the same $J$+1$\rightarrow$$J$ quantum number may be a more reliable thermometer than NH$_3$(1,1)$\&$(2,2) in warm molecular gas located in the surroundings of massive young stellar objects or, more generally, in massive star-forming regions.

astro-ph.GA↗

arXiv2026

MAJORS II: HCO+& HCN Abundances in W40

We present observations of HCN and HCO$^+$ J = $3 - 2$ in the central $424'' \times 424''$ region of the W40 massive star forming region. The observations were taken as part of a pilot project for the MAJORS large program at the JCMT telescope. By incorporating prior knowledge of N(H$_2$) and $T_K$, assuming a constant density, and using the RADEX radiative transfer code we found that the HCN and HCO$^+$ abundances range from $X$(HCN) = $0.4-7.0 \times 10^{-8}$ and $X$(HCO$^+$) = $0.4-7.3 \times 10^{-9}$. Additional modelling using the NAUTILUS chemical evolution code, that takes H$_2$ density variations into account, however, suggests the HCN and HCO$^+$ abundances may be fairly constant. Careful modelling of three different positions finds $X$(HCN) = $1.3-1.7 \times 10^{-8}$, $X$(HCO$^+$) = $1.3-3.1 \times 10^{-9}$. Cross-comparison of the two models also provides a crude estimate of the gas density producing the HCN and HCO$^+$ emission, with H$_2$ densities in the range $5 \times 10^4 - 5 \times 10^5$ cm$^{-3}$, suggesting that the HCN and HCO$^+$ emission does indeed arise from dense gas. High UV intensity (e.g. $G_o >$ a few thousand) has no effect on the abundances in regions where the visual extinction is large enough to effectively shield the gas from the UV field. In regions where $A_V < 6$, however, the abundance of both species is lowered due to destructive reactions with species that are directly affected by the radiation field.

astro-ph.GA↗

arXiv2026

The ALMA-ATOMS survey: Methanol emission in a large sample of hot molecular cores

Methanol (CH$_{3}$OH) is a key complex organic molecule (COM) in the interstellar medium, widely used as a tracer of dense gas and hot molecular cores (HMCs). Using high-resolution ALMA observations from the ATOMS survey, we investigate the excitation and abundance of methanol nuclear spin isomers and their relationship to chemical complexity in massive star-forming cores. We identify 20 methanol transitions, including A- and E-type lines in the v=0 state and E-type lines in the v$_{t}$=1 state, and detect 94 HMC candidates. Rotational temperature analysis under the LTE assumption yields average values of 194 $\pm$ 33 K for CH$_{3}$OH-E v$_{t}$=1, 178 $\pm$ 33 K for CH$_{3}$OH-A v=0, and 75 $\pm$ 33K for CH$_{3}$OH-E v=0. Emission from COMs other than methanol is detected in 87 of the 94 cores, with the CH$_{3}$OH-E v$_{t}$=1 line intensity showing a strong correlation with the channel detection ratio (CDR). These results demonstrate that CH$_{3}$OH-E v$_{t}$=1 lines are reliable tracers of HMCs and chemical complexity, and that the CDR provides a robust indicator of molecular richness. The temperature difference between A- and E-type methanol transitions is driven by anomalously strong J(2,J-2)$-$J(-1,J-1) lines, highlighting the importance of analyzing methanol symmetry types separately.

astro-ph.GA↗

arXiv2026

Spectuner-D1: Spectral Line Fitting of Interstellar Molecules Using Deep Reinforcement Learning

Spectral lines from interstellar molecules provide crucial insights into the physical and chemical conditions of the interstellar medium. Traditional spectral line analysis relies heavily on manual intervention, which becomes impractical when handling the massive datasets produced by modern facilities like ALMA. To address this challenge, we introduce a novel deep reinforcement learning framework to automate spectral line fitting. Using observational data from ALMA, we train a neural network that maps both molecular spectroscopic data and observed spectra to physical parameters such as excitation temperature and column density. The neural network predictions can serve as initial estimates and be further refined using a local optimizer. Our method achieves consistent fitting results compared to global optimization with multiple runs, while reducing the number of forward modeling runs by an order of magnitude. We apply our method to pixel-level fitting for an observation of the G327.3-0.6 hot core and validate our results using XCLASS. We perform the fitting for typical complex organic molecules of hot cores, including CH$_3$OH, CH$_3$OCHO, CH$_3$OCH$_3$, C$_2$H$_5$CN, and C$_2$H$_3$CN. For a 100 $\times$ 100 region covering 5 GHz bandwidth, the fitting process requires 4.9 to 41.9 minutes using a desktop with 16 cores and one consumer-grade GPU card.

astro-ph.GA↗

arXiv2026

HOPS-288: A Laboratory for Complex Organics in Proto-multiple Systems

Complex organic molecules (COMs) in young stellar objects (YSOs) have attracted significant attention in recent years due to their potential connection to pre-biotic chemistry and their utility as tracers of warm or shocked gas components. Proto-binary and multiple systems with close separations are particularly valuable targets for investigating chemical inheritance and reaction, as their members are expected to form from similar material in their parental cloud. We present ALMA observations of the hierarchical proto-triple system HOPS-288, focusing on the physical structure, kinematics, and COM compositions. The system is treated as a proto-binary system consisting of HOPS-288-A and HOPS-288-B due to the limited spatial resolutions, with a separation of 200~au. Three COM-rich features are revealed: two hot corinos associated with the two members, rich in a variety of COMs, and an intervening component between the two members traced by CH$_3$OH and tentatively by CH$_3$CHO. The hot corino in HOPS-288-A exhibits rotational features and might trace a disk. The hot corino in HOPS-288-B is also possibly exhibiting rotational motion. The intervening component could possibly trace a shocked region in the circumbinary disk or a bridge between the two members. The column densities of COMs, including $^{13}$CH$_3$OH, CH$_2$DOH, CH$_3$CHO, HCOOCH$_3$, C$_2$H$_5$OH, $^{13}$CH$_3$CN, and NH$_2$CHO, are broadly similar between the two sources, possibly suggesting the complex organic similarities among proto-binary/multiple systems. Given the complexity of the studied physical structures, further detailed investigations will be essential to confirm this result.

astro-ph.SR↗