The calculation of longitude and latitude from geodesic measurements

The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. [This is an English translation of F. W. Bessel, Astronomische Nachrichten 4(86), 241-254 (1825). The mathematical notation has been updated to conform to current conventions and, in a few places, the equations have been rearranged for clarity. Several errors have been corrected, a figure has been included, and the tables have been recomputed.]Comment: 11 pages, including 1 figure and 4 pages of tables. Version 2 and 3 fix some minor errors. This translation was edited by Charles F. F. Karney and Rodney E. Deakin. A transcription of the original paper is available at arXiv:0908.1823 . For links to other 18th and 19th century papers on geodesics, see http://geographiclib.sourceforge.net/geodesic-papers/biblio.htm

Quasar Parallax: a Method for Determining Direct Geometrical Distances to Quasars

We describe a novel method to determine direct geometrical distances to quasars that can measure the cosmological constant, Lambda, with minimal assumptions. This method is equivalent to geometric parallax, with the `standard length' being the size of the quasar broad emission line region (BELR) as determined from the light travel time measurements of reverberation mapping. The effect of non-zero Lambda on angular diameter is large, 40% at z=2, so mapping angular diameter distances vs. redshift will give Lambda with (relative) ease. In principle these measurements could be made in the UV, optical, near infrared or even X-ray bands. Interferometers with a resolution of 0.01mas are needed to measure the size of the BELR in z=2 quasars, which appear plausible given reasonable short term extrapolations of current technology.Comment: 13 pages, with 3 figures. ApJ Letters, in press (Dec 20, 2002

\"Uber die Berechnung der geographischen L\"angen und Breiten aus geod\"atischen Vermessungen

The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. [This is a transcription of F. W. Bessel, Astronomische Nachrichten 4(86), 241-254 (1825). The text follows the original; however the mathematical notation has been updated to conform to current conventions. Several errors have been corrected and the tables have been recomputed.]Comment: 11 pages, including 4 pages of tables. Versions 2 and 3 fixes some broken links. A facsimile of the original paper by F. W. Bessel is available at http://adsabs.harvard.edu/full/1825AN......4..241B . This transcription is by Charles F. F. Karney and Rodney E. Deakin. An English translation of this paper is available at arXiv:0908.182

Are Proxima and Alpha Centauri Gravitationally Bound?

Using the most recent kinematic and radial velocity data in the literature, we calculate the binding energy of Proxima Centauri relative to the center of mass of the Alpha Centauri system. When we adopt the centroids of the observed data, we find that the three stars constitute a bound system, albeit with a semi-major axis that is on order the same size as Alpha Centauri AB's Hill radius in the galactic potential. We carry out a Monte Carlo simulation under the assumption that the errors in the observed quantities are uncorrelated. In this simulation, 44% of the trial systems are bound, and systems on the 1-3 sigma tail of the radial velocity distribution can have Proxima currently located near the apastron position of its orbit. Our analysis shows that a further, very significant improvement in the characterization of the system can be gained by obtaining a more accurate measurement of the radial velocity of Proxima Centauri.Comment: 10 pages total, 4 pages of text, 1 page of references, 3 figures, and 2 tables This article will be published in The Astronomical Journa

Sub-Subgiants in the Old Open Cluster M67?

We report the discovery of two spectroscopic binaries in the field of the old open cluster M67 -- S1063 and S1113 -- whose positions in the color-magnitude diagram place them approximately 1 mag below the subgiant branch. A ROSAT study of M67 independently discovered these stars to be X-ray sources. Both have proper-motion membership probabilities greater than 97%; precise center-of-mass velocities are consistent with the cluster mean radial velocity. S1063 is also projected within one core radius of the cluster center. S1063 is a single-lined binary with a period of 18.396 days and an orbital eccentricity of 0.206. S1113 is a double-lined system with a circular orbit having a period of 2.823094 days. The primary stars of both binaries are subgiants. The secondary of S1113 is likely a 0.9 Mo main-sequence star, which implies a 1.3 Mo primary star. We have been unable to explain securely the low apparent luminosities of the primary stars; neither binary contain stars presently limited in radius by their Roche lobes. We speculate that S1063 and S1113 may be the products of close stellar encounters involving binaries in the cluster environment, and may define alternative stellar evolutionary tracks associated with mass-transfer episodes, mergers, and/or dynamical stellar exchanges

