![Page 1: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/1.jpg)
Stellar Oscillations in Giant Stars
1. K giants
2. Mira
3. RV Tau stars
![Page 2: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/2.jpg)
K giants occupy a „messy“ region of the H-R diagram
Progenitors are higher mass stars than the sun
Giant stars are A-K starts that have evolved off the main sequence and on to the giant branch
![Page 3: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/3.jpg)
![Page 4: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/4.jpg)
A 2 Mּס star on the main sequence
Giant stars are of particular interest to planet hunters. Why? Because they have masses in the range of 1-3 Mּס
Stars of higher mass than the Sun are ill-suited for RV searches. However the problem with this is getting a good estimate for the mass of the star
A 2 Mּס star on the giant branch
![Page 5: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/5.jpg)
The story of variability in K giant stars began in 1989:
Smith et al. 1989 found a 1.89 d period variation in the radial velocity of Arcturus:
![Page 6: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/6.jpg)
1989 Walker et al. Found that RV variations are common among K giant stars
These are all IAU radial velocity standard stars !!!
Inspired by the Walker et al. Paper, Hatzes & Cochran began a radial velocity survey of a small sample of K giant stars.
![Page 7: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/7.jpg)
The Long Period Variability: Planets?
![Page 8: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/8.jpg)
1990-1993 Hatzes & Cochran surveyed 12 K giants with precise radial velocity measurements and found significant period
![Page 9: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/9.jpg)
Many showed RV variations with periods of 200-600 days
The „3 Muskateers“
![Page 10: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/10.jpg)
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
![Page 11: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/11.jpg)
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
=
![Page 12: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/12.jpg)
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
![Page 13: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/13.jpg)
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
![Page 14: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/14.jpg)
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
![Page 15: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/15.jpg)
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:
![Page 16: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/16.jpg)
CFHT
McDonald 2.1m
McDonald 2.7m TLS
The Planet around Pollux ( Gem)
The RV variations of Gem taken with 4 telescopes over a time span of 26 years. The solid line represents an orbital solution with Period = 590 days, m sin i = 2.3 MJup.
![Page 17: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/17.jpg)
Ca II H & K core emission is a measure of magnetic activity:
Active star
Inactive star
![Page 18: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/18.jpg)
Ca II emission variations for Gem
If there are no Ca II variations with the RV period, it probably is not activity
![Page 19: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/19.jpg)
Hipparcos Photometry
If there are no photometric variations with the RV period, spots on the surface are not causing the variations.
![Page 20: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/20.jpg)
Test 2: Bisector velocity
From Gray (homepage)
Spectral Line Bisectors
For most phenomena like spots, surface structure, or stellar pulsations, the radial velocity variations are all accompained by changes in the shape of the spectral lines. Planets on the other hand cause an overall Doppler shift of the line without an accompanying change in the lines.
Spectral line bisectors are a common way to measure line shapes
![Page 21: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/21.jpg)
The Spectral line shape variations of Gem.
![Page 22: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/22.jpg)
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 = 1.9 Msun
[Fe/H] = –0.07
The Star
Planets have been found around ~ 30 Giant stars
![Page 23: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/23.jpg)
Frink et al. 2002
P = 1.5 yrs
M = 9 MJ
The Planet around Dra
![Page 24: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/24.jpg)
From Michaela Döllinger‘s thesis
M sin i = 3.5 – 10 MJupiter
P = 272 d
m = 6.6 MJ
e = 0.53
M* = 1.2 Mּס
P = 159 d
m = 3 MJ
e = 0.03
M* = 1.15 Mּס
P = 477 d
m = 3.8 MJ
e = 0.37
M* = 1.0 Mּס
P = 517 d
m = 10.6 MJ
e = 0.09
M* = 1.84 Mּס
P = 657 d
m = 10.6 MJ
e = 0.60
M* = 1.2 Mּס
P = 1011 d
m = 9 MJ
e = 0.08
M* = 1.3 Mּס
JD - 2400000
RV
(m
/s)
![Page 25: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/25.jpg)
Tau
![Page 26: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/26.jpg)
Period 653.8 ± 1.1 d RV Amplitude 133 ± 11 m/se 0.02 ± 0.08a 2.0 AUMsin i 10.6 MJupiter
The Planet around Tau
M = 2.5 Msun
[Fe/H] = –0.34
The Star
![Page 27: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/27.jpg)
Dra
![Page 28: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/28.jpg)
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
![Page 29: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/29.jpg)
Setiawan et al. 2005
The evidence supports that the long period RV variations in many K giants are due to planets…so what?
