Tangential Motions and Spectroscopy within NGC 6720, the Ring Nebula

We have combined recent Hubble Space Telescope WFPC2 images in the [O III] 5007 and [N II] 6583 lines with similar images made 9.557 years earlier to determine the motion of the Ring Nebula within the plane of the sky. Scaled ratio images argue for homologous expansion, that is, larger velocities scale with increasing distance from the central star. The rather noisy pattern of motion of individual features argues for the same conclusion and that the silhouetted knots move at the same rate as the surrounding gas. These tangential velocities are combined with information from a recent high resolution radial velocity study to determine a dynamic distance, which is in basic agreement with the distance determined from the parallax of the central star. We have also obtained very high signal to noise ratio moderate resolution spectra (9.4 Angstrom) along the major and minor axes of the nebula and from this determined the electron temperatures and density in the multiple ionization zones present. These results confirm the status of the Ring Nebula as one of the older planetary nebulae, with a central star transitioning to the white dwarf cooling curve. (Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA Contract No. NAS 5-26555 and the San Pedro Martir Observatory operated by the Universidad Nacional Autonoma de Mexico.)Comment: Astronomical Journal, in pres

A Keck High Resolution Spectroscopic Study of the Orion Nebula Proplyds

We present the results of spectroscopy of four bright proplyds in the Orion Nebula obtained at a velocity resolution of 6 km/s. After careful isolation of the proplyd spectra from the confusing nebular radiation, the emission line profiles are compared with those predicted by realistic dynamic/photoionization models of the objects. The spectral line widths show a clear correlation with ionization potential, which is consistent with the free expansion of a transonic, ionization-stratified, photoevaporating flow. Fitting models of such a flow simultaneously to our spectra and HST emission line imaging provides direct measurements of the proplyd size, ionized density and outflow velocity. These measurements confirm that the ionization front in the proplyds is approximately D-critical and provide the most accurate and robust estimate to date of the proplyd mass loss rate. Values of 0.7E-6 to 1.5E-6 Msun/year are found for our spectroscopic sample, although extrapolating our results to a larger sample of proplyds implies that 0.4E-6 Msun/year is more typical of the proplyds as a whole. In view of the reported limits on the masses of the circumstellar disks within the proplyds, the length of time that they can have been exposed to ionizing radiation should not greatly exceed 10,000 years - a factor of 30 less than the mean age of the proplyd stars. We review the various mechanisms that have been proposed to explain this situation, and conclude that none can plausibly work unless the disk masses are revised upwards by a substantial amount.Comment: 23 pages, 8 figures, uses emulateapj.sty, accepted for publication in The Astronomical Journal (scheduled November 1999

Impurity in a Bose-Einstein condensate in a double well

We compare and contrast the mean-field and many-body properties of a Bose-Einstein condensate trapped in a double well potential with a single impurity atom. The mean-field solutions display a rich structure of bifurcations as parameters such as the boson-impurity interaction strength and the tilt between the two wells are varied. In particular, we study a pitchfork bifurcation in the lowest mean-field stationary solution which occurs when the boson-impurity interaction exceeds a critical magnitude. This bifurcation, which is present for both repulsive and attractive boson-impurity interactions, corresponds to the spontaneous formation of an imbalance in the number of particles between the two wells. If the boson-impurity interaction is large, the bifurcation is associated with the onset of a Schroedinger cat state in the many-body ground state. We calculate the coherence and number fluctuations between the two wells, and also the entanglement entropy between the bosons and the impurity. We find that the coherence can be greatly enhanced at the bifurcation.Comment: 19 pages, 17 figures. The second version contains minor corrections and some better figures (thicker lines

Collective excitation frequencies and stationary states of trapped dipolar Bose-Einstein condensates in the Thomas-Fermi regime