HST, VLT, and NTT imaging search for wide companions to bona-fide and candidate brown dwarfs in the Cha I dark cloud

We present results from a deep imaging search for companions around the young bona-fide and candidate brown dwarfs Cha Ha 1 to 12 in the Cha I dark cloud, performed with HST WFPC2 (R, I, Ha), VLT FORS1 (VRI), and NTT SofI (JHK). We find 16 faint companion candidates around five primaries with separations between 1.5" and 7" and magnitudes in R & I from 19 to 25 mag, i.e. up to 8 mag fainter than the primaries. While most of these companion candidates are probably unrelated background objects, there is one promising candidate, namely 1.5" SW off the M6-dwarf Cha Ha 5. This candidate is 3.8 to 4.7 mag fainter than the primary and its colors are consistent with an early- to mid-L spectral type. Assuming the same distance (140 pc) and absorption (0.47 mag in I) as towards the primary, the companion candidate has log (L(bol)/L(odot) = -3.0 +- 0.3. At the age of the primary (1 to 5 Myrs), the faint object would have a mass of 3 to 15 Jupiter masses according to Burrows et al. (1997) and Chabrier & Baraffe (2000) models. The probability for this companion candidate to be an unrelated fore- or background object is smaller than 0.7%, its colors are marginally consistent with a strongly reddened background K giant. One other companion candidate has infrared colors consistent with an early T-dwarf. In addition, we present indications for Cha Ha 2 being a close (0.2") binary with both components very close to the sub-stellar limit. Our detection limits are such that we should have detected all companions above 1 Jup with separations above 2" (320 AU) and all above 5 Jup at 0.35" (50 AU).Comment: A&A 384, 999-1011. appeared 2002, A&A 384, 999-101

A Rich Cluster of Galaxies Near the Quasar B2 1335+28 at z=1.1: Color Distribution and Star-Formation Properties

We previously reported a significant clustering of red galaxies (R-K=3.5--6) around the radio-loud quasar B2 1335+28 at z=1.086. In this paper, we establish the existence of a rich cluster at the quasar redshift, and study the properties of the cluster galaxies through further detailed analysis of the photometric data. The color distribution of the galaxies in the cluster is quite broad and the fraction of blue galaxies (\sim 70%) is much larger than in intermediate-redshift clusters. Using evolutionary synthesis models, we show that this color distribution can be explained by galaxies with various amounts of star-formation activity mixed with the old stellar populations. Notably, there are about a dozen galaxies which show very red optical-NIR colors but also show significant UV excess with respect to passive-evolution models. They can be interpreted as old early-type galaxies with a small amount of star formation. The fact that the UV-excess red galaxies are more abundant than the quiescent red ones suggests that a large fraction of old galaxies in this cluster are still forming stars to some extent. However, a sequence of quiescent red galaxies is clearly identified on the R-K versus K color-magnitude (C-M) diagram. The slope and zero point of their C-M relation appear to be consistent with those expected for the precursors of the C-M relation of present-day cluster ellipticals when observed at z=1.1. We estimate the Abell richness class of the cluster to be R \sim 1. New X-ray data presented here place an upper limit of L_x < 2 10^{44} erg s^{-1} for the cluster luminosity. Inspections of the wider optical images reveal some lumpy structure, suggesting that the whole system is still dynamically young.Comment: 54 pages including 13 Postscript figures, 1 jpg figure, and 1 table, uses aasms4.sty and epsf.sty. Accepted for publication in ApJ: Replaced as the older verison was missed to include the figure 2c, 2d, and figure

