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Photometry

Photometry. …Getting the most from your photon. Very Brief History:. Hipparcos in 130 B.C. created catalog of stars and the magnitude scale used to this day In 1800s astronomers decided that the magnitude scale should be logarithmic, determined by physiological response of eye.

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Photometry

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  1. Photometry …Getting the most from your photon

  2. Very Brief History: • Hipparcos in 130 B.C. created catalog of stars and the magnitude scale used to this day • In 1800s astronomers decided that the magnitude scale should be logarithmic, determined by physiological response of eye m1 – m2 = –2.5 log (f1/f2) Dm = 5 → 100 x decrease in brightness Remember: Larger magnitude, the fainter the object

  3. What do Astronomers use photometric measurements for? • Brightness of objects (Luminosity) • Color of objects (temperature, Hertzprung-Russel Diagrams) • Variability of Objects (variable stars, transiting planets, etc) Photometry usually requires only small (< 1m diameter) telescopes.

  4. Useful terms Apparent magnitude m: the brightness of a star in traditional magnitude system standard magnitude U,B,V, I, R: the standard brightness of a star in traditional magnitude system absolute magnitude M: the magnitude of a star if it is at a distance of 10 parsecs Bolometric magnitude: Total power of the source Bolometric correction: must be added to the visual magnitude to get the bolometric magnitude.

  5. Useful terms Bandwidth : wavelength range over which observations are made: Dl/l Broadband: ~ 1/4 Narrow band: Dl/l ~ 10–2 Color index: difference of two magnitudes at two different wavelengths Standard star: star that provide a reference to a magnitude system Metallicity index m1 : index that is a measure of the relative abundance of a star Extinction k: reduction in light due to passage through the Earth‘s atmosphere Interstellar extinction: reduction in light due to passage through interstellar material (dust, gas).

  6. The Hertzsprung-Russel (H-R) Diagram Astronomers usually measure the color instead of temperature. For stars in a cluster (all at same distance) the apparent magnitude is a measure of the relative luminosity

  7. From http://cas.sdss.org/dr5/en/proj/advanced/color/making.asp Color indices are a measure of the shape of the black body curve and thus the temperature

  8. ∫ ∫ ∫ ∫ Fn WB(n) dn Fn WB(n) dn Fn WU(n) dn Fn WV(n) dn Magnitudes and color indices Color Index: ) ( B–V = –2.5 log + 0.710 ) ( U–B = –2.5 log – 1.093 O5 G0M0 B-V –0.35 +0.58 +1.45 –1.15 +0.05 +1.28 U-B

  9. Black Body Curves B V B–V < 0 T = 10000 K T = 4000 K Flux B–V > 0 Temperature

  10. U-B = –1.33 B-V = –0.46 For T= ∞

  11. Filter Characteristics of Astronomical Photometry Systems

  12. From http://www.ucolick.org/~kcooksey/CTIOreu.html Giant stars Main sequence stars For field stars the apparent magnitude does not tell you the true luminosity. Therefore, color-color magnitude diagrams are often employed

  13. Detectors for Photometric Observations • Photographic Plates 1.7o x 2o Advantages: large area Disadvantages: low quantum efficiency

  14. Detectors for Photometric Observations 2. Photomultiplier Tubes Advantages: blue sensitive, fast response Disadvantages: Only one object at a time

  15. 2. Photomultiplier Tubes: observations • Are reference stars really constant? • Transperancy variations (clouds) can affect observations

  16. Detectors for Photometric Observations 3. Charge Coupled Devices From wikipedia Advantages: high quantum efficiency, digital data, large number of reference stars, recorded simultaneously Disadvantages: Red sensitive, readout time

  17. Get data (star) counts Get sky counts Aperture Photometry Magnitude = constant –2.5 x log [Σ(data – sky)/(exposure time)] Instrumental magnitude can be converted to real magnitude by looking at standard stars

  18. Aperture photometry is useless for crowded fields

  19. Term: Point Spread Function PSF: Image produced by the instrument + atmosphere = point spread function Camera Atmosphere Most photometric reduction programs require modeling of the PSF

  20. Crowded field Photometry: DAOPHOT Computer program developed to obtain accurate photometry of blended images (Stetson 1987, Publications of the Astronomical Society of the Pacific, 99, 191) DAOPHOT software is part of the IRAF (Image Reduction and Analysis Facility) IRAF can be dowloaded from http://iraf.net (Windows, Mac, Intel) or http://star-www.rl.ac.uk/iraf/web/iraf-homepage.html (mostly Linux) In iraf: load packages: noao -> digiphot -> daophot Users manuals: http://www.iac.es/galeria/ncaon/IRAFSoporte/Iraf-Manuals.html

  21. In DAOPHOT modeling of the PSF is done through an iterative process: • Choose several stars as „psf“ stars • Fit psf • Subtract neighbors • Refit PSF • Iterate • Stop after 2-3 iterations

  22. Original Data Data minus stars found in first star list Data minus stars found in second determination of star list

  23. Improvements to daophot and psf fitting: SExtractor (Source Extractor). Allows for elliptical apertures. Better at finding galaxies which can have none circular shapes Bertin & Arnouts, Astron. Astroph. Suppl. Ser 117, 393-404, 1996