We present a general method for obtaining the exact static solutions and collective excitation frequencies of a trapped Bose-Einstein condensate (BEC) with dipolar atomic interactions in the Thomas-Fermi regime. The method incorporates analytic expressions for the dipolar potential of an arbitrary polynomial density profile, thereby reducing the problem of handling non-local dipolar interactions to the solution of algebraic equations. We comprehensively map out the static solutions and excitation modes, including non-cylindrically symmetric traps, and also the case of negative scattering length where dipolar interactions stabilize an otherwise unstable condensate. The dynamical stability of the excitation modes gives insight into the onset of collapse of a dipolar BEC. We find that global collapse is consistently mediated by an anisotropic quadrupolar collective mode, although there are two trapping regimes in which the BEC is stable against quadrupole fluctuations even as the ratio of the dipolar to s-wave interactions becomes infinite. Motivated by the possibility of fragmented BEC in a dipolar Bose gas due to the partially attractive interactions, we pay special attention to the scissors modes, which can provide a signature of superfluidity, and identify a long-range restoring force which is peculiar to dipolar systems. As part of the supporting material for this paper we provide the computer program used to make the calculations, including a graphical user interface.Comment: 23 pages, 11 figure

An optical spectroscopic H-R diagram for low-mass stars and brown dwarfs in Orion

The masses and temperatures of young low mass stars and brown dwarfs in star- forming regions are not yet well established because of uncertainties in the age of individual objects and the spectral type vs. temperature scale appropriate for objects with ages of only a few Myr. Using multi-object optical spectroscopy, 45 low-mass stars and brown dwarfs in the Trapezium Cluster in Orion have been classified and 44 of these confirmed as bona fide cluster members. The spectral types obtained have been converted to effective temperatures using a temperature scale intermediate between those of dwarfs and giants, which is suitable for young pre-main sequence objects. The objects have been placed on an H-R diagram overlaid with theoretical isochrones. The low mass stars and the higher mass substellar objects are found to be clustered around the 1 Myr isochrone, while many of the lower mass substellar objects are located well above this isochrone. An average age of 1 Myr is found for the majority of the objects. Assuming coevality of the sources and an average age of 1 Myr, the masses of the objects have been estimated and range from 0.018 to 0.44Msun. The spectra also allow an investigation of the surface gravity of the objects by measurement of the sodium doublet equivalent width. With one possible exception, all objects have low gravities, in line with young ages, and the Na indices for the Trapezium objects lie systematically below those of young stars and brown dwarfs in Chamaeleon, suggesting that the 820 nm Na index may provide a sensitive means of estimating ages in young clusters.Comment: 19 pages, accepted by MNRA

Dynamical diffraction in sinusoidal potentials: uniform approximations for Mathieu functions

Eigenvalues and eigenfunctions of Mathieu's equation are found in the short wavelength limit using a uniform approximation (method of comparison with a `known' equation having the same classical turning point structure) applied in Fourier space. The uniform approximation used here relies upon the fact that by passing into Fourier space the Mathieu equation can be mapped onto the simpler problem of a double well potential. The resulting eigenfunctions (Bloch waves), which are uniformly valid for all angles, are then used to describe the semiclassical scattering of waves by potentials varying sinusoidally in one direction. In such situations, for instance in the diffraction of atoms by gratings made of light, it is common to make the Raman-Nath approximation which ignores the motion of the atoms inside the grating. When using the eigenfunctions no such approximation is made so that the dynamical diffraction regime (long interaction time) can be explored.Comment: 36 pages, 16 figures. This updated version includes important references to existing work on uniform approximations, such as Olver's method applied to the modified Mathieu equation. It is emphasised that the paper presented here pertains to Fourier space uniform approximation