Distances, ages, and epoch of formation of globular clusters

We review the results on distances and absolute ages of galactic globular clusters (GCs) obtained after the release of the Hipparcos catalogue. Several methods for the Population II local distance scale are discussed, exploiting NEW RESULTS for RR Lyraes in the Large Magellanic Cloud (LMC). We find that the so-called Short and Long Distance Scales may be reconciled whether a consistent reddening scale is adopted for Cepheids and RR Lyrae variables in the LMC. Distances and ages for the 9 clusters discussed in Paper I are re-derived using an enlarged sample of local subdwarfs, which includes about 90% of the metal-poor dwarfs with accurate parallaxes (Delta p/p < 0.12) in the whole Hipparcos catalogue. On average, our revised distance moduli are decreased by 0.04 mag with respect to Paper I. The corresponding age of the GCs is t=11.5+-2.6 Gyr (95% confidence range). The relation between Mv(ZAHB) and metallicity for the nine programme clusters turns out to be Mv(ZAHB)=(0.18+-0.09)([Fe/H]+1.5)+(0.53+-0.12).Thanks to Hipparcos the major contribution to the total error budget associated with the subdwarf fitting technique has been moved from parallaxes to photometric calibrations, reddening and metallicity scale. This total uncertainty still amounts to about +-0.12 mag. Comparing the corresponding (true) LMC distance modulus 18.64+-0.12 mag with other existing determinations, we conclude that at present the best estimate for the distance of the LMC is: 18.54+-0.03+-0.06, suggesting that distances from the subdwarf fitting method are 1 sigma too long. Consequently, our best estimate for the age of the GCs is revised to: Age = 12.9+-2.9 Gyr (95% confidence range). The best relation between Mv(ZAHB) and [Fe/H] is: Mv(ZAHB) =(0.18+-0.09)([Fe/H]+1.5)+(0.63+-0.07).Comment: 76 pages, 6 encapsulated figures and 6 tables. Latex, uses aasms4.sty. Revised and improved version, with new data on field RR Lyraes in LMC. Accepted in the Astrophysical Journa

Detection of eccentric supermassive black hole binaries with pulsar timing arrays:Signal-to-noise ratio calculations

We present a detailed analysis of the expected signal-to-noise ratios of supermassive black hole binaries on eccentric orbits observed by pulsar timing arrays. We derive several analytical relations that extend the results of Peters and Mathews [Phys. Rev. D 131, 435 (1963)] to quantify the impact of eccentricity in the detection of single resolvable binaries in the pulsar timing array band. We present ready-to-use expressions to compute the increase/loss in signal-to-noise ratio of eccentric single resolvable sources whose dominant harmonic is located in the low/high frequency sensitivity regime of pulsar timing arrays. Building upon the work of Phinney (arXiv:astro-ph/0108028) and Enoki and Nagashima [Prog. Theor. Phys. 117, 241 (2007)], we present an analytical framework that enables the construction of rapid spectra for a stochastic gravitational-wave background generated by a cosmological population of eccentric sources. We confirm previous findings which indicate that, relative to a population of quasicircular binaries, the strain of a stochastic, isotropic gravitational-wave background generated by a cosmological population of eccentric binaries will be suppressed in the frequency band of pulsar timing arrays. We quantify this effect in terms of signal-to-noise ratios in a pulsar timing array.Comment: 18 pages, 9 figures, 3 Appendices. Submitted to PRD. v2: typos corrected, references added. Accepted to PR

GJ 900: A new hierarchical system with low-mass components

Speckle interferometric observations made with the 6 m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences in 2000 revealed the triple nature of the nearby ($\pi_{Hip}=51.80\pm1.74$ mas) low-mass young ($\approx200$ Myr) star GJ 900. The configuration of the triple system allowed it to be dynamically unstable. Differential photometry performed from 2000 through 2004 yielded $I$- and $K$-band absolute magnitudes and spectral types for the components to be $I_{A}$=6.66$\pm$0.08, $I_{B}$=9.15$\pm$0.11, $I_{C}$=10.08$\pm$0.26, $K_{A}$=4.84$\pm$0.08, $K_{B}$=6.76$\pm$0.20, $K_{C}$=7.39$\pm$0.31, $Sp_{A}$$\approx$K5--K7, $Sp_{B}$$\approx$M3--M4, $Sp_{C}$$\approx$M5--M6. The ``mass--luminosity'' relation is used to estimate the individual masses of the components: $\mathcal{M}_{A}$$\approx0.64\mathcal{M}_{\odot}$, $\mathcal{M}_{B}$$\approx0.21\mathcal{M}_{\odot}$, $\mathcal{M}_{C}$$\approx0.13\mathcal{M}_{\odot}$. From the observations of the components relative motion in the period 2000--2006, we conclude that GJ 900 is a hierarchical triple star with the possible orbital periods P$_{A-BC}$$\approx$80 yrs and P$_{BC}$$\approx$20 yrs. An analysis of the 2MASS images of the region around GJ 900 leads us to suggest that the system can include other very-low-mass components.Comment: 7 pages, 5 figure