AST325/6 – Praccal Astronomy 2014-2015

Lecture #8: Introducon to Photometry and Astrometry

Shelley Wright (Dunlap/DAA, University of Toronto)

November 3, 2014

S. Wright - AST325 Brian Schmidt (Nobel Prize Winner)

• Howard Yee scheduling meeng for undergraduates to meet with Brian Schmidt during his visit • Can everyone meet at 11AM – 12PM on Thursday, Nov 20th? • Tuesday Nov 18: 11AM-12PM, 2-3PM, 3-4PM, 4-5PM??? • Thursday Nov 20: same slots??

S. Wright - AST325 Goals of Lab #3: Astrometry

• Learn more about imaging properes of a CCD and coordinate systems • Further applicaons of least-square fing • Query astronomical databases and catalogs • Plan and execute observaons • Data reducon techniques for imaging data • Learn about proper moons and astrometry

S. Wright - AST325 I. Stellar Photometry

S. Wright - AST325 What are the essenal factors that define what an “image” looks like?

• Diffracon-limit: – telescope and/or imaging system (e.g., your eye’s pupil), f(λ) • Sensivity: – total collecng area of the telescope, f(λ) – throughput of opcs and atmosphere, f(λ) – QE of detector, f(λ) – Frame rate of detector – Detector spaal sampling (pixel size and plate scale) • Seeing: – Atmospheric turbulence, f(λ)

S. Wright - AST325 Point Spread Funcon of DI Telescope Star Field

S. Wright - AST325 NGC 6397, Hubble S. Wright - AST325 Why do bright stars “look” bigger than faint stars? • The FWHM of the stars are the same, but the intensity of the stars are different with respect to the background (or image stretch)

Sensivity limit (or image stretch)

S. Wright - AST325 Principles of photometry

• The light from a star is spread over several pixels non-uniformly • How do we sum the light to get a measure of the total flux from the star? – Idenfy the locaon of the star – Select the associated pixels that contain the stellar flux by generang a masking region – Sum up the light • Ensure that the noise and background is not included

S. Wright - AST325 Determining the center

• For each star we can find its centroid by determining the first moments along a 2d array, y I ∑xiIi ∑ j j x = i y = j I ∑Ii ∑ j i j

where I is the intensity at each pixel locaon (x,y)

S. Wright - AST325 Aperture photometry

• How would you define the aperture mask on the star? – What radius of an aperture? – Where would you define the sky region?

Sky annulus aperture Sky annulus

aperture

S. Wright - AST325 Photometric Model

• Star – Brightness

– Center (x0, y0) – Width (σ) • Sky background in annulus – B • Detector r1 – QE, readnoise, dark current r2 • Aperture sizes r3

– r1, r2, r3

S. Wright - AST325 Photometric Model

• Write down an expression for the signal, Si , in units of photoelectrons – In an individual pixel

Si = Fi + Bi + Qi + Ei

- – Fi is the stellar signal = fi t at pixel i [e ] • Different for every pixel - – Qi is the dark charge = ii t [e ] in a given pixel • The dark current iivaries from pixel to pixel • For SNR model assume constant - – Bi is the sky background = bit assumed uniform [e ] • Varies from pixel to pixel, for SNR model assume constant - – Ei is the readout electronic offset or bias [e ] • Varies from pixel to pixel, for SNR model assume constant

S. Wright - AST325 The Stellar Signal

• The stellar signal is found by subtracng the background from Si and summing over the N pixels that contain the star

; Flux per pixel Fi = Si − (Bi + Qi + Ei )

N1 N1 ; Total flux of star in FN = ∑ Fi = ∑Si − (Bi + Qi + Ei ) i=1 i=1 circular aperture 2 N1 = πr1

• Error in FN is due to noise in the signal itself, FN • Noise due to dark charge per pixel, Qi • Noise from the background per pixel (e.g., from atmosphere), Bi 2 • The read out noise σRO can define the Error, Ei

S. Wright - AST325 Noise in the stellar aperture

• The total noise is a funcon of the Poisson noise of the stellar signal and noise (background, dark current, readnoise) in the stellar aperture (N1)

N1 N1 # & N1 % ( FN = ∑Fi = ∑ Si −(Bi +Qi + Ei ) i 1 i 1 % ( = = $ Background '

