the cosmic distance ladder: moving cluster methodcrenshaw/moving_clusters.pdfthe cosmic distance...
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The Cosmic Distance Ladder:Moving Cluster Method
Mary Geer DetheroExtragalactic Astronomy, Georgia State University
April 13, 2020
Images: NASA 1
Outline
• Terms to Know• The Basic Technique•Relevant Distances•Benefits/Sources of Error•Recent Results• Summary
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Terms to Know:
• Proper motion - ! = !" (‘’/yr)
• Space velocity - " (km/s)
• Transverse velocity - "" (km/s)
• Radial velocity - "# (km/s) !!
!"
!
"
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The Moving Cluster Method
(Top-down view)
Converging Point
!
4
#
The Moving Cluster Method
Celestial Sphere
Converging Point
#
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$
The Moving Cluster Method
Converging Point6
!"
!!"
sin " = !!$
Small AngleApproximation:
" = !!$
Equation 1:!!= 4.74 " #
(Top-down view)
$
The Moving Cluster Method
(Top-down view)
Converging Point
#
$!"
!!!
Equation 2:!!=!" tan(*)
tan & = """#
#
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The Distance Equation
• Set Equation 1 and Equation 2 equal:
Equation 2:!!=!" tan *
Equation 1:!!= 4.74 " #
4.74 " # = !" tan ,
# = #! tan $4.74 %
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Relevant Distances
•We need:
•Proper motion (!) – motion across the sky•Radial velocity ("!) – how fast cluster moves away
• Few hundred parsecs! # = #! tan $
4.74 %
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Benefits of this Method• Cluster has a larger angular size
than a star• Hyades served as major step in
distance ladder:
• 1952 • Standard for main sequence fitting• 46.34 ⁄$ % 0.27 pc
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Image: University of Nebraska-Lincoln
HR Diagram
Sources of Error
•We assume clusters not contracting/expanding/rotating.•We assume all stars have same velocity vector.•We may be including not enough/extra stars in the cluster.•We assume a random velocities are minimal.
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Recent Work• Reino et al. 2018• “A Gaia study of the Hyades open cluster”• D = 46.75 ⁄$ % 0.7 pc (compare to 46.34 ⁄$ % 0.27 pc)• Gaia adds stars not included in previous studies, more error
• Galli et al. 2017• “A revised moving cluster distance to the Pleiades open cluster”• D = 134.4 ⁄$ % 2.9 pc (compare to…)
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Recent Work
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• Galli et al. 2017
Summary
• Historically important for main sequence fitting• Need "# and ! to find distance• Key to the Method:• Angle between cluster and CP = Angle between ! and "#
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# = #! tan $4.74 %