Intro to Photometry and Astrometry Goals'of'Lab'#3:'Astrometry'' • Learn more about imaging proper/es of a CCD & & &&& & & & &&& & and coordinate systems &&& • Further applica/ons of least-square fi=ng &&&&& &&&&& • Query astronomical databases and catalogs && & & • Data reduc/on techniques for imaging data &&& & & & & &&& • Learn about proper mo/ons and astrometry & &&& & & & & The Needs of Astronomers What are the physical laws that govern these objects? Astronomical Object Does it move? Astrometry Measure gravitational interactions between Detection objects Do we see it? Spectroscopy Initial discovery of astronomical Photometry objects What kinds of How bright is it? light Does it vary with time? does it emit? Measure rudimentary Look at astrophysical properties of processes that govern astronomical objects astronomical objects I.'Stellar'Photometry' What'are'the'essen/al'factors'that' define'what'an'“image”'looks'like?' • DiffracHonIlimit:& – telescope&and/or&imaging&system& (e.g.,&your&eye’s&pupil),&f(λ)& • SensiHvity:& – total&collecHng&area&of&the&telescope,& f(λ)& – throughput&of&opHcs&and&atmosphere,& f(λ)& – QE&of&detector,&f(λ)& – Frame&rate&of&detector& – Detector&spaHal&sampling&(pixel&size& and&plate&scale)& • Seeing:&& – Atmospheric&turbulence,&f(λ)& Point'Spread'Func/on'' of'DI'Telescope'Star'Field' NGC&6397,&Hubble& 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)& SensiHvity&limit&& (or&image&stretch)& Principles'of'photometry' • The&light&from&a&star&is&spread&over&several& pixels&nonIuniformly& • How&do&we&sum&the&light&to&get&a&measure&of& the&total&flux&from&the&star?& – IdenHfy&the&locaHon&of&the&star& – Select&the&associated&pixels&that&contain&the&stellar& flux&by&generaHng&a&masking&region& – Sum&up&the&light& • Ensure&that&the&noise&and&background&is&not&included& 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&locaHon&(x,y)& 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& '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& Photometric'Model' • Write&down&an&expression&for&the&signal,&Si&,&in&units&of& photoelectrons& – In&an&individual&pixel& Si = Fi + Bi + Qi + Ei I& – Fi&is&the&stellar&signal&=&fi&t&&at&pixel&i&[e ]& • Different&for&every&pixel& I – 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& I& – Bi&&is&the&sky&background&=&bit&assumed&uniform&[e ]& • Varies&from&pixel&to&pixel,&for&SNR&model&assume&constant& I& – Ei&&is&the&readout&electronic&offset&or&bias&[e ]& • Varies&from&pixel&to&pixel,&for&SNR&model&assume&constant& & The'Stellar'Signal' • The&stellar&signal&is&found&by&subtracHng&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& Noise'in'the'stellar'aperture' • The&total&noise&is&a&funcHon&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&<B>&and&<Q>&is&the&mean&background&and&dark&current&per& 2& pixel&and&N1&=&πr1 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 <r<r3 SignalMtoMnoise'ra/o'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”& How'does'flux'change'' with'aperture'radius?' • Suppose&the&stellar&signal&has&a&2Id& 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& 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& correcHon”&& • When&the&total&flux&is& outside&the&aperture,& like&for&crowded&field& photometry& – Useful&for&defining&SNR& per&radius& II.'Astrometry' Astrometry' • Astrometry&is&the&measurement&of& posiHon&and&moHon&of&celesHal& objects& • Oldest&branch&of&astronomy&& – In&129&BC&Hipparcos&generated&the& 1st&catalog&of&stars&with&apparent& brightness&and&posiHonal&accuracy&to& 1°& – RevoluHonized&by&Tycho&Brahe&in& 16th&century&and&measured&posiHons& of&stars&to&1&arcminute& – PosiHons&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”& & Importance'of'astrometry' • Astrometry&is&used&to&determine:& – Distances&to&nearby&stars&using&parallax& – Proper&moHons&of&stars&& • KinemaHc&structure&of&the&galaxy& – Distance&scale&of&the&Milky&Way&and&beyond& • Stellar&formaHon&and&evoluHon&& – Orbits&of&solar&system&objects,&binary&stars,&exoplanets,&stellar& populaHons& • Direct&way&of&determining&the&mass&of&celesHal&objects& • Determine&the&mass&of&stellar&black&holes&and&the&supermassive&black& hole&at&the&GalacHc&Center& • Determine&the&orbit&of&asteroids&and&comets& – Probability&of&Earth&gePng&slammed!& – Solar&System&formaHon&& – Astrometric microlensing • Determine the mass of the lens source accurately • Number density compact objects Proper Mo(on (from Lecture #7) ''''' • Objects&in&our&solar&system,&galaxy,&and&extragalacHc& sources&have&their&own&velociHes& – Closer&the&source&and&higher&the&velociHes&the&greater& moHon&on&the&projecHon&of&the&sky,&which&is&known&as& “proper&moHon”& • Typical&proper&moHon&of&nearby&stars&is&0.1”&per&year& • Typical&proper&moHon&of&main&belt&asteroids&is&~0.5I1’&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&moHon& 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& Astrometry'determined'the'mass'of' the'MW’s'supermassive'black'hole''' • Using&adapHve& opHcs&and&8I10m& groundIbased& telescope&the& relaFve&astrometric& precision&is&100&μas& (0.0001”)& • Monitor&the&stellar& orbits&over&15+& years& UCLA&GalacHc&Center&Group& Reference'frames' • The&concept&of&posiHon&in&space&is&relaHve& – You&need&to&define&a&coordinate&system&(e.g.,&CelesHal& coordinates,&standard&coordinates)& – You&need&to&define&posiHon&relaHve&to&other&celesHal& objects&for&given&Equinox& • Everything&in&the&Universe&is&moving!& • A&“reference&frame”&is&a&catalog&of&known& posiHons&and&proper&moHons&of&celesHal&objects& – For&astrometry&you&use&reference&frames&to&define&the& posiHon&and&moHon&of&the&object&of&study& Reference'star'catalogs' • AllIsky&surveys&have&generated&catalogs&of&stars& with&posiHons&per&Equinox&and&proper&moHons&& – Hipparcos&contains&posiHons,&proper&moHon,& parallaxes&of&118,218&stars.&Complete&to&V=7.5&mag.& – TychoM2'contains&posiHons&and&proper&moHon&of&over& 2&million&stars.&Complete&to&V=11.0&mag.& – USNOMB1&contains&posiHons&and&proper&moHon&of& over&1&billion&objects.&AllIsky&coverage&to&V=21&mag.& – Sloan'Digital'Sky'Survey'mapped&¼&of&the&sky&in&5& opHcal&filters&and&contains&287&million&objects& We&will&be&using&the&USNOIB1&catalog&in&Lab&#3& Interna/onal'Celes/al'Reference' System'and'Frame'(ICRS)' • Fundamental&reference&system&adopted&by& InternaHonal&Astronomical&Union&(IAU)& – Reference&system&of&celesHal&sphere&defined&by& the&barycenter&of&the&solar&system&& – Reference&frame&is&with&respect&to&distant& extragalacHc&objects&that&are&considered&fixed& • Based&on&radio&posiHons&from&the&VLBI&of&Quasars& • PosiHonal&accuracy&is&0.5&mas&(0.0005”)& ICRS&–&VLBI&Quasar&reference& Coordinate'transforma/ons'' to'the'image'plane' • CelesHal&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&