σ 2 = F + N B + Q +σ 2 F N 1 ( RO ) Poisson signalnoise  Poisson noisewithin r1

• Where and is the mean background and dark current per 2 pixel and N1 = πr1

S. Wright - AST325 Including all noise sources

• You must also include the noise N1 from the background annulus (N23),

2 2 σ Sky = ( B + Q +σ RO ) / N23

r1 2 2 2 N1 = πr1 , N23 = πr3 − πr2   r2 Star Sky r3 N23 • Then you get the total noise source from stellar aperture and sky annulus,

σ 2 = F + N B + Q +σ 2 + N B + Q +σ 2 / N F N 1 ( d RO ) 1 ( d RO ) 23 Poisson signalnoise   Poisson noisewithinr1 Poisson noisewithinr2

S. Wright - AST325 Signal-to-noise rao for aperture photometry

Signal F SNR = N F + N B + Q + σ 2 + N B + Q + σ 2 / N N 1 (       RO ) 1 (       RO )  23 Signal Noise SkyDark& RON SkyDark& RON instar aperture inskyaperture

• How do we choose r1 , r2 , r3? – Signal increases with N1 – Noise increases with N1 and decreases with N23

For more generalized with N number of frames see Mclean, “Electronic Imaging in Astronomy”

S. Wright - AST325 How does flux change with aperture radius?

• Suppose the stellar signal has a 2-d Gaussian shape

2 F0 ⎡ 1 ⎛ ri ⎞ ⎤ 2 2 2 Fi = 2 exp⎢ − ⎥ , ri = (x − x0 ) + (y − y0 ) 2πσ 2 ⎝ σ ⎠ ⎣ ⎦ i

r1 F = 2π rFdr N ∫0 i

– This tells us how FN changes with aperture radius

S. Wright - AST325 Stellar profile and integral

• You can determine what percentage of light is found per aperture radius – Useful for determining aperture radii – Useful when you need to use “aperture correcon” • When the total flux is outside the aperture, like for crowded field photometry – Useful for defining SNR per radius

S. Wright - AST325 II. Astrometry

S. Wright - AST325 Astrometry • Astrometry is the measurement of posion and moon of celesal objects • Oldest branch of astronomy – In 129 BC Hipparcos generated the 1st catalog of stars with apparent brightness and posional accuracy to 1° – Revoluonized by Tycho Brahe in 16th century and measured posions of stars to 1 arcminute – Posions were measured to 1 arcsecond precision by the 18th century with new instruments and the telescope – In 1989 Hipparcos satellite launched Courtesy ESA and had an astrometric precision of 0.001” S. Wright - AST325 Importance of astrometry

• Astrometry is used to determine: – Distances to nearby stars using parallax – Proper moons of stars • Kinemac structure of the galaxy – Distance scale of the Milky Way and beyond • Stellar formaon and evoluon – Orbits of solar system objects, binary stars, exoplanets, stellar populaons • Direct way of determining the mass of celesal objects • Determine the mass of stellar black holes and the supermassive black hole at the Galacc Center • Determine the orbit of asteroids and comets – Probability of Earth geng slammed! – Solar System formaon – Astrometric mircolensing • Determine the mass of the lens source accurately • Mumber density compact objects

S. Wright - AST325 Proper Moon • Objects in our solar system, galaxy, and extragalacc sources have their own velocies – Closer the source and higher the velocies the greater moon on the projecon of the sky, which is known as “proper moon” • Typical proper moon of nearby stars is 0.1” per year • Typical proper moon of main belt asteroids is ~0.5-1’ per hour • NEO’s can move have as fast as 2.5° per day Arcturus radial velocity

Δt Radial velocity

μ Star’s velocity Sun

Proper moon S. Wright - AST325 Barnard’s star, 10.3” per year Astrometry discovered the dwarf planet Eris (the “Pluto killer”!) • Eris moves at 1.75” per hour and was discovered by 1.2m telescope (Brown et al. 2005, ApJL) – 27% more massive than Pluto

Eris

Eris’s moon Dysnomia Palomar (1.2m telescope) Discovery Image! Hubble S. Wright - AST325 Astrometry determined the mass of the MW’s supermassive black hole • Using adapve opcs and 8-10m ground-based telescope the relave astrometric precision is 100 μas (0.0001”) • Monitor the stellar orbits over 15+ years UCLA Galacc Center Group S. Wright - AST325 Future Space-Based Astrometry Missions • GAIA telescope launches in 2013 and will be next all-sky survey telescope – Measure the posion and radial velocity of 1 billion stars and galaxies in the Local Group – Astrometric precision to 0.00002” (20μas) • The width of human hair at 1,000 km distance Courtesy ESA

