Forming an O Star via Disk Accretion?

We present a study of outflow, infall, and rotation in a ~10^5 Lsun (solar luminosity) star-forming region, IRAS 18360-0537, with Submillimeter Array (SMA) and IRAM 30m observations. The 1.3 mm continuum map shows a 0.5 pc dust ridge, of which the central compact part has a mass of ~80 Msun (solar mass) and harbors two condensations, MM1 and MM2. The CO (2--1) and SiO (5--4) maps reveal a biconical outflow centered at MM1, which is a hot molecular core (HMC) with a gas temperature of 320+/-50 K and a mass of ~13 Msun. The outflow has a gas mass of 54 Msun and a dynamical timescale of 8,000 yr. The kinematics of the HMC is probed by high-excitation CH3OH and CH3CN lines, which are detected at sub-arcsecond resolution and unveil a velocity gradient perpendicular to the outflow axis, suggesting a disk-like rotation of the HMC. An infalling envelope around the HMC is evidenced by CN lines exhibiting a profound inverse P-Cygni profile, and the estimated mass infall rate, 1.5x10^{-3} Msun/yr, is well comparable to that inferred from the mass outflow rate. A more detailed investigation of the kinematics of the dense gas around the HMC is obtained from the 13CO and C18O (2--1) lines; the position-velocity diagrams of the two lines are consistent with the model of a free-falling and Keplerian-like rotating envelope. The observations suggest that the protostar of a current mass ~10 Msun embedded within MM1 will develop into an O star via disk accretion and envelope infall.Comment: Accepted for publication in the Ap

L-series and their 2-adic and 3-adic valuations at s=1 attached to CM elliptic curves

$L-$series attached to two classical families of elliptic curves with complex multiplications are studied over number fields, formulae for their special values at $s=1,$ bound of the values, and criterion of reaching the bound are given. Let $E_1: y^{2}=x^{3}-D_1 x$ be elliptic curves over the Gaussian field K=\Q(\sqrt{-1}), with $D_1 =\pi_{1} ... \pi_{n}$ or $D_1 =\pi_{1} ^{2}... \pi_{r} ^{2} \pi_{r+1} ... \pi_{n}$, where $\pi_{1}, ..., \pi_{n}$ are distinct primes in $K$. A formula for special values of Hecke $L-$series attached to such curves expressed by Weierstrass $\wp-$function are given; a lower bound of 2-adic valuations of these values of Hecke $L-$series as well as a criterion for reaching these bounds are obtained. Furthermore, let $E_{2}: y^{2}=x^{3}-2^{4}3^{3}D_2^{2}$ be elliptic curves over the quadratic field \Q(\sqrt{-3}) with $D_2 =\pi_{1} ... \pi_{n},$ where $\pi_{1}, ..., \pi_{n}$ are distinct primes of \Q(\sqrt{-3}), similar results as above but for $3-adic$ valuation are also obtained. These results are consistent with the predictions of the conjecture of Birch and Swinnerton-Dyer, and develop some results in recent literature for more special case and for $2-adic$ valuation