Comp Astron 2010 Study guide - things I will expect you to know. =============================================== General: ++++++++ * How to estimate whether a value is 'significant' (ie significantly different from zero). * The formula for propagation of uncertainties, in the case that the variables are uncorrelated. * How to present graphical data in a correct and professional manner, including: - How to transform one or both axes, and reasons for doing so. - When to use symbols vs error bars vs a connecting line. - Clear and informative axis labels. * How to generate a frequency histogram, including: - How to calculate its uncertainties. - How to normalize it for comparison to a probability density function (PDF). - How to accumulate its values for comparison to a survival function. Probability and statistics: +++++++++++++++++++++++++++ * The formula for a Gaussian PDF (including the normalization). * The formula for a Poisson PDF. * The chi squared formula for Gaussian-PDF data. * Given N bins, each containing a data value (of any probability distribution), how to calculate the nett likelihood. * To be able to prove that the log of the nett likelihood for Gaussian-PDF data is proportional to chi squared for those data. * What the Null Hypothesis is in any particular case, and how to test it. * How to calculate the degrees of freedom when using the chi squared formula. * How to calculate uncertainties in the model parameters from the Hessian matrix values at the minimum of an objective function. Source catalogs: ++++++++++++++++ * In respect of a catalog of source detections, to be able to explain/describe/define the following concepts: - Reliability. - Completeness. - Sensitivity. - Confusion. - Eddington bias. - Malmquist bias. - Dynamic range. - LogN-logS. - Luminosity (and/or mass) function. * The formula for the 'Euclidean' probability of occurrence of a source as a function of flux. - Also the relation between this and Olbers' paradox. Fourier: ++++++++ * How to estimate the frequency of a repeated signal using a discrete Fourier transform (DFT). Plus, in this connection: - The use of zero-padding. - How to calculate a power spectrum from the FT. * How to calculate a (cyclic) convolution via DFT. Optics: +++++++ * Given the diameter of a single mirror, or the maximum baseline of a synthesis array, and the observing wavelength, how to estimate the resolution, aka the 'beam width'. - Also to estimate the 'beam area' (actually a solid angle). * How to convert from one angular (or solid-angle) unit to another. * What sidelobes are. Radiometry: +++++++++++ * To know that, of all the principal radio emission mechanisms, only the syncrotron process is expected to generate polarised radiation. * Given an averaged noise temperature T, plus the bandwidth and an observing duration over which it was averaged, how to calculate the uncertainty in T. * Given the mirror area and/or the observing wavelength, the connection between measured noise temperature T and: - the flux density S of a point source; - the brightness B of a uniform radiator. (See the example on slides 29-31 of lecture 13.) * How to use these results to calculate the approximate time needed to achieve a specified sensitivity, given the instrumentatl noise temperature and the observing bandwidth. * The relation between the 'optical depth' tau, the true temperature of a medium and the 'effective' temperature (ie the measured noise temperature) of the medium. Polarimetry: ++++++++++++ * The meaning of the 4 Stokes parameters. * Given values of the Stokes parameters, how to calculate: - the polarization fraction; - the PA of the linearly polarized component. * How to calculate the amount of Faraday rotation of the plane of polarisation, given the 'rotation measure' and the wavelength. Interferometry: +++++++++++++++ * Given 2 antennas at the same height, know the relation between the zenith angle of a source, the wavelength of the observing radiation, the distance between the antennas and the phase difference between the detected signals. * Know the desired properties of an ideal calibrator object for interferometry, and the reasons why this ideal is so hard to find. * To know why the field of view of a synthesis array is different from its resolution, and how to estimate each. * To be able to sketch the basics of a standard process for generating 'clean', calibrated images from raw interferometer data. * To be able to describe the meaning of: - Baseline; - Visibility function; - Visibility measurement; - Dirty beam; - Dirty image; - Clean components; - Aperture synthesis; - Multi-frequency synthesis. * To be able to describe what is meant by a non-coplanar array and the main restriction to observing with one. * To be able to explain why frequent phase calibration is both more necessary and more important than frequent flux calibration. * In interferometry, discuss the advantages/disadvantages of the following choices: - Direct Fourier inversion vs. gridding followed by discrete FT. - Natural vs. Uniform weighting of visibilities. - Wide- vs. narrow-band observing. Coord transforms: +++++++++++++++++ * How to convert between RA/dec and its Cartesian representation (= 'direction cosines') * Given the attitude matrix of a spacecraft, plus optionally the boresight matrix of an instrument on that spacecraft, how to convert between the position of a source on the detector and its RA and dec. High-energy astronomy: ++++++++++++++++++++++ * To be able to calculate a hardness ratio. * Convert between photon and spectral index. * Explain why often only 1 of two paired jets is visible. * How to calculate fluence of a GRB (or anything else) given (i) the light curve, (ii) the spectral index, (iii) the energy band of the detector and (iv) the collecting area of the detector. * The essential difference between practical CCD detection of visible light vs x-rays. * The function of the filter(s) on XMM-Newton. * To be able to describe: - Pileup. - Out-Of-Time Events (OOTEs). * To know the significance of event patterns/grades and broadly how to distinguish between plausible and non-plausible ones. * Know the 4 main sources of background in XMM-Newton. * Describe charge redistribution and its effect on XMM-Newton EPIC spectra. * The advantages/disadvantages of RGA vs. EPIC spectra.