Photometry Stellar Photometry: Implementation • Select a detector and a suite of filters • Define a “zero point” in both brightness and in colors, based on fundamental reference stars • Measure a network of standard stars around the sky relative to the reference stars • You now have a “photometric system” • Measure your unknown stars relative to the network of standards • Correct for various influences on the data that make it depart from the ideal (for example, atmospheric absorption) • Compare the properties of the unknown stars with those of well measured ones A “Heritage” Photometer You may never use one, but a lot of the concepts are based on this type of instrument A pupil is formed on the photomultiplier photocathode, since it can have highly non-uniform response. The wide field eyepiece allows finding the star, and the microscope lets the observer verify it is centered within the aperture. Harold Johnson’s UBVRI System Why the photometer gives accurate results: • Allows accurate guiding • Every star measured the same way • Generally took multiple repetitions • Filters far away from a focus • Detector (photomultiplier) placed at a pupil • Detector cooled so dark current was negligible Measurements with Detector Arrays • Start with well-reduced data (as discussed under imagers) • Aperture photometry: • Measure signal within an aperture centered on the source and sky/background in an annulus around the source • Simplest method, reliable with clean data • Subject to errors if have artifacts in the image (they come through unattenuated as signal) • Can be adapted to extended sources • Point spread function (PSF) fitting • Fit an idealized image of an unresolved source to the image • Best for crowded fields • More immune to artifacts (fits tend to de-emphasize them) • Determining PSF may be difficult (it may be dependent on where a source is within the FOV, or on time of observation in a night) • More difficult to adapt to extended sources • Array measurements • Allow accurate differential measurements (e.g., through clouds) • But are subject to detector artifacts (e.g., fringing, intra pixel response) Photometry : Terms • Magnitude system • Response of the eye is roughly logarithmic • Hipparchos: 150 BC, sorted stars into bins by apparent brightness, or magnitudes, from 1 to 6 (brightest to faintest) • Pogson, 1856, defined m1 – m2 = -2.5 log(f1/f2), where m is the apparent magnitude and f is the flux • As fainter and brighter objects came within reach, astronomers extrapolated Procedure for Stellar Photometry • Establishing the photometric system • Set the zero point (Johnson used six A0 stars averaged, but that was quickly forgotten and his work became the “Vega system” • Get accurate standard star measurements over the entire sky relative to the zero point defining stars • m = apparent magnitude = -2.5 log (fstar/fzero pt. ) • Then in terms of the network of well-measured standard stars, m=-2.5 log (fstar/fstandard) + mstandard Procedure for Stellar Photometry - II •Air mass corrections – have to correct for different paths through the atmosphere • Can assume plane parallel atmosphere for a crude correction sec(zenith angle) (cos cos HA cos sin sin)1 (1) • A more accurate formula is given in the text • If the extinction is exponential: dI I , (3) ds • Then m (am) m (am 1) 2.5 (am 1). (4) • However, the atmospheric effects may be more complex, like shifting the center wavelength of the spectral band (a major issue for M and Q in the infrared) Is the system based exclusively on an instrument – the defining photometer? • If so, how do you maintain it? One solution: Harold Johnson maintaining the defining UBVRI photometer A Truly Great Review • Johnson, H. L. 1966, ARAA, 4, 193 • What makes this review so great? You need to read it (posted on class web site). Some Issues: What is the System, Really???? The following slides compare real Johnson with “other Johnson” Cousins came up with his own R and I bands Barr used to sell this filter set Another example: Stromgren uvby systems. These are all supposed to be the same!! J H K Extending to the infrared – Johnson comes to the Lunar and Planetary Laboratory and sets up JKLM, Frank N Low adds N (OP) Q. Eric Becklin L M (CalTech grad student) adds H. These bands are pretty well determined by the atmospheric windows, but to get cheap filters people often used to buy stock ones that are not identical from one system to another. To a large extent Q this issue has been resolved at JHK by 2MASS defining a standard. The bands are also significantly influenced by atmospheric conditions (mostly water vapor). Some of these problems can be addressed with transformations – fits to the trend of magnitudes with colors, or colors vs. colors, or etc. etc. These work well only when you are dealing with closely related objects, i.e., stars. Using transformations determined on stars when studying AGN at high redshift is