Observational Astronomy

Transcription

1 Observational Astronomy Photometry...2 Magnitude system...2 Observing procedure...3 Relation magnitude-flux...4 Atmospheric extinction correction...6 Transforming to standard system...6 Photometric System...7 UBV system...7 Morgan-Keenan spectral classification system...10 Second parameter of MK system: luminosity classes...11 Relationship between color indices and absolute magnitude...13 Effect of reddening...14 Absolute calibration...16 Other systems...17 Strömgren system...17 Narrow band filters...19 Practical case...20 Calculation of instrumental magnitudes and colors...20 Extinction correction...20 First order extinction...21 Second order extinction...21 Zero point values...22 Transformation coefficients

2 Photometry Magnitude system Based on human eye Þ non linear response to light eye suppress difference in brightness Pogson scale (Pogson N. R. 1856): redefine magnitude scale so that a difference of 5 magnitudes Þ 100 in variation of flux Light flux ratios: 1 magnitude difference: or 25 2 magnitudes difference: ( 10 ) magnitudes difference: ( 10 ) or f 1 f m ( ) 2 -m 1 = or m1- m2 =- 2.5log f1 f2 To make system consistent with old: Adebaran and Altair have magnitude 1.0 First photometer (19 th century - Zöllner): light from artificial star adjusted to same brightness as object measured error 0.1 magnitude Photography (1850 s Bond et al. at Harvard): photographic magnitudes sensible to blue part of spectrum visual magnitudes sensible to yellow-green part Photovisual = panchromatic photographic plates obtained using yellow filters Ex. North Polar Sequence (NPS) or International System Mount Wilson Observatory: 139 secondary standards as faint as 19 magnitudes but not accurate because of non linearity of photographic plates Advantage of photographic plates = multiplexing = 1000 of images recorded at the same time 1800 s photoelectric method: based on photoconductive cells: change resistance upon exposure to light low sensitivity + narrow spectral response not commercially made 2

3 Photoelectric cell (1911) work at high voltage (300V) linear not available commercially until 1930 limited of sensitivity 7 magnitudes Photoelectric photometer Photon multiplier (1930): photocell + cascade secondary electrons Þnoiseless amplification RCA 931 photomultiplier (before WWII) + RCA 1P21 (after WWII) Kron 11 th magnitude stars measured on Lick 36 inch Photoelectric magnitudes Þ new magnitude system Based on choice of filters Various standard stars Late 1990 s : Charge Coupled Device (CCD) revolutionize astrometry Linear and digital High sensitivity over large wavelength range Commercially available Þ increasing quality and lowering price Observing procedure Depends on goal of project: Differential photometry o Most accurate technique for measuring small variations in brightness error magnitude o Used for variable stars eclipsing binary systems o Principles: target observed in sequence with second stars (same brightness + color within 1 of target Þ extinction correction not necessary) o Changes in magnitude observed as difference between target and comparison star o Usually use second comparison star for check Absolute photometry o general + demanding on time and quality of sky o numerous target in different region of sky Þ extinction correction important o set of stars for extinction 3

4 o set of stars for transformation coefficients Relation magnitude-flux m = m - 2.5log f + 2.5log f Choosing stars 2 with zero magnitudes: m = q - 2.5log f l l l Where f l refer to observed flux convolved with: extinction + scattering due to atmosphere departure of detecting instrument from ideal one Two sources of extinction: 1. Interstellar = dust 2. Atmosphere ÞUV mostly absorbed + scattering of light in blue Response of telescope: Variation in coating + dust + quality Lens in optical path or filters (no two filters alike) No two observations measure the same flux Þ calibration process necessary to homogenize observations If F l * F l is the actual flux out of atmosphere, the measure flux F l : ò 0 ( ) ( ) ( ) ( ) * = F l F l F l F l Fdl A T F D F A : Fractional transmission of atmosphere F : Fractional transmission of telescope T F : Fractional transmission of filters F F : Fractional transmission of detector D l Expression can be very complicated and many factors are usually poorly known Þabsolute calibration very difficult 4

5 Magnitude scheme requires only that certain stars be defined to have magnitudes so that magnitudes of other stars can be determined from observed fluxes corrected for atmospheric absorption Remaining problems = Telescope + filters + detector set of standard stars Þ allows to determine transformation coefficients to transform instrumental magnitude into common standard system Recorded quantity d l is proportional to observed flux: F [ ] -1-1 d l counts s electrons s =ADU*GAIN l = kd = =, where ADU is Analog to Digital Unit and GAIN is the ratio electrons ADU (depends on CCD) m = q -2.5logk- 2.5log f = q - 2.5log f l l l l l Where q l is the instrumental zero point constant and m l the instrumental magnitude l Color index: ml1- ml2= q l1-q l2-2.5logdl1+ 2.5logdl 2 or ml1- ml2 = ql12-2.5log dl 1 dl2 5

