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)