Transcript PresentationAstrox

INTRODUCTION TO
HELIOSEISMOLOGY AND
ASTEROSEISMOLOGY
Meryem Berrada
1
Introduction
• Helioseismology is the study of the sun’s structure
• Asteroseismology is the study of other stellar bodies
• Identify the internal structure
• Variations of brightness  oscillations within the structure
• Convection occurring in the deep interior of a star
• Observe Doppler shifts in spectrum lines
• Standing sound waves  Boundaries : beginning of the convection
zone to the surface of the sun
2
Three different types of sound waves
1) Acoustic waves
• p-modes
• adiabatic process
2) Internal gravity waves
• g-modes
• Complex: imply a pressure gradient
• adiabatic as one of the possible solution
3) Surface gravity waves
• f-modes
• Incompressible liquid
• Constant density
3
Technique
• Earthquake is recorded by different stations all around the earth’s
surface
• In Helioseismology, the source is estimated to any point of the
surface
• Assume that this point aligns on some great circle
• Gives displacement function of the oscillations on that particular
great circle.
4
Relationship between Luminosity and
Temperature;
𝐿 = 𝑅2 𝑇 4
(1)
Mass-Luminosity relationship ;
L
L⨀
=
M
M⨀
4
(2)
Time wave at speed c takes to travel
stellar medium;
𝑡𝑑𝑦𝑛 =
𝑅3
𝐺𝑀
(3)
5
Spherical harmonics
• Model the oscillations
• Two types of modes : radial & non radial
•
Sun modes are non-radial: the shape of the star is not preserved
during oscillation
• Defined by three wavenumbers.
1)
n: radial order, the number of nodes in the radial direction
2)
l: angular degree, the number of nodal lines
3)
m: angular order, the number of nodal lines that cross the
equator
6
Doppler shift
•
Many combinations of wavenumbers that can lead to a similar oscillation
•
From the Doppler shift analysis, approximate the complexity of the
oscillations
7
Fourier Transform
• Oscillations are detected as functions of position on the solar disk.
• Fourier Transform in time will filter the corresponding frequencies.
𝐹 𝑣 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ∗
• Fundamental frequency:
• Oscillation frequencies:
𝑁
−𝑖𝑡𝑛(2𝜋𝑣)
𝑛=1 𝑦𝑛 (𝑡𝑛 )𝑒
period-1h  n=0
period- 5 min  n= 20-30
8
Power Spectrum
• Plot of power (energy per unit time ) relative to frequency
• Filter noise by setting limits of energy per unit time that can be
received from the observed object:
1) Analyze the signal to noise ratio
2) Maximum energy per unit time for a frequency
𝐴
𝐴0
=
𝐿
𝑇 𝑠
(
)
𝑀 𝑇𝑒𝑓𝑓
9
Assumptions
• Adiabatic process is occurring
• Pressure caused by the dynamics of convection is neglected
• No transition zone between the convection zone and the interior
• Acoustic waves have specific boundary conditions
• Effects of magnetic field are also neglected
10
Simulation of spherical harmonics
11
Quality factor Q
↑ 𝑄 ∶ Low energy loss = almost no damping
↓ 𝑄 ∶ Great energy loss = damped oscillation
𝑄=Π
𝑀
𝑀⊙
𝜌~
1
2
𝑅
𝑅⊙
−
3
2
𝑀
𝑅3
𝑀
𝑔 ~ 𝑅2
1/2
𝜌
𝑔 𝑅
𝑔 𝐿⨀ 𝑇 2
=
=
𝜌⨀ 𝑔⨀ 𝑅⊙ 𝑔⨀ 𝐿1/2 𝑇⨀2
Gives direct relationship between the observed values and the stellar
density.
12
Asteroseismology
O-C diagram (Tool to check model )
Observed parameters [O] - Calculated parameters [C] vs time
• Curvature= period is changing with time
• Quadratic O-C curve = constant rate of change in the period
• Upward parabolic curve = steadily increasing period
• Increasing slope = real period > that used in model
•
The calculated part comes from forward and reverse modelling
13
Example of model analysis:
variable star Tau V1370
• Constellation of Taurus (401 ly)
• Decreasing slope = real period (0.295523 𝑑𝑎𝑦𝑠)
< that used in model
V1370 Tau - O-C Diagr.
-0.04
-0.045
O-C (days)
-0.05
-0.055
-0.06
-0.065
-0.07
-0.075
14000
14500
15000
15500
16000
16500
17000
17500
18000
Cycle
IBVS
Nelson
S3
S4
S5
S6
Misc
Lin Fit
14
Conclusion
• Data: luminosity, temperature, intensity, period and velocity of the
sun’s oscillations.
• Fourier time transforms : the wavenumbers’ corresponding
frequencies
• Power spectrum : Oscillation modes
• Forward modelling : spherical harmonics, parameters estimation
• Inverse modelling : more precise values for parameters
• Perspective: diffusion, angular momentum, magnetic fields,
transition zone, perturbations
15
REFERENCES
•Breger, M. "Uncertainties in the Calculated Pulsation Constant Q." DSSN 2. Delta Scuti Star
Newsletter, 2 Mar. 1990. Web. 13 Mar. 2016.
