ast443, lecture 15 stanimir metchev
TRANSCRIPT
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Astrometry
AST443, Lecture 15Stanimir Metchev
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Administrative• Reading:
– Howell, chapters 5.8• Project 4, part II:
– you now have positions and instrumental magnitudes for all your stars– calibrate your photometry
• relative to the standard stars (open clusters)• relative to the mean change in magnitude of field stars (transiting planet)
– begin data analysis• plot CMDs and CCDs; separate known cluster members (open clusters)• eliminate variable stars; plot time variation of observed flux (transiting
planet)– complete by Mon, Nov 23
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Outline
• Reference system• Apparent stellar motions due to Earth’s orbital
motion and axial rotation• Proper stellar motion• Measuring positions and motions
– tangent-plane geometry– PSF sampling– focal plane distortion
• Example: the HR 8799 triple planetary system
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Reference (from Lecture 3):Equatorial Coordinate Systems• FK4
– precise positions and motions of 3522 stars– adopted in 1976– B1950.0
• FK5– more accurate positions (± 50 milli-arcsec), fainter stars– adopted in 1988– J2000.0
• ICRS (International Celestial Reference System)– extremely accurate (± 0.5 milli-arcsec)– adopted in 1998– 250 extragalactic radio sources
• Very-Long Baseline Interferometry (VLBI) measurements• negligible proper motions
– J2000.0
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Reference Point
• first point of Aries– a.k.a., “vernal
equinox”– R.A. = 0, DEC = 0– λ = 0, β = 0
• this is a fictitious,moving point!
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Precession and Nutation(from Lecture 3)
• The Earth precesses…– Sun’s and Moon’s tidal forces– precession cycle: 25,800 years– rate is 1º in 72 years (along
precession circle) = 50.3″/year
• … and nutates– Sun and Moon change relative
locations– largest component has period of
18.6 years (19″ amplitude)
eclipticcoords
NE
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Precession• Vernal equinox follows a retrograde motion
– 25725 year cycle (Platonic year)– ecliptic coordinates increase monotonically
• In ecliptic coordinates:P0 = 50.3878″ + 0.000049″ T lunisolarP1 = –0.1055″ + 0.000189″ T planetaryP = P0 + P1 cosε = 50.2910″ + 0.000222″ T total
T = number of tropical years since 1900ε = 23.439281º (obliquity of the ecliptic = Earth’s axial tilt)
• In equatorial coordinatesm = 46.124″ + 0.000279″ Tn = 20.043″ + 0.000085″ TPα = m + n sinα tanδPδ = n cosα
• Nutation: periodic change in rate of precession– e.g., NCP traces a 9.2″ ellipse every 18.6 yr due to inclination of Moon’s orbit
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Outline
• Reference system• Apparent stellar motions due to Earth’s orbital
motion and axial rotation• Proper stellar motion• Measuring positions and motions
– tangent-plane geometry– PSF sampling– focal plane distortion
• Example: the HR 8799 triple planetary system
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Annual Stellar Aberration
• Earth’s orbital motion causes a periodaberration in an object’s position– velocity of light is finite– angular size of correction is ~v/c
• over a year, star traces ellipse with axesk, k sinβ!
"# = $k cos(# $ #0)sec%
"% = $k cos(# $ #0)sin%
k = 20.49 & & 6
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Diurnal Stellar Aberration
• due to Earth’s axial rotation
• both annual and diurnal aberration shift entirefield– needed for pointing a telescope with ~1″ accuracy– not of concern if required relative positional
accuracy is >0.05″
!
"# = $k cos% cosh sec&
"& = $k cos% sinh sin&
k = $0.319 ' ' 8
% $ latitude, h $ hour angle
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Parallactic Motion
• annual– due to Earth’s annual orbital motion around Sun– i.e., same as in measuring trigonometric parallax
• diurnal– difference in zenith distance seen from Earth’s
surface vs. from geocenter– amplitude: (REarth / d) cos l
• d – distance to object in units of REarth, l – latitude• 57′ for Moon, 8.8″ for Sun
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Outline
• Reference system• Apparent stellar motions due to Earth’s orbital
motion and axial rotation• Proper stellar motion• Measuring positions and motions
– tangent-plane geometry– PSF sampling– focal plane distortion
• Example: the HR 8799 triple planetary system
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Apparent Proper Motion(from Lecture 3)
• µ ≡ annual proper motion• θ ≡ position angle (PA) of
proper motion
Barnard’s star, 1.8 pc, µ =10.3″/yr
equatorial coords
N
E
θ
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Apparent Proper Motion(from Lecture 3)
• µ ≡ annual proper motion• θ ≡ position angle (PA) of
proper motion
• relative to Local Standard ofRest (LSR) or heliocenter– average reference frame from
motions of nearby stars– Sun’s peculiar velocity w.r.t.
