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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. - PowerPoint PPT Presentation
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Stellar ContinuaStellar 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 Measuring Stellar Flux DistributionsDistributions
• Low resolution spectroscopy• Wide spectra coverage• Access to fainter stars• Typically R~600• Use a large (but not too large)
entrance aperture• Correct for sky brightness and
telluric extinction
Primary Photometric StandardsPrimary Photometric Standards
• Vega (A0V)• Compared 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
Calculating FCalculating F from V from V
• Best estimate for F at V=0 at 5556A is
F = 3.54 x 10-9 erg s-1 cm-2 A-1
F = 990 photon s-1 cm-2 A-1
F = 3.54 x 10-12 W m-2 A-1
• We can convert V magnitude to F:
Log F= -0.400V – 8.451 (erg s-1 cm-2 A-1)
Log F = -0.400V – 19.438 (erg s-1 cm-2 A-1)
• With color correction for 5556 > 5480 A:
Log F =-0.400V –8.451 – 0.018(B-V) (erg s-1 cm-2 A-1)
Class ProblemsClass 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?
Interpreting Stellar Flux DistributionsInterpreting Stellar Flux DistributionsI. The Paschen ContinuumI. 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. The Paschen Continuum vs. TemperatureTemperature
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 DistributionsInterpreting Stellar Flux DistributionsII – The Balmer JumpII – 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=8000Flux 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 FluxBolometric 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
dFFBol
0
bolFRL 24
Bolometric CorrectionsBolometric 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
constant5.2 V
bol
F
FBC
Bolometric CorrectionsBolometric Corrections
Bolometric Corrections from AQ
-5
-4
-3
-2
-1
0
-0.5 0 0.5 1 1.5 2
B-V
BC
(m
agn
itu
des
)
Class ProblemClass 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 magnitude. – Which star has the larger bolometric
flux? – What is the difference between the
stars in Mbol?