6 Atmospheric extinction correction Amount of light lost depends on height of stars above the horizon + wavelength of observation + atmospheric conditions Correction: ml0 = ml- ék l kcx ù ë + l û Where k l : principal extension coefficient k l : second order extinction coefficient c : observed color index X : airmass X = sec z where z is the zenith distance ( 90 - altitude) Corrected color index: c0 = c-kx c - kxc c Where k l, k l, k c and k c are determined observationally Transforming to standard system Defined by set of standard stars (particular filter + detectors) Standard stars Þallows determining transformation from instrumental to standard system m = m + b C+ g l l0 l l C : Standard color index b : Color coefficient l g : zero point constant of instrument l C= dc 0 + g c c 0: Observed color index d : Color coefficient g : Zero point constant c 6

7 Photometric System Defined by specifying Detector + filters + standard stars Wide band system: filters width ~ 900Å - Ex. UBV Intermediate filters: filters width ~ 200Å Ex. Strömgren Narrow-band filters: filters width ~ 30Å Ex. Ha or Hb yields very specific information needs large aperture telescope UBV system Established by H. L. Johnson & W. W.Morgan 1. Photoelectric system yielding comparable results as yellow + blue magnitudes of International System 2. Third color for better discrimination of stellar attributes 3. Consistent to Morgan-Keenan (MK) spectral classification Developed around RCA 1P21 photomultiplier tube + 3 broad filters = VBU 7

8 V filter Peak at 5500Å Magnitude almost identical to IS Cutoff produced by RCA 1P21 B filter Peak at 4300Å most of sensitivity range of 1P21 Corresponds well with earlier blue photographic magnitudes B + blocking UV filter Þnot affected by Balmer discontinuity U filter Peak at 3500Å Red-leak Þtransmit light in NIR o must be block or measured + subtracted Cutoff set by earth s atmosphere o Depends on altitude of observatory + atmosphere condition (UV transmittance) UBV standards Measured by Johnson s original photometer without any transformation Instrumental system of this photometer Zero points of (B-V) and (U-B) defined by 6 A0V stars: a Lyr, g UMA, 109 Vir, a Crb, g Oph, HR 3314 Þ average (B-V) = (U-B) = 0 10 primary standards + secondary standards + 3 open clusters 8

9 UBV transformation equations Magnitudes: v=- 2.5log d b=- 2.5log d b u=- 2.5log d u Colors: b- v =- d d ( ) 2.5log b v ( u- b) =- 2.5logd u d b Correction for atmosphere: v = v- kx 0 v ( ) ( )( ) ( u- b) = ( u-b) - k X v b- v = b-v -k X - k X 0 1 bv bv 0 ub Where k ub = 0 and k v very small Transformations V = v + e B- V + z ( ) 0 v ( B- V) = m( b- v) 0 + zbv ( U - B) = y( u- b) 0 + zub Where e, m, y = transformation coefficients zv, zbv, z ub = zero point constants 9

10 Morgan-Keenan spectral classification system 1920s Harvard College Observatory Henry Draper Catalog ~ stellar spectra Classification based on decreasing strength of hydrogen lines ( A P) Groups dropped because of poor quality of spectra or because no logical sequence Remaining groups: OBAFGKM from Early Late Higher quality Þ10 subclasses 0-9, Ex. Sun G2, Vega A0 Spectral sequence corresponds to surface temperature Because of Balmer discontinuity, k bv and k uv do not vary smoothly with spectral typeþto avoid correction defined to be zero Þerror of 0.03 in U-B 10

11 Second parameter of MK system: luminosity classes Some stars show narrower absorption line for their spectra class Mount Wilson Observatory Þorder spectra by strength of absorption line Narrower line Þlower density of atmosphere Larger atmosphere Brighter lines Luminosity indicator = Luminosity classes I - Supergiants II Bright giants III Giants IV Subgiants V Main sequence (dwarfs) VI Subdwarfs Subdivision: a (brightest), ab, b (dimmest) Low density in larger stars alters percentage of ionized atom such that spectra looks earlier 11

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13 Relationship between color indices and absolute magnitude 2 steps process: 1. Measure color indices of nearby stars with accurately known parallaxes 2. since few AFG stars fill gaps using stars in clusters (NGC 2362, Pleiades, Praesepe) after correcting for extinction ÞMain sequence fitting In Color-Color diagram (unredened) MS stars deviate from BB because of absorption line From O to A0 hydrogen increases + Balmer discontinuity ÞU decreases and U-B increases After A0, Balmer lines + discontinuity weaken ÞU-B decreases After F5 metal lines + Molecular bands become strong Þ U-B increases again Near bump F5 abnormal abundance cause stars to plot higher than normal 13

14 Effect of reddening Color excess: E( B V) Slope of reddening line: For early stars ( B V) - and EU ( - B) ( B) ( -V) EU- = ( B - V) E B ( ) ( ) EU -B - nearly zero Þ = 0.72 E B-V Stars later than A0 not possible to use CC diagram to determine intrinsic color Þcolor excess obtained by comparing colors to that of spectra 14

