THE MAGELLANIC CLOUDS NEWSLETTER

An electronic publication dedicated to the Magellanic Clouds, and astrophysical phenomena therein

No. 85 — 1 February 2007

http://www.astro.keele.ac.uk/MCnews

Editors: Jacco van Loon and Snežana Stanimirović

Editorial

Dear Colleagues,

It is our pleasure to present the 85^{th} issue of the Magellanic Clouds Newsletter. Two very interesting contributions discuss the tidal effects on the Magellanic Clouds, creating the Magellanic Bridge (Harris) and causing tidal heating of the disk of the LMC (Olsen & Massey). Several other contributions shed new light on the late stages of stellar evolution from studies in the Magellanic Clouds

There are two job announcements, one for a postdoctoral fellowship and another one for PhD studentships. And you might well be interested in the release of shape, a powerful tool for interpreting position-velocity datacubes.

The next issue will be distributed on the 1^{st} of April; the deadline for contributions is the 31^{st} of March.

Editorially Yours,

Jacco van Loon and Snežana Stanimirović

Refereed Journal Papers

Confirmation of New Planetary Nebulae in the Large Magellanic Cloud

Richard A. Shaw^{1}, Warren A. Reid^{2,3} and Quentin A. Parker^{2,3}

1National Optical Astronomy Observatory 2Department of Physics, Macquarie University, Sydney, NSW 2109, Australia 3Anglo-Australian Observatory, PO Box 296, Epping, NSW 1710, Australia

We present Hubble Space Telescope (HST) images of new planetary nebulae (PNe) that were discovered in the Reid-Parker AAO/UKST Hα survey of the Large Magellanic Cloud. These serendipitous observations from various HST programs yield independent confirmations of 6 PNe; one other detected nebula may also be a PN, and one appears to be a region of diffuse emission. The high resolution HST archival images enable us to determine the physical sizes, the nebular morphology, and related features of these new PNe in detail for the first time. In a few cases we were also able to identify the central star, which was impossible with the lower resolution, wide-field discovery data. The confirmation of faint, extended halos surrounding many PNe in the RP catalog must await the acquisition of new deep, high-resolution, narrow-band imagery.

Accepted for publication in PASP Available from astro-ph/0612008

The Magellanic Bridge: The Nearest Purely Tidal Stellar Population

Jason Harris^{1}

1Steward Observatory, USA

We report on observations of the stellar populations in twelve fields spanning the region between the Magellanic Clouds, made with the Mosaic-II camera on the 4-meter telescope at the Cerro-Tololo Inter-American Observatory. The two main goals of the observations are to characterize the young stellar population (which presumably formed in situ in the Bridge and therefore represents the nearest stellar population formed from tidal debris), and to search for an older stellar component (which would have been stripped from either Cloud as stars, by the same tidal forces which formed the gaseous Bridge). We determine the star-formation history of the young inter-Cloud population, which provides a constraint on the timing of the gravitational interaction which formed the Bridge. We do not detect an older stellar population belonging to the Bridge in any of our fields, implying that the material that was stripped from the Clouds to form the Magellanic Bridge was very nearly a pure gas.

Accepted for publication in Astrophysical Journal Available from astro-ph/0612107

Hubble Space Telescope Fine Guidance Sensor Parallaxes of Galactic Cepheid Variable Stars: Period-Luminosity Relations

G. Fritz Benedict^{1}, Barbara E. McArthur^{1}, Michael W. Feast^{2}, Thomas G. Barnes^{1}, Thomas E. Harrison^{3}, Richard J. Patterson^{4}, John W. Menzies^{5}, Jacob. L. Bean^{1} and Wendy L. Freedman^{6}

1McDonald Observatory, University of Texas, USA 2Astronomy Dept., University of Cape Town, South Africa 3Dept. Astronomy, New Mexico State University, USA 4Dept. Astronomy, University of Virginia, USA 5South African Astronomical Observatory, South Africa 6The Observatories, Carnegie Institution of Washington, USA

