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ASTRONOMICAL DATA ANALYSIS

ASTRONOMICAL DATA ANALYSIS. Andrew Collier Cameron acc4@st-and.ac.uk Text: Press et al, Numerical Recipes. Astronomical Data. (Almost) all information available to us about the Universe arrives as photons. Photon properties: Position x Time t Direction  Energy E = h  = hc/ 

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ASTRONOMICAL DATA ANALYSIS

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  1. ASTRONOMICAL DATA ANALYSIS Andrew Collier Cameron acc4@st-and.ac.uk Text: Press et al, Numerical Recipes

  2. Astronomical Data • (Almost) all information available to us about the Universe arrives as photons. • Photon properties: • Position x • Time t • Direction  • Energy E = h = hc/ • Polarization (linear, circular) • Observational data are functions of (some subset of) these properties: • f (x, t,p)

  3. Observations I • Direct imaging: f() • size • structure • Astrometry: f(, t) • distance • parallax • motion • proper motion • visual binary orbits

  4. Interferometry f(x, t) • Uses information about wavefront arrival time and structure at different locations to infer angular structure of source. • Picture: 6 cm radio map of “mini-spiral” in Sagittarius A.

  5. Integral-field spectroscopy f() • Uses close-packed array of fibres or lenslets to obtain spectra on a honeycomb grid of positions on the sky, to probe spatial and spectral structure simultaneously.

  6. Eclipse mapping: f(t) • Uses modulation of broad-band flux to infer locations and brightnesses of eclipsed structures.

  7. Starspots Prominences -v sin i +v sin i -v sin i +v sin i Starspot signatures in photospheric lines Prominence signatures in H alpha Doppler tomography f(, t) • Uses periodically changing Doppler shifts of fine structure in spectral lines to infer spatial location of structures in rotating systems

  8. Zeeman-Doppler Imaging f(,t,p) • Uses time-series spectroscopy of left and right circularly polarized light to map magnetic fields on surfaces of rotating stars. Latitude Longitude

  9. Noise • No two successive repetitions of the same observation ever produce the same result. • e.g. spectral-line profile: • Two main sources of noise: • Quantum noise • arises through the fact that we only detect a finite number of photons • Thermal noise • arises in system electronics or due to background sources.

  10. Random variables • Consider repetitions of identical measurements. • Value of each data point jiggles around in some range • Statistical error arises from random nature of measurement process. • Systematic error (bias) can arise through the measurement technique itself, e.g. error in estimating background level. • How can we describe this “jiggling”?

  11. f(x) x a b Probability density distributions • Probability density function f(x) is used to define probability that x lies in range a<x≤b: • Probabilities must add up to 1, i.e. if x can take any value between - and + then

  12. f(x) x a Cumulative probability distributions • Integrate PDF to get probability that x ≤ a: F(x) 1 0 x a

  13. Discrete probability distributions • e.g. • Exam marks • Photons per pixel

  14. Example: boxcar distribution U(a,b) • Also known as a uniform distribution: U(a,b) x b a

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