  24. Special Techniques: Image Subtraction If you are only interested in changes in the brightness (differential photometry) of an object one can use image subtraction (Alard, Astronomy and Astrophysics Suppl. Ser. 144, 363, 2000) • Applications: • Nova and Supernova searches • Microlensing • Transit detections

  25. S ([R*K](xi,yi) – I(xi,yi))2 i Image subtraction: Basic Technique • Get a reference image R. This is either a synthetic image (point sources) or a real data frame taken under good seeing conditions (usually your best frame). • Find a convolution Kernal, K, that will transform R to fit your observed image, I. Your fit image is R*Iwhere * is the convolution (i.e. smoothing) • Solve in a least squares manner the Kernal that will minimize the sum: Kernal is usually taken to be a Gaussian whose width can vary across the frame.

  26. Special Techniques: Frame Transfer What if you are interested in rapid time variations? • some stellar oscillations have periods 5-15 min • CCD Read out times 30-120 secs Solution: Window CCD and frame transfer E.g. exposure time = 10 secs readout time = 30 secs efficiency = 25%

  27. Store data Mask Target Frame Transfer Reference Transfer images to masked portion of the CCD. This is fast (msecs) While masked portion is reading out, you expose on unmasked regions Can achieve 100% efficiency Data shifted along columns

  28. Sources of Errors Sources of photometric noise: 1. Photon noise: error = √Ns (Ns = photons from source) Signal to noise ratio = Ns/ √ Ns = √Ns rms scatter in brightness = 1/(S/N)

  29. Sources of Errors 2. Sky: Sky is bright, adds noise, best not to observe under full moon or in downtown Jena. Error = (Ndata + Nsky)1/2 S/N = (Ndata)/(Ndata + Nsky)1/2 rms scatter = 1/(S/N) Ndata = counts from star Nsky = background

  30. Nsky = 1000 Nsky = 100 Nsky = 10 Nsky = 0 rms Ndata

  31. Sources of Errors 3. Dark Counts and Readout Noise: Electrons dislodged by thermal noise, typically a few per hour. This can be neglected unless you are looking at very faint sources Readout Noise: Noise introduced in reading out the CCD: Typical CCDs have readout noise counts of 3–11 e–1 (photons)

  32. Sources of Errors 4. Scintillation Noise: Amplitude variations due to Earth‘s atmosphere s~ [1 + 1.07(kD2/4L)7/6]–1 D is the telescope diameter L is the length scale of the atmospheric turbulence

  33. For larger telescopes the diameter of the telescope is much larger than the length scale of the turbulence. This reduces the scintillation noise.

  34. Light Curves from Tautenburg taken with BEST

  35. Sources of Errors 4. Atmospheric Extinction Atmospheric Extinction can affect colors of stars and photometric precision of differential photometry since observations are done at different air masses Major sources of extinction: • Rayleigh scattering: cross section s per molecule ∝ l–4

  36. Aerosol Extinction • Absorption by gases

  37. Atmospheric extinction can also affect differential photometry because reference stars are not always the same spectral type. A-star Wavelength K-star Wavelength Atmospheric extinction (e.g. Rayleigh scattering) will affect the A star more than the K star because it has more flux at shorter wavelength where the extinction is greater

  38. 6. Interstellar reddening (extinction): One of the problems of the 1920s was that the observation of O-B stars had red colors. This was later found to be caused by interstellar material. To measure accurate „real“ colors and to put a star in the Hertzprung-Russel diagram this must be corrected

  39. 6. Interstellar reddening: To correct: assume that stars with identical spectra have similar colors. A(li) = amount of interstellar absorption in magnitudes. Then the observed magnitudes mi and mj at two different wavelengths li and lj are related to the intrinsic magnitudes, mi0 and mj0 by the expressions: mi = mi0 + A(li) mj = mj0 + A(lj) The observed color index Cij≡ mi– mj is related to the intrinsic color index Cij ≡ mi0 – mj0 by Cij = Cij0 + [A(li) – A(lj)] ≡ Cij + Eij

  40. 6. Interstellar reddening: In the UBV system the notation for color excess is: E(B – V) ≡ (B – V) – (B – V)0 E(U – B) ≡ (U – B) – (U – B)0 Eij is postive, i.e. colors become redder

  41. Usually can be neglected 6. Interstellar reddening: The reddening lines for stars of different spectral types originate at different points in the two color diagram E(U – B) = 0.72 + 0.05 E(B – V) E(B – V)

  42. 6. Interstellar reddening: In many cases we do not have spectral types of the stars. The slope of the reddening line can be used to define a photometric parameter that depends only on spectral type and independent of the amount of reddening. In the UBV system: E(U – B) Q ≡ (U – B) – (B – V) E(B – V) Q ≡ (U – B) – 0.72(B – V)

  43. 6. Interstellar reddening: Using expressions for color excess: E(U – B) – Q = (U – B)0 + E(U – B) [(B – V)0 + E(B – V)] E(B – V) E(U – B) – Q = (U – B)0 (B – V)0 ≡ Qo E(B – V)

  44. 6. Interstellar reddening: (B – V)0 = 0.322 Q We can determine (B – V)0 (= intrinsic color) for early-type stars from Q

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