We present new absolute trigonometric parallaxes and relative proper motions for nine Galactic Cepheid variable stars: l Car, zeta Gem, beta Dor, W Sgr, X Sgr, Y Sgr, FF Aql, T Vul, and RT Aur. We obtain these results with astrometric data from Fine Guidance Sensor 1r, a white-light interferometer on Hubble Space Telescope. We find absolute parallaxes with an average σ_{π}/π = 8%. Two stars (FF Aql and W Sgr) required the inclusion of binary astrometric perturbations, providing Cepheid mass estimates. With these parallaxes we compute absolute magnitudes in V, I, K, and Wesenheit W_{V I} bandpasses corrected for interstellar extinction and Lutz-Kelker-Hanson bias. Adding our previous absolute magnitude determination for delta Cep, we construct Period-Luminosity relations for ten Galactic Cepheids. We compare our new Period-Luminosity relations with those adopted by several recent investigations, including the Freedman and Sandage H_{0} projects. Adopting our Period-Luminosity relationship would tend to increase the Sandage H_{0} value, but leave the Freedman H_{0} unchanged. Comparing our Galactic Cepheid PLR with those derived from LMC Cepheids, we find the slopes for K and W_{V I} identical in the two galaxies within their respective errors. Our data lead to a W_{V I} distance modulus for the Large Magellanic Cloud, m − M = 18.50 ± 0.03, uncorrected for any metallicity effects. Applying recently derived metalllcity corrections yields a corrected LMC distance modulus of (m − M)_{0} = 18.40 ± 0.05. Comparing our Period-Luminosity relationship to solar-metallicity Cepheids in NGC 4258 results in a distance modulus, 29.28 ± 0.08, which agrees with that derived from maser studies.

Accepted for publication in Astronomical Journal Available from astro-ph/0612465

First detection of photospheric depletion in the LMC

M. Reyniers^{1} and H. Van Winckel^{1}

1Instituut voor Sterrenkunde, Departement Natuurkunde en Sterrenkunde, K.U.Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium

Context. Recent photospheric abundance studies of galactic field RV Tauri stars show that depletion of refractory elements is rather common in these evolved objects. Aims. The process that creates this chemical anomaly is not understood well, but it probably requires the presence of gravitationally bound dust in a binary system. We test for the presence of depletion in extra-galactic objects. Methods. A detailed photospheric abundance study on the basis of high-quality UVES spectra was performed on the RV Tauri star in the LMC: MACHO 82.8405.15. Abundances were derived using a critically compiled line list with accurate log(gf) values and the latest Kurucz model atmospheres. Results. With [Fe/H] = −2.6 in combination with [Zn/Fe] = +2.3 and [S/Ti] = +2.5, MACHO 82.8405.15 displays a strong depletion abundance pattern. The effect of the depletion is comparable to the strongest depletions seen in field Galactic RV Tauri stars. Conclusions. The chemical analysis of MACHO 82.8405.15 proves that the depletion process also occurs in the extragalactic members of the RV Tauri pulsation class. Our program star is a member of a larger sample of LMC RV Tauri objects. This sample is unique, since the distances of the members are wellconstrained. Further studies of this sample are therefore expected to gain deeper insight into the poorly understood depletion phenomenon and of the evolutionary status of RV Tauri stars in general.

Accepted for publication in A&A Letters Available from astro-ph/0701327

A hypervelocity star from the Large Magellanic Cloud

Alessia Gualandris^{1} and Simon Portegies Zwart^{1}

1University of Amsterdam, The Netherlands

We study the acceleration of the star HE 0437–5439 to hypervelocity and discuss its possible origin in the Large Magellanic Cloud (LMC). The star has a radial velocity of 723 km s^{−1} and is located at a distance of 61 kpc from the Sun. With a mass of about 8 M_{⊙}, the travel time from the Galactic centre is of about 100 Myr, much longer than its main sequence lifetime. Given the relatively small distance to the LMC (18 kpc), we consider it likely that HE 0437– 5439 originated in the cloud rather than in the Galactic centre, like the other hypervelocity stars. The minimum ejection velocity required to travel from the LMC to its current location within its lifetime is about 500 km s^{−1}. Such a high velocity can only be obtained in a dynamical encounter with a massive black hole. We perform 3-body scattering simulations in which a stellar binary encounters a massive black hole and find that a black hole more massive than 10^{3} M_{⊙} is necessary to explain the high velocity of HE 0437–5439. We look for possible parent clusters for HE 0437–5439 and find that NGC 2100 and NGC 2004 are young enough to host stars coeval to HE 0437–5439 and dense enough to produce an intermediate mass black hole able to eject an 8 M_{⊙} star with hypervelocity.