S. Wright - AST325 Reference frames

• The concept of posion in space is relave – You need to define a coordinate system (e.g., Celesal coordinates, standard coordinates) – You need to define posion relave to other celesal objects for given Equinox • Everything in the Universe is moving! • A “reference frame” is a catalog of known posions and proper moons of celesal objects – For astrometry you use reference frames to define the posion and moon of the object of study

S. Wright - AST325 Reference star catalogs

• All-sky surveys have generated catalogs of stars with posions per Equinox and proper moons – Hipparcos contains posions, proper moon, parallaxes of 118,218 stars. Complete to V=7.5 mag. – Tycho-2 contains posions and proper moon of over 2 million stars. Complete to V=11.0 mag. – USNO-B1 contains posions and proper moon of over 1 billion objects. All-sky coverage to V=21 mag. – Sloan Digital Sky Survey mapped ¼ of the sky in 5 opcal filters and contains 287 million objects

We will be using the USNO-B1 catalog in Lab #3 S. Wright - AST325 Internaonal Celesal Reference System and Frame (ICRS) • Fundamental reference system adopted by Internaonal Astronomical Union (IAU) – Reference system of celesal sphere defined by the barycenter of the solar system – Reference frame is with respect to distant extragalacc objects that are considered fixed • Based on radio posions from the VLBI of Quasars • Posional accuracy is 0.5 mas (0.0005”)

ICRS – VLBI Quasar reference

S. Wright - AST325 Absolute astrometry

• “Absolute astrometry” is the posion of celesal object with respect to an absolute reference frame – Like the reference frame of ICRS – Defines the posion and moon with a “stable” reference frame • Absolute astrometric accuracy: how well one can measure the posion of an object on the sky with respect to a known coordinate system – Important for matching observaons from different telescopes and instruments

S. Wright - AST325 Relave astrometry

• “Relave astrometry” is astrometry measured with respect to other objects in the same observaonal field • Relave astrometric precison; how well we can measure the separaon between two sources • Relave astrometric accuracy; repeatability of relave astrometric precision and the systemacs between observaons on long term mescales

S. Wright - AST325 Coordinate transformaons to the image plane • Celesal coordinates are defined on spherical coordinate system, but a CCD image is a Cartesian coordinate system on the plane of the sky

Celestial pole The projected coordinates (X, Y) of a Y posion on the celesal sphere (α, δ) X in the vicinity of a field centered at (α0, δ0) are,

(α, δ) δ0 cosδ sin(α −α 0 ) X = − α cosδ 0 cosδ cos(α −α 0 ) + sinδ sinδ 0 0 Celestial equator ! sinδ 0 cosδ cos(α −α 0 ) − cosδ 0 sinδ Y = − cosδ 0 cosδ cos(α −α 0 ) + sinδ sinδ 0

! Derivaon in the Lab #3 write-up S. Wright - AST325 Converng to pixel coordinates (x,y) of the CCD • The CCD has plate scale (pixel per arcseconds) that is defined by the focal length (f) of the camera and the size of the CCD pixels (p) • For an “ideal” camera and detector the x, y posion on the detector can be found by,

x = f (X p) + x0

y = f (Y p) + y0

• Of course a number of factors make this non- ideal with opcal distoron, anamorphic magnificaon and the CCD rotaon on sky

S. Wright - AST325 Lab #3 proper moon of asteroids • The key steps of the lab: 1. Read FITS files from the CCD on the 50-cm telescope and display the data using the Python PyFITS library (§3.1); 2. Apply systemac correcons including dark and flat field (§3.3); 3. Compare your field image with the digital sky survey and confirm that field is correct (§4); 4. Measure the posions of the stars in your CCD image (§4.1); 5. Cross-correlate the stars in your image with those in the USNO B-1 star catalog (4.2); 6. Compute the “standard coordinates” for the USNO B-1 stars and match the two lists (§4.3); 7. Perform a linear least squares fit to find the “plate constants”(§5); 8. Examine the residuals between the measurements and the fit; 9. Schedule observaons with the DI Telescope of a field including an asteroid; 10. Reduce your DI telescope observaons using your observed darks and flat field; 11. Use your Python code to compute the posion (and associated errors) of the asteroid; 12. Determine your observed asteroid’s proper moon (i.e., arcsec per hour) and its measured error, and generate figure(s) that illustrates its observed moon on the plane of the sky.

Nov 3- 17: Steps 1-6 Nov 17 – 24 : Steps 7-9 Nov 24 – Dec 3 : Steps 10-12 S. Wright - AST325