LSR is 19.5 km/s in direction of18.0h, 30° equatorial coords
N
E
θ!
µ" = µcos#
µ$ cos" = µsin#
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Radial Motion (or Velocity)
• blueshift, redshift• modulated by
– Sun’s motion (v = 220 km/s) around centerof Galaxy
– Earth’s motion around Sun (v = 29.8 km/s)– Earth’s axial rotation (v = 0.47cosl km/s)
!
vr
= c"#
#$ cz
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Stellar Space Motions
• UVW galacticcoordinates
• at Sun’slocation, moststars in diskhave– V ~ –20 km/s– U ~ 0 km/s– W ~ 0 km/s
U
V
W
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UVW Motions Example:Young Moving Groups
Zuckerman & Song (2004)
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Young Moving Groups
• <0.1 Gyr-old starscluster in adistinct UVW“box”
Zuckerman & Song (2004)
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Outline
• Reference system• Apparent stellar motions due to Earth’s orbital
motion and axial rotation• Proper stellar motion• Measuring positions and motions
– tangent-plane geometry– PSF sampling– focal plane distortion
• Example: the HR 8799 triple planetary system
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Tangent-Plane Geometry• sky is curved; images of it are flat
– measured X, Y positions do not translate linearly to angular coordinates onsky
– see map of Moving Groups (slide 17)
RA, DEC to X, Y X, Y to RA, DEC
αt, δt – RA, DEC of tangent point (where image is tangent to sky; usually, center of image)!
X = "1
S
cos# sin($ "$t)
sin# sin#t+ cos#cos#
tcos($ "$
t)
Y =1
S
sin#cos#t" cos# sin#
tcos($ "$
t)
sin# sin#t+ cos#cos#
tcos($ "$
t)
!
" = tan(#X /Y ) ; $ = tan S X2 +Y 2( )
% =%t+ arcsin
sin$ sin"
cos&tcos$ # sin&
tsin$ cos"
& = arcsin(sin&tcos$ + cos&
tsin$ cos")
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UVW Motions Example:Young Moving Groups
Zuckerman & Song (2004)
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Astrometry: Limitations(from Lecture 8)
• limiting precision– δr ~ FWHM / SNR– unattainable in practice
• systematic effects– differential atmospheric refraction– pixel sampling– focal plane curvature, distortion
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Atmospheric Refraction(from Lecture 4)
n (3200 Å) = 1.0003049n (5400 Å) = 1.0002929n (10,000 Å) = 1.0002890
differential atmosphericrefraction D between3200 Å and 5400 Å
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Astrometry: Pixel Sampling (from Lecture 8)
• r = FWHM / (pixel size)• r < 1.5: under-sampled• Nyquist sampling: r ~ 2 (r = 2.355, precisely)
– optimal SNR, error rejection, positional precision
• r > 2 desirable for best photometry, astrometry onbright point sources
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Hayward et al. (2001)
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Focal Plane Distortion: Beam Tilt
• in reality focal plane has a high-order curvatureMetchev (2006)
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Distortion of the Wide Field Camera onthe HST Advanced Camera for Surveys
HST ACS Instrument Handbook
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Distortion of the Wide Field Camera onthe HST Advanced Camera for Surveys
HST ACS Instrument Handbook
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HST Focal Plane
• HSTfocalplane
HST ACS Instrument Handbook
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Example: HR 8799 Planets
Marois et al. (2008)
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HR 8799bcd: Detection throughAngular Differential Imaging
Marois et al. (2008)
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HR 8799bcd: Astrometry
Marois et al. (2008)
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HR 8799bcd: Orbital Motions
Metchev et al. (2009); Konopacky et al. (2010)