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 F vs. )

– 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

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

Stellar SEDs

Calculating F from V

• Best estimate for F at V=0 at 5556Å isF = 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)

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 DistributionsI. 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

Flux Distributions

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

300 400 500 600 700 800 900 1000

Wavelength (nm)

Lo

g F

lux

4000 K

50,000 K

Interpreting Stellar Flux DistributionsII – 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 Pe)

• Works for 5000 < Teff < 10,000 (where Hbf opacity is significant)

Flux Distributions at T=8000

1.00E-06

1.00E-05

1.00E-04

200 300 400 500 600 700 800

Wavelength (nm)

Flux

Log g = 4.5

Log g = 1.5

Bolometric Flux

• Bolometric flux (Fbol) is the integral of F over all wavelengths

• 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 is measured in units of erg s-1, R is distance, r is radius

dFFBol

0

422 44 TrFRL bol

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:

BC = mV – mbol = Mv - Mbol

constantlog5.2 V

bol

F

FBC

Bolometric Corrections from AQ-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

-0.5 0 0.5 1 1.5 2B-V

BC

Main Sequence

Giants

Supergiants

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?