Week8

•  MidterminclassonThursday–  Reviewdocumentposted–  Prepara;onemphasizedinTue/Wedsessionsthisweek–  Expect½;mespentonconceptualques;ons,½spentoncalcula;on

•  DayAssignment4wasposted–  WatchoutforthatMoon

•  Lab4pending,butnothinghappensun;laJermidterm–  (howdoesApril1or2lookforyou?)

•  Topics–  PhotometryandFilters–  Magnitudes–  Imagecalibra;on–  Sourceextrac;on(aperturevs.PSFphotometry)

StellarPhotometry

•  Why?Precisionstellarphotometryisthegatewaytoobserva;onalastrophysics.

HR Diagram in Omega Centauri

StellarPhotometry

•  Why?Precisionstellarphotometryisthegatewaytoobserva;onalastrophysics.

HR Diagram in Omega Centauri

StellarPhotometry

•  Why?Precisionstellarphotometryisthegatewaytoobserva;onalastrophysics.

•  Time variability in pulsating stars (top) and eclipsing binaries (bottom).

•  Variable stars are key “standard candles” calibrated by amplitude and period measurements.

•  Eclipsing binaries permit direct measurement of stellar dimensions and masses, putting stellar models to the test.

StellarPhotometry

•  Why?Precisionstellarphotometryisthegatewaytoobserva;onalastrophysics.

Planetary Transits

StellarPhotometry

•  Why?Precisionstellarphotometryisthegatewaytoobserva;onalastrophysics.

Planetary Transits…. with precision

Mul;-PlanetSystemsandPowerSpectralAnalysis

StellarPhotometry

•  Why?Precisionstellarphotometryisthegatewaytoobserva;onalastrophysics.

Asteroid Light Curves

MagnitudesforReal

•  FromASTR2110,2120,etc…considertwotargetswithmeasuredfluxesf1andf2

•  Afluxra;oof10isadifferenceof2.5magnitudes,afluxra;oof100

is5magnitudes.

•  But,exactlywhatiswhatisf???

m1 − m2 = − 2.5 log f1f2

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Fluxvs.FluxDensity

•  Fluxistheamountofenergyfromasourcethatpassesthroughasquarecen;meteradistance,d,awayintegratedoverallwavelengths.–  Alsoreferredtoas“bolometricflux”.Unitsareerg/cm2/sorwa^s/m2

•  Fluxdensityaccountsforthefactthattheenergypassingthroughthatsquarecen;meteriswavelengthdependentandwemaycare,forexample,abouttheenergytraversingthatsquarecen;meterinapar;cularfilterbandpass.–  Unitsareerg/cm2/s/µmorwa^s/m2/Hz

Flux = Luminosity4πd 2

Integra;ngFluxAcrossaFilterBandpass•  Measuringafluxrequireslookingthroughafilteratan

astronomicalsource.–  Thatfilterhasabandpass(variabletransmissionwithwavelength)–  Thetargethasaspectrum(structurewithinthefilterbandpass)

Integra;ngFluxAcrossaFilterBandpass•  Measuringafluxrequireslookingthroughafilteratan

astronomicalsource.–  Thatfilterhasabandpass(variabletransmissionwithwavelength)–  Thetargethasaspectrum(structurewithinthefilterbandpass)

filter_fluxBand = filter_transmission(λ)*0

∞

∫ target_flux_density(λ) dλ

Integra;ngFluxAcrossaFilterBandpass•  Measuringafluxrequireslookingthroughafilteratan

astronomicalsource.–  Thatfilterhasabandpass(variabletransmissionwithwavelength)–  Thetargethasaspectrum(structurewithinthefilterbandpass)

filter_fluxBand = filter_transmission(λ)*0

∞

∫ target_flux_density(λ) dλ

Integra;ngFluxAcrossaFilterBandpass•  Measuringafluxrequireslookingthroughafilteratan

astronomicalsource.–  Thatfilterhasabandpass(variabletransmissionwithwavelength)–  Thetargethasaspectrum(structurewithinthefilterbandpass)–  Tobestrictlycorrectonemustaccountforatmosphericandtelescope/

instrumenttransmissionasafunc;onofwavelength.

•  Observingtwostarssimultaneously(inthesameimageforexample)calibratesoutthe;mevariableterms,atm_transinpar;cular.

filter_fluxBand = filter_transmission(λ)*0

∞

∫ target_flux_density(λ)

* atm_trans(λ) * inst_trans(λ) dλ

FilterCharacteris;cs/Terminology

•  Cutoffandcut-onwavelengths–  Definedby½powerpointsatfilteredges

•  Centerwavelength:½(cutoff+cut-on)•  Bandpass:(cutoff–cut-on)•  Effec;vewavelength:Weightedaverageofproductoftransmission

andwavelength(centroidwavelengthaccoun;ngfortransmission)

•  Refertoon-boarddiscussion

Hertzvs.Nanometers

•  Conver;ngabandpassfromwavelengthunitstoHertzisnotassimpleasdividingthewavelengthintothespeedoflight…Onemustdifferen;atethewavelength/frequencyequa;ontogettheproperconversion:

λν = c ν =cλ

Δν =cλ 2

Δλ

FilterWheels

FilterTechnologies

•  Filterscansimplybecoloredglasswiththedye/glasstransmissionenforcingatransmissionspectrumvs.wavelength.

