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Table of contents

Volume 126

Number 6, 2003 December 1

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2579

, , , , , , , , , et al

We present the second edition of the Sloan Digital Sky Survey (SDSS) Quasar Catalog. The catalog consists of the 16,713 objects in the SDSS First Data Release that have luminosities larger than Mi = -22 (in a cosmology with H0 = 70 km s-1 Mpc-1, ΩM = 0.3, and ΩΛ = 0.7), have at least one emission line with FWHM larger than 1000 km s-1, and have highly reliable redshifts. The area covered by the catalog is ≈1360 deg2. The quasar redshifts range from 0.08 to 5.41, with a median value of 1.43. For each object, the catalog presents positions accurate to better than 0farcs2 rms per coordinate, five-band (ugriz) CCD-based photometry with typical accuracy of 0.03 mag, and information on the morphology and selection method. The catalog also contains some radio, near-infrared, and X-ray emission properties of the quasars, when available, from other large-area surveys. Calibrated digital spectra of all objects in the catalog, covering the wavelength region 3800–9200 Å at a spectral resolution of 1800–2100, are available. This publication supersedes the first SDSS Quasar Catalog, which was based on material from the SDSS Early Data Release. A summary of corrections to current quasar databases is also provided. The majority of the objects were found in SDSS commissioning data using a multicolor selection technique. Since the quasar selection algorithm was undergoing testing during the entire observational period covered by this catalog, care must be taken when assembling samples from the catalog for use in statistical studies. A total of 15,786 objects (94%) in the catalog were discovered by the SDSS; 12,173 of the SDSS discoveries are reported here for the first time. Included in the new discoveries are five quasars brighter than i = 16.0 and 17 quasars with redshifts larger than 4.5.

2594

, , , , , , , , and

We investigate the continuum and emission-line properties of 224 broad absorption line quasars (BALQSOs) with 0.9 ≲ z ≲ 4.4 drawn from the Sloan Digital Sky Survey Early Data Release, which contains 3814 bona fide quasars. We find that low-ionization BALQSOs (LoBALs) are significantly reddened as compared with normal quasars, in agreement with previous work. High-ionization BALQSOs (HiBALs) are also more reddened than the average non-BALQSO. Assuming SMC-like dust reddening at the quasar redshift, the amount of reddening needed to explain HiBALs is E(B-V) ∼ 0.023 and LoBALs is E(B-V) ∼ 0.077 (compared with the ensemble average of the entire quasar sample). We find that there are differences in the emission-line properties between the average HiBAL, LoBAL, and non-BAL quasar. These differences, along with differences in the absorption-line troughs, may be related to intrinsic quasar properties such as the slope of the intrinsic (unreddened) continuum; more extreme absorption properties are correlated with bluer intrinsic continua. Despite the differences among BALQSO subtypes and non-BALQSOs, BALQSOs appear to be drawn from the same parent population as non-BALQSOs when both are selected by their UV/optical properties. We find that the overall fraction of traditionally defined BALQSOs, after correcting for color-dependent selection effects due to different SEDs of BALQSOs and non-BALQSOs, is 13.4% ± 1.2% and shows no significant redshift dependence for 1.7 ≤ z ≤ 3.45. After a rough completeness correction for the effects of dust extinction, we find that approximately one in every six quasars is a BALQSO.

2608

, , , , , , , , , et al

We present the results of a study of the host galaxies of high-redshift Type Ia supernovae (SNe Ia). We provide a catalog of 18 hosts of SNe Ia observed with the Hubble Space Telescope (HST) by the High-z Supernova Search Team, including images, scale lengths, measurements of integrated (Hubble-equivalent) BVRIZ photometry in bands where the galaxies are brighter than m ≈ 25 mag, and galactocentric distances of the supernovae. We compare the residuals of SN Ia distance measurements from cosmological fits with measurable properties of the supernova host galaxies that might be expected to correlate with variable properties of the progenitor population, such as host-galaxy color and position of the supernova. We find mostly null results; the current data are generally consistent with no correlations of the distance residuals with host-galaxy properties in the redshift range 0.42 < z < 1.06. Although a subsample of SN hosts shows a formally significant (3 σ) correlation between apparent V-R host color and distance residuals, the correlation is not consistent with the null results from other host colors probed by our largest samples. There is also evidence for the same correlations between SN Ia properties and host type at low redshift and high redshift. These similarities support the current practice of extrapolating properties of the nearby population to high redshifts, pending more robust detections of any correlations between distance residuals from cosmological fits and host properties.

2622

, , and

We use the Tully-Fisher relation (TFR) to compare the behavior of S0 and late-type spiral galaxies. We determine circular velocities based on stellar kinematics derived from stellar absorption line spectroscopy for 10 S0's in the Coma Cluster and eight S0's in the Virgo Cluster. We combine these results with similar measurements of 13 Coma S0 galaxies obtained previously. We find that there is only a small offset, ΔmH ∼ 0.2, in the H-band luminosity at a given circular velocity, vc ∼ 200 km s-1, between S0 and late-type spirals. This result implies a similar total H-band mass-to-light ratio (within an effective radius) among disk galaxies of different Hubble types. As the older stellar population in S0's is dimmer, this suggests a somewhat larger fraction of stellar mass in these S0's than in late-type spirals. We also find that the relation between (I- and H-band) luminosity and vc for the S0 galaxies is at best poorly defined and has a scatter of ∼1 mag, significantly larger than the TFR for late-type spirals, where the observed I- and H-band scatter is σ ∼ 0.3–0.5 mag. This substantial scatter confirms the original findings of Dressler & Sandage and is similar to that found in a study by Neistein and coworkers of 18 nearby S0 galaxies in the field where σI ∼ 0.7 mag, but differs from the small scatter found by Mathieu and coworkers, σI ∼ 0.3 mag, for six nearby S0's. Our results suggest that differing formation histories can lead to S0's with diverse properties and that S0's are more likely to be the outcomes of minor mergers or some "preprocessing" in groups of galaxies falling into clusters, rather than simply late-type spirals that have been stripped of their gas but are kinematically preserved. We suggest that it is likely that many mechanisms, such as slow encounters, tidal interactions, and gas stripping, may have occurred in the lifetimes of the galaxies and produced the heterogeneous class of S0's that are observed today.

