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Observations Phenomenology
Stars — Theory and Applications
Achim Weiss
Max-Planck-Institute fur Astrophysik
Ludwig-Maximilians-Universitat — Summer 2020
Part II: Observations and Phenomenology
Observations Phenomenology
Outline
1 Observations
Photometry
Astrometry
Spectroscopy
Seismology
2 Phenomenology
Single stars
Binaries
Observations Phenomenology
How to obtain information about stars?
photometry → brightness, colour
spectroscopy → Teff , g , v , ~X , M, vrot , activities, magnetic fields, . . .
astrometry → distance, proper motion
eclipsing binaries → mass ratios, orbital elements, geometricquantities
occultations & interferometry → angular diameter → R
pulsations and seismology → global properties (mean density, L/M);
interior structure, c , ρ, Γ1 =(∂ ln P∂ ln ρ
)S
gravitational lensing: existence, mass
neutrino experiments: interior conditions
Observations Phenomenology
Photometry: Basics - 1
Photometry: Astronomical observations make use of several broad- ornarrow-band filters to measure the flux of a star in differentwavelength-bands.
Best-known filter system: Johnson-Cousins-Glass UBVRIJHK ; the Vfilter is similar to the human eye.
Illustration of the UBV-filter response functions
Observations Phenomenology
Photometric filters of surveys
The Sloan Digital Sky Survey(SDSS) system
The Gaia system
Observations Phenomenology
Photometry: Basics - 2
Stars are almost perfect Black Body radiators; spectrum is characterizedby temperature TFlux in several bands → stellar temperature Teff (Infrared Flux Method)
Iλ =2c2h
λ5
(exp
hc
λkT− 1
)−1 ( erg
cm3s
)Planck′s law
F =
∫ ∞0
Iλdλ = σT 4( erg
cm2s
)2π5k4
15c2h3=
ac
4= σ = 5.67 · 10−5 erg
cm2 sK4Stefan− Boltzmann− constant
Photometric observations of interest for this lecture yield
V ≡ mv : apparent brightness (luminosity)
B − V or V − I : colour (temperature)
Observations Phenomenology
Luminosity, magnitudes, etc.:
For the Sun,L� = 4πR2
�F
is the solar luminosity (integrated flux through solar surface).
Flux on earth: S = 1.36 · 106 ergcm2s (solar constant):
S = F (R2�/d
2) ⇒L� = 3.82 · 1033erg/s
with Stefan-Boltzmann law
L� = 4πσR2�T
4eff → Teff = 5770K.
L, Teff , mass M (or g , R) are the basic global stellar parameters.
Observations Phenomenology
HRD & CMD
Hertzsprung-Russell-Diagram (HRD): log L – logTeff
Colour-Magnitude-Diagram (CMD): V – (B − V )(more general: brightness vs. colour index)
Magnitudes measure stellar brightness in log F -system.
m2 −m1 = 2.5 log f1/f2
m: apparent magnitude; M: absolute magnitude:
M −m ≡ 5− 5 log d
d : distance in parsec (3.08 · 1018 cm);
M is m at 10 pc.
Observations Phenomenology
HRD & CMD
distance modulus m −M: 0.2(m −M) + 1 = log d .
(the distance modulus to the LMC is 18.50→compute the distance)
Indices to m and M denote filter, e.g. MV or mB .
Bolometric luminosity or brightness is Mbol = Mbol,� − 2.5 log(L/L�).
Bolometric correction B.C. (here in V ): Mbol −MV
For the sun, B.C.V ,� = −0.12 (Alonso et al. 1996) and MV ,� = 4.82± 0.02 →Mbol = 4.70 and therefore
Mbol = −2.5 logL
L�+ 4.70
A further convention is that for a star of spectral class A0 V (e.g. α Lyr = Vega),
MV = MB = MU . This defines the bolometric corrections and scales for U and B bands.
Observations Phenomenology
Colour-Magnitude-DiagramsA globular cluster — variable mass:
A dwarf spheroidal galaxy —
variable composition, age, distance
The HIPPARCOS solar neighbourhood —
variable mass, composition, age
Observations Phenomenology
Colour-Magnitude-DiagramsA globular cluster — variable mass:
A dwarf spheroidal galaxy —
variable composition, age, distance
The HIPPARCOS solar neighbourhood —
variable mass, composition, age
Observations Phenomenology
Colour-Magnitude-DiagramsA globular cluster — variable mass:
A dwarf spheroidal galaxy —
variable composition, age, distance
The HIPPARCOS solar neighbourhood —
variable mass, composition, age
Observations Phenomenology
CMD of the galactic bulge (Surot Madrid et al., 2018)left: “Hess”-diagram, center: completeness map, right: after reddeningcorrection
problems: crowding, absorption and reddening, different population,foreground disk stars, distance . . .aim of such papers: to learn about the galactic history
Observations Phenomenology
Gaia Colour-Magnitude-Diagrams
Gaia (2013–2019/22) is an astrometric satellite to measure accurate positions
of about 109 stars (1% of all galactic stars) out to almost 10 kpc; plus radial
velocities (spectrometer) for 1.5 108 stars.