15 For B0 to A0 stars: Q= U B 0.72 B V ( ) ( ) Where ( U B) and ( B V) are the observed colors and Q is independent of reddening Total absorption in the visual: AV R = A B A V Where AV and AB are the absorption in magnitude in V and B, reciprocally Since B0 = B+ AB and V0 = V + AV E B V = B V B V ( ) ( ) ( ) 0 ( B A ) ( V A ) ( B V) = + = = AB AV AV R = AV = RE B V E B V ( ) B 0 V ( ) Where R 3.0 for most direction in the galaxy 15

16 Absolute calibration Convert magnitude into flux: m = q 2.5log F = 10 λ λ λ 0.4( mλ qλ) Fλ Ex. flux reaching earth from star with V 0 = 3.0 = q v ( ) = 10 = F V W 2 cm Å Total flux multiplied by band width of filter ( 1000 Å): W F V Å cm Å W cm Total power: P = F π R 2 V V tel 16

17 Other systems Strömgren system Defined based on intermediate width filters Totally filter defined (no cutoff due to detector) y : b : matches visual or V no strong spectral features in early-type stars 300Å to the red of B Reduces effect of line blanketing Since for types later than A0, metal absorptions become strong Temperature indicator; strong in later types For early type stars, b and y are free of blanketing. In later type both are affected by the same amount. v : u : Centered in region of strong line blanketing but longwards of Balmer s crowding measure line blanketing + Balmer discontinuity not affected by atmospheric condition 17

18 Since the system is filter defined no second order color term in extinction correction ( b y) ( v b) : Good indicator of color and temperature : affected by blanketing Metal index: m = ( v b) ( b y) 1 Measures the strength of line blanketing In absence of line blanketing m1 0 ( ) ( ) ( ) c = u v v b = u v+ b 1 2 Measures continuum slope affected by Balmer discontinuity Subtracting 2v cancels effect of line blanketing Measure Balmer discontinuity Drawback of the system: faint stars difficult to measure large aperture telescope 18

19 Narrow band filters Narrow width filters centered on spectral features Ex. Hα, H β or [ OIII ] λ 5007, [ SII ] λλ 6717,6739 Measures the strength of these features related to star formation rate, age of stellar population or level ionization and density At least wo filters needed: Centered on the line Centered on nearby continuum Drawback: need large aperture telescope 19

20 Practical case Calculation of instrumental magnitudes and colors v= c 2.5log d v d b v= cbv 2.5log d d u b= cub 2.5log d v Where the constants are arbitrarily b v u b e count e = = GAIN s s ADU IMPORTANT: [ d] ( ADU ) Extinction correction More than 30 above the horizon ( z < 60 ) plane parallel model ± 0.2% Airmass: X = sec z Where secz = [ sinϑsinδ + cosϑcosδ cos H] 1 Where: ϑ : Latitude of observatory δ : Declination of target H : Hour angle in degrees For zenith distance z > 60 : [ ] [ ] [ ] 2 3 X = secz secz secz sec z 1 Ex. for an object 10 above the horizon, airmass

21 First order extinction v = v kx 0 v ( ) ( ) ( ) ( ) b v = b v k X 0 bv u b = u b k X Where [ k ] 0 ub magnitude = airmass The value of the extinction coefficient is found by observing 1 or more standard stars through changing airmass and plotting the color index or magnitude vs X The slope = extinction coefficient Intercept = color index v= kx + v v 0 ( b v) = k bv X + ( b v) 0 ( u b) = k ub X + ( u b) 0 Second order extinction + ( ) and k k + k ( b v) k k k b v v v v bv bv bv ( ) and ( ) = ( ) + ( ) 0 bv bv v = v k + k b v X 0 v v b v b v k k b v X Solve the equations observing close pairs with different colors (but airmass is the same) ( ) ( ) v v = v k + k b v X v k k b v X v v v v 2 0 v v ( ) ( ) v = v k b v X v= k b v X + v b v = k b v X + b v And ( ) bv ( ) ( ) 0 0 In practice k v very small and k bv is stable (only need to determine it once) 21

22 Zero point values V = ε( B V) + v0 + ζv ζv = V v0 ε ( B V) ( B V) = µ ( b v) 0 + ζbv ζ bv = ( B V) µ ( b v) 0 ( U B) = ψ ( u b) 0 + ζub ζub = ( U B) ψ ( u b) 0 Zero points = standard values transformed values (corrected for extinction) One as to solve equation for each standard and take the mean Zero points must be determined nightly Transformation coefficients Determined by measuring several stars whose magnitudes and colors are known Since V v = ε( B V) + ζ a plot of ( ) vs ( B V) For the color terms: 0 v 1 ζ = 0 + µ µ ( B V) ( b v) ( B V ) Plot of left side vs ( B V) 1 bv ( U B) ( u b) ( U B) V v 0 yields a slope related to µ 1 ζ = 0 + ψ ψ Plot of left side vs ( U B) 1 ub yields a slope related to ψ yields the slope ε 22