2635

, , , and

We investigate the properties of the B-band Tully-Fisher (T-F) relation for 25 compact group galaxies, using Vmax derived from two-dimensional velocity maps. Our main result is that the majority of the Hickson Compact Group galaxies lie on the T-F relation. However, about 20% of the galaxies, including the lowest-mass systems, have higher B luminosities for a given mass, or alternatively, a mass that is too low for their luminosities. We favor a scenario in which outliers have been brightened because of either enhanced star formation or merging. Alternatively, the T-F outliers may have undergone truncation of their dark halo due to interactions. It is possible that in some cases both effects contribute. The fact that the B-band T-F relation is similar for compact group and field galaxies tells us that these galaxies show common mass-to-size relations and that the halos of compact group galaxies have not been significantly stripped inside R25. We find that 75% of the compact group galaxies studied (22 out of 29) have highly peculiar velocity fields. Nevertheless, a careful choice of inclination, position angle, and center, obtained from the velocity field, and an average of the velocities over a large sector of the galaxy enabled the determination of fairly well-behaved rotation curves for the galaxies. However, two of the compact group galaxies HCG 91a and HCG 96a, which are the most massive members in M51-like pairs, have very asymmetric rotation curves, with one arm rising and the other one falling, indicating most probably a recent perturbation by the small close companions.

2644

, , and

Wide-field (20' × 20') UBVI images of intermediate-redshift (z = 0.39), Butcher-Oemler cluster Cl 0024+1654 have been obtained. These data probe the rest-frame mid-UV properties over a much larger area than previous studies of Cl 0024+1654. Using these data, a multicolor catalog of nonstellar objects, assumed to be galaxies, has been constructed and analyzed. Using statistical arguments, the observed galaxy sample is separated into field and cluster populations. The basic photometric properties of these populations are presented and discussed. The "dropout" objects (i.e., objects undetected in one or more photometric bands) in our catalog are also discussed. A description of the final UBVI images, as well as the object catalog, is provided in an appendix. In a second appendix the use of SExtractor in crowded fields, such as the core of Cl 0024+1654, is discussed. The specific issues of the mid-UV properties of red envelope cluster galaxies, as well as the possible detection of a faint blue cluster population, are discussed in a forthcoming companion paper by Silva, Alexov, & Pierce.

2662

, , , , , , and

We report on the morphological luminosity functions (LFs) and radial profiles derived for the galaxy population within the rich cluster Abell 868 (z = 0.153) based purely on Hubble Space Telescope imaging in F606W. We recover Schechter functions (-24.0 < MF606W - 5 log h0.65 < -16.0) within a 0.65h0.65 Mpc radius for early (E/S0) , mid (Sabc), and late (Sd/Irr) type galaxies of

The early, mid, and late types are all consistent with the recent field morphological LFs based on recent analysis of the Sloan Digital Sky Survey Early Data Release. From a detailed error analysis, including clustering of the background population, we note that improved statistics can only come from combining data from many clusters. We also examine the luminosity-density and number-density profiles as a function of morphology and draw the following conclusions: (1) the galaxies responsible for the steep faint-end slope are predominantly of late-type morphology; (2) the cluster core is dominated by elliptical galaxies; (3) the core is devoid of late-type systems; (4) the luminosity density as a function of morphological type is skewed toward early types when compared with the field; (5) up to half of the elliptical galaxies may have formed from the spiral population through core disk-destruction process(es). We believe the most plausible explanation is the conventional one that late types are destroyed during transit through the cluster core and that mid types are converted into early types through a similar process, which destroys the outer disk and results in a more tightly bound population of core elliptical galaxies.

2677

, , and

We present submillimeter continuum observations at 870 μm of the cores of low-redshift 3CRR radio galaxies, observed at the Heinrich Hertz Submillimeter Telescope. The cores are nearly flat-spectrum between the radio and submillimeter, which implies that the submillimeter continuum is likely to be synchrotron emission and not thermal emission from dust. The emitted power from nuclei detected at optical wavelengths and in the X-rays is similar in the submillimeter, optical, and X-rays. The submillimeter-to-optical and X-ray power ratios suggest that most of these sources resemble misdirected BL Lac–type objects with synchrotron emission peaking at low energies. However, we find three exceptions, the FR I galaxy 3C 264 and the FR II galaxies 3C 390.3 and 3C 338 with high X-ray–to–submillimeter luminosity ratios. These three objects are candidate misdirected high- or intermediate-energy peaked BL Lac–type objects. With additional infrared observations and from archival data, we compile spectral energy distributions for a subset of these objects. The steep dips observed near the optical wavelengths in many of these objects suggest that extinction inhibits the detection and reduces the flux of optical continuum core counterparts. High-resolution near- or mid-infrared imaging may provide better measurements of the underlying synchrotron emission peak.

2687

, , , , , , , , , et al

We discuss the IAU resolutions B1.3, B1.4, B1.5, and B1.9 that were adopted during the 24th General Assembly in Manchester, 2000, and provides details on and explanations for these resolutions. It is explained why they present significant progress over the corresponding IAU 1991 resolutions and why they are necessary in the light of present accuracies in astrometry, celestial mechanics, and metrology. In fact, most of these resolutions are consistent with astronomical models and software already in use. The metric tensors and gravitational potentials of both the Barycentric Celestial Reference System and the Geocentric Celestial Reference System are defined and discussed. The necessity and relevance of the two celestial reference systems are explained. The transformations of coordinates and gravitational potentials are discussed. Potential coefficients parameterizing the post-Newtonian gravitational potentials are expounded. Simplified versions of the time transformations suitable for modern clock accuracies are elucidated. Various approximations used in the resolutions are explicated and justified. Some models (e.g., for higher spin moments) that serve the purpose of estimating orders of magnitude have actually never been published before.

2707

, , and

Current understanding of the secular evolution of galactic disks suggests that this process is dominated by two or more "heating" mechanisms, which increase the random motions of stars in the disk. In particular, the gravitational influence of giant molecular clouds and irregularities in the spiral potential have been proposed to explain the observed velocity dispersions in the solar neighborhood. Each of these mechanisms acts on different components of the stellar velocity, which affects the ratio σzR of the vertical and radial components differently. Since the relative strengths of giant molecular clouds and spiral irregularities vary with Hubble type, a study of σzR as function of Hubble type has the potential to provide strong constraints on disk heating mechanisms. We present major- and minor-axis stellar kinematics for four spiral galaxies of Hubble type from Sa to Sbc and use the data to infer the ratios σzR in the galaxy disks. We combine the results with those for two galaxies studied previously with the same technique, with Milky Way data, and with estimates obtained using photometric techniques. The results show that σzR is generally in the range 0.5–0.8. There is a marginally significant trend of decreasing σzR with advancing Hubble type, consistent with the predictions of disk heating theories. However, the errors on individual measurements are large, and the absence of any trend is consistent with the data at the 1 σ level. As a by-product of our study, we find that three of the four galaxies in our sample have a central drop in their stellar line-of-sight velocity dispersion, a phenomenon that is increasingly observed in spiral galaxies.

