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Inferred Through Ca II H K emission

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Title: 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
5
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
6
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
7
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
8
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
9
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
10
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

11
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
12
Chart of Program Stars
13
Chart Continued
14
Teff, Radius, Mass Graphs
15
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
16
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
17
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

18
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
19
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
20
Pcyc vs Age and Ro
Correlation 0.0164058 Confidence 7.22
Correlation -0.00853774 Confidence 3.76
21
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
Bibliography
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