and Magda Stavinschi - UNAM

An Introduction to Astrometry and Celestial Mechanics: A Proposed Syllabusp y

William van AltenaYale University

and

Magda StavinschiAstronomical Institute of the

Romanian Academy

ADeLA IV, Mexico, Feb. 12, 2008 1

Micro-arcsecond Astrometry:Micro arcsecond Astrometry:How did we get there?Hipp s k d th ld t th • Hipparcos awakened the world to the scientific potential of milli-arcsecond astrometry– Stellar structure & evolution local galactic Stellar structure & evolution, local galactic

structure and kinematics• VERA & VLBA showed us that micro-arcsecond

radio astrometry can be doney– Distance to the Orion cluster, proper motions in

jets• Gaia & SIM have excited us with the

p ssibilit f micr rcs c nd ptic l possibility of micro-arcsecond optical astrometry– Galactic structure and kinematics on a grand

scalescale– Definitive cosmological distance scales– Masses of exoplanets


Astrometry and Celestial Mechanics (ACM)Astrometry and Celestial Mechanics (ACM)A one-semester introductory syllabus

• Broad introduction to the fields to provide a basis for:– More specialized courses, where available

F ll s lf st d b st d ts h th s s ist– Follow-on self study by students when no other courses exist– Advanced international workshops on specialized topics– International summer research programs at institutes with

sp ci liz ti ns in st m t nd c l sti l m ch nics specializations in astrometry and celestial mechanics • Scaled to a 40-hour lecture course, but easily revised to other

standards like a 20-hour course by:d h d h d h – Reducing the depth covered in each section, or

– Selectively omitting some subject areas• Relative stress on subject areas will have to be adjusted to meet j j

the special needs of different institutions


Wh t till d t b dd d f ACMWhat still needs to be addressed for ACM

Th di• The audience– Ph.D. versus Masters degree

• Topic stress should probably vary according to the endpoint • Topic stress should probably vary according to the endpoint degree desired

• Training style– Lecture style course– Lecture plus observatory internship– Internships at institutes and observatoriesInternships at institutes and observatories– International Workshops on specific topics

• Course content– Topics need to be revised by specialists in each specific area


T i i t d ti f ACMTopic introductions for ACM• Astrometry and Celestial Mechanics are small Astrometry and Celestial Mechanics are small,

specialized fields– Course should be taught in conjunction with courses

h d d d l l whose science is aided by astrometry and celestial mechanics

• Stellar formation structure and evolutionStellar formation, structure and evolution• Solar and exo-planetary system discovery, formation,

structure and evolutionG l f ti t t (ki ti l d i l d • Galaxy formation, structure (kinematical, dynamical and spatial) and evolution

– Science introductions to each topic are critical to pmotivating students


ACM: General Organization

• Section 1: Opportunities and challenges for Astrometry in the 21st Century (3 hours)

• Section 2: Relativistic Foundations of Astrometry and Celestial Mechanics (10 hours)

• Section 3: Observing through the Atmosphere (7 hours)

• Section 4: From detected photons to the Celestial Sphere (14 hours)

• Section 5: Applications of Astrometry to Astronomical Topics (9 hours)


ACM 1: Opportunities and Challenges • (1.5 hr) Motivational lecture on why one should study

Astrometry using hot science topics that can now be addressed– Cosmological distance scaleg

• Galactic center• Cepheids and RR Lyraes• Magellanic clouds

– Dynamics of merging dwarf galaxy remnants– The Milky Way Galaxy

• The Galactic center Black Hole• Stellar census and the search for Dark Matter• Rotation of the Galaxy• Understanding the Disk, Thick Disk and Halo kinematics and dynamics

E l l di bi d h i i i– Extra-solar planets: discovery, orbits, masses and their origin– Stellar masses to 1% and stellar evolution constraints


ACM 1: The Modern Tools of Astrometry • (1.5 hr) Review of astrometric

satellites and telescopes that will be the tools of modern Astrometry

Large Synoptic Survey Telescope

Hi G i SIMADeLA IV, Mexico, Feb. 12, 2008 8

Hipparcos Gaia SIM

ACM 2: Relativity in yAstrometry and Celestial

MechanicsQuickTime™ and a

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• (3 hrs) Relativistic foundations of Astrometry and Celestial Mechanics:

– Basics of special and general relativity– Post-Newtonian approximation scheme– Relativistic astronomical reference systems and framesRelativistic astronomical reference systems and frames– Coordinate-dependent and measurable quantities– Relativistic astronomical time scales and their

li ti nsrealizations– Relativistic data reduction modeling– Relativistic equations of motion (test body around a q y

spherically symmetric body and N-body problem)


ACM 2: Celestial Mechanics of the N-body problem

• (4 hrs) Celestial Mechanics of th N b d blthe N-body problem

– The Sun, solar oblatenessMajor planets planetary rings– Major planets, planetary rings

– Minor planets, asteroid belts– The role of analytic techniques and numerical The role of analytic techniques and numerical

methods– The role of pulsar timing, laser and radio rangingp g, g g– High-resolution radial velocities– Analyzing binary and multiple systems from