2717

, , , , , , and

We report on the properties of nuclear regions in the Toomre sequence of merging galaxies, based on imaging data gathered with the Hubble Space Telescope WFPC2 camera. We have imaged the 11 systems in the proposed evolutionary merger sequence in the F555W and F814W broadband filters, and in Hα+[N II] narrowband filters. The broadband morphology of the nuclear regions varies from nonnucleated starburst clumps through dust-covered nuclei to a nucleated morphology. There is no unambiguous trend in the morphology with merger stage. The emission-line morphology is extended beyond the nucleus in most cases, but centrally concentrated (within 1 kpc) emission-line gas can be seen in the four latest-stage merger systems. We have quantified the intrinsic luminosity densities and colors within the inner 100 pc and 1 kpc of each identified nucleus. We find little evidence for a clear trend in nuclear properties along the merger sequence other than a suggestive rise in the nuclear luminosity density in the most evolved members of the sequence. The lack of clear trends in nuclear properties is likely due both to the effects of obscuration and geometry, as well as the physical variety of galaxies included in the Toomre sequence.

2740

, , , and

We present an analysis of the X-ray emission for a complete sample of 288 Abell clusters spanning the redshift range 0.016 ≤ z ≤ 0.09 from the ROSAT All-Sky Survey. This sample is based on our 20 cm VLA survey of nearby Abell clusters. We find an X-ray detection rate of 83%. We report cluster X-ray fluxes and luminosities and two different flux ratios indicative of the concentration and extent of the emission. We examine correlations between the X-ray luminosity, Abell richness, and Bautz-Morgan and Rood-Sastry cluster morphologies. We find a strong correlation between LX and cluster richness coupled with a dependence on the optical morphological type. These results are consistent with the observed scatter between X-ray luminosity and temperature and a large fraction of cooling flows. For each cluster field, we also report the positions, peak X-ray fluxes, and flux ratios of all X-ray peaks above 3 σ significance within a box of 2 × 2 h Mpc centered on Abell's position.

2752

, , , , and

We infer the star formation history in different regions of the blue compact dwarf NGC 1705 by comparing synthetic color-magnitude diagrams with the Hubble Space Telescope optical and near-infrared photometry. We find that NGC 1705 is not a young galaxy, because its star formation commenced at least 5 Gyr ago. On the other hand, we confirm the existence of a recent burst of star formation between 15 and 10 Myr ago. We also find evidence for new strong activity, which started 3 Myr ago and is still continuing. The old population is spread across the entire galaxy, while the young and intermediate stars are more concentrated in the central regions. We derive an almost continuous star formation with variable rate and exclude the presence of long quiescent phases between the episodes during the last ≈1 Gyr. The central regions experienced an episode of star formation of ∼0.07 M yr-1 (for a Salpeter initial mass function [IMF]) 15 to 10 Myr ago. This coincides with the strong activity in the central super–star cluster. We find a rate of ∼0.3 M yr-1 for the youngest ongoing burst, which started ∼3 Myr ago. This is higher than in other dwarfs and comparable to the rate of NGC 1569. The star formation rate of earlier episodes is not especially high and falls in the range 10-3 to 10-1M yr-1. The IMF is close to the Salpeter value or slightly steeper.

2774

, , , and

A new installment of neutral hydrogen mappings of blue compact dwarf (BCD) galaxies, as defined by optical morphology, in and near the Virgo Cluster is presented. The primary motivation was to search for outlying clouds of H I as potential interactive triggers of enhanced star formation, and therefore the mapped galaxies were selected for large H I mass, large optical diameter, and large velocity profile width. Approximately half the sample proved to have one or more small, low column density, star-free companion clouds, either detached or appearing as an appendage in our maps, at a resolution on the order of 4 kpc. Comparison is made with a sample of similarly mapped field BCD galaxies drawn from the literature; however, the Virgo Cluster sample of mapped BCDs is still too small for conclusive comparisons to be made. We found, on the one hand, little or no evidence for ram-pressure stripping nor, on the other, for extremely extended low column density H I envelopes. The H I rotation curves in most cases rise approximately linearly and slowly, as far out as we can trace the gas.

2797

, , and

We present results on the X-ray properties of IC 342 using a 10 ks XMM-Newton observation. Thirty-five sources are detected coincident with the disk of IC 342 (more than tripling the number known), of which ≈31 are likely to be intrinsic to IC 342. This point-source population exhibits a diverse range of spectral properties and has an X-ray luminosity function slope and infrared luminosity comparable to that of starburst galaxies such as M82 and the Antennae, while its relative lack of extended X-ray emission is similar to the properties of quiescent spirals. Although we find no evidence of short-term variability in any of the X-ray sources, we do detect long-term variability between this observation and the 1991 ROSAT and 1993/2000 ASCA observations for five sources. Notably, the second most luminous source in IC 342 (X-2) is found to have an absorption-corrected 0.5–10 keV luminosity of 5.75 × 1039 ergs s-1 and a spectrum best fitted by an absorbed multicolor accretion disk model with Tin = 2.17 keV and NH = 15.3 × 1021 cm-2. This is the lowest luminosity state observed for X-2 to date, although the slope of the spectrum is intermediate between the previously observed low/hard and high/soft states. IC 342 X-1, on the other hand, is found to be in an identical state to that observed in 2000 with ASCA. Assuming X-1 is in an anomalous very high (VH) state, then either (1) X-1 has remained in this state between 2000 and 2002 and is therefore the longest duration VH-state binary ever observed, or (2) it was simply caught in a VH state by chance in both the 2000 ASCA and 2002 XMM-Newton observations. We have also confirmed the ROSAT HRI result that the nucleus of IC 342 is made up of both pointlike and extended emission, with the extended emission contributing ≈55% and ≈35% in the 0.3–2.0 keV and 2.0–10.0 keV bands, respectively. The spectrum of the nucleus is best fitted by an absorbed two-component model consisting of a thermal plasma with a temperature of kT ≈ 0.3 and a power law with a photon index of Γ ≈ 2.53. The relative fluxes of the two spectral components suggest that the nucleus is complex, with a soft extended component contributing approximately half of the total luminosity.

