Inferred Through Ca II H K emission

1
Modeling of Stellar Magnetic Activity
Inferred Through Ca II HK emission
Solar Physics REU 2005
Sarah Lakatos, Villanova University
2
Objectives

• To create a subset of stars with similar
  properties to the sun, with a wide range of ages
• To look at the Ca II HK emission data and see
  how the stars emission changes with age
• To compare the x-ray data to that of the Ca II
  HK
• To determine and use the relationships between
  the stellar parameters to help understand the
  evolution of the dynamo from a younger sun to an
  older sun

3
http//earth.ast.smith.edu/courses/ast224/ColorMag
nitude.htm
http//www.enchantedlearning.com/subjects/astronom
y/stars/startypes.shtml
4
Background Info.

• Dynamo Cycle of Stars

• A stars magnetic dynamo is governed by many
  parameters.
• Most important are the depth of the Convection
  Zone, the Rotation Period, and t(c)
• As the star ages it spins down due to the loss
  of angular momentum through the outflow of
  magnetized stellar winds

ds9.ssl.berkeley.edu/.../ 6/images_6/sun_350.jpg
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Background Info. Cont.

• This spin down effects the amount of magnetic
  field activity
• By studying the Ca II HK data and x-ray
  emission which is caused by magnetically mediated
  heating we can determine how the activity depends
  on various stellar parameters and evolves with
  age.

Mt. Wilson 100in Telescope ROSAT satellite
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Mt. Wilson Ca II HK Project
Ca II K line
http//www.mtwilson.edu/hk/Overview/

• Sun like stars show strong absorption lines from
  singly ionized calcium (Ca II)
• These important lines were named by Joesph von
  Fraunhofer, and are found in the near-UV at 3969
  Å (H) and 3934 Å (K)

Ca II H line
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Mt. Wilson Data

• Measurements were taken on the 100in Telescope,
  using a two channel Photometer and the 1.5m
  telescope.
• Measured the variations of the Ca II H and K
  lines (chromospheric activity) over at total of
  25 years, to help determine the Magnetic Activity
  Cycle.
• The cycles are classified as, excellent, good,
  fair, poor, variable, or flat.
• The S index was used to graph the Ca II HK data
  vs. Age for the program stars.

Baliunas et. al. 1995ApJ...438..269B
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Magnetic Dynamo of the Sun

• Two Magnetic Fields

Pictures from www-solar.mcs.st-andrews.ac.uk/...
/ gif/mlast.gif
Omega Effect Differential Rotation
lt-----------------------
Poloidal Field
Toroidal Field
Dynamo Cycle
lt-----------------------
Helical turbulence and Coriolis Force Alpha Effect
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Magnetic Dynamo Equations
Equation for Toroidal field
Bf stands for Toroidal field A stands for
Poloidal field ?? / L stands for the differential
rotation, or sheer (how fast the rotation is
changing) ? stands for the diffusivity
Equation for Poloidal field
a stands for the alpha effect
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Magnetic Dynamo Equations
Dynamo Number Equation

• Dynamo is the ratio of the source term to the
  sink term in the dynamo equations.

Diffusivity Equation

• L length of the convection zone
• tc convective turnover time

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Magnetic Dynamo Equations
Ro Prot
tc
Rossby Number Equation
Prot 2p/O tc L2/?

• sub in the ? equation into the ND equation
• assume the differential rotation is proportional
  to the rotation rate, which is inversely
  proportional to the period of rotation.
• ?? a O Prot a 1/ O
• with these substitutions you get the relation
  below

Dynamo related to Ro
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Chart of Program Stars
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Chart Continued
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Teff, Radius, Mass Graphs
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Finding Ages
Log Prot 0.658log T 1.0152 Prot
10.36T0.658
Correlation 0.976617 Confidence 1.08784x10-8
99.99
Correlation 0.9948870 Confidence 1.88358x10-39
99.99
Prot is directly proportional to Age
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Ro and t(c) vs. Age Graphs
tc 0.712T 13.194
Ro 0.796T0.525
Correlation 0.434408 Confidence 99.09
Correlation 0.935513 Confidence 99.99
Ro Prot
tc
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Emission Measures
RHK RHK - Rphot

• Ca II HK flux minus the photospheric
  contamination divided by the stellar bolometric
  luminosity

• H K are counts in combined Ca II passbands
• V R are counts in violet and red continuum
  bands

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Emission vs. Rossby Graphs
Correlation -0.946848 Confidence 99.99 RHK
2.333x10-5Ro-0.798
Correlation -0.814515 Confidence 99.99 ltSgt
0.283Ro-0.533
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Emission vs. Age Graphs
Fx 2.33x106T-0.681 Correlation -0.878234
Confidence 99.99
RHK 2.71x10-5T-0.352 Correlation -0.852168
Confidence 99.99
ltSgt 0.310T-0.202 Correlation -0.6047830
Confidence 99.98
??
a
Prot
ND a??L3
?2
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Pcyc vs Age and Ro
Correlation 0.0164058 Confidence 7.22
Correlation -0.00853774 Confidence 3.76
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Conclusions
vs. Age
vs. Rossby
Prot 10.36T0.658
ltSgt 0.283Ro-0.533
Ro 0.796T0.525
RHK 2.333x10-5Ro-0.798
tc 0.712T 13.194
Fx 2.33x106T-0.681
RHK 2.71x10-5T-0.352
ltSgt 0.310T-0.202
22
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