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Stellar Continua • • • • How do we measure stellar continua? How precisely can we measure them? What are the units? What can we learn from the continuum? – – – – Temperature Luminosity Metallicity Presence of binary companions • Bolometric corrections Measuring Stellar Flux Distributions • Low resolution spectroscopy (R~600 or 50-100 Å) • Wide spectral coverage • Access to fainter stars (why?) • Use a large (but not too large) entrance aperture (why?) • Correct for sky brightness and telluric extinction Measuring Stellar Flux Distributions • Four steps – Select a standard star (Vega) – Measure the shape of standard star’s energy distribution (relative Fn vs. l) – Measure the standard star’s absolute flux at (at least) one wavelength – Correct for line absorption Primary Photometric Standards • Vega (A0V) • For absolute flux, compare to standard laboratory sources, usually black bodies • Flux measured in ergs cm-2 s-1 A-1 at the top of the Earth’s atmosphere • Often plotted as – – – – Fl vs. A Fn vs. wavenumber (cm-1 = 1/l in cm) Log Fl + constant vs. A Log Fn + constant vs. wavenumber Stellar SEDs Calculating Fl from V • Best estimate for Fl at V=0 at 5556Å is Fl = 3.36 x 10-9 erg s-1 cm-2 Å-1 Fl = 996 photon s-1 cm-2 Å-1 Fl = 3.56 x 10-12 W m-2 Å-1 • We can convert V magnitude to Fl: Log Fl = -0.400V – 8.449 (erg s-1 cm-2 Å-1) Log Fn = -0.400V – 19.436 (erg s-1 cm-2 Å-1) • To correct from 5556 to 5480 Å: Log [Fl (5556)/Fl(5480)]=-0.006– 0.018(B-V) What about the Sun? • Absolute flux uncertain by about 2% • Mv (~4.82) uncertain by about 0.02 mags • B-V even more uncertain • values range from 0.619 to 0.686 Practice Problems • Assuming an atmosphere + telescope + spectrograph+ detector efficiency of 10%, how many photons would be detected per Angstrom at 5480A using a 1.2-m telescope to observe a star with V=12 (and B-V=1.6) for one hour? • Using the CTIO 4-m telescope, an astronomer obtained 100 photons per A at 5480 A in a one hour exposure. Again assuming an overall efficiency of 10%, what was the magnitude of the star if B-V=0? Bound Free Continua • Lyman – far UV • Balmer – UV • Paschen – optical • Brackett – IR • Pfund – more IR Interpreting Stellar Flux Distributions I. The Paschen Continuum • The Paschen continuum slope (B-V) is a good temperature indicator • Varies smoothly with changing temperature • Slope is negative (blue is brighter) for hot stars and positive (visual is brighter) for cooler stars • B-V works as a temperature indicator from 3500K to 9000K (but depends on metallicity) • For hotter stars, neutral H and H- opacities diminish, continuum slope dominated by Planck function, and the Rayleigh-Jeans approximation gives little temperature discrimination The Paschen Continuum vs. Temperature 1.00E-02 50,000 K Flux Distributions Log Flux 1.00E-03 1.00E-04 1.00E-05 4000 K 1.00E-06 1.00E-07 300 400 500 600 700 Wavelength (nm) 800 900 1000 Interpreting Stellar Flux Distributions II – The Balmer Jump • The Balmer Jump is a measure of the change in the continuum height at 3647A due to hydrogen bound-free absorption • Measured using U-B photometry • Sensitive to temperature BUT ALSO • Sensitive to pressure or luminosity (at lower gravity, the Balmer jump is bigger – recall that kbf depends on ionization, and hence on Pe) • Works for 5000 < Teff < 10,000 (where Hbf opacity is significant) Flux Distributions at T=8000 Flux 1.00E-04 Log g = 4.5 1.00E-05 Log g = 1.5 1.00E-06 200 300 400 500 Wavelength (nm) 600 700 800 Bolometric Flux • Bolometric flux (Fbol) is the integral of Fn over all wavelengths FBol Fn dn 0 • Fbol is measured in erg cm-2 s-1 at the Earth • Luminosity includes the surface area (where R is the distance from the source at which Fbol is measured): L 4R Fbol 4r T 2 2 4 • L is measured in units of erg s-1, R is distance, r is radius Bolometric Corrections • Can’t always measure Fbol • Compute bolometric corrections (BC) to correct measured flux (usually in the V band) to the total flux • BC is usually defined in magnitude units: Fbol BC 2.5 log constant FV BC = mV – mbol = Mv - Mbol Bolometric Corrections from AQ -5 -4.5 Main Sequence -4 Giants Supergiants -3.5 BC -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 -0.5 0 0.5 1 B-V 1.5 2 Class Problem • A binary system is comprised of an F0V star (B-V=0.30) and a G3IV star (B-V=0.72) of equal apparent V magnitude. – Which star has the larger bolometric flux? – What is the difference between the stars in Mbol?