2806

, , , , , and

New Hubble Space Telescope WFPC2 imaging of the dwarf starburst galaxy NGC 625 is presented. These data, which are 80% complete to V and I magnitudes of 26.0 and 25.3, respectively, allow us to study the recent star formation history of NGC 625. Using outlying red giant stars, we derive a tip of the red giant branch (TRGB) distance modulus of 27.95 ± 0.07. This corresponds to a distance of 3.89 ± 0.22 Mpc, placing this system on the far side of the Sculptor Group. NGC 625 has a well-defined radial stellar population gradient, evidenced by a central concentration of young main-sequence stars and a red giant branch (RGB)/asymptotic giant branch (AGB) ratio that increases with galactocentric distance. The prominent AGB is very red, similar to the population found in the Local Group dwarf irregular galaxy NGC 6822. The RGB stars can be detected out far from the central star-forming activity and show an elliptical distribution in agreement with the galaxy's outer H I distribution. Using Hα and Hβ narrowband imaging and previous optical spectroscopy, we identify substantial and varying internal extinction associated with the central active star formation regions. This extinction, which varies from AV = 0.0 to 0.6 mag, hampers efforts to derive a detailed recent star formation history. To better understand the effects of internal extinction on the analysis of young stellar populations, synthetic models are presented that, for the first time, examine and account for this effect. Using the luminous blue helium-burning stars, we construct a simple model of the recent (<100 Myr) star formation in which an elevated but declining star formation rate has been present over this entire period. This is at odds with the presence of spectroscopic Wolf-Rayet (W-R) features in the major star formation region, which implies a short duration (≤5 Myr) for the recent starburst. This suggests that starbursts displaying W-R features are not necessarily all of a short duration. Finally, we speculate on the possible causes of the present burst of star formation in this apparently isolated galaxy and compare it with other nearby, well-studied dwarf starburst systems.

2831

, , and

In the inner 3 kpc of M51, we find that logarithmic spirals provide good fits to the peak intensities in molecular gas observed by the Berkeley-Illinois-Maryland Association array in the CO (J = 1–0) emission line along the spiral arms. However, we measure significant asymmetries between the location and density of the arms observed on one side of the galaxy compared with those on the opposite side. Between a radius of 1 and 2.2 kpc, the gas distribution traced in CO is lopsided with densities twice as large in one arm than the opposite one. In the same region, the spiral arms are offset by 20° from the position of the arm on the opposite side of the galaxy after a rotation of 180°. We use the ratio of CO emission to the emission in the Paα hydrogen recombination line to estimate the efficiency of star formation along each arm. Except for a narrow region at about 2 kpc in which star formation is surprisingly inefficient, the gas depletion time is approximately 200 million years despite large variations in the molecular gas density in the arms. We account for the deviations from two-armed bisymmetric structure with a simple model that includes an additional three-armed spiral density wave. This model accounts for the angular offset between the arm on one side compared with its opposite, the lopsided distribution in molecular gas, and interarm star formation to the northeast of the galaxy nucleus. Since the star formation efficiency is unaffected by the variations in gas density, and the variations in gas density can be accounted for by the presence of an additional three-armed density wave, we suggest that the star formation rate is variable and is highest where and when the maxima of the two spiral density waves coincide or constructively add. The inner region of M51 provides good evidence for the presence of more than one spiral density wave and a resulting variable rate of star formation.

2840

, , , , , , , , , et al

We present deep wide-field VI CCD photometry of the Sextans dwarf spheroidal galaxy (dSph) in the Local Group, covering a field of 42' × 28' located at the center of the galaxy (supplemented by short B photometry). The limiting magnitudes with 50% completeness are V = 24.4 mag and I = 23.6 mag. Color-magnitude diagrams of the Sextans dSph show a well-defined red giant branch (RGB), blue horizontal branch (BHB), prominent red horizontal branch (RHB), and asymptotic giant branch (AGB), as well as ∼120 variable star candidates including RR Lyrae stars and anomalous Cepheids, ∼230 blue stragglers (BSs), and main-sequence (MS) stars. The main-sequence turnoff (MSTO) of the old population is found to be located at V ≈ 23.7 mag and V-I ≈ 0.56. The distance to the galaxy is derived using the I-band magnitude of the tip of the RGB at ITRGB = 15.95 ± 0.04: (m - M)0 = 19.90 ± 0.06, for an adopted reddening of E(B-V) = 0.01. This estimate agrees well with the distance estimate based on the mean V-band magnitude of the HB at V(HB) = 20.37 ± 0.04. The mean metallicity of the RGB is estimated from the V-I color: [Fe/H] = -2.1 ± 0.1 (statistical error) ±0.2 (standard calibration error) dex, with a dispersion of σ[Fe/H] = 0.2 dex. The age of the MSTO of the main old population is estimated to be similar to that of the metal-poor Galactic globular cluster M92, and some stellar populations with younger age are seen. There is found to be one RGB bump at V = 19.95 ± 0.05 mag (MV = 0.03 mag) and a weak brighter bump at V = 19.35 ± 0.05 mag (MV = -0.58 mag), which is probably an AGB bump. The V-band luminosity function of the RGB and MS stars is in general similar to that of the globular cluster M92, with a slight excess of stars in the magnitude range brighter than the MSTO with respect to that of M92. The bright BSs are more centrally concentrated than the faint BSs. The V-band luminosity function of the BSs in the inner region is found to extend to a brighter magnitude and to have a flatter slope compared with that of the BSs in the outer region. Significant radial gradients are seen for several kinds of populations: the RHB, the red RGB, the red subgiant branch (SGB), and the bright BSs are more centrally concentrated toward the center of the galaxy compared with the BHB, the blue RGB, the blue SGB, and the faint BSs, respectively.