<https://www.univie.ac.at/tops/CoAst/archive/DSSN2/QConstant.html>.
•Brown, Jeff. "Re: What Is a Variable Star Observed minus Calculated (O-C) Diagram?" MadSci.
Faculty of Astronomy, 9 Feb. 2000. Web. 7 Mar. 2016. <http://www.madsci.org/posts/archives/200002/950129794.As.r.html>.
•"Dynamical Time Scale." Physics and Universe. N.p., 23 June 2013. Web. 7 Mar. 2016.
<http://physicsanduniverse.com/dynamical-time-scale/>.
•Fratarcangeli, Marco. "Spherical Harmonics." YouTube. YouTube, 9 Dec. 2014. Web. 17 Mar. 2016.
<https://www.youtube.com/watch?v=4TPvXHqa0Xc>.
•Ghosh, Pallab. "Team Records 'music' from Stars." BBC News. BBC, 23 Oct. 2008. Web. 17 Mar. 2016.
<http://news.bbc.co.uk/2/hi/science/nature/7687286.stm>.
•Guenther, D. B. "Age of the Sun." Age of the Sun. Astrophysical Journal, Part 1 (ISSN 0004-637X), Vol.
339, April 15, 1989:1156-1159, Apr. 1989. Web. 7 Mar. 2016.
<http://adsabs.harvard.edu/doi/10.1086/167370>.
• Harvey, John. "Helioseismology." Physics Today. N.p., 1 Oct. 1995. Web. 7 Mar. 2016: 32-38.
<https://www.deepdyve.com/lp/aip/helioseismology-UQ0SUm3iCD?key=AIP>.
•Jørgen Christensen-Dalsgaard, Jørgen. "Problems of Solar and Stellar Oscillations." Stellar
Oscillations 5 (1983). Phys.au.dk. Institut for Fysik Og Astronomi, Aarhus Universitet Teoretisk
Astrofysik Center, Danmarks Grundforskningsfond, Jan. 2015. Web. 7 Mar. 2016. <http://usersphys.au.dk/jcd/oscilnotes/print-chap-full.pdf>.
• "Kepler: Graphics for 2010 Oct 26 Webcast." Kepler: Graphics for 2010 Oct 26 Webcast. Ames
Research Center, 26 Oct. 2010. Web. 7 Mar. 2016.
<http://kepler.nasa.gov/news/nasakeplernews/20101026webcast/>.
16
•"Main Sequence Stars." Atnf.csiro. Australia Telescope National Facility, n.d. Web. 7 Mar. 2016.
<http://www.atnf.csiro.au/outreach/education/senior/astrophysics/stellarevolution_mainsequence
.html>.
• Minard, Anne. "The Case of the Missing Sunspots: Solved? - Universe Today." Universe Today Space and Asronomy News. Universe Today, 17 June 2009. Web. 7 Mar. 2016.
<http://www.universetoday.com/32642/the-case-of-the-missing-sunspots-solved>.
•Nave. "Composition of the Sun." HyperPhysics. Georgia State University, Departement of Physics
and Astronomy, n.d. Web. 7 Mar. 2016. <http://hyperphysics.phyastr.gsu.edu/hbase/tables/suncomp.html>.
•Nave. "Red Shift." HyperPhysics. Georgia State University, Departement of Physics and
Astronomy, 2000. Web. 7 Mar. 2016. <http://hyperphysics.phyastr.gsu.edu/hbase/astro/redshf.html#c1>.
•Nelson, Bob. "Eclipsing Binary O-C Files." Aavso. American Association of Variable Stars
Observers, 29 Mar. 2015. Web. 7 Mar. 2016. <https://www.aavso.org/bob-nelsons-o-c-files>.
•"Power Spectrum." Wolfram MathWorld. Wolfram Research, Inc., 2016. Web. 7 Mar. 2016.
<http://mathworld.wolfram.com/PowerSpectrum.html>.
•"Singing Stars." YouTube. Ed. Nature Video. YouTube, 21 Aug. 2013. Web. 17 Mar. 2016.
<https://www.youtube.com/watch?v=IzeJq3CbiZM>.
•"Spherical Harmonics Symmetries." Ambisonics. Plone Foundation, 2016. Web. 13 Mar. 2016.
<http://ambisonics.iem.at/xchange/fileformat/docs/spherical-harmonics-symmetries>.
•"Spherical Harmonic." Wolfram MathWorld. Wolfram Research, Inc., 2016. Web. 13 Mar. 2016.
<http://mathworld.wolfram.com/SphericalHarmonic.html>.
• "Stars - Stellar Evolution." Astronomyonline. N.p., 2013. Web. 13 Mar. 2016.
<http://astronomyonline.org/Stars/Evolution.asp>.
• Tong, Vincent C.H, and Rafael A. Garcia, eds. Extraterrestrial Seismology. N.p.: Cambridge UP,
2015. Ebooks.cambridge. McGill Livrary, July 2015. Web. 7 Mar. 2016: 11-122.
<http://ebooks.cambridge.org.proxy3.library.mcgill.ca/ebook.jsf?bid=CBO9781107300668>.
17