Lab 6: Color Magnitude Diagram For M 45 ✓ Solved

Lab 6 Colour Magnitude Diagram For M 45

Analyze photometric data of the Pleiades (M45) to calculate the Colour Index for each star, plot the stars on a Colour-Magnitude diagram, interpret the stellar population's characteristics, compute absolute magnitudes, examine the relationships between colour, spectral class, and stellar evolution, and compare with other clusters to understand their relative ages and origins. Use provided magnitude data, perform calculations with the distance modulus formula, and analyze the plots to identify the main sequence, giant, dwarf, and other stellar classifications.

Sample Paper For Above instruction

Introduction

The Pleiades cluster (M45) is a well-studied open star cluster located relatively close to Earth, offering an excellent opportunity to analyze stellar properties and evolution. Its bright, young stars provide insight into the early stages of stellar development and the characteristics of main sequence stars. Understanding the cluster involves photometric measurements, plotting the stars on a Colour-Magnitude diagram, and interpreting their evolutionary status.

Photometric Data and Calculations

The provided data includes the apparent magnitudes in the visual (V) and blue (B) filters for each star within the Pleiades cluster. Using these data, we calculate the Colour Index (CI) for each star, defined as CI = B – V. This value indicates the star's colour and temperature, with lower CI values representing hotter (bluer) stars and higher CI values corresponding to cooler (redder) stars.

For example, if a star has B = 11.52 and V = 10.44, then the CI = 11.52 – 10.44 = 1.08.

Once the Colour Index is determined, plotting these against the apparent magnitude (V) creates a Colour-Magnitude diagram, which visually reveals the distribution of stellar types within the cluster.

Plotting the Colour-Magnitude Diagram

Using spreadsheet software or manual plotting, the stars are plotted to show V magnitude (vertical axis) versus the Colour Index (horizontal axis). Since lower V magnitudes correspond to brighter stars, the scale for V should be inverted, with brighter (lower V) values higher on the plot.

After plotting, the majority of stars should form a recognizable main sequence, showcasing the typical relationship between stellar colour and luminosity. Notably, the plot should reveal a curve resembling an "S" shape, known as the Main Sequence, where most stars reside.

Interpreting the Plot and Stellar Evolution

The trend in the plot indicates that most stars in the Pleiades are located along the main sequence, consistent with a young, active stellar population. Blue, massive stars are found to the left (lower CI and bright V magnitudes), while red, less massive stars occupy the right (higher CI and dimmer V magnitudes).

Bright, blue stars are the most massive and youngest among the cluster members. Conversely, the red segment contains less massive, older, and often less luminous stars.

By marking the most massive stars in blue and the least massive in red, the trend demonstrates stellar mass distribution within the cluster.

A fitted Curved line (Main Sequence) following this trend emphasizes the evolutionary track of stars from high-mass, hot, blue stars to lower-mass, cooler, red stars.

Analysis of Images and Cluster Age

Internet images of the Pleiades reveal a striking, neat arrangement with bright blue stars and surrounding nebulosity. The presence of dust and gas clouds indicates these stars are relatively young, still located within their birth molecular clouds. Typically, open clusters like the Pleiades are young (

Supporting Evidence and Star Formation Theories

The visible dust and gas around the Pleiades suggest ongoing or recent star formation activity within or near the cluster. Molecular clouds are the birthplaces of stars, and the residual gas and dust imply that the cluster's stars formed relatively recently. This aligns with current theories that star clusters originate from collapsing molecular clouds, supporting the idea that star formation is an ongoing process in the Galaxy.

Calculations of Absolute Magnitude and Distance Modulus

Assuming the Pleiades are approximately 126 parsecs away (from Hipparcos data), the distance modulus (m – M) can be computed for each star using the formula:

m – M = 5 log₁₀(d) – 5

Where d is the distance in parsecs.

For d = 126 parsecs, approximate distance modulus:

m – M ≈ 5 log₁₀(126) – 5 ≈ 5 × 2.1004 – 5 ≈ 10.502 – 5 ≈ 5.50.

This means that the apparent magnitude (m) minus the absolute magnitude (M) for each star is roughly 5.50, allowing the calculation of M from m as M = m – 5.50.

Applying this calculation to each star's V magnitude yields the absolute magnitudes, which are intrinsic brightnesses unaffected by distance.

Creating the Absolute Magnitude Plot

Using the calculated Mv values, plot the stars again on a new diagram with the same axis orientation—V magnitude (now replaced by absolute magnitude)—inverted so that brighter (lower M) stars are at the top.

This new plot provides a clearer picture of the stars' intrinsic luminosities and helps compare the cluster to theoretical models of stellar evolution.

Distance Modulus and Cluster Distance

The distance modulus (m – M) for the Pleiades, based on the Hipparcos data, is approximately 5.50. For a more distant cluster at 200 parsecs:

m – M = 5 log₁₀(200) – 5 ≈ 5 × 2.3010 – 5 ≈ 11.505 – 5 ≈ 6.50.

This higher value indicates that more distant clusters have larger distance moduli, reflecting greater distance and dimmer apparent magnitudes for stars of similar intrinsic brightness.

Spectral Classification and Stellar Evolution

The correlation between Colour Index and spectral class allows the assignment of spectral types to the stars on the plot. For example, stars with CI ≈ 0.00 are of spectral type A0, while those with higher CI values are K or M dwarfs. The Sun, with a spectral type G2V, typically corresponds to a CI near 0.58.

Marking the Sun's position on the plot provides a reference point for understanding the stellar population, indicating where our Sun would fall among the cluster members.

Identifying Stellar Types in the Diagram

Red giants and supergiants appear higher and to the right of the main sequence, characterized by larger radii and luminosities despite cooler temperatures. White dwarfs are located below and to the left, representing old, compact stars with low luminosity and high temperature.

Drawing and labeling these regions helps contextualize different stellar evolutionary stages within the plot, illustrating the diversity of the stellar population.

Comparing Open and Globular Clusters

The colour-magnitude diagram for the globular cluster M5 indicates an older stellar population with a well-developed red giant branch and an absence of bright main sequence stars. This contrasts with the younger, more prominent main sequence in the Pleiades, confirming that globular clusters are typically much older (

Conclusion

This analysis of the Pleiades cluster employs photometric data, plotting techniques, and stellar classification concepts to elucidate the properties and evolutionary status of its stars. The presence of young, hot, blue stars alongside more evolved stars underscores the cluster's youth. Comparing to globular clusters further enhances appreciation for the diversity of stellar systems in our galaxy.

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