2867

and

We investigate the red supergiant (RSG) content of the SMC and LMC using multiobject spectroscopy on a sample of red stars previously identified by BVR CCD photometry. We obtained high-accuracy (<1 km s-1) radial velocities for 118 red stars seen toward the SMC and 167 red stars seen toward the LMC, confirming most of these (89% and 95%, respectively) as red supergiants. Spectral types were also determined for most of these RSGs. We find that the distribution of spectral types is skewed toward earlier type at lower metallicities: the average (median) spectral type is K5–K7 I in the SMC, M1 I in the LMC, and M2 I in the Milky Way. Our examination of the Kurucz ATLAS9 model atmospheres suggests that the effect that metallicity has on the appearance on the TiO lines is probably sufficient to account for this effect, and we argue that RSGs in the Magellanic Clouds are 100 K (LMC) and 300 K (SMC) cooler than Galactic stars of the same spectral types. The colors of the Kurucz models are not consistent with this interpretation for the SMC, although other models (e.g., Bessell et al.) show good agreement. A finer grid of higher resolution synthetic spectra appropriate to cool supergiants is needed to better determine the effective temperature scale. We compare the distribution of RSGs in the H-R diagram to that of various stellar evolutionary models; we find that none of the models produce RSGs as cool and luminous as what is actually observed. This result is much larger than any uncertainty in the effective temperature scale. We note that, were we to simply adopt the uncorrected Galactic effective scale for RSGs and apply this to our sample, then the SMC's RSGs would be underluminous compared with the LMC's, contrary to what we expect from stellar evolution considerations. In all of our H-R diagrams, however, there is an elegant sequence of decreasing effective temperatures with increasing luminosities; explaining this will be an important test of future stellar evolutionary models. Finally, we compute the blue-to-red supergiant ratio in the SMC and LMC, finding that the values are indistinguishable (∼15) for the two Clouds. We emphasize that "observed" B/R values must be carefully determined if a comparison with that predicted by stellar models is to be meaningful. The nonrotation Geneva models overestimate the number of blue to red supergiants for the SMC, but underestimate it for the LMC; however, given the inability to produce high-luminosity RSGs in the models that match what is observed in the H-R diagram, such a disagreement is not surprising.

2887

, , and

We report the first likely detections of erupting dwarf novae (DNe) in an external galaxy: the Large Magellanic Cloud. Six candidates were isolated from approximately a million stars observed every second night over 11 nights with the Cerro Tololo Inter-American Observatory 8K × 8K Mosaic2 CCD imager. Artificial dwarf nova and completeness tests suggest that we are seeing only the brightest of the LMC DNe, probably SS Cygni–like cataclysmic variables (CVs), but possibly SU UMa type cataclysmics undergoing superoutbursts. We derive crude but useful limits on the LMC DN surface density and on the number of DNe in the LMC. Many thousands of CVs in the Magellanic Clouds can be discovered and characterized with 8 m class telescopes.

2896

, , , , and

We have reestimated the surface density of the Galactic disk in the solar neighborhood within ±0.4 kpc of the Sun using the parallaxes and proper motions of a kinematically and spatially unbiased sample of 1476 old bright red giant stars from the Hipparcos catalog with measured radial velocities from Barbier-Brossat & Figon. We determine the vertical distribution of the red giants as well as the vertical velocity dispersion of the sample (14.4 ± 0.3 km s-1) and combine these to derive the surface density of the gravitating matter in the Galactic disk as a function of the Galactic coordinate z. The surface density of the disk increases from 10.5 ± 0.5 M pc-2 within ±50 pc to 42 ± 6 M pc-2 within ±350 pc. The estimated volume density of the Galactic disk within ±50 pc is about 0.1 M pc-3 which is close to the volume density estimates of the observed baryonic matter in the solar neighborhood.

2910

, , and

We present a (V-R)-based reddening map of about 43 deg2 of the Galactic bulge/bar. The map is constructed using template image photometry from the MACHO microlensing survey, contains 9717 resolution elements, and is based on V-R color averages of the entire color-magnitude diagrams (CMDs) in 4' × 4' tiles. The conversion from the observed color to the reddening follows from an assumption that CMDs of all bulge fields would look similar in the absence of extinction. Consequently, the difference in observed color between various fields originates from varying contribution of the disk extinction summed along different lines of sight. We check that our V-R colors correlate very well with infrared and optical reddening maps. We show that a dusty disk obeying a csc |b| extinction law, E(V-R) = 0.0274 csc |b|, provides a good approximation to the extinction toward the MACHO bulge/bar fields.

2922

, , , , and

We present techniques for obtaining precision astrometry using old photographic plates from assorted large-aperture reflectors in combination with recent CCD Mosaic Imager frames. At the core of this approach is a transformation of plate/CCD coordinates into a previously constructed astrometric reference frame around the open cluster NGC 188. This allows us to calibrate independently the optical field angle distortion for all telescopes and field correctors used in this study. Particular attention is paid to computing the differential color refraction, which has a marked effect in the case of NGC 188 as a result of the large zenith distances at which this cluster has been observed. Our primary result is a new catalog of proper motions and positions for 7812 objects down to V = 21 in the 0.75 deg2 area around NGC 188. The precision for well-measured stars is 0.15 mas yr-1 for proper motions and 2 mas for positions on the system of the Tycho-2 catalog. In total, 1490 stars have proper-motion membership probabilities Pμ ≥ 10%. The sum of membership probabilities indicates that NGC 188 contains ∼1050 stars down to V = 21. Comprehensive lists of the candidate blue stragglers and red giant stars substantially enlarge the number of such stars known in NGC 188. We have also obtained a small correction to the proper motions from the mean "motion" of background galaxies. Thus, the absolute proper motion of NGC 188 is μ = -2.56 ± 0.2 and μ = +0.18 ± 0.2 mas yr-1.

2936

and

We report the discovery of two young stars in the NGC 2264 star-forming molecular cloud whose physical and morphological characteristics are similar to FU Orionis objects. The objects form a close pair and exhibit a curved reflection nebula in the near-IR. The brighter of the two stars, AR 6A, is optically visible but considerably reddened, has a small 3 μm IR excess, shows pronounced 2.294 μm CO overtone band head absorption, and is the brightest near-IR object in the region. The fainter star, AR 6B, located 2farcs8 south, has a much larger thermal IR excess and shows considerably deeper CO band head absorption identical to that seen in several known FU Orionis stars (FUors). Both stars therefore resemble FUors in terms of thermal excess, near-IR spectral features, and morphology. Here we discuss the characteristics of AR 6A and AR 6B in relation to the FUor population and propose that both stars are likely additional members of this class of young stellar outburst objects. We speculate that the simultaneous appearance of two FUor–like objects in a binary system, which would be highly unlikely if unrelated, could be caused by orbital evolution in a newly formed hierarchical quadruple system.

2949

and

The optical light curve of the Be–neutron star binary AX J0049.4-7323 has been investigated using data from the MACHO and OGLE-II projects. This X-ray source, whose neutron star has a very slow rotation rate (Ppulse = 755.5 s), shows optical outbursts every ∼394 days. The regularity of these outbursts suggests that their recurrence time is the orbital period of the system. During the outbursts, the system brightens and becomes slightly redder. A possible interpretation is that a portion of the equatorial disk is excited as the neutron star passes through it during periastron passage. In the intervals between outbursts, the light curve shows ∼11 day quasi-periodic variability, which may be associated with the rotation of the Be star's extended disk.

