Extrasolar Planets and Stellar Oscillations in K Giant Stars

Notes can be downloaded from

www.tls-tautenburg.de→Teaching

20000 14000 10000 7000 5000 3500 2500

1.000.000

10.000

100

1

0.01

0.0001

O B A F G K M

+20

+15

+10

+5

0

-5

-10

Abs

olut

e M

agni

tude

Lum

inos

it y (

Sol

ar L

um. )

Effective Temparature

Spectral Class

White Dwarfs

Main Sequence Giants

Supergiants

Why the interest in K giants for exoplanets and asteroseismology?

K giants occupy a „messy“ region of the H-R diagram

Progenitors are higher mass stars

Evolved A-F stars

The story begins:

Smith et al. 1989 found a 1.89 d period in Arcturus

1989 Walker et al. Found that RV variations are common among K giant stars

These are all IAU radial velocity standard stars !!!

First, planets around K giants stars…

1990-1993 Hatzes & Cochran surveyed 12 K giants with precise radial velocity measurements

Footnote: Period Analysis

Lomb-Scargle Periodogram:

Power is a measure of the statistical significance of that frequency (period):

1

2Px() =

[ Xj sin tj–]2

j

Xj sin2 tj–

[ Xj cos tj–]2

j

Xj cos2 tj–j

+1

2

False alarm probability ≈ 1 – (1–e–P)N = probability that noise can create the signal

N = number of indepedent frequencies ≈ number of data points

tan(2) = sin 2tj)/cos 2tj)j j

If a signal is present, for less noise (or more data) the power of the Scargle periodogram increases. This is not true with Fourier transform -> power is the related to the amplitude of the signal.

Many showed RV variations with periods of 200-600 days

Her has a 613 day period in the RV variations

But what are the variations due to?

The nature of the long period variations in K giants

Three possible hypothesis:

1. Pulsations (radial or non-radial)

2. Spots (rotational modulation)

3. Sub-stellar companions

What about radial pulsations?

Pulsation Constant for radial pulsations:

Q = PM

Mּס

( )0.5 R

Rּס

( )–1.5

For the sun:

Period of Fundamental (F) = 63 minutes = 0.033 days (using extrapolated formula for Cepheids)

Q = 0.033

Pּס

( )0.5

=

Footnote:

The fundamental radial mode is related to the dynamical timescale:

d2R

The dynamical timescale is the time it takes a star to collapse if you turn off gravity

dt2=

GM

R2

Approximate: R ≈ G R is the mean

density

For the sun = 54 minutes

= (G)–0.5

What about radial pulsations?

K Giant: M ~ 2 Mּס , R ~ 20 Rּס

Period of Fundamental (F) = 2.5 days

Q = 0.039

Period of first harmonic (1H) = 1.8 day

→ Observed periods too long

What about radial pulsations?

Alternatively, let‘s calculate the change in radius

V = Vo sin (2t/P),

R =2 Vo sin (2t/P) = ∫0

/2 VoP

Gem: P = 590 days, Vo = 40 m/s, R = 9 Rּס

R ≈ 0.9 RּסBrightness ~ R2

m = 0.2 mag, not supported by Hipparcos photometry

What about non-radial pulsations?

p-mode oscillations, Period < Fundamental mode

Periods should be a few days → not p-modes

g-mode oscillations, Period > Fundamental mode

So why can‘ t these be g-modes?

Hint: Giant stars have a very large, and deep convection zone

Recall gravity modes and the Brunt–Väisälä Frequency

The buoyancy frequency of an oscillating blob:

N2 = g (1

P

dPdr

–ddr )

g is local acceleration of gravity

is density

P is pressure

Where does this come from?

P

dPd( )

adFirst adiabatic exponent

Brunt Väisälä Frequency

*

00

T

r

Change in density of surroundings:

= 0 + ( ddr ) r

* = 0 + ( ddP ) r

Change in density due to adiabatic expansion of blob:

dPdr

* = 0 + ( 11

) rdPdr

P

Brunt Väisälä Frequency

*

00

T

r

Difference in density between blob and surroundings :

= – *

= r( 11

)dPdr

P

ddr

–

Buoyancy force fb = – g r

= –( 1

)ddr

1

1

dP

drP–

F = –kx → 2 = k/mRecall

This is just a harmonic oscillator with 2 = N2

r

Brunt Väisälä Frequency

Criterion for onset of convection:

However if * < , the blob is less dense than its surroundings, buoyancy force will cause it to continue to rise

( 11

) dPdr

P

ddr

In convection zone buoyancy is a destabilizing force, gravity is unable to act as a restoring force → long period RV variations in K giants cannot be g modes

What about rotation? Spots can cause RV variations

Radius of K giant ≈ 10 Rּס

Rotation of K giant ≈ 1-2 km/s

Prot ≈ 2R/vrot

Prot ≈ 250–500 days

Its possible!