Accepted for publication in MNRAS Available from astro-ph/0612673

Long Secondary Periods and Binarity in Red Giant Stars

I. Soszynski^{1}

1Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa, Poland

Observational arguments supporting the binary explanation of the long secondary periods (LSP) phenomenon in red giants are presented. Photometry of about 1200 semiregular variables with the LSP in the Large Magellanic Cloud are analyzed using the MACHO and OGLE photometry. For about 5% of these objects additional ellipsoidal-like or eclipsing-like modulation with the same periods as the LSP is detectable. These double-humped variations are usually shifted in phase comparing to the LSP light curves. I discuss the model of binary system with a red giant as the primary component and a low-mass object as the secondary one. The mass lost by the red giant through the wind follows the spiral pattern in the orbit around the primary star and obscures it causing the LSP variations.

Accepted for publication in Astrophysical Journal Available from astro-ph/0701463

Evidence for Tidal Effects in the Stellar Dynamics of the Large Magellanic Cloud

Knut A.G. Olsen^{1} and Philip Massey^{2}

1NOAO, USA 2Lowell Observatory, USA

We present a combined analysis of the kinematics of the Large Magellanic Cloud through its H i gas, carbon stars, and red supergiant stars. After correcting the line-of-sight velocities for the recent accurate measurement of the LMC’s space motion, we find that each kinematic tracer clearly defines a flat rotation curve with similar shape but different amplitude for each tracer: 61 km s^{−1} for the carbon stars, 80 km s^{−1} for the H i, and 107 km s^{−1} for the red supergiants. Previously identified tidal H i features are seen to harbor numerous carbon stars, with the tidally disturbed stars comprising 7-15% of the total sample. This discovery implies that we cannot depend on the carbon star sample alone to construct a reliable model of the LMC’s gravitational potential. We also find red supergiants with peculiar kinematics, but their association with tidal features is unclear, and may instead be interacting with supergiant H i shell SGS4. In addition, although the local velocity dispersion of the red supergiants is small, ∼8 km s^{−1}, their velocity dispersion about the carbon star rotation solution is 17 km s^{−1}, equal to the velocity dispersion of the carbon stars themselves. We thus appear to be witnessing the tidal heating of the LMC’s stellar disk.

Accepted for publication in ApJ Letters Available from astro-ph/0701500

The globular cluster NGC 1978 in the Large Magellanic Cloud

A.Mucciarelli^{1}, F.R.Ferraro^{1}, L.Origlia^{2} and F.Fusi Pecci^{2}

1Dipartimento di Astronomia, Università di Bologna, Italy 2INAF - Osservatorio Astronomico di Bologna, Italy

We have used deep high-resolution Hubble Space Telescope ACS observations to image the cluster NGC 1978 in the Large Magellanic Cloud. This high-quality photometric data set allowed us to confirm the high ellipticity (∼ 0.30±0.02) of this stellar system. The derived Color Magnitude Diagram allowed a detailed study of the main evolutionary sequences: in particular we have detected the so called Bump along the Red Giant Branch (at V_{555} = 19.10 ± 0.10). This is the first detection of this feature in an intermediate-age cluster. Moreover the morphology of the evolutionary sequence and their population ratios have been compared with the expectations of different theoretical models (namely BaSTI, PEL and Padua) in order to quantify the effect of convective overshooting. The best agreement (both in terms of morphology and star counts) has been found the PEL ( Pisa Evolutionary Library) isochrone with Z = 0.008 (consistenly with the most recent determination of the cluster metallicity, [M/H]= −0.37 dex) and a mild overshooting efficiency (Λ_{os} = 0.1). By adopting this theoretical set an age of 1.9 ± 0.1 Gyr has been obtained.