2954

and

We have discovered that the star S986 in the old open cluster M67 has detectable total eclipses of depth 0.08 mag for the primary eclipse and 0.011 mag for the secondary eclipse (in I only). We confirm the detection of a third star in spectra contributing (11.5 ± 1.5)% of the total light in V band. The radial velocity of the third star indicates that it is a cluster member, but it is unclear whether it is physically associated with the eclipsing binary. Using spectroscopic and photometric data, we deconvolve the photometry of the three stars and find that the primary star in the eclipsing binary is significantly hotter than the turnoff. The two most likely explanations are that the primary star is in a rapid phase of evolution near core hydrogen exhaustion (associated with the turnoff gap in M67's color-magnitude diagram) or that it is a blue straggler created during a stellar collision earlier in the cluster's history. Our detection of Li in the primary star tightly constrains possible formation mechanisms in the blue straggler explanation. Because S986 is often used to constrain tidal dissipation models, this may imply that the strength of tidal effects is underestimated.

2963

and

New spatiokinematic observations were undertaken of the planetary nebula NGC 1514 in the [O III] line at 5007 Å using an imaging Fabry-Pérot spectrometer. Our results show an inner ellipsoidal shell and polar blobs that do not conform to bipolar morphology. It is argued that the nebula is a descendant of a common envelope binary system the periodicity of which is estimated to be about 10 days, with a progenitor mass of 4.5 M.

2971

, , , , , , , and

We present a new catalog of 108 Herbig Ae/Be candidate stars identified in the Pico dos Dias Survey, together with 19 previously known candidates and four objects selected from the IRAS Faint Source Catalog. These 131 stars were observed with low- and/or medium-resolution spectroscopy, and we complement these data with high-resolution spectra of 39 stars. The objects present a great variety of Hα line profiles and were separated according to them. Our study suggests that most of the time a Herbig Ae/Be star will present a double peak Hα line profile. Correlations among different physical parameters, such as spectral type and v sin i with Hα line profiles were searched. We found no correlation among Hα line profiles and spectral type or v sin i except for stars with P Cygni profiles, where there is a correlation with v sin i. We also use preliminary spectral energy distributions to seek for any influence of the circumstellar medium in the Hα line profiles. The presence of [O I] and [S II] forbidden lines is used together with the Hα line profiles and these preliminary spectral energy distributions to discuss the circumstellar environment of the Herbig Ae/Be candidates. The distribution of the detected [O I] and [S II] forbidden lines among different spectral types points to a significantly higher occurrence of these lines among B stars, whereas the distribution among different Hα profile types indicates that forbidden lines are evenly distributed among each Hα line-profile type. Combining the distance estimates of the Herbig candidates with the knowledge of the interstellar medium distribution, we have found that 84 candidates can be associated with some of the more conspicuous SFRs, being in the right direction and at a compatible distance. As a further means of checking the properties of the HAeBe candidates, as well as their present evolutionary status, the derived luminosities and effective temperatures of the stars with possible association to the star-forming regions and/or Hipparcos distances were plotted together with a set of pre–main-sequence evolutionary tracks on an HR diagram. A set of 14 stars were found out of their expected positions in the HR diagram.

2988

, , , and

We present new spectroscopic and photometric data on the early-type overcontact binary TU Muscae. The analysis of the spectroscopic data shows that the line of sight to the system crosses three kinematically sharp and well-separated interstellar reddening sources and that the stars rotate synchronously. We present new radial velocities that are in good agreement with earlier optical velocities and, thus, do not confirm the systematically smaller velocities obtained from IUE spectra. The optical velocities are analyzed simultaneously with the photometric data to derive accurate absolute dimensions for the binary components. The results show that TU Mus consists of an O7.5 primary with M1 = 23.5 ± 0.8 M and R1 = 7.48 ± 0.08 R and an O9.5 secondary with M2 = 15.3 ± 0.4 M and R2 = 6.15 ± 0.07 R in an overcontact configuration, and that the orbital period has remained constant over the three decades covered by the observations. These results might imply that the mass transfer seen in late-type overcontact binaries does not occur in their early-type counterparts.

2997

and

We have compiled and studied photometric and spectroscopic data published in the literature of several star-forming regions and young open clusters (Orion, Taurus, IC 348, Sco-Cen complex, Chamaeleon I, TW Hydrae association, σ Orionis cluster, IC 2391, α Persei cluster, and the Pleiades). Our goal was to seek the definition of a simple empirical criterion to classify stars or brown dwarfs that are accreting matter from a disk on the sole basis of low-resolution optical spectroscopic data. We show that, using Hα equivalent widths and spectral types, we can statistically classify very young stars and brown dwarfs as classical T Tauri stars and substellar analogs. As a boundary between accreting and nonaccreting objects, we use the saturation limit of chromospheric activity at log [L(Hα)/L(bol)] = -3.3 (determined in the open clusters). We discuss the uncertainties in the classification scheme due to the occurrence of flares. We have used this spectroscopic empirical criterion to classify objects found in the literature, and we compute the fraction of accreting objects in several star-forming regions. The fraction of accreting objects appears to decrease from about 50% to about 5% from 1 to 10 Myr for both stars and brown dwarfs.

3007

, , , , , , , , , and

We present low-resolution optical spectroscopy and BVRI photometry of 453 candidate nearby stars drawn from the NLTT proper-motion catalog. The stars were selected based on optical/near-infrared colors, derived by combining the NLTT photographic data with photometry from the 2MASS Second Incremental Data Release. Based on the derived photometric and spectroscopic parallaxes, we identify 111 stars as lying within 20 pc of the Sun, including nine stars with formal distance estimates of less than 10 pc. A further 53 stars have distance estimates within 1 σ of our 20 pc limit. Almost all of those stars are additions to the nearby-star census. In total, our NLTT-based survey has so far identified 496 stars likely to be within 20 pc, of which 195 are additions to nearby-star catalogs. Most of the newly identified nearby stars have spectral types between M4 and M8.

3017

I used the 2.4 m Hiltner Telescope at MDM Observatory in an attempt to measure trigonometric parallaxes for 14 cataclysmic variable stars. Techniques are described in detail. In the best cases the parallax uncertainties are below 1 mas, and significant parallaxes are found for most of the program stars. A Bayesian method that combines the parallaxes together with proper motions and absolute magnitude constraints is developed and used to derive distance estimates and confidence intervals. The most precise distance derived here is for WZ Sge, for which I find 43.3 pc. Six Luyten Half-Second stars with previous precise parallax measurements were remeasured to test the techniques, and good agreement was found.