guaranteed to get you into trouble!!!!! • Here is how a simple set of transformations might look: (K S )2MASS KCIT (0.000 0.005)(J K)CIT (0.024 0.003) (J H)2MASS (1.076 0.010)(J H)CIT (0.043 0.006) (J K S )2MASS (1.056 0.006)(J K)CIT (0.013 0.005) (H K S )2MASS (1.026 0.020)(H K)CIT (0.028 0.005) (5) • You may find that they are based on a shockingly small number of stars well- measured in the two systems. • Trying to put Johnson’s photometry on the 2MASS system is very difficult, as an example • Transformations work pretty well in the infrared where stellar spectra are relatively simple • However, transformations are not nearly so good in the optical because of the complexity of stellar spectra there A Happier Solution • Use all-sky surveys • Near infrared: 2MASS, accurate to about 2 – 3% • Not quite as good as it seems because of ~ 2% offsets between read 1 and read 2, plus some general calibration drift over the sky (but < 2%) • BV: Tycho, accurate to better than 1% (but sometimes gets confused by stars with small separations) • These surveys are as uniform over the whole sky as the best previous standard systems were over limited regions and with very small numbers of stars. • It used to be necessary to take photometry of widely spaced standards, including at large air mass, and solve for the instrumental zero point plus the air mass corrections. Now there is an option of tying in directly with these all sky networks. Common Terms: • CI = color index = difference in magnitudes at two bands, e.g., CI = mB – mV, or B-V • E = color excess = the difference between observed CI and standard CI for the star • M = absolute magnitude, that is the magnitude the object would have at 10pc • m-M = distance modulus = 5 log (distance in pc) – 5 = 5 log (d/10pc) • Mbol = bolometric magnitude = absolute magnitude integrated over all wavelengths to provide the luminosity of the object • BC = bolometric correction = the correction to the apparent magnitude at some wavelength to give the apparent bolometric magnitude Physical Photometry • When not studying stars (and at z = 0), there are serious shortcomings in the approaches just described • Therefore, we use physical photometry, where we reduce the measurements to physical units rather than just making color and brightness comparisons • Our measurements are made through a spectral band with certain characteristics: • We would like to characterize this band by a single wavelength. One candidate is the mean: T() d 0 . (6) T() d • This works to first order, but we will find that some corrections are necessary Overview of Absolute Calibration • Optical/IR • Absolute calibration tied to measures of local sources relative to celestial ones (or local emitting spheres in the case of MSX) • A clever round-about devised by Harold Johnson: the solar analog method • 1 – 2%, 0.4 to 25 microns • Radio • Primary standards measured with horn antennas, which have cleaner beams and are easier to model than a paraboloid with a feed antenna. • Performance confirmed by measurements of local sources • Calibrators then tied in with other standards with conventional radio telescope • Accuracies achieved are ~ 10 – 15% (Maddalena & Johnson) • X-ray • Calibrate telescope throughput on the ground • Illumination not exactly parallel, so there is an uncertainty in telescope throughput • Celestial sources also used (e.g., Crab) but very dependent on models • ACIS: 5% 2 – 7kev, 10% 0.5 – 2 kev (Bautz) The most famous horn antenna antenna pattern for a horn antenna antenna pattern for a paraboloidal antenna with a horn feed X-Ray Calibration Facility at Marshall Space Flight Center Optical/Infrared Absolute Calibration Ultimate goal is about 1% for supernova dark energy experiments. • Direct calibrations One transfers a calibrated blackbody reference source to one or more members of the standard star network. Ideally, one would use the same telescope and detector system to view both, but often the required dynamic range is too large and it is necessary to make an intermediate transfer. • Indirect calibrations One can use physical arguments to estimate the calibration, such as the diameter and temperature of a source. A more sophisticated approach is to use atmospheric models for calibration stars to interpolate and extrapolate from accurate direct calibrations to other wavelengths. • Hybrids The solar analog method uses absolute measurements of the sun, assumes other G2V stars have identical spectral energy distributions, and normalizes the solar measurements to other G2V stars at some wavelength where both have been measured, such as mV • Current "best" methods The calibrations in the visible are largely based upon comparisons of a standard source (carefully controlled temperature and emissivity) with a bright star, often Vega itself. Painstaking work is needed to be sure that the very different paths through the atmosphere are correctly compensated.