The Cosmic Distance Ladder: Moving Cluster Methodcrenshaw/Moving_Clusters.pdfThe Cosmic Distance Ladder: Moving Cluster Method Mary Geer Dethero Extragalactic Astronomy, Georgia State

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 %