3030

and

We describe a technique for deriving effective temperatures, surface gravities, rotation velocities, and radial velocities from high-resolution near-IR spectra. The technique matches the observed near-IR spectra to spectra synthesized from model atmospheres. Our analysis is geared toward characterizing heavily reddened pre–main-sequence stars, but the technique also has potential applications in characterizing main-sequence and post–main-sequence stars when these lie behind thick clouds of interstellar dust. For the pre–main-sequence stars, we use the same matching process to measure the amount of excess near-IR emission (which may arise in the protostellar disks) in addition to the other stellar parameters. The information derived from high-resolution spectra comes from line shapes and the relative line strengths of closely spaced lines. The values for the stellar parameters we derive are therefore independent of those derived from low-resolution spectroscopy and photometry. The new method offers the promise of improved accuracy in placing young stellar objects on evolutionary model tracks. Tests with an artificial noisy spectrum with typical stellar parameters and a signal-to-noise ratio of 50 indicate a 1 σ error of 100 K in Teff, 2 km s-1 in v sin i, and 0.13 in continuum veiling for an input veiling of 1. If the flux ratio between the sum of the Na, Sc, and Si lines at 2.2 μm and the (2–0) 12CO band head at 2.3 μm is known to an accuracy of 10%, the errors in our best-fit value for log g will be Δ log g = 0.1–0.2. We discuss the possible systematic effects on our determination of the stellar parameters and evaluate the accuracy of the results derivable from high-resolution spectra. In the context of this evaluation, we quantitatively explore the degeneracy between temperature and gravity that has bedeviled efforts to type young stellar objects using low-resolution spectra. The analysis of high-resolution near-IR spectra of MK standards shows that the technique yields very accurate values for the effective temperature. The greatest uncertainty in comparing our results with optical spectral typing of MK standards is in the spectral type–to–effective temperature conversion for the standards themselves. Even including this uncertainty, the 1 σ difference between the optical and infrared temperatures for dwarfs at 3000–5800 K is only 140 K. In a companion paper, we present an analysis of heavily extincted young stellar objects in the ρ Ophiuchi molecular cloud.

3043

, , and

We present high-resolution (R = 50,000) spectra at 2.2 μm of 16 young stars in the ρ Ophiuchi dark cloud. Photospheric features are detected in the spectra of 11 of these sources, all Class II young stellar objects. The five featureless spectra consist of two Class I, two Class I.5, and one Class II. One star, GSS 29, is identified as a spectroscopic binary based on radial velocity variations. The radial velocities for the remaining sample are consistent with 12CO and H2CO gas velocities and further confirm the membership of the sources in the ρ Oph cluster. For the 10 spectroscopically single Class II sources, we measure effective temperatures, continuum veiling, and v sin i rotation from the shapes and strengths of atomic photospheric lines by comparison with spectral synthesis models at 2.2 μm. We measure surface gravities in two stars from the integrated line flux ratio of the 12CO line region at 2.3 μm and the Na I line region at 2.2 μm. Although the majority (8/10) of the Class II stars have similar effective temperatures (3530 ± 100 K), they exhibit a large spread in bolometric luminosities (a factor of ∼8), as derived from near-IR photometry. In the two stars for which we have surface gravity measurements from spectroscopy, the photometrically derived luminosities are systematically higher than the spectroscopic luminosities. The spread in the photometrically derived luminosities in our other sources suggests either a large spread in stellar ages or nonphotospheric emission in the J band since anomalous and significant veiling at J has been observed in other T Tauri stars. Our spectroscopic luminosities result in older ages on the Hertzsprung-Russell diagram than are suggested by photometry at J or K. Most of our sources show a larger amount of continuum excess (FK ex) than stellar flux at 2.2 μm (FK*), substantially higher in many cases (rKFK ex/FK* = 0.3–4.5). The derived veiling values at K (rK) appear correlated with mid-IR disk luminosity and with Brackett γ equivalent width, corrected for veiling. The derived v sin i rotation is substantial (12–39 km s-1), but systematically less than the rotation measured in Class I.5 (flat) and Class I sources from other studies in Ophiuchus. In four stars (Class I and I.5 sources), the absence of any photospheric lines is likely due to large continuum excess and/or rapid rotation if the stars have late-type photospheres.

3058

and

We use new high-dispersion spectroscopic and precise photometric observations to identify 12 new γ Doradus stars. Two of the 12 systems are double-lined binaries that show obvious velocity variability. Five other stars have metallic lines with composite profiles characterized by a narrow feature near the center of each broad component. Spectrograms of the Hα line indicate that all five stars are binaries rather than shell stars. The remaining five stars in our sample are probably single. All 12 stars are photometrically variable with amplitudes between 6 and 87 mmag in Johnson B and periods between 0.3 and 1.2 days. Four stars are monoperiodic; the rest have between two and five independent periods. The variability at all periods approximates a sinusoid. Although many of the stars lie within the δ Scuti instability strip, none exhibit the higher frequency variability seen in δ Scuti stars. We have increased the sample of known γ Doradus stars by 40% and revised the positions of a number of variables in the H-R diagram by accounting for duplicity. Our list of 42 confirmed γ Doradus variables gives some of their properties. All are dwarfs or subgiants and lie within a well-defined region of the H-R diagram that overlaps the cool edge of the δ Scuti instability strip. We compare the observed location of the γ Doradus variables with a recently published theoretical γ Doradus instability strip and find good agreement.

3076

, , , , , , , , and

We have obtained three long-slit, far-UV spectra of the pre–main-sequence system T Tauri. These Hubble Space Telescope STIS spectra show a strong and variable on-source spectrum composed of both fluoresced H2 and stellar chromospheric lines. Extended H2 emission is seen up to 10'' from the T Tau system. The on-source and extended H2 are both pumped by H I Lyα. The on-source H2 is pumped by the red wing of a broad, self-absorbed Lyα line, while the progressions seen in the extended gas are pumped from near line center. This suggests that the extended H2 is pumped locally and not by the stellar Lyα line. The H2 to the north and west coincides with the evacuated cavity bounded by the optical reflection nebulosity; to the south the extended H2 coincides with the HH 255 outflow from the embedded infrared companion T Tau S. The spatial profile of the extended gas shows a prominent dip coincident with the position of T Tau S. This may be absorption by a disk associated with T Tau S. There is no evidence for absorption by a disk surrounding T Tau N large enough to obscure T Tau S.

