Background

The H-R Diagram is usually portrayed as a plot of the color or temperature of a star (x- axis) vs. its energy output (y-axis). There are many variations of this plot. While H-R Diagrams are useful in providing a broad visualization of star properties, this investigation uses color-magnitude diagrams (CMD), the astronomers' tool for analyzing data from direct observations of stars.

The groups of stars on the H-R Diagram represent different stages of stellar evolution. Most of the stars on an H-R Diagram occupy a region from upper left to lower right, the main sequence. Stars on the main sequence are fusing hydrogen in their cores. About 90% of a star’s lifetime is on the main sequence. Most of the stars above the main sequence (the giants and supergiants) represent the next phase of evolution that begins when the pressure generated by hydrogen fusion fails to maintain a stable equilibrium with gravitational forces. Giant stars form at the onset of helium fusion, and continue to produce successively heavier elements, potentially up to iron. White dwarfs are located below the main sequence. These stellar remnants have ceased fusion and represent the endpoint for most stars having an initial mass less than eight times that of the Sun.

Giants and supergiants are brighter than main sequence stars of similar temperature because of their larger size, while white dwarfs are dimmer than main sequence stars of similar temperