Spectral energy distribution of the sun

400 600 800 1000 1200 [nm]

Astrophysics I, Lecture Slides – Chapter 2, ETH Zurich

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Wien's displacement lawBlack body curves for different temperatures

250 500 750 1000 1250 nm

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Low resolution spectra of stars

3500350 400 450 500 550wavelength [nm]

rel.

flux

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''Mindmap'' for plane-parallel atmosphere

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formal solution + Taylor expansion for source funct. I(τ) as function of B(τ)

~ U ~ F~aT4 ~σTeff

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isotr. anisotr.

B(τ): - grey atmosphere approximation- RT-equation (pp-atmosphere) rad.pressure ~ flux + Eddington approximation

approx.Temperature structure

U or B(τ) decreasewith τ

F or dB(τ)/dτ= const

approximation: very good good not so good

surface

τ=2/3τ>>1 τ>1

Comparison of detailed models with grey atmosphere and Eddington approximation

• Temperature structure as function of optical depths at 500nm, for two modern 1-D models (red and green) and the mean of a 3D-model (blue). The dashed lines give the rms variations of the 3-D model (because of surface structures). Asplund et al. 2009, ARA&A 47,481

Temperature structure T(τ) for the solar atmosphere

grey atmosphere withEddington approximationTeff=5780 K adopted

4 43 2( ) ( )4 3effT Tτ τ= +

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Limb darkening for the sun

from Choudhuri

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Limb darkening

Grey atmosphere + Eddington approximation

Two parameter description (for diff. λ )

from Wikipedia, Photosphäre, 6.10.2017

sun during Venus transit 2012

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Planet transits yield limb darkening for stars

from Knutson et al., ApJ 655, 564 (2007)

HST observations of the color dependence of the transit of the planet around HD 209458

HD 209458 G0V (Teff=6000 K)Planet, 0.7 MJ, 1.3 RJ, P=3.5 d, Teq=1000K

wavelengths from top to bottom:950nm, 870nm, 770nm, 680nm, 580nm540nm, 480nm, 430nm, 380nm, 330nm

(curves not corrected for finite size of planet)

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Line formation in stars

from Choudhuri

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Spectral atlas for the sun

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Fe I (Fe0) and FeII (Fe+)

The atomic transitions of FeI and FeII which are partly responsible for the many absorption lines in the solar spectrum

Energy given in cm-1

E/hc = 1/λ (hν=hc/λ)λ = wavelength of line

from F. Thevenin, T.P. Idiart,

arXiv:astro-ph/9906433

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Curve of growth (interstellar/intergalactic Lyα)

• Curve of grows for HI Lyα line

b: Doppler widths b/c=ΔνD/ν

Top: line profiles for b=23 km/s(with HI column density log x=12,13,…,21 in cm2)

Middle: curves of growthdifferent b-parameters

Bottom: lines profiles with different b-parameters

https://ned.ipac.Caltech.edu/level5/Charlton/Charlton1_1.html 12

Curve of growths analysis

Arcturus (K-giant , 4000K) relative to empirical curves from the sun

yields differential abundancese.g. NaIArcturus/NaIsun

(from Griffin and Griffin)

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Solar photospheric elemental abundances (by number) normalized to nH = 1012

Asplund et al. 2009, ARA&A 47,481 14

there are stars with very peculiar abundances

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Warning: sun and stars have complex structures

A monster quiescent prominence photographed through a SolarMax II 60 H-alpha scope on September 17, 2015. Two days later, when the prominence rotated onto the disk, it appeared as a prominent, dark filament. Bright white patches are "plages", described below.

Bob Antol / stargate4173.com 16

https://ase.tufts.edu/cosmos/print_images.asp?id=28

Outer structure of the solar atmosphere- Photosphere- Chromosphere- Transition region- Corona

Complex magneticfield processesheat thehigher layers

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