Jeremiah Horrocks Institute University of Central

Asteroseismology

A new revolution with the Kepler and TESS

space missions

Emeritus Professor Donald Kurtz Jeremiah Horrocks Institute

University of Central Lancashire

At first sight it would seem that the deep interior of the Sun and stars

is less accessible to scientific investigation

than any other region of the universe.

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Our telescopes may probe farther and farther

into the depths of space; but how can we ever obtain

certain knowledge of that which is hidden

behind substantial barriers?

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What appliance can pierce through

the outer layers of a star and test

the conditions within?

Asteroseismology

The Kepler Mission Space Telescope

Main mission: March 2009 – May 2013K2: May 2013 – October 30 2018

TESS2018

7 days of Kepler data for one of ~200,000 starsKIC10799291

The light curve

Radial modesCepheidsP1/P0= 0.7

organ pipeP1/P0= 0.33

Structure of stellar pulsation modes

• n = number of radial nodes

• l = total number of surface nodes

• m = number of surface nodes that are lines of longitude

• l – m = number of surface nodes that are lines of latitude

Ylm q,j( ) = Nl

mPlm cosq( )eimj

Nonradial modes-Dipole modes( ) ( ) jqjq immm ePY cos, 11 µ

l = 1, m = -1 l = 1, m = 0 l = 1, m = +1

Animations courtesy of Rich Townsend

Nonradial modes -Quadrupole modes

( ) ( ) jqjq immm ePY cos, 22 µ

l = 2, m = -1l = 2, m = 0 l = 2, m = -2

Animations courtesy of Rich Townsend

Asteroseismology –how does it work?

• Turning radius

• Acoustic cavity

c 2 =G1p

r=

G1kT

m

• Sound speed

Driving mechanisms

Heat engine mechanism

• Gains heat on compression

• κ-mechanism (κappa = opacity)

• H, He, Fe main drivers

• Cepheids, RR Lyr stars,δ Sct stars, β Cep stars, SPB stars, roAp stars, pulsating white dwarfs, sdB variables, …

Stochastic driving

• Star resonates with acoustic noise

• Solar-like oscillators

• Main interest in exoplanet finding

Early versions of this figure were made by JørgenChristensen-Dalsgaard

(Aarhus University) and by Pieter Degroote (KU Leuven).

This updated version was produced by Peter Papicsbased on the version in his PhD Thesis (Papics, 2013).

The sun as a star - BiSON

The sun as a star - GOLF

large separationsmall separation

Saxo

Java

Gemma

Chaplin et al. 2010, ApJ, 713, L169

Dn µ r µM

R3nmax µ

g

Teff=GM / R2

Teff

Stellar Age

White et al. 2011, ApJ, 743. 161

p modes and g modes

Aerts, Christensen-Dalsgaard, Kurtz 2010, Asteroseismology, Springer

The Sun

KIC 11145123

g modes

g modes

g mode splitting

• For high overtone dipole g modes Cn,l asymptotically approaches 0.5

• Cn,l ≈ l/(l+1) = 0.5 for KIC 11145123 g modes

• This is model independent

• The splitting between the g mode sectoral m = +1 and -1 frequencies measures the “average” rotation rate in the core.

• Pcore ≥ 105.13 ± 0.02 days

kernels

Dipole triplet

Quadrupole quintuplet

Radialsinglet

p modes

p mode triplet

p mode quintuplet

p mode splitting

• For the p modes Cn,l < 0.03 ≈ 0

• This is model independent

• The splitting between the p mode frequencies measures the “average” rotation rate near the surface.

• Psurface ≤ 98.57 ± 0.02 days

• The surface rotates more quickly than the core

The Ap stars

The roAp stars

• Teff: 6600 – 8500 K

• Ppul: 4.68 – 23.6 min

• Aphot B: < 10 mmag

• Arv: < 8000 m s-1

• Bs: < 30 kG

• Very peculiar: atomic diffusion

• Oblique pulsators

• Chemically stratified atmospheres

log 5000

-5

-4

-3

-2

-1

0

Pr, Nd

H

Fe

HD154708 – 24.5 kG

Hubrig, Mathys, Kurtz et al., 2009, MNRAS, 396, 1018 1/18/2021IAC WS 2010 – Lecture 2

Heartbeat Stars – KOI-54

Animation courtesy of Jim Fuller

Tidal Asteroseismology • HD 74423

• V = 8.6

• A7VkA0mA0 lambda Boo star

• Ellipsoidal variable

• Tidally trapped dipole oblique pulsator

• Pulsation axis = tidal axisFirst one!

• Essentially only one side of the star pulsates

1926

What appliance can pierce through

the outer layers of a star and test

the conditions within?

Asteroseismology

A new revolution with the Kepler and TESS

space missions

Emeritus Professor Donald Kurtz Jeremiah Horrocks Institute

University of Central Lancashire