Accepted for publication in AJ Available from astro-ph/0701649

X-ray bright sources in the Chandra Small Magellanic Cloud Wing Survey - detection of two new pulsars

Katherine E. McGowan^{1}, Malcolm J. Coe^{1}, Matthew Schurch^{1}, Vanessa A. McBride^{1}, Jose L. Galache^{2}, William R.T. Edge^{1}, Robin H.D. Corbet^{3}, Silas Laycock^{2}, Andrzej Udalski^{4} and David A.H. Buckley^{5,6}

1University of Southampton, UK 2Harvard-Smithsonian CfA, USA 3USRA/GSFC, USA 4Warsaw University Observatory, Poland 5South African Astronomical Observatory, South Africa 6Southern African Large Telescope Foundation, South Africa

We investigate the X-ray and optical properties of a sample of X-ray bright sources from the Small Magellanic Cloud (SMC) Wing Survey. We have detected two new pulsars with pulse periods of 65.8 s (CXOU J010712.6−723533) and 700 s (CXOU J010206.6−714115), and present observations of two previously known pulsars RX J0057.3−7325 (SXP101) and SAX J0103.2−7209 (SXP348). Our analysis has led to three new optical identifications for the detected pulsars. We find long-term optical periods for two of the pulsars, CXOU J010206.6−714115 and SXP101, of 267 and 21.9 d, respectively. Spectral analysis of a sub-set of the sample shows that the pulsars have harder spectra than the other sources detected. By employing a quantile-based colour-colour analysis we are able to separate the detected pulsars from the rest of the sample. Using archival catalogues we have been able to identify counterparts for the majority of the sources in our sample. Combining this with our results from the temporal analysis of the Chandra data and archival optical data, the X-ray spectral analysis, and by determining the X-ray to optical flux ratios we present preliminary classifications for the sources. In addition to the four detected pulsars, our sample includes two candidate foreground stars, 12 probable active galactic nuclei, and five unclassified sources.

Accepted for publication in MNRAS Available from astro-ph/0701184

HV 11423: The Coolest Supergiant in the SMC

Philip Massey^{1}, Emily M. Levesque^{2}, K. A. G. Olsen^{3}, Bertrand Plez^{4} and B. A. Skiff^{1}

1Lowell Observatory, USA 2Institute for Astronomy, University of Hawaii at Manoa, USA 3Cerro Tololo Inter-American Observatory, NOAO, USA 4GRAAL, Université de Montpellier II, France

We call attention to the fact that one of the brightest red supergiants in the SMC has recently changed its spectral type from K0-1 I (December 2004) to M4 I (December 2005) and back to K0-1 I (September 2006). An archival spectrum from the Very Large Telescope reveals that the star was even cooler (M4.5-M5 I) in December 2001. By contrast, the star was observed to be an M0 I in both October 1978 and October 1979. The M4-5 I spectral types is by far the latest type seen for an SMC supergiant, and its temperature in that state places it well beyond the Hayashi limit into a region of the H-R diagram where the star should not be in hydrostatic equilibrium. The star is variable by nearly 2 mag in V, but essentially constant in K. Our modeling of its spectral energy distribution shows that the visual extinction has varied during this time, but that the star has remained essentially constant in bolometric luminosity. We suggest that the star is currently undergoing a period of intense instability, with its effective temperature changing from 4300 K to 3300 K on the time-scale of months. It has one of the highest 12μm fluxes of any RSG in the SMC, and we suggest that the variability at V is due primarily to changes in effective temperature, and secondly, due to changes in the local extinction due to creation and dissipation of circumstellar dust. We speculate that the star may be nearing the end of its life.

Accepted for publication in Astrophysical Journal Available from astro-ph/0701769 and from http://www.lowell.edu/users/massey/hv11423.pdf.gz

Spectroscopy of SMC Wolf-Rayet Stars Suggests that Wind-Clumping does not Depend on Ambient Metallicity

S.V. Marchenko^{1}, C. Foellmi^{2,3}, A.F.J. Moffat^{4}, F. Martins^{5}, J.-C. Bouret^{6} and E. Depagne^{3,7}

1Department of Physics and Astronomy, Western Kentucky University, 1906 College Heights Blvd., 11077, Bowling Green, KY 42101-1077, USA 2Laboratoire d’Astrophysique, Observatoire de Grenoble, BP 53, 38041 Grenoble Cedex 9, France 3European Southern Observatory, 3107 Alonso de Cordova, Casilla 19001, Vitacura, Santiago, Chile 4Departement de Physique and Observatoire du Mont Megantic, Université de Montreal, CP 6128, Succursale Centre-Ville, Montreal, QC H3C 3J7, Canada 5Max-Planck-Institut für extraterrestrische Physik, Postfach 1312, D-85741 Garching, Germany 6Laboratoire d’Astrophysique de Marseille, Traverse du Siphon - BP 8, 13376 Marseille Cedex 12, France 7Departamento de Astronomía y Astrofisica, Pontificia Universidad Catolica de Chile, Campus San Joaquin, Vicuña Mackenna 4860 Casilla 306, Santiago 22, Chile