Large Scale Flows from Orion-South

Multiple optical outflows are known to exist in the vicinity of the active star formation region called Orion-South (Orion-S). We have mapped the velocity of low ionization features in the brightest part of the Orion Nebula, including Orion-S, and imaged the entire nebula with the Hubble Space Telescope. These new data, combined with recent high resolution radio maps of outflows from the Orion-S region, allow us to trace the origin of the optical outflows. It is confirmed that HH 625 arises from the blueshifted lobe of the CO outflow from 136-359 in Orion-S while it is likely that HH 507 arises from the blueshifted lobe of the SiO outflow from the nearby source 135-356. It is likely that redshifted lobes are deflected within the photon dominated region behind the optical nebula. This leads to a possible identification of a new large shock to the southwest from Orion-S as being driven by the redshifted CO outflow arising from 137-408. The distant object HH 400 is seen to have two even further components and these all are probably linked to either HH 203, HH 204, or HH 528. Distant shocks on the west side of the nebula may be related to HH 269. The sources of multiple bright blueshifted Herbig-Haro objects (HH 202, HH 203, HH 204, HH 269, HH 528) remain unidentified, in spite of earlier claimed identifications. Some of this lack of identification may arise from the fact that deflection in radial velocity can also produce a change in direction in the plane of the sky. The best way to resolve this open question is through improved tangential velocities of low ionization features arising where the outflows first break out into the ionized nebula.Comment: Astronomical Journal, in press. Some figures are shown at reduced resolution. A full-resolution version is available at http://ifront.org/wiki/Orion_South_Outflows_Pape

High-resolution x-ray telescopes

High-energy astrophysics is a relatively young scientific field, made possible by space-borne telescopes. During the half-century history of x-ray astronomy, the sensitivity of focusing x-ray telescopes-through finer angular resolution and increased effective area-has improved by a factor of a 100 million. This technological advance has enabled numerous exciting discoveries and increasingly detailed study of the high-energy universe-including accreting (stellar-mass and super-massive) black holes, accreting and isolated neutron stars, pulsar-wind nebulae, shocked plasma in supernova remnants, and hot thermal plasma in clusters of galaxies. As the largest structures in the universe, galaxy clusters constitute a unique laboratory for measuring the gravitational effects of dark matter and of dark energy. Here, we review the history of high-resolution x-ray telescopes and highlight some of the scientific results enabled by these telescopes. Next, we describe the planned next-generation x-ray-astronomy facility-the International X-ray Observatory (IXO). We conclude with an overview of a concept for the next next-generation facility-Generation X. The scientific objectives of such a mission will require very large areas (about 10000 m2) of highly-nested lightweight grazing-incidence mirrors with exceptional (about 0.1-arcsecond) angular resolution. Achieving this angular resolution with lightweight mirrors will likely require on-orbit adjustment of alignment and figure.Comment: 19 pages, 11 figures, SPIE Conference 7803 "Adaptive X-ray Optics", part of SPIE Optics+Photonics 2010, San Diego CA, 2010 August 2-

PPAK Integral Field Spectroscopy survey of the Orion Nebula: Data Release

We present a low-resolution spectroscopic survey of the Orion nebula which data we release for public use. In this article, we intend to show the possible applications of this dataset analyzing some of the main properties of the nebula. We perform an integral field spectroscopy mosaic of an area of ~5' X 6' centered on the Trapezium region of the nebula, including the ionization front to the south-east. The analysis of the line fluxes and line ratios of both the individual and integrated spectra allowed us to determine the main characteristics of the ionization throughtout the nebula.The final dataset comprises 8182 individual spectra, which sample each one a circular area of \~2.7" diameter. The data can be downloaded as a single row-stacked spectra fits file plus a position table or as an interpolated datacube with a final sampling of 1.5"/pixel. The integrated spectrum across the field-of-view was used to obtain the main integrated properties of the nebula, including the electron density and temperature, the dust extinction, the Halpha integrated flux (after correcting for dust reddening), and the main diagnostic line ratios. The individual spectra were used to obtain line intensity maps of the different detected lines. These maps were used to study the distribution of the ionized hydrogen, the dust extinction, the electron density and temperature, and the helium and oxygen abundance...Comment: 13 pages, 8 figures, accepted for publishing in Astronomy & Astrophysic