How Volatile is ENSO?

The El Niños Southern Oscillations (ENSO) is a periodical phenomenon of climatic interannual variability which could be measured through either the Southern Oscillation Index (SOI) or the Sea Surface Temperature (SST) Index. The main purpose of this paper is to analyze these two indexes in order to capture ENSO volatility. The empirical results show that both the ARMA(1,1)-GARCH(1,1) and ARMA(3,2)-GJR(1,1) models are suitable for modelling ENSO volatility. Moreover, 1998 is a turning point for the volatility of SOI, and the ENSO volatility has became stronger since 1998 which indicates that the ENSO strength has increased.GARCH;Volatility;EGARCH;GJR;ENSO;SOI;SOT

Finite Form of the Quintuple Product Identity

The celebrated quintuple product identity follows surprisingly from an almost-trivial algebraic identity, which is the limiting case of the terminating q-Dixon formula.Comment: 1 pag

Resolving SNR 0540-6944 from LMC X-1 with Chandra

We examine the supernova remnant (SNR) 0540-697 in the Large Magellanic Cloud (LMC) using data from the Chandra ACIS. The X-ray emission from this SNR had previously been hidden in the bright emission of nearby X-ray binary LMC X-1; however, new observations with Chandra can finally reveal the SNR's structure and spectrum. We find the SNR to be a thick-shelled structure about 19 pc in diameter, with a brightened northeast region. Spectral results suggest a temperature of 0.31 keV and an X-ray luminosity (0.3-3.0 keV) of 8.4 x 10^33 erg/s. We estimate an age of 12,000-20,000 yr for this SNR, but note that this estimate does not take into account the possibility of cavity expansion or other environmental effects.Comment: 8 pages, 2 GIF figures. Submitted to ApJL. Replaced with minor revisions from referee comment

A Critical Examination of Hypernova Remnant Candidates in M101. II. NGC 5471B

NGC 5471B has been suggested to contain a hypernova remnant because of its extraordinarily bright X-ray emission. To assess its true nature, we have obtained high-resolution images in continuum bands and nebular lines with the Hubble Space Telescope, and high-dispersion long-slit spectra with the Kitt Peak National Observatory 4-m echelle spectrograph. The images reveal three supernova remnant (SNR) candidates in the giant HII region NGC 5471, with the brightest one being the 77x60 pc shell in NGC 5471B. The Ha velocity profile of NGC 5471B can be decomposed into a narrow component (FWHM = 41 km/s) from the background HII region and a broad component (FWHM = 148 km/s) from the SNR shell. Using the brightness ratio of the broad to narrow components and the Ha flux measured from the WFPC2 Ha image, we derive an Ha luminosity of (1.4+-0.1)x10^39 ergs/s for the SNR shell. The [SII]6716,6731 doublet ratio of the broad velocity component is used to derive an electron density of ~700 cm^-3 in the SNR shell. The mass of the SNR shell is thus 4600+-500 Mo. With a \~330 km/s expansion velocity implied by the extreme velocity extent of the broad component, the kinetic energy of the SNR shell is determined to be 5x10^51 ergs. This requires an explosion energy greater than 10^52 ergs, which can be provided by one hypernova or multiple supernovae. Comparing to SNRs in nearby active star formation regions, the SNR shell in NGC 5471B appears truly unique and energetic. We conclude that the optical observations support the existence of a hypernova remnant in NGC 5471B.Comment: 27 pages, 9 figures, to appear in May 2002 issue of The Astronomical Journa