Today in Astronomy 241: radial stellar pulsation

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Today in Astronomy 241 radial stellar pulsation

• Todays reading Carroll and Ostlie Chap.
  14.1-14.3, on
• Review of types of pulsating stars
• The distance ladder pulsating stars Cepheids,
  RR Lyrae stars, and W Virginis stars
• The ?, ?, and ? mechanisms and the physics of
  pulsation
• One-zone model of linear radial pulsation

Pattern of one particular p-mode solar
oscillation, amplitude greatly exaggerated.
(GONG/NSO)
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Special Talkscelebrating400th anniversary of
Galileos first observations with the telescope

• Thursday March 26 430-630 Robbins Library
• 4th floor, Rush Rhees
• Galileo The Father of Modern Science
• Jack Thomas (UR)
• Galileo A Literary Master in XVII Century
  Italy
• Erminia Ardissino (Univ. Turin, Italy)

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Actually, all stars are thought to pulsate.

• Even the Sun, for which the strongest modes
  comprise the famous 5-minute oscillation.
• And thats a good thing. Stellar pulsations have
  two crucial uses in astrophysics
• Probes of stellar structure. The frequencies of
  oscillation modes are very sensitive to the
  internal structure and state of stars.
• Standard candles. For some stars the oscillation
  frequency is related to the stars luminosity. If
  one knows the relationship, one can use a
  measurement of the frequency and average apparent
  flux to calculate the stars distance.

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Notable stellar pulsations
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HR diagram of pulsating stars the instability
strip
Cepheids W Vir stars RR Lyr stars ? Scu
stars ZZ Cet stars
A. Gautschy and H. Saio 1995
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Next few slides are courtesy of Brad Carroll (BOB
co-author)
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In 1784, John Goodricke of York discovered that
d Cephei is variable P 5 days, 8 hours
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d Cephei is the prototype of the Classical
Cepheids
From Wycombe Astronomical Society,
wycombeastro.org.uk/news.shtm
magnitude varies from 3.4 to 4.3,so luminosity
changes by factor of100(Dm/5) 100(0.9/5) 2.3
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Edward Charles Pickerings Computersat Harvard
Observatory
From left to right Ida Woods, Evelyn Leland,
Florence Cushman, Grace Brooks,Mary Van,
Henrietta Leavitt, Mollie O'Reilly, Mabel Gill,
Alta Carpenter, Annie Jump Cannon, Dorothy
Black, Arville Walker, Frank Hinkely,
andProfessor Edward King (1918).
www.astrogea.org/surveys/dones_harvard.htm
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Henrietta Swan Leavitt
(1868 1921)
Found 2400 Classical Cepheids In 1912,
discovered the Period-Luminosity Relation
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Small Magellanic Cloud
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Cepheids in the SMC
From Shapley, Galaxies, Harvard University Press,
Cambridge, MA, 1961.
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Calibration The Distance to a Cepheid
The nearest Cepheid is Polaris (over 90 pc), too
far for trigonometric parallax. d (pc) 1/p (in
arcsec)
In 1913, Ejnar Hertzsprung of Denmark used least
squares mean parallax to determine the average
magnitude M -2.3 for a Cepheid with P 6.6
days. d (pc) 4.16/slope (in arcsec/yr)(4.16
AU/yr is the Suns motion)
www.cnrt.scsu.edu/dms/cosmology/DistanceABCs/dist
ance.htm
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Period Luminosity Relation
MltVgt -2.81 log10 Pd 1.43
d (pc) 10(m-M5)/5
Sandage and Tammann, The Astrophysical Journal,
151, 531, 1968.
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How to Find the Distance to aPulsating Star

• Find the stars apparent magnitude m (just by
  looking)
• Measure the stars period (bright-dim-bright)
• Use the Period-Luminosity relation to find the
  stars absolute magnitude M
• Calculate the stars distance (in parsecs) using

d (pc) 10(m-M5)/5
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In 1913, Hertzsprung calculated that the distance
to the Small Magellanic Cloud was 33,000 light
years. This was the greatest distance ever
determined for an astronomical object. In 1917,
Harlow Shapley used Hertzsprungs calibration of
the period-luminosity relation to determine the
distance to the globular clusters (some of which
contain Cepheids).
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The Milky Way has about 120 globular
clusters,each containing perhaps 500,000
stars. One-third of all known globular
clusters covers only 2 of the sky, in the
constellation Sagittarius. Shapley found the
globular clusters had a spherical distribution.
homepage.mac.com/kvmagruder/bcp/aster/constellatio
ns/Sgr.htm
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The Sun was removed from the center of the
universe, and placed at an inconspicuous spot
near the edge.
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HR diagram of pulsating stars the instability
strip
Cepheids W Vir stars RR Lyr stars ? Scu
stars ZZ Cet stars
A. Gautschy and H. Saio 1995
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Physics of stellar pulsation

• Rough estimate of pulsation period sound
  crossing time

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Physics of stellar pulsation (continued)

• Paradigms for radial-mode stellar pulsation
• standing waves in wind instruments and organ
  pipes
• thermodynamic heat engines
• Driving heat enters gas near maximum compression
• Damping heat dissipates (leaves the gas)
• Types of pulsation
• e-mechanism in core of star, driven by
  temperature and energy-generation rate rise
  toward center.
• k-mechanism opacity increases with increasing
  density thus soaks up radiative energy near
  maximum compression. (Usually this mechanism
  dominates.)
• g-mechanism same as k, plus conduction.

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Physics of stellar pulsation (continued)

• One-zone model with linearization of equations of
  motion specialize to small oscillations, write P
  P0dP, ignore terms in (dP)2 or higher.
• Assume adiabatic compression and expansion (i.e.
  polytrope equation of state)

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Physics of stellar pulsation (continued)

• Resulting equation of motion for dR

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Periods goes as 1/root(density)!
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Todays in-class problems

• Problems 14.7 and 14.8 in BOB
• Prob. 14.7 derive Eqn. 14.11 by linearizing the
  adiabatic relation PV? constant