On the scalar nonet in the extended Nambu Jona-Lasinio model

We discuss the lightest scalar resonances, $f_0(600)$, $\kappa(800)$, $a_0(980)$ and $f_0(980)$ in the extended Nambu Jona-Lasinio model. We find that the model parameters can be tuned, but unnaturally, to accommodate for those scalars except the $f_0(980)$. We also discuss problems encountered in the K Matrix unitarization approximation by using $N_c$ counting technique.Comment: 23 pages 3 eps figures, To appear in Nucl. Phys.

On indecomposable modules over the Virasoro algebra

It is proved that an indecomposable Harish-Chandra module over the Virasoro algebra must be (i) a uniformly bounded module, or (ii) a module in Category $\cal O$, or (iii) a module in Category ${\cal O}^-$, or (iv) a module which contains the trivial module as one of its composition factors.Comment: 5 pages, Latex, to appear in Science in China

The first 40 million years of circumstellar disk evolution: the signature of terrestrial planet formation

We characterize the first 40 Myr of evolution of circumstellar disks through a unified study of the infrared properties of members of young clusters and associations with ages from 2 Myr up to ~ 40 Myr: NGC 1333, NGC 1960, NGC 2232, NGC 2244, NGC 2362, NGC 2547, IC 348, IC 2395, IC 4665, Chamaeleon I, Orion OB1a and OB1b, Taurus, the \b{eta} Pictoris Moving Group, \r{ho} Ophiuchi, and the associations of Argus, Carina, Columba, Scorpius-Centaurus, and Tucana-Horologium. Our work features: 1.) a filtering technique to flag noisy backgrounds, 2.) a method based on the probability distribution of deflections, P(D), to obtain statistically valid photometry for faint sources, and 3.) use of the evolutionary trend of transitional disks to constrain the overall behavior of bright disks. We find that the fraction of disks three or more times brighter than the stellar photospheres at 24 {\mu}m decays relatively slowly initially and then much more rapidly by ~ 10 Myr. However, there is a continuing component until ~ 35 Myr, probably due primarily to massive clouds of debris generated in giant impacts during the oligarchic/chaotic growth phases of terrestrial planets. If the contribution from primordial disks is excluded, the evolution of the incidence of these oligarchic/chaotic debris disks can be described empirically by a log-normal function with the peak at 12 - 20 Myr, including ~ 13 % of the original population, and with a post-peak mean duration of 10 - 20 Myr.Comment: accepted for publication, the Astrophysical Journal (2017

A Study of H2 Emission in Three Bipolar Proto-Planetary Nebulae: IRAS 16594-4656, Hen 3-401, and Rob 22

We have carried out a spatial-kinematical study of three proto-planetary nebulae, IRAS 16594-4656, Hen 3-401, and Rob 22. High-resolution H2 images were obtained with NICMOS on the HST and high-resolution spectra were obtained with the Phoenix spectrograph on Gemini-South. IRAS 16594-4656 shows a "peanut-shaped" bipolar structure with H2 emission from the walls and from two pairs of more distant, point-symmetric faint blobs. The velocity structure shows the polar axis to be in the plane of the sky, contrary to the impression given by the more complex visual image and the visibility of the central star, with an ellipsoidal velocity structure. Hen 3-401 shows the H2 emission coming from the walls of the very elongated, open-ended lobes seen in visible light, along with a possible small disk around the star. The bipolar lobes appear to be tilted 10-15 deg with respect to the plane of the sky and their kinematics display a Hubble-like flow. In Rob 22, the H2 appears in the form of an "S" shape, approximately tracing out the similar pattern seen in the visible. H2 is especially seen at the ends of the lobes and at two opposite regions close to the unseen central star. The axis of the lobes is nearly in the plane of the sky. Expansion ages of the lobes are calculated to be approximately 1600 yr (IRAS 16594-4656), 1100 yr (Hen 3-401), and 640 yr (Rob 22), based upon approximate distances

What Sets the Radial Locations of Warm Debris Disks?

The architectures of debris disks encode the history of planet formation in these systems. Studies of debris disks via their spectral energy distributions (SEDs) have found infrared excesses arising from cold dust, warm dust, or a combination of the two. The cold outer belts of many systems have been imaged, facilitating their study in great detail. Far less is known about the warm components, including the origin of the dust. The regularity of the disk temperatures indicates an underlying structure that may be linked to the water snow line. If the dust is generated from collisions in an exo-asteroid belt, the dust will likely trace the location of the water snow line in the primordial protoplanetary disk where planetesimal growth was enhanced. If instead the warm dust arises from the inward transport from a reservoir of icy material farther out in the system, the dust location is expected to be set by the current snow line. We analyze the SEDs of a large sample of debris disks with warm components. We find that warm components in single-component systems (those without detectable cold components) follow the primordial snow line rather than the current snow line, so they likely arise from exo-asteroid belts. While the locations of many warm components in two-component systems are also consistent with the primordial snow line, there is more diversity among these systems, suggesting additional effects play a role