• Micro-arcsecond positions• High-resolution radial velocities


ACM 2: Stellar Coordinate ACM 2: Stellar Coordinate Systems and Positions

• (2 hrs) Stellar Coordinate Systems and PositionsGl f t d d d fi iti– Glossary of terms used and definitions

– Transformation from ICRS to Observed Places of Starsof Stars

– Flow charts and formulae for the transformations

– IAU Nomenclature for Fundamental Astronomy - "Explanatory Document B, July 2006" -http://syrte obspm fr/iauWGnfa/NFA B pdfhttp://syrte.obspm.fr/iauWGnfa/NFA_B.pdf


ACM 3:The AtmosphereACM 3:The Atmosphere• (1 hr) The Earth’s atmosphere (troposphere):

– Models of the atmosphere and turbulencep– Refraction through a turbulent atmosphere– Refraction and absorption as a function of wavelength– The effect of refraction on positions– Special cases for Radio Astronomy

• (1 hr) Atmospheric limits to positional precision (optical and radio):– Beating the atmosphere at its game– Observational determinations of the limits– Theoretical interpretation of the observations– Tip-tilt and adaptive optics correction systems

I i– Image reconstruction– Phase referencing

• (0.5 hr) Diffraction-limited imaging:

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are needed to see this picture.

– Getting the ultimate resolution from your optics– HST, Gaia and Hipparcos– Speckle Imaging

G nd b s d bs ti ns in th inf dADeLA IV, Mexico, Feb. 12, 2008 12

– Ground-based observations in the infra-red

ACM 3: Optical Interferometry• (2 hrs) Beating the atmosphere(2 hrs) Beating the atmosphere

– Sparse apertures work since the sky is mostly empty

– Michelson interferometers: theory and Michelson interferometers: theory and calibration

• Existing systems: VLT, Keck, CHARA, NPOI, …

• Planned systems: PRIMA, SIM– Intensity interferometers– White-light interferometers, such as the

/HST/FGS– Speckle Interferometers– Imaging– Coronagraphy


ACM 3: Radio InterferometryQuickTime™ and a


• (2 hrs) Interferometry (Radio)– Highlights: The first micro-arcsecond parallaxesg g p

• Sharpless 269 result from VERA: π = +189 ± 8 µas!!!• http://veraserver.mtk.nao.ac.jp/hilight/pub070711/pub070711-e.html

Th d lib i f i i – Theory and calibration of existing systems• Connected-element, VLA, VLBI, VLBA, VERA

– Phase referencingPhase referencing– Physics of water masers– Gravitational deflection of light– Future instruments

• ALMA, SKA


ACM 4: Geometrical Optics for AstrometryACM 4: Geometrical Optics for Astrometry

• (3 hrs) Geometrical optics for Astrometry:– Refracting optics

• Filters & CCD windows– Beam shift, focus and image position errors

S id l b i• Seidel aberrations– Theory– Aberrations relevant to optical astrometry– Observational examplesObservat onal examples

– Reflecting optics• Conic sections• Seidel aberrations

– Two-mirror telescopes• Aberrations• Alignmentg

– Astrometric compensation for optical aberrations


ACM 4: Imaging detectorsg g• (1.5 hrs) Complexities of our modern detectors:

– Characteristics of astronomical CCD and CMOS detectorsCalibratin– Calibrating

• The signal sources• Noise sources (flat, bias, dark and read-out)• Charge transfer efficiency• Charge-transfer efficiency• Linearity and saturation• Fringing

– Optimizing the signal-to-noise Optimizing the signal to noise – Astrometry

• Image centers and centroids– PhotometryPhotometry

• Surface, Aperture and PSF photometry– Statistical techniques useful for CCD analyses

• (0 5 hr) Time delayed integration:• (0.5 hr) Time-delayed integration:– Letting the sky drift by and observing efficiently– Gaia, CTI, Sloan, and Quest.


ACM 4 M i l tACM 4: Measuring platesQuickTime™ and a


• (1 hr) Plate measuring machines– Scanning machines

C sm s PDS • Cosmos, PDS, …• Calibrating for thermo-mechanical drifts

– Step-and-repeat imaging of a plate• PMM, Star Scan, …• Stitching the “footprints” together

– Algorithms for photographic images• Astrometry• Photometry

– Calibration• Orthogonality of axes, periodic errors, detector time lags, etc.


