1. Atmospheric extinction Suppose that Earth’s atmosphere has mass absorption coefficient  at wavelength. If f 0 is flux of incoming beam above atmosphere, then observed flux: Convert f/ f 0 to a magnitude difference: where z ds dh

2. Continuous extinction Produced by continuum scattering processes in Earth’s atmosphere (mainly Rayleigh+aerosols). Use calibration of a c ( ) for site, together with expression just derived to get: Vertical extinction at Roque de los Muchachos Observatory, La Palma

3. Telluric-line extinction Water, O 2 other molecules produce rotation/vibration bands composed of many saturated absorption lines. e.g. Near-IR spectrum of B3V star: Individual lines almost resolved in this high-resolution spectrum

4. Unresolved telluric lines At low/moderate resolution (  ≥ 1Å) each spectral pixel holds several saturated lines with continuum gaps in between. How does extinction scale with sec z? Note how unresolved lines no longer appear saturated at low resolution Same spectrum as before, degraded in wavelength resolution by factor 11.

5. Curve of growth for telluric lines Stellar flux is diminished by the equivalent width of the lines. Telluric lines have saturated Voigt profiles due to thermal Doppler+pressure-broadening. On saturated part of curve of growth, slope=1 Log W Log (sec z) Optically thin Doppler core Lorentzian wings slope=0.5 Saturated

6. Calibrating telluric-line extinction Extinction relation in spectral regions affected by saturated telluric lines is therefore: Calibrate a L ( ) by measuring B stars (and flux- calibration standards) at several different airmasses (sec z). At each wavelength, fit a relation of the form: Do this by converting flux to magnitude and plotting versus log(sec z). Then fit slope B  and intercept log A 0 ( )

7. Flux calibration Observed monochromatic “OB” magnitude: Flux-calibrated monochromatic “AB” magnitude: where f is the flux in erg cm –2 s –1 Hz –1. Calibrate target spectrum by observing a flux standard spectrum with known AB( ) Apply line + continuum airmass corrections to both stars. Then fit polynomial to OB-AB( ) versus.

8. Slit-loss corrections If observing a variable object faint enough to have a nearby non-variable comparison star: Rotate spectrograph slit to observe comparison and variable simultaneously. Observe comparison star once with wide slit. Ratio narrow/wide calibrates slit losses vs : Slit loss

9. Synthetic photometry Monochromatic flux distributions: Unit of received flux density: –1 Jansky (Jy)=10 –26 W m –2 Hz –1 –mJy commonly used, esp. in radio astronomy.

10. Monochromatic magnitude systems Palomar: Hubble Space Telescope: Conversion from AB magnitude to mJy: Conversion from ST to AB magnitude: AB = 16.4 ST = 16.4 f f = 1 mJy 5500 Å erg cm –2 s –1 Å –1

11. Broadband magnitudes Conventional magnitudes are defined relative to Vega = 0: Useful in early days before good absolute calibrations of stellar photometry were available. In the Johnson V band at 5500Å = 550 nm, Vega (m=0) produces –~10 8 photons m –2 s –1 nm –1 at 550 nm, or equivalently –~1000 photons cm –2 s –1 Å –1 at 550 nm (Johnson V) Zero points of AB and ST magnitudes are chosen so that in V band, AB(V) = ST(V) = m(V).