Path-factors involving paths of order seven and nine

In this paper, we show the following two theorems (here $c_{i}(G-X)$ is the number of components $C$ of $G-X$ with $|V(C)|=i$): (i)~If a graph $G$ satisfies $c_{1}(G-X)+\frac{1}{3}c_{3}(G-X)+\frac{1}{3}c_{5}(G-X)\leq \frac{2}{3}|X|$ for all $X\subseteq V(G)$, then $G$ has a $\{P_{2},P_{7}\}$-factor. (ii)~If a graph $G$ satisfies $c_{1}(G-X)+c_{3}(G-X)+\frac{2}{3}c_{5}(G-X)+\frac{1}{3}c_{7}(G-X)\leq \frac{2}{3}|X|$ for all $X\subseteq V(G)$, then $G$ has a $\{P_{2},P_{9}\}$-factor.Comment: 29 pages, 4 figure

A 1000 AU Scale Molecular Outflow Driven by a Protostar with an age of <4000 Years

To shed light on the early phase of a low-mass protostar formation process, we conducted interferometric observations towards a protostar GF9-2 using the CARMA and SMA. The observations have been carried out in the CO J=3-2 line and in the continuum emission at the wavelengths of 3 mm, 1 mm and 850 micron. All the continuum images detected a single point-like source with a radius of 250+/-80 AU at the center of the previously known ~3 Msun molecular cloud core. A compact emission is detected towards the object at the Spitzer MIPS and IRAC bands as well as the four bands at the WISE. Our spectroscopic imaging of the CO line revealed that the continuum source is driving a 1000 AU scale molecular outflow, including a pair of lobes where a collimated "higher" velocity red lobe exists inside a poorly collimated "lower" velocity red lobe. These lobes are rather young and the least powerful ones so far detected. A protostellar mass of M~<0.06 Msun was estimated using an upper limit of the protostellar age of (4+/-1)x10^3 yrs and an inferred non-spherical steady mass accretion rate of ~10^{-5} Msun/yr. Together with results from an SED analysis, we discuss that the outflow system is driven by a protostar whose surface temperature of~3,000K, and that the natal cloud core is being dispersed by the outflow.Comment: 27 pages, 14 figures, accepted for publication in Astrophysical Journa

The Initial Conditions for Gravitational Collapse of a Core: An Extremely Young Low-Mass Class 0 Protostar GF9-2

We present a study of the natal core harboring the class 0 protostar GF9-2 in the filamentary dark cloud GF 9 (d = 200 pc). GF9-2 stands unique in the sense that it shows H2O maser emission, a clear signpost of protostar formation, whereas it does not have a high-velocity large-scale molecular outflow evidenced by our deep search for CO wing emission. These facts indicate that GF9-2 core is early enough after star formation so that it still retains some information of initial conditions for collapse. Our 350 um dust continuum emission image revealed the presence of a protostellar envelope in the center of a molecular core. The mass of the envelope is ~0.6 Msun from the 350 um flux density, while LTE mass of the core is ~3 Msun from moleuclar line observations. Combining visibility data from the OVRO mm-array and the 45m telescope, we found that the core has a radial density profile of $\rho(r)\propto r^{-2}$ for 0.003 < r/pc < 0.08 region. Molecular line data analysis revealed that the velocity width of the core gas increases inward,while the outermost region maintains a velocity dispersion of a few times of the ambient sound speed. The broadened velocity width can be interpreted as infall. Thus, the collapse in GF9-2 is likely to be described by an extension of the Larson-Penston solution for the period after formation of a central star. We derived the current mass accretion rate of ~3E-05 Msun/year from infall velocity of ~ 0.3 km/s at r~ 7000 AU. All results suggest that GF9-2 core has been undergoing gravitational collapse for ~ 5000 years since the formation of central protostar(s), and that the unstable state initiated the collapse ~2E+05 years (the free-fall time) ago.Comment: ApJ Accepted. The preprint including figures with the original quality is available at http://subarutelescope.org/staff/rsf/publication.htm