ACM 4: Statistical AstronomyACM 4: Statistical Astronomy• (1.5 hrs) Statistics and errors:

– Introduction to error analysis– The Malmquist bias– The Lutz-Kelker corrections

• Luminosity• Masses

– Monte-Carlo modelingg– Statistical and Secular parallaxes


ACM 4: Image DeconvolutionACM 4: Image Deconvolution• (0.5 hr) Analyzing poorly-sampled images

– HST imaging astrometry and photometryHS mag ng astrom try an photom try

• (1 hr) Image deconvolution– Theory– Noise sourcesNoise sources– Aberrated PSF’s– Good PSF’s but correcting for atmospheric degradation

Potential gain in precision– Potential gain in precision– Potential gain in limiting magnitude– Cost in computing CPU needed


ACM 4: Modeling the Focal PlaneACM 4: Modeling the Focal Plane• (3 hrs) From measures to celestial coordinates:

– Telescope-modeling techniques– Telescope-modeling techniques.• Gnomonic to focal plane calibrations• Focal-plane arrays of CCD’s

L ki f t ti • Looking for systematic errors– Extending astrometric calibration regions to fainter objects

and to different passbands.• (1 hr) Calibration of imaging detectors:

– Mosaic cameras – HST imaging cameras– HST imaging cameras– Time-delayed integration systems

• Sloan, QuEST, etc.


ACM 4: CatalogsACM 4: Catalogs• (2 hrs) Catalogs

– FundamentalFun am nta• ICRF and radio astrometry

– Optical reference system• ICRS, Hipparcos and Tycho, pp y• Looking to Gaia• Extending to fainter magnitudes

– UCAC, NPM & SPM• Value of “non-astrometric” catalogs: 2MASS, DENIS, Sloan

– Schmidt-based catalogs• GSC, Digital Sky Survey, USNO A2.0 & B-1, Cosmos, SRC, …h l b– The Virtual Observatory• National versions of the VO• NOMAD - the “astrometric” VO


ACM 5: Galactic StructureACM 5: Galactic Structure• (2 hrs) Galactic Structure

astrometry:– The role that astrometry plays

in defining parameters of:g p• Spatial structure• Kinematical and dynamical

structurestructure• Local Group of galaxies• Galactic cannibalism

M difi i h d i l – Modifications to the dynamical equations required by Micro-arcsecond proper motions


ACM 5: Luminosities of stars ACM 5: Luminosities of stars • (2.0 hr) Trigonometric Parallaxes:

– Highlights: Gaia and SIM give parallaxes of Cepheids, RR L th G l ti C t d Lyraes, the Galactic Center and the Magellanic Clouds!

– Absolute vs relative parallaxes– Absolute vs relative parallaxes– Calibration of luminosities and

masses– The Lutz-Kelker statistical

corrections to luminosity


ACM 5: Masses of starsACM 5: Masses of stars• (2.5 hrs) Binary and multiple stars

H hl h f h lk ’ – Highlights: Mass of the Milky Way’s Black Hole, …

– Determining orbital parameters from b ti

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observations– Speckle interferometric observations– Space-based methods and the principal

ltresults– Long baseline optical interferometry

(CHARA, VLTI, Keck, PRIMA, …)S s f bi t s– Surveys of binary parameters

– The Lutz-Kelker statistical corrections to mass


ACM 5: Star clusters & the Solar system

• (0.5 hr) Star clusters:QuickTime™ and a

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– Highlights: Gaia and SIM give definitive:• Distances• Membership determinationsp• Internal motion determinations

• (1.0 hr) Solar System astrometry:– Finding Extra-solar planetsFinding Extra solar planets– Moving object astrometry

• NEO’s, Minor planets and comets• Algorithms• Algorithms

– Observing in the glare of a bright planet– Lunar occultations

Ext s l l ts– Extra-solar planets• Optical astrometry• Radial velocity observations

b d d ( M G l )ADeLA IV, Mexico, Feb. 12, 2008 25

• Space-based discovery (SIM, Gaia, Kepler, …)

ACM 5: Astrometry & CosmologyACM 5: Astrometry & Cosmology

• (0.5 hr) How astrometry can help even at the edge of th i s :the universe:– Constraining critical

cosmological parameters.QuickTime™ and a


– Search for primordial gravitational waves

– Astrometry of gamma-y gray bursters


ConclusionsConclusions• The evolution of Astrometry from ground- to

space-based has resulted in greatly increased space based has resulted in greatly increased accuracy and that requires:– Reformulation of the equations in the context of special

d l l ti itand general relativity– Our old curricula are outdated and need to be completely

revised• This is especially critical in countries with direct access to

space-based observations– A range of teaching methods and opportunities are g g pp

needed• Lecture courses, internships, workshops, summer schools


Acknowledgements• Colleagues who provided us with many suggestions • Colleagues who provided us with many suggestions

for the one-semester syllabus in Astrometry and Celestial Mechanics:– Sergei Kopeikin, Sergei Klioner, Nicole Capitaine, Ana

Gomez, Wenjing Jin, Stephen Unwin, Elliott Horch, Michael Perryman, Catherine Turon, Michael Efroimsky, y yKenneth Seidelmann, Steve Majewski and others

• NSF, NASA, ESA, & ESO, who provide us with outstanding facilities for astrometric researchoutstanding facilities for astrometric research.

ReferenceEducating astrometry and celestial g ymechanics students for the 21st centuryvan Altena, W. F., Stavinschi, M.IAU Symposium 248, Shanghai, October 2007.


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and Magda Stavinschi - UNAM