K giants can tell us about planet formation around stars more massive than the sun. The problem is the getting the mass. This is where stellar oscillations can help.
![Page 30: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/30.jpg)
And now for the stellar oscillations…
![Page 31: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/31.jpg)
Hatzes & Cochran 1994
Short period variations in Arcturus consistent with radial pulsations
n = 1 (1H)
n = 0 (F)
![Page 32: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/32.jpg)
Ari velocity variations:
Alias
n≈3 overtone radial mode
![Page 33: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/33.jpg)
Photometry of UMa with WIRE guide camera (Buzasi et al. 2000)
Equally spaced modes in frequency → p-modes. Observed = 2.94 Hz
![Page 34: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/34.jpg)
Buzasi et al get a mean spacing of 2.94 Hz and a lowest frequency mode of 1.82 Hz (P = 6.35 d).
UMa has an interferometric radius of 28 Rּס
The Fundamental radial mode is given by:
0 ≈ 135M1/2
R3/2
Hz
Q = P0 √/ּס
Where the pulsation constant Q = 0.038 – 0.116, so P = 2.8, to 8.6 days, if M ≈ 4 Mּס , close to the first frequency. But…
Based on the known radius and observed spacing, this gives M ≈ 10 Mּס. So actual spacing may be one-half as a large and one is not seeing all modes (odd or even radial order, n)
![Page 35: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/35.jpg)
Dra
![Page 36: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/36.jpg)
Dra : June 1992
![Page 37: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/37.jpg)
Dra : June 2005
![Page 38: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/38.jpg)
Dra
The short period variations of Dra can also be explained by radial pulsations, but only n order modes?
![Page 39: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/39.jpg)
Dra: A planet hosting K giant
P1 = 7 hrs A1= 5 m/s
P2 = 6.4 hrs A2=6.35 m/s
P3 = 5.9hrs d A3=4 m/s
1 = 39.7 Hz
2 = 43.4 Hz
2 = 47.8 Hz
Mean = 4.05 Hz
![Page 40: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/40.jpg)
Recall our Scaling Relations
max = M/Mּס
(R/Rּס)2√Teff/5777K
Frequency spacing:
3.05 mHz
0 ≈ 135M1/2
R3/2Hz n,l = (n + l/2 +
R ≈ ( mHzmax/3.05 )(135/Hz)2
Thes can be solved for the radius of the star:
![Page 41: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/41.jpg)
max ≈ 40 Hz (max peak at P = 7 hrs) = 0.04 mHz
Mean = 4.05 Hz
We have two cases:
1. These are nonradial modes and the observed spacing is one-half the large spacing
2. These are radial modes and the observed spacing is the large spacing
We have 2 equations and 2 unknowns, these can be solved for M, R
Case 2:
R = 14.5 Rּס
M = 2.9 Mּס
Case 1:
R = 3.6 Rּס
M = 0.17 Mּס
Case 1 is in disagreement with evolutionary tracks (they cannot be that wrong!) and Hipparcos distance. Conclusion: this is a giant star and we are detecting radial modes.
![Page 42: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/42.jpg)
Stellar Oscillations in Gem
Nine nights of RV measurements of Gem. The solid line represents a 17 sine component fit. The false alarm probability of these modes is < 1% and most have FAP < 10–5. The rms scatter about the final fit is 1.9 m s–1
![Page 43: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/43.jpg)
Am
plit
ude
(m/s
)
Window
DFT Velocities
![Page 44: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/44.jpg)
Amplitude in m/s
Observed RV Frequencies in Gem
![Page 45: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/45.jpg)
DFT Fit
![Page 46: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/46.jpg)
The Oscillation Spectrum of Pollux
The p-mode oscillation spectrum of Gem based on the 17 frequencies found via Fourier analysis. The vertical dashed lines represent a grid of evenly-spaced frequencies on an interval of 7.12Hz
![Page 47: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/47.jpg)
0 ≈ 135M1/2
R3/2Hz
0 ≈ 7.12 Hz
Inteferometric Radius of Gem = 8.8 Rּס
For radial modes → M = 1.89 ± 0.09 Mּס
Frequency Spacing
Evolutionary tracks give M = 1.94 Mּס
For nonradial modes→ M = 7.5 Mּס
![Page 48: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/48.jpg)
MOST Photometry for Gem
For = 87 mHz 2K/m = 65 km/s/mag
![Page 49: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/49.jpg)
Observed Photometric Frequencies in Gem
![Page 50: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/50.jpg)
![Page 51: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/51.jpg)
For modes for modes found in both photometry and radial velocity the 2K/m ratio is consistent with values found for Cepheids (2K/m ≈ 55) and thus radial pulsators.
The Radial Velocity – to – Photometric Amplitude Ratio
![Page 52: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/52.jpg)
HD 13189
P = 471 d
Msini = 14 MJ
M* = 3.5 s.m.
The first Tautenburg planet:
![Page 53: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/53.jpg)
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
![Page 54: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/54.jpg)
P = 5.8 days
Periodogram of RV residuals for Tau after subtracting the long period orbit
![Page 55: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/55.jpg)
Aldebaran with MOST
Period consistent with fundamental radial mode for M = 2.5 Mּס
5.8 days
But isochrones give M = 1.2 Mּס→ overtone?
![Page 56: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/56.jpg)
MOST: I/I = 0.019 = 0.02 mag
Radial Velocity 2K ~ 300 m/s
2K/m ≈ 15 Nonradial?
The Radial Velocity – to – Photometric Amplitude Ratio
![Page 57: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/57.jpg)
Radial Velocities of Boo in
Estimates of the mass for Arcturus have been controversial and have ranged from 0.1 to 3 Mּס. Can stellar oscillations resolve this?
![Page 58: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/58.jpg)
P1 = 3.57 d A1=34.7 m/s
P2 = 12.8 d A2=27.2 m/s
P3 = 2.08 d A3=23.2 m/s
P4 = 2.50 d A3=11.5 m/s
P5 = 1.74 d A5 =6.93 m/s
P6 = 5.77d A6 =6.23 m/s
P7 = 1.38d A7 =6.27 m/s
P8 = 1.19d A8 =5.4 m/s
Multi-period Fit
![Page 59: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/59.jpg)
Mean spacing = 1.16 Hz
The Oscillation Spectrum of Arcturus?
![Page 60: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/60.jpg)
Mozurkowich et al. 2003:
Limb darkened diameter = 21.373 mas = 25.65 Rּס
= 1.16 Hz → 1.24 Mּס for radial modes
= 2.32 Hz → 5 Mּס for nonradial modes
The higher mass is inconsistent with the spectroscopic analysis which indicate M ≈ 1 Mּס
![Page 61: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/61.jpg)
Boo in 2005
P = 3.36d
At any given time not all modes are visible → need lots of observing time over a very long time base → CoRoT and Kepler
![Page 62: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/62.jpg)
A new planet hosting K giant star: 11 UMa
P = 657 d
Msini = 3.6 MJupiter
e = 0.6
Döllinger et al. In preparation
![Page 63: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/63.jpg)
M* = 1.2 Mּס
R* = 36.3 Rּס
P1 = 4.1 d
P2 = 3.1 d
P3 = 7.1 d
Consistent with fundamental and low overtone radial modes
Oscillations in 11 UMa in 2007
![Page 64: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/64.jpg)
M* = 1.2 Mּס
R* = 36.3 Rּס
P1 = 6.2 d
P2 = 14.2 d
F = 10.8 d1H = 6.2 d2H = 4.1 d3H = 3.7 d
Oscillations in 11 UMa in 2009
We need a radius!