•  Alterna;velyfilterbandpassescanbecustomdesignedusingmul;-layerreflec;ve(!)coa;ngs.–  Theconspiracyofreflectedandtransmi^edwavesinterferingwitheachother

canproducearemarkably“square”hightransmissionbandpass.

InterferenceFiltersvs.AngleofIncidence

•  Thetransmissionofbulkcoloredglassisindependentofangle.•  Becauseinterferencefiltersrelyonphasedelaybetweenmul;ply

reflectedwaves,anglesincreasepathlengthsanddecrease(!)theeffec;vewavelengthofthefilter.

PhotometryisUl;mately“Compara;ve”(eventhoughitstrivestobeabsolute!)

•  Themagnitudeequa;onalwaysquan;fiesadifference(whichisactuallyafluxra;o)anditis“easy”tomeasurera;os.

•  Asphysicists,however,wewouldliketoknowtheanswersinSIunits.–  Fluxesinerg/cm2/sorfluxdensi;esinerg/cm2/s/µm…

•  InrareinstancesaninstrumentcalibratedtoSIunitsgetspointedatastar.–  ForthemostpartweareleJtomeasuremagnitudedifferencesbetweenstars

(viainstrumentalcounts–whicharepropor;onaltofluxes)andbootstrapourwaytoaphysicallycalibratedstandard.

–  Modernskysurveysprovidebillionsofcalibratedsourcesatavarietyofwavelengths(theremightalwaysbeacalibratorinyourfieldofview).

–  Imagetwostarsatthesame;me,extractthecounts,andyougetthefluxra;o/magnitudedifferenceindependentoftheatmosphere(tofirstorder).

m1 − m2 = − 2.5 log f1f2

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MagnitudeZeropoints

•  0thmagnituderequiresadefini;on(acomparisonposter-child).•  Sincemeasuringrela;vefluxesis“easy”thestarVegaisdefinedto

bemagnitude0.00inallbands.

•  AtsomepointVegahasbeenquan;ta;velyassessedineveryfilter

mstar = − 2.5 log fstarfVega

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Magnitudes,Percentages,andSNR

•  Considerthefluxdifferenceoftwostarsthatdifferby0.1magnitude–  Sincemagnitudesarelogarithmicamagnitudedifferencecorrespondstoa

mul;plica;ve/factordifferenceinbrightnesssoitdoesn’tma^erifwearetalkingaboutmagnitude10.0vs.10.1or4.0vs.4.1

•  Itturnsoutan0.1magdifferenceisclosetoa10%differenceinfluxandan0.01magdifferenceisclosetoa1%differencebecause….

•  Consideran0.1magdifference

•  Taylorseriesexpandthissmalldifference:•  Expandingaboutx=0

f (x +Δx) = f (x) + ʹf (x)*Δx + ...

m1 −m2 = 0.1 = − 2.5log f1f2

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f1f2=10

−0.12.5⎛

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10x = 1 + ln(10)*Δx for   x = −0.1 / 2.5 10x = 1− 2.3* 0.12.5⎛

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Magnitudes,Percentages,andSNR

•  Expandingaroundx=0

•  So,thankstothefactthatln(10)ispre^ycloseto2.5thefluxra;ofor0.1magdifferencecorrespondstoabouta10%differenceinflux.

•  Similarly,ifamagnitudemeasurementisuncertainby+/-0.1magthatuncertaintytranslatesto10%orSNR=10.–  10.73+/-0.01magisabouta1%uncertaintyinmagnitudecorrespondingto

SNR=100

f1f2=10

−0.12.5⎛

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10x = 1 + ln(10)*Δx for   x = − 0.12.5⎛

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⎠⎟ 10x =1− 2.3* 0.1

2.5⎛

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⎠⎟ = 0.91

ABMagnitudes

•  Justtomakethingsmoreconfusing,about20yearsagoaseparatesetofmagnitudezeropointswereestablishedtotaketheempiricalmeasurementofVega“outoftheequa;on”and;eittothefundamentalunitsoffluxdensity.

•  fν hereisinunitsoferg/s/cm2/Hertz–  One“Jansky”is10-26Wa^s/m2/Hz

•  Theconstant,48.600,makesAB=Vforaflatspectrumsource•  Seeh^p://adsabs.harvard.edu/doi/10.1086/160817

mAB = − 2.5log fν +  48.600 =− 2.5log fv3631 Jy⎛

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RegisteringABandVegaMagnitudes

InstrumentalMagnitudes

•  Sincemagnitudesarera;os,anyconstantofpropor;onalitythatscalesthemeasurement(forexampleconver;nginstrumentalcountstophysicalfluxunits)cancelsout.

•  Thesimpleimplica;onisthatyoucanevaluatemagnitudedifferencessimplybyapplyingthemagnitudeequa;ontoextractedinstrumentalcounts.

m1 − m2 = − 2.5 log φ f1φ f2

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minstrumental = − 2.5 log counts( )