ASTR_4170 Special Topics: Photometry & Filter Systems Day-6

Announcements This week: Dark Night Observing tonight First “Astro-group” meeting. - Friday, 9/11; 2:30-3:30 E-109

Definitions & Terms -1 Photometric Conditions: Differential Photometry Absolute Relative Photometry Absolute Photometry Standard Star Zenith Angle Airmass Atmospheric Extinction

Light is an Electromagnetic Wave

Basic Properties of Waves Wavelength = in meters Frequency = in cycles per second or Hertz (Hz) Speed = c in meters per second

Each “color” is characterized by its wavelength Using c = we can see that the frequency of visible light is in the Hz range

Visible light is only a very small part of the Electromagnetic Spectrum

Flux Amount of light energy per unit area per unit time in a specific wavelength band Recall that Energy is usually measured in Electron Volts; 1 eV = X J

Blackbody Spectra

Two laws govern blackbody radiation Wein’s Displacement Law Where T is in Kelvin and is in meters Planck’s Law with B in Watts per square meter per Hz per steradians or Watts per square meter per meter per steradians, T in Kelvin, c in meters per second and is in meters. h is Planck’s constant and k is Boltzmann’s constant

Stellar Classification Annie Jump Cannon developed a stellar classification system based on temperature and the women of Harvard Observatory classified hundreds of thousands of stars. The project spanned several decades and was funded by a grant from the widow of Henry Draper. The resulting catalogue is the Henry Draper Catalogue

Stellar Classification Scheme

Magnitudes §2, 3, 4 – EMR, Definitions, Magnitudes

Magnitude Originally devised by Hipparchus around 140 BC. Based on when stars become visible after sunset. Sunset to astronomical twilight (complete dark) is divided into six equal time periods 1 st mag…visible in first 2 nd mag…visible in second = End Civil Twilight 3 rd mag…visible in third 4 th mag…visible in fourth = End Nautical Twilight 5 th mag…visible in fifth 6 th mag…visible in sixth = End Astronomical Twilight

Modern definition of magnitude is based on light flux Note that this compares two stars. If a “zero point” is defined then where C is the zero point offset Vega Magnitude System

Zero Points N.R. Pogson, originator of the modern magnitude definition, proposed an average of the sixth magnitude stars in certain star catalogues. Result: m Sirius = -1.6 North Polar Sequence…system of “standard stars” with known magnitudes to compare against m Vega ≡ 0.0 but problems with variability and dust leads modern values to m Vega = 0.03 Most common systems now are standard star systems

Absolute magnitude Defined as the magnitude of the object if it was located at a distance of 10 parsecs. This gives a distance (d) relationship between apparent magnitude (m) and absolute magnitude (M). Distance is measured in parsecs

Types of Magnitude  Visual Magnitude (m v )…measured over the visible spectrum  Monochromatic magnitude(m )…measured over a narrow wavelength range  Bolometric magnitude (m bol )…measured over the entire E/M spectrum  Photographic magnitude (m pg )…magnitude measured with photographic plate

Johnson-Cousins Filter System

Now, A0V stars have relevant colors. AB Magnitude System The Vega system has issues: notably the arbitrary assigning of 0.00 color to all A0V stars, and a magnitude on the Vega system does NOT translate to a physical understanding of the physics of the body. The SDSS used the “AB Magnitude” system (Fukugita et al. 1996, AJ, 111, 1748) where the definition of a magnitude is:Fukugita et al. 1996, AJ, 111, 1748 and

The asinh magnitudes are characterized by a softening parameter b, the typical 1-sigma noise of the sky in a PSF aperture in 1" seeing. The relation between flux density f and asinh magnitude m is: m=[-2.5/ln(10)][asinh((f/f 0 )/(2b)) + ln(b)]. or f=2bf 0 sinh(m/[-2.5/ln(10)] - ln(b)). Here, f 0 is the zero point of the magnitude scale, i.e., f 0 is the flux density of an object with magnitude of zero, given in the table below. The quantity b is measured relative to f 0, and thus is dimensionless. The corresponding flux density uncertainty is df= abs[(fdm/[-2.5/ln(10)])/tanh((m/[-2.5/ln(10)])-ln(b))]. where dm is the uncertainty in SDSS magnitude m. AB Magnitude System There is still an issue, especially for modern detectors working near the “plate limit” of zero (or negative) flux. To circumvent this issue (the log function becomes undefined), Robert Lupton created a new way to calculate magnitude for the SDSS, the asinh magnitude. Within SDSS we called these “Luptitudes”.

asinh Softening Parameters and Zero Points (b and f0) Bandbf 0 (Jy)mzpc Zero-Flux- Density Magnitude [m(f/f 0 = 0)]m(f/f 0 = 10b) u1.4 × (CModel magnitudes only) g0.9 × r1.2 × i1.8 × z7.4 × (PSF and Model magnitudes only) From the SDSS DR6 photometry page.