The mass-loss rates of hot, massive, luminous stars are considered a decisive parameter in shaping the evolutionary tracks of such stars and influencing the interstellar medium on galactic scales. The small-scale structures (clumps) omnipresent in such winds may reduce empirical estimates of mass-loss rates by an evolutionarily significant factor of ≥ 3. So far, there has been no direct observational evidence that wind-clumping may persist at the same level in environments with a low ambient metallicity, where the wind-driving opacity is reduced. Here we report the results of time-resolved spectroscopy of three presumably single Population I Wolf-Rayet stars in the Small Magellanic Cloud, where the ambient metallicity is ∼ \frac{1}{5} Z_{⊙}.We detect numerous small-scale emission peaks moving outwards in the accelerating parts of the stellar winds. The general properties of the moving features, such as their velocity dispersions, emissivities and average accelerations, closely match the corresponding characteristics of small-scale inhomogeneities in the winds of Galactic Wolf-Rayet stars.

Accepted for publication in ApJ Letters Available from astro-ph/0701516

Conference Paper

SN 1987A at the end of its second decade

Karina Kjaer^{1}, Per Groeningsson^{2}, Rubina Kotak^{1}, Claes Fransson^{2} and Bruno Leibundgut^{1}

1ESO, Karl-Schwarzschild-Str. 2, D-85748 Garching b. Munich, Germany 2Stockholm Observatory, Department of Astronomy, AlbaNova, SE-106 91 Stockholm, Sweden

After nearly two decades at least five emission mechanisms can be found in SN 1987A. The ejecta continue to glow as a result of the radioactive decay of long-lived nuclei (mostly ^{44}Ti), but is fading continuously because of the expansion and the reduced opacity. The nearly stationary rings around SN 1987A are still fluorescing from the recombination of matter originally excited by the soft X-ray emission from the shock breakout at explosion. The supernova shock reached the inner circumstellar ring about ten years ago and the forward shock is moving through the inner ring and leaves shocked material behind. This material is excited and accelerated. The reverse shock illuminates the fastmoving supernova ejecta as it catches up. And, finally light echoes in nearby interstellar matter can still be observed. We present here high resolution spectroscopy in the optical and integral-field spectroscopy in the near infrared of SN 1987A and its rings.

Oral contribution, published in the Cefalu conference, ”The Multicoloured Landscape of Compact Objects and their Explosive Origins” Available from astro-ph/0612177

Job Adverts

Postdoctoral Fellowship in Astrophysics

Applications are invited for a post-doctoral fellowship in the Astrophysics Group at Keele University. We are looking for a researcher with expertise and interests at the intersection of stellar nucleosynthesis, evolution and hydrodynamics. The appointee will work with Dr. Falk Herwig and research team members at the Joint Institute for Nuclear Astrophysics (JINA) and Los Alamos National Laboratory (LANL) in the US. To realize the collaborative aspects of this project it is expected that the appointee takes advantage of the opportunity to spend one quarter of each year at these participating institutions.

Our group (see http://www.astro.keele.ac.uk) is currently expanding to ten academic staff. We work in a wide range of fields mostly related to stars and their environments. The group is supported by a PPARC rolling grant.

The post is jointly funded 75% by a European Union grant to Keele and 25% by JINA, and is available initially for 2 years, with the a possibility for a third year depending on project progress and continued availability of funding. We have excellent computational resources for this project as well as adequate travel support. The position is open immediately.

Job packs are available from Human Resources Department, Keele University, vacancies@keele.ac.uk or www.keele.ac.uk/depts/uso/hr/cwisvacs.htm. Inquiries: Dr Falk Herwig (fherwig@astro.keele.ac.uk) or Prof Nye Evans (ae@astro.keele.ac.uk). Electronic applications to be submitted to vacancies@keele.ac.uk by March 5^{th}, 2007. Applicants should arrange to have three letters of reference sent to this address by that date as well.