Low-Mass Star Forming Cores in the GF9 Filament

We carried out an unbiased mapping survey of dense molecular cloud cores traced by the NH3 (1,1) and (2,2) inversion lines in the GF9 filament which contains an extremely young low-mass protostar GF9-2 (Furuya et al. 2006, ApJ, 653, 1369). The survey was conducted using the Nobeyama 45m telescope over a region of ~1.5 deg with an angular resolution of 73". The large-scale map revealed that the filament contains at least 7 dense cores, as well as 3 possible ones, located at regular intervals of ~0.9 pc. Our analysis shows that these cores have kinetic temperatures of $\lesssim$ 10 K and LTE-masses of 1.8 -- 8.2 Msun, making them typical sites of low-mass star formation. All the identified cores are likely to be gravitationally unstable because their LTE-masses are larger than their virial masses. Since the LTE-masses and separations of the cores are consistent with the Jeans masses and lengths, respectively, for the low-density ambient gas, we argue that the identified cores have formed via the gravitational fragmentation of the natal filamentary cloud.Comment: accepted by pas

Warm Extended Dense Gas Lurking At The Heart Of A Cold Collapsing Dense Core

In order to investigate when and how the birth of a protostellar core occurs, we made survey observations of four well-studied dense cores in the Taurus molecular cloud using CO transitions in submillimeter bands. We report here the detection of unexpectedly warm (~ 30 - 70 K), extended (radius of ~ 2400 AU), dense (a few times 10^{5} cm^{-3}) gas at the heart of one of the dense cores, L1521F (MC27), within the cold dynamically collapsing components. We argue that the detected warm, extended, dense gas may originate from shock regions caused by collisions between the dynamically collapsing components and outflowing/rotating components within the dense core. We propose a new stage of star formation, "warm-in-cold core stage (WICCS)", i.e., the cold collapsing envelope encases the warm extended dense gas at the center due to the formation of a protostellar core. WICCS would constitutes a missing link in evolution between a cold quiescent starless core and a young protostar in class 0 stage that has a large-scale bipolar outflow.Comment: Accepted for publication in The Astrophysical Journal Letter

Water Maser Survey toward Low‐Mass Young Stellar Objects in the Northern Sky with the Nobeyama 45 Meter Telescope and the Very Large Array

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Spectroscopic Evidence for Gas Infall in GF9-2

We present spectroscopic evidence for infall motion of gas in the natal cloud core harboring an extremely young low-mass protostar GF9-2. We previously discussed that the ongoing collapse of the GF9-2 core has agreement with the Larson-Penston-Hunter (LPH) theoretical solution for the gravitational collapse of a core (Furuya et al.; paper I). To discuss the gas infall on firmer ground, we have carried out On-The-Fly mapping observations of the HCO+ (1--0) line using the Nobeyama 45m telescope equipped with the 25 Beam Array Receiver System. Furthermore, we observed the HCN (1--0) line with the 45m telescope, and the HCO+ (3--2) line with the Caltech Submillimeter Observatory 10.4 m telescope. The optically thick HCO+ and HCN lines show blueskewed profiles whose deepest absorptions are seen at the peak velocity of optically thin lines, i.e., the systemic velocity of the cloud (paper I), indicating the presence of gas infall toward the central protostar. We compared the observed HCO+ line profiles with model ones by solving the radiative transfer in the core under LTE assumption.We found that the core gas has a constant infall velocity of ~0.5 km/s in the central region, leading to a mass accretion rate of 2.5x10^{-5} Msun/yr. Consequently, we confirm that the gas infall in the GF9-2 core is consistent with the LPH solution.Comment: 13 pages, 5 figure, full resolution version of the figures are available at http://subarutelescope.org/staff/rsf/publication.htm