![Page 65: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/65.jpg)
Oph: G9.5 III (de Ridder et al. A&A 448, 689-695, 2006)
![Page 66: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/66.jpg)
Amplitude Spectra of Oph
![Page 67: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/67.jpg)
Best Fitting Models for Oph
![Page 68: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/68.jpg)
Radial or Nonradial pulsations?
So far we have seen evidence for radial pulsations in K giants, but are there nonradial modes?
Two tales of the same star, Oph
![Page 69: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/69.jpg)
MOST Photometry of Oph
![Page 70: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/70.jpg)
This power spectrum is typical for giants. You have a Gaussian envelope of excess power due to the p-mode oscillations, and an exponential rise to low frequencies believed to be due to convection motion.
![Page 71: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/71.jpg)
Conclusion: Mean spacing of 5.3 Hz which are radial modes of short lifetime (~3 days).
The autocorrelation function shows peaks at possible frequency spacings
![Page 72: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/72.jpg)
Conclusion using the same data set: radial and nonradial modes but with a long (10-20 d) lifetime.
The model reproduces Oph position in the HR diagram and the interferometric radius
Echelle diagram for Oph
![Page 73: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/73.jpg)
So why did two different groups get different answers using the same data set?
The answer lies in how you interpret the wings of a peak in the power spectrum.
The lifetime of a mode is not infinite and damping results in each mode being split into a number of peaks under a Lorentzian profile whose full width at half maximum (FWHM) is given by:
= 1 = lifetime of mode
L(x,) =
(2 + 2)
The shorter the mode lifetime, the broader the Lorentzian.
![Page 74: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/74.jpg)
Barban et al. Smoothed the power spectrum and intepreted the broad wings around each peak as due to a short lifetime modes.
Kallinger at al. Intepreted the wings as being individual modes that were quite narrow in width, ie. that had long lifetimes
So who is correct? We will have to wait for CoRoT and Kepler!
![Page 75: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/75.jpg)
Stellar Oscillations in HD 20884 (K2III) Observerved with MOST
(Kallinger et al. 2008, CoAst.153, 84K)
![Page 76: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/76.jpg)
The Observed Frequencies
![Page 77: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/77.jpg)
The Echelle Diagram and Best Fit Model
Conclusion: Photometric space-based observations show evidence for radial and non-radial modes in giant stars
![Page 78: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/78.jpg)
Mira Variables
• Red Giant Stars
• Mass less than 2 solar masses
• Pulsating in periods longer than 100 days
• Light amplitudes greater than 1 magnitude
Short History from Dorrit Hoffleit David Fabricius (1564_1617), an amateur astronomer and native of Friesland, The Netherlands, is recognized as the first to have discovered a long period variable in 1596, later called o (omicron) Ceti by Johann Bayer in 1603. Fabricius (Wolf 1877) observed the star from August 3, when he had used it as a comparison star for the determination of the position of the planet he assumed to be Mercury (later identified by Argelander, 1869, as more probably Jupiter), until August 21, when it had increased from magnitude 3 to magnitude 2. In September it faded, disappearing entirely by October (Clerke 1902). At the time Fabricius assumed the star was a nova. However, he observed it to reappear on February 15, 1609. Although Pingré saw it October 14, 1631, the star was practically forgotten until Johann Fokkens Holwarda (1618_1651), also of Friesland, rediscovered it in 1638 and determined its period as eleven months. Johannes Hevelius of Danzig (1611_1687) also observed the star on November 7, 1639, and in 1642 named it Mira, "The Wonderful." Fabricius unfortunately did not live to enjoy this appreciation for his discovery. Fabricius, a minister, had been murdered by a peasant whom he had cited from the pulpit as having stolen one of the minister's geese (Poggendorff 1863)!
