1. 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

2. 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

3. Measuring Stellar Flux Distributions Four steps –Select a standard star (Vega) –Measure the shape of standard star’s energy distribution (relative F vs. ) –Measure the standard star’s absolute flux at (at least) one wavelength –Correct for line absorption

4. 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 –F vs. A –F vs. wavenumber (cm -1 = 1/ in cm) –Log F + constant vs. A –Log F + constant vs. wavenumber

5. Stellar SEDs

6. Calculating F from V Best estimate for F at V=0 at 5556Å is F = 3.36 x 10 -9 erg s -1 cm -2 Å -1 F = 996 photon s -1 cm -2 Å -1 F = 3.56 x 10 -12 W m -2 Å -1 We can convert V magnitude to F : Log F  = -0.400V – 8.449 (erg s -1 cm -2 Å -1 ) Log F = -0.400V – 19.436 (erg s -1 cm -2 Å -1 ) To correct from 5556 to 5480 Å: Log [F (5556)/F (5480)]=-0.006– 0.018(B-V)

7. What about the Sun? Absolute flux uncertain by about 2% M v (~4.82) uncertain by about 0.02 mags B-V even more uncertain values range from 0.619 to 0.686

8. 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?

9. Bound Free Continua Lyman –far UV Balmer –UV Paschen –optical Brackett –IR Pfund –more IR

10. 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

11. The Paschen Continuum vs. Temperature 4000 K 50,000 K

12. 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  bf depends on ionization, and hence on P e ) Works for 5000 < Teff < 10,000 (where H bf opacity is significant)

13. Flux Distributions at T=8000 Log g = 4.5 Log g = 1.5

14. Bolometric Flux Bolometric flux (F bol ) is the integral of F over all wavelengths F bol 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 F bol is measured): L is measured in units of erg s -1, R is distance, r is radius

15. Bolometric Corrections Can’t always measure F bol Compute bolometric corrections (BC) to correct measured flux (usually in the V band) to the total flux BC is usually defined in magnitude units: BC = m V – m bol = M v - M bol

16. Bolometric Corrections from AQ

17. 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 M bol ?