Observations Phenomenology
Astrometry → distances
The Hyades main sequence
Distances allow brightness calibrations,mass determinations, helpspectroscopic analyses, . . .and here resolve 3d-structure of theopen cluster Hyades (Reino et al. 2018)
Observations Phenomenology
Spectroscopy - examples
Spectroscopy gives: abundances (element ratios, ~X ), log g , Teff ,velocities
The Li- (Spite-) plateau
(Spite & Spite 1982; Ryan et al. 2001)
age of Milky Way halo stars from SDSS spectroscopy (Jofre, 2011)
Observations Phenomenology
The “Kiel-diagram” - spectroscopist’s HRD
Analysis of nearby disk stars (Fuhrmann 1998)
The Stagger-Grid of 3d-atmospheres in the Kiel-diagram
(Magic et al. 2013)
Observations Phenomenology
An example for abundance determinations
Comparison of abundances in both components of the α Cen system (de Melloet al., 2008)
. . . and in comparison to other analyses [A/B] := log(A/B)? − log(A/B)�
What does [Fe/H]=-2 for a globular cluster mean? What to conclude about other elements?
Observations Phenomenology
(Detached) Eclipsing binaries — fundamental method
Double-lined detached eclipsing binaries allow determination of M and R for
both components. Evolve models for these masses (with known composition),
and if both reach observed radius at same time → system age! (Additionally:
check model physics.)
V453 Cyg (Higl 2018), M1 = 14.4 M� , M2 = 11.1 Msun
Observations Phenomenology
Eclipsing binaries → masses and radii
Procyon A (α Can Min):astrometric mass (1.478 ± 0.012 M� ; Bond et al. 2015) and
theoretical evolution tracks to obtain age (about 2.7 Gyr);
(β is an overshooting parameter)
Three detached eclipsing binaries in NGC 6791 (with isochrones):
mass, age, helium content (Brogaard et al. 2011)
Observations Phenomenology
Seismology & oscillations → ν & c
Power in solar oscillation modes
Solar sound speed and an adiabatic exponent Γ1 =(d ln Pd ln ρ
)S
and: hydrogen mass on white dwarfs, evolutionary state,size of convective regions, stellar mass, helium content, . . .
Observations Phenomenology
Seismology & oscillations → M & R
For solar-type oscillations, scaling-relations hold:
M
M�=
(∆ν
∆ν�
)−4(νmax
νmax,�
)3(Teff
Teff,�
)3/2
R
R�=
(∆ν
∆ν�
)−2(νmax
νmax,�
)(Teff
Teff,�
)1/2
Silva Aguirre et al. (2012)
Together with Teff (and models!)allows age determination, evolutionarystate identification, . . .
Observations Phenomenology
Seismology & oscillations → evolutionary state
Separation of H-shell and He-core burning stars (Vrard & Mosser 2016)Determination of mixing in stellar core of 3.25 M�
star (Moravveji et al. 2016)
Observations Phenomenology
Cepheids: pulsational mass → discrepant with evolution
Evolutionary tracks (withoutand with core overshooting)that match the luminosity ofCepheid Polaris (Evans etal. 2008)The pulsational mass wasdetermined to be≈ 5.0± 0.4M�This “Cepheid mass
discrepancy” amounts to about
15% on average.
Observations Phenomenology
Solar Neighbourhood
range: 12-15 pc aroundSun
α Cen is nearest star at4.36 ly
α Cen A is G2 star of1.1M� and 1.52 L�
most nearby stars arered M-type dwarfs
56 stars, of which are 24single, 10 binary sytems,4 triple
⇒ ∼ 1/2 of all stars are inmultiples
stellar density: 4 starsper 1000 ly3
Observations Phenomenology
Proxima Cen in comparison to Sun
Prox Cen is a red(dwarf) main-sequencestar of spectral classM5.5
mass: M = 0.12M�
radius: R = 0.15R�
luminosity: 0.0017 L�(100x fainter than eyecan see)
Observations Phenomenology
The luminosity function of the solar neighbourhood
The SolarNeighbourhood isdominated by faint stars
most of them are on themain-sequence
since luminosity scaleswith mass, this is also amass distribution
⇒ low-mass stars dominate
this is confirmed by theuniversal Initial MassFunction
Observations Phenomenology
Extending the solar neighbourhood
Stars within 35 ly Stars within 100 ly
Observations Phenomenology
Binary systems
about 1/2 of all stars are in multiple systems
binaries are the most frequent ones
wide binaries: stars don’t interact and evolve as single stars
close binaries: stars may be affected (slightly) by tidal forces andstellar winds
interacting binaries: stars transfer mass and angular momentum,also repeatedly and in both directions, and system may lose massand angular momentum
→ separate and specialized lecture
theoretical treatment very rudimentary; needs 3d-radiationhydrodynamics!
Observations Phenomenology
Phenomenological types of binary systems – 1
ζ UMa, visual binary Mizar:
components A and B are themselves
binaries; A resolved here by
interferometry ( c©J. Benson and USNO)
α Cen, visual binary ( c©Charles Sturt Univ., Bathurst, Austr.)
Sirius is an astrometric binary (first detetcted
by 1844 by Friedrich Bessel) ( c©M. Guidry, Univ. Tennessee)
Observations Phenomenology
Phenomenological types of binary systems – 2
spectroscopic binaries revealthemselves by the Doppler shift ofspectral lines
( c©CSIRO (Commonwealth Scientific and Industrial
Research Organisation, 2015-2017))
lightcurve of HIP 59683, an eclipsing binary,
detected by photometry ( c©ESA)