Transcript Stellar Continua

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  4R Fbol  4r 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?