3090

, , , , and

Using the Very Large Array, we have measured the proper motions of 28 radio pulsars. On average, the pulsars studied are fainter and more distant than those studied in earlier work, reducing the selection biases inherent in surveys restricted to the solar neighborhood. The typical measurement precision achieved is a few milliarcseconds per year, corresponding to a few tens of kilometers per second for a pulsar a kiloparsec away. While our results compare well with higher precision measurements done using very long baseline interferometry, we find that several earlier proper-motion surveys appear to have reported overly optimistic measurement uncertainties, most likely because of a failure to fully account for ionospheric effects. We discuss difficulties inherent in estimating pulsar velocities from proper motions given poorly constrained pulsar distances. Our observations favor a distribution with 20% of pulsars in a low-velocity component (σrm1D = 99 km s-1) and 80% in a high-velocity component (σ1D = 294 km s-1). Furthermore, our sample is consistent with a scale height of pulsar birthplaces comparable to the scale height of the massive stars that are their presumed progenitors. No evidence is found in our data for a significant population of young pulsars born far from the plane. We find that estimates of pulsar ages based on kinematics agree well with the canonical spin-down age estimate, but agreement is improved if braking indexes are drawn from a Gaussian distribution centered at n = 3 with width 0.8.

3099

, , , and

We present the first results from our planet-search program using the 9.2 m Hobby-Eberly Telescope (HET) at McDonald Observatory to detect planets around M-type dwarf stars by means of high-precision radial velocity (RV) measurements. Although more than 100 extrasolar planets have been found around solar-type stars of spectral type F–K, there is only a single M dwarf (GJ 876) known to harbor a planetary system. With the current incompleteness of Doppler surveys with respect to M dwarfs, it is not yet possible to decide whether this is due to a fundamental difference in the formation history and overall frequency of planetary systems in the low-mass regime of the Hertzsprung-Russell diagram, or simply an observational bias. Our HET M dwarf survey plans to survey 100 M dwarfs in the next 3 to 4 years, with the primary goal being to answer this question. Here we present the results from the first year of the survey, which show that our routine RV precision for M dwarfs is 6 m s-1. We found that GJ 864 and GJ 913 are binary systems with as yet undetermined periods, while five out of 39 M dwarfs reveal a high RV scatter and represent candidates for having short-period planetary companions. For one of them, GJ 436 (rms = 20.6 m s-1), we have already obtained follow-up observations, but no periodic signal is present in the RV data.

3108

, , and

By implementing a version of the dissipative mapping technique introduced by R. Malhotra, we have developed a new integration code for the N-body problem that incorporates the effects of radiation pressure, Poynting-Robertson (P-R) drag, and solar wind drag. The advantage of employing the dissipative mapping technique is that it modifies the basic N-body symplectic integration algorithm developed by Wisdom & Holman to allow certain nongravitational effects to be modeled and therefore retains the speed of execution common to codes based upon this algorithm. To achieve this, we have adapted the dissipative mapping technique to the requirements of the forces being modeled. We present the results of tests that demonstrate the suitability of this new dissipative integration code for investigating the dynamical behavior of micron-sized dust particles in heliocentric orbits in the solar system and, more generally, of particles in exosolar planetary systems where the dominant nongravitational perturbations to the particles' astrocentric orbits are due to the effects of radiation pressure, P-R drag, and solar wind drag.

3122

and

We have numerically investigated the long-term dynamical behavior of known Centaurs. This class of objects is thought to constitute the transitional population between the Kuiper belt and the Jupiter-family comets (JFCs). In our study, we find that over their dynamical lifetimes these objects diffuse into the JFCs and other sinks, and they also make excursions into the scattered disk, but (not surprisingly) do not diffuse into the parameter space representing the main Kuiper belt. These Centaurs spend most of their dynamical lifetimes in orbits of eccentricity 0.2–0.6 and perihelion distance 12–30 AU. Their orbital evolution is characterized by frequent close encounters with the giant planets. Most of these Centaurs will escape from the solar system (or enter the Oort cloud), while a fraction will enter the JFC population and a few percent will impact a giant planet. Their median dynamical lifetime is 9 Myr, although there is a wide dispersion in lifetimes, ranging from less than 1 Myr to more than 100 Myr. We find the dynamical evolution of this sample of Centaurs to be less orderly than the planet-to-planet "handoff" described in previous investigations. We discuss the implications of our study for the spatial distribution of the Centaurs as a whole.

3132

A model of the origin of the solar system is described based on equations obtained from a complex electromechanical stress tensor applied to a rotating, spherical primeval protosphere containing a low-density plasma. Ionization of the protosphere stems from a supernova displaced far from the sphere but sufficiently intense to ionize the sphere. The sphere collapses under gravity to a disklike domain. The lowest-order results of the expansion of the electromechanical relations yield an inhomogeneous differential equation for the electromechanical potential function. The solutions are shown to reduce to Bessel functions. A localized perturbation of a matter ring in a trough of the electromechanical potential grows to a protoplanet. The resulting planets out to Pluto are all found to have mean radii to the Sun in good agreement with measured values. The related magnetic field components are normal to the ecliptic plane. A number of properties, including orbital resonance between adjacent planets, are proposed to lend stability to two otherwise metastable orbits. Newtonian and Coulomb interactions enter in the electromechanical equations, and a unit dimensional constant contributes to the dimensional consistency of these relations. Five intervals are defined in the formation of the solar system. It is proposed that during the third interval outer coalescing matter rings comprise the precursors of the Jovian planets and that the asteroid belt, likewise formed in this interval, defines the spatial domain separating the regular lower matter rings and the coalescing higher matter rings. It is further proposed that to compensate for an increase in angular momentum in the fourth interval, Venus goes into retrograde spin rotation. Reasonable agreement with the observed disparity between mass and angular momentum for the Sun and the planets is obtained as well. The analysis is found to imply the existence of a 10th planet at a mean radius from the Sun of ≈51 AU.

3138

By adding the orbital angular momentum vector as another auxiliary quantity to be integrated, we extend our scaling methods to integrate quasi-Keplerian orbits numerically in order to suppress the growth of integration errors in the inclination and the longitude of the ascending node. This time, the method follows the time evolution of the angular momentum vector, as well as the time development of the Kepler energy and/or the Laplace integral, in addition to integrating the usual equation of motion. By using a rotation that is independent of the application of the spatial scaling, the new method adjusts the position and velocity integrated rigorously at each integration step in order to align both perpendicular to the integrated angular momentum vector. The direction and the angle of the rotation are determined uniquely from the position, the velocity, and the angular momentum vector integrated. As with the original scaling methods, the new method is simple to implement, fast to compute, and applicable to a wide variety of integration methods, perturbation types, and complexities of problems. Although this addition provides no significant decrease in the position error, the new method is superior to the original scaling methods in the sense that it enhances the quality of the integration by significantly reducing the errors of the orbital plane at the cost of a negligibly small amount of additional computation.