Rotation (and pulsations) should be accompanied by other forms of variability

1. Have long lived and coherent RV variations

2. No chromospheric activity variations with RV period

4. No spectral line shape variations with the RV period

3. No photometric variations with the RV period

Planets on the other hand:

Case Study Gem

CFHT McDonald 2.1m

McDonald 2.7m TLS

Ca II H & K core emission is a measure of magnetic activity:

Active star

Inactive star

Ca II emission variations

Hipparcos Photometry

Test 2: Bisector velocity

From Gray (homepage)

Spectral line shape variations

Period 590.5 ± 0.9 d

RV Amplitude 40.1 ± 1.8 m/s

e 0.01 ± 0.064

a 1.9 AU

Msin i 2.9 MJupiter

The Planet around Gem

M = 1.7 Msun

[Fe/H] = –0.07

The Star

Frink et al. 2002

P = 1.5 yrs

M = 9 MJ

P = 711 d

Msini = 8 MJ

Setiawan et al. 2005

Setiawan et al. 2002:

P = 345 de = 0.68 M sini = 3.7 MJ

Tau

Tau has line profile variations, but with the wrong period

Hatzes & Cochran 1998

Period 653.8 ± 1.1 d

RV Amplitude 133 ± 11 m/s

e 0.02 ± 0.08

a 2.0

Msin i 10.6 MJupiter

The Planet around Tau

M = 2.5 Msun

[Fe/H] = –0.34

The Star

Dra

Period 712 ± 2.3 d

RV Amplitude 134 ± 9.9 m/s

e 0.27 ± 0.05

a 2.4

Msin i 13 MJupiter

The Planet around Dra?

M = 2.9 Msun

[Fe/H] = –0.14

The Star

Setiawan et al. 2005

The evidence supports that the long period RV variations in many K giants are due to planets…so what?

B1I V

F0 V

G2 V

Planets around massive K giant stars

Dra 2.9 13 2.4 712 0.27 –0.14

Tau 2.5 10.6 2.0 654 0.02 –0.34

Period

Characteristics:

1. Supermassive planets: 3-11 MJupiter

Theory: More massive stars have more massive disks

2. Many are metal poor

Theory: Massive disks can form planets in spite of low metallicity

3. Orbital radii ≈ 2 AU

Theory: Planets in metal poor disks do not migrate because they take so long to form.

And now for the stellar oscillations…

Hatzes & Cochran 1994

Short period variations in Arcturus

n = 1 (1H)

n = 0 (F)

n

0 F1 1H2 2H

Ari

Alias

n≈3 overtone radial mode

Dra

Dra : June 1992

Dra : June 2005

Dra

Photometry of a UMa with WIRE guide camera (Buzasi et al. 2000)

0

1

23

Radial modes n =

Conclusion: most (all?) K giant stars pulsate in the radial and low-overtone modes.

So what?

HD 13189

P = 471 d

Msini = 14 MJ

M* = 3.5 s.m.

P = 4.8 days

P = 2.4 days

HD 13189 short period variations

For M = 3.5 Mּס

R = 38 R

F = 4.8 d

2H = 2.7 d

→ oscillations can be used to get the stellar mass

Current work on K giants

1. TLS survey of 62 K giants (Döllinger Ph.D.)

2. Multi-site campaigns planned (GLONET)

3. MOST campaign on Oph and Gem

4. CoRoT additional science program (150 days of photometry)

5. Lots of theoretical work to model pulsations needs to be done

Döllinger Ph.D. work: 62 K giants surveyed from TLS

≈ 10% show long period variations that may be due to planetary companions

Time (days)

Inte

nsit

y5.7 days

Aldebaran with MOST

Summary

• K giant (IAU radial velocity standards) are RV variable stars!

• Multi-periodic on two time scales: 200-600 days and 0.25 – 8 days

• Long period variations are most likely due to giant planets around stars with Mstar > 1 Mּס

• Short period variations are due to radial pulsations in the fundamental and overtone modes

• Pulsations can be used to get funamental parameters of star