Lecture 18: Star Clusters, Introduction to the Milky Way

-- come in two flavors: globular and open

-- are a natural laboratory for checking models of stellar evolution

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-- both types are assumed to have stars that formed at the same time and with the same composition so that color-magnitude diagrams can be used to determine their ages

-- globular clusters are very old, ~1010 yrs, while open clusters are young

-- open clusters are always found close to the plane of the Milky Way, may not be bound by their own gravity, typically have a 1000 members, frequently found in association with interstellar matter

-- globular clusters are more broadly distributed, are gravitationally bound, may have ~100,000 members, are spherical in shape

Distribution of Open Clusters:

clust_dist.jpg (634712 bytes)Open clusters are the asterisks.

Open clusters delineate spiral arms:

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Globular clusters are found in the direction of the center of the galaxy:

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Globular clusters form a halo around the galaxy:

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In 1908 the period-luminosity relationship for RR Lyrae stars, commonly found in globular clusters, wasdiscovered by Henrietta Leavitt.

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She was studying these variable stars in the Large Magellanic Cloud so she could assume that her stars were all at the same distance. By plotting their average apparent magnitudes versus their periods, she discovered the relationship between period and luminosity. Note that the distance to at least one RR Lyrae star is required to complete the derivation.

These pulsating variables can be found in globular clusters and therefore can be used to measure the distances to these clusters. This lead to a new understanding of the size of our galaxy, the Milky Way.

The true size and nature of our home galaxy was not recognized until this century when galaxies were demonstrated to be isolated objects scattered throughout the Universe. The size of the Milky Way was underestimated for a long time because dust extinction was unknown.

Size and Shape of the Milky

-- looks like a band with dark features from naked-eye or visible light imaging

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Herschel in ~1780 attempted a quantitative derivation of the Milky Way’s properties by counting stars in equal area samples distributed across the sky.

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Herschel's Milky Way:Hersch.gif (13995 bytes)

More sophisticated counting techniques yielded similar results including a careful model by Kapteyn in 1922.

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Shapley's Model of the Milky Way

Shapley observed a number of globular clusters and discovered that the center of the Milky Way is some distance (now known to be 8.5kpc) from the Sun.

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Shapley's Method:

1) Observe globular clusters which are visible over large distances. Determine the periods and hence luminosity's (equivalent to M) of the RR Lyrae stars in the clusters. This yielded distances to the clusters via m-M=5logd -5. He relied upon Ms. Leavitt's discovery and calibration of the period-luminosity relation.

2) Plot the locations of globular clusters relative to the Sun.

3) Make the correct assumption that the globular clusters outline a spherical shape around the Milky Way.

4) Determine the center of the globular cluster distribution and assume that this is the center of the Milky Way.

-- Shapley's value for the distance of the Sun from the center of the galaxy was wrong because he didn't know how to take proper account of interstellar dust

Measuring Ages of Star Clusters

Recall that the lifetime of a star on the main sequence is inversely proportional to a power of the star's mass:

 

A star cluster is a group of stars that form most likely from the same parent cloud of interstellar material. We can assume

      1. That the stars all have about the same age (an assumption which can be checked to some extent).
      2. That the stars all have about the same chemical composition and hence will follow the same suite of tracks through the HR diagram.
      3. The stars are all the same distance from us so their apparent magnitudes are indicative of their relative luminosities.

If we observe a representative sampling of the stars in the cluster, we can define the main sequence for that cluster observationally in a form of HR diagram where apparent magnitude (frequently V) is plotted against a measure of temperature (frequently B-V or spectral type). Such a diagram is a called a color-magnitude diagram.

Both a cluster's age and its distance can be derived from such a diagram.

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The age comes from determining the location of the tip of the main sequence which is defined as the last star still on the main sequence. The main sequence lifetime of this star is then taken to be the cluster's age.

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The distance comes from a technique closely associated to that of spectroscopic parallaxes. With the main sequence defined, one can read off the apparent magnitude of a star on the main sequence and compare it with what the absolute magnitude is for such a main sequence star.

HR Diagrams for Open star clusters:

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HR Diagram for a globular cluster:

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Difficulties in Measuring Cluster Ages

Nonetheless, the marching of observed color-magnitude diagrams for star clusters with computed stellar evolutionary models is one of the triumphs of 20th century astrophysics.