![Page 79: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/79.jpg)
Light curve of Mira Variables
![Page 80: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/80.jpg)
Joy, 1926:
Velocity and Light Curves for Mira from 1926
Integrating the radial velocity curve, the change in radius of the star is ~70 Rּס, or 0.33 AU!
![Page 81: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/81.jpg)
Radial velocity curves of some Mira variables.
2K (peak to peak amplitude): 4 km/s
V ≈ 1 mag
2K/m ~ 2-3, significantly different from Cepheids
![Page 82: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/82.jpg)
From I.S. Glass: Miras in the LMC
Miras do not show an obvious Period – Luminosity Relationship in the Optical, but a clear one in the Infrared
A Period-Luminosity Relationship for Miras
![Page 83: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/83.jpg)
Mira is not a symmetric star!
Asymmetry is most likely related to non-symmetric mass loss coupled to the pulsations
![Page 84: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/84.jpg)
RV Tau Variables
• Spectral Type G-K giants (F-G at minimum, G-K at maximum)
• Pulsating in periods 60-100 days
• Light amplitudes 0.2 magnitudes or greater
• Stars in transition between the AGB and white dwarf stars
![Page 85: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/85.jpg)
Red Giant Branch (RGB) star leaves the main sequence and ascends the giant branch
Asymptotic Giant Branch (AGB): After core burning He (horizontal branch stars), the star moves back up the giant branch
![Page 86: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/86.jpg)
RV Tau Variables in the HR Diagram
![Page 87: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/87.jpg)
Oscillations in the M supergiant Betelgeuse ( Ori)
![Page 88: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/88.jpg)
3D simulation of convection in a Ori
![Page 89: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/89.jpg)
http://www.aip.de/groups/sternphysik/stp/box_simulation.html
Convection cells on a supergiant are large, only a few cells at any given time, whereas the sun has millions (size~700 km). These cells are also long-lived (years)
![Page 90: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/90.jpg)
RV Measurements from McDonald
AVVSO Light Curve
![Page 91: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/91.jpg)
Period of Ori abruptly changed from 317 days to 714 days. This coincided with an abrupt drop in the brightness of Ori.
Fourier transform of red points:
Fourier transform of blue points:
![Page 92: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/92.jpg)
Ori has dust shells surrounding it.
These shells may be related to these incidents of changing pulsation modes.
![Page 93: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/93.jpg)
vosc = L/Lּס
M/Mּס
(23.4 ± 1.4) cm/sec
max=
M/Mּס
(R/Rּס)2√Teff/5777K3.05 mHz
How well do the Scaling Relationships do?
Star Period VoscM R L Vpred Ppred
Gem 3.2 hrs 4 m/s 1.9 8.8 33 4 m/s 3.7 hrs
Dra 4 days 42 m/s 2.9 47.4 516 41 m/s 3 d
Ori 330-700 d
2 km/s 19 836 105000 1.2 km/s 174 d
Mira 330 d 6 km/s 0.4 500 8500 5 km/s 2370 d
In spite of the large range in mass and radius the scaling relationships are reasonably good predictors
![Page 94: Stellar Oscillations in Giant Stars K giants Mira RV Tau stars](https://reader036.vdocuments.us/reader036/viewer/2022062723/56813c02550346895da56099/html5/thumbnails/94.jpg)
Ori
Today we looked at stellar oscillations of stars up the giant branch.
In general: Periods get longer, and amplitudes get higher as the star evolves. Most modes are dominated by radial modes.
Next week: The stellar graveyard