Please quote post reference: RE07/05

See also http://www.jobs.ac.uk/jobfiles/SH383.html

PhD positions

INSTITUTE OF COSMOLOGY AND GRAVITATION UNIVERSITY OF PORTSMOUTH UNITED KINGDOM

PhD Studentships 2007

Research Projects in Stellar Population Modelling and Galaxy Evolution (supervisor: Dr Claudia Maraston)

Contact: Chris Jones, Research Administrator email: chris.jones@port.ac.uk tel: +44 23 9284 5151 fax: +44 23 9284 5626 web: www.icg.port.ac.uk

The Institute of Cosmology & Gravitation at the University of Portsmouth is a young, dynamic research department with RAE grade 5. We have 10 academic staff, 12 postdoctoral researchers and 18 PhD students. The ICG is a member of the Sloan Digital Sky Survey and of the UK cosmology supercomputer consortium. Group members participate in many international research collaborations, and we have a very active visitor programme.

The two studentships are funded by the European Community through a Marie Curie Excellence Grant and offer a salary including social insurances and pensions to students. The positions are open to students of any nationality.

Applications should reach us by 23^{rd} February 2007, but will be considered until the positions are filled.

PhD applicants should have or expect to obtain a good honours degree or equivalent in Astronomy or Physics. Applicants should send a CV and application form (see ICG website), a brief statement of general research interests, and arrange for 2 letters of recommendation to be emailed directly to

chris.jones@port.ac.uk,

or posted to:

Chris Jones, Research Administrator Institute of Cosmology and Gravitation Mercantile House University of Portsmouth Portsmouth, PO1 2EG UK

Scientific staff members:

Prof Roy Maartens, Head Prof Bob Nichol Prof David Wands Dr David Bacon Dr Marco Bruni Dr Rob Crittenden Dr Kazuya Koyama Dr Claudia Maraston Dr Will Percival Dr Daniel Thomas

See also http://www.icg.port.ac.uk

Announcement

SHAPE: New software for the modeling of astronomical objects in 3D

Software release announcement

Instituto de Astronomía, Universidad Nacional Autónoma de México, Ensenada, Baja California

Ensenada, January 24, 2007

The Institute of Astronomy at the Universidad Nacional Autónoma de México has released Version 1.0 of a new software system called Shape for general use by the scientific community. Shape is a morpho-kinematic modeling tool for astrophysical nebulae. The main application of Shape is to assist in the interpretation of observations. The morpho-kinematic 3D modeling is done with commonly available 3D modeling software like 3D Studio Max, Blender or the built-in 3D-module. Using a comfortable graphical interface, the user generates images and position-velocity (pv-) diagrams, channel maps and one dimensional spectral line shapes based on the Doppler-effect. The design purpose of Shape is the analysis of the 3D structure and kinematics of spatially resolved astrophysical nebulae in a way that can be compared directly with observations. It is particularly suited for the study of expanding nebulae like planetary nebulae and other structures with clear kinematical signatures like bow-shocks or accretion disks and other streaming flows that can be analyzed using the Doppler-effect. Shape may be applied to the interpretation of existing observations or the planning and prediction of observations based on a proposed model.

More information about Shape, including the software download, the current development status, published papers, examples and the user manual can be found on the ShapeSite:

http://www.astrosen.unam.mx/shape.

Shape has been designed and developed by Wolfgang Steffen from the Instituto de Astronomía, Universidad Nacional Autónoma, Ensenada, Baja California, Mexico, with scientific contributions to the design by José Alberto López (also from the IA-UNAM). The development of the public version of Shape has been in collaboration with Nicholas Koning from the University of Calgary (Canada).

Reference: Steffen, W., López, J.A., 2006, Morpho-kinematic modeling of gaseous nebulae with SHAPE, Revista Mexicana de Astronomía y Astrofísica 42, 99-105

Disclaimer: This software release is a Beta release and the software is provided ”as is”. No warranty is given for its fitness for a particular purpose. Neither the authors nor their employers can be held responsible in any way for incorrect scientific or other results that may follow from the usage and interpretation of models produced with Shape.

Acknowledgements: This project has obtained financial support by Universidad Nacional Autónoma de México (DGAPA PAPIIT projects IN108506, IN111803, IN112103), the Consejo Nacional de Ciencia y Tecnología CONACYT (project 49447) and the University of Calgary through a grant from the Natural Sciences and Engineering Council of Canada awarded to Sun Kwok.

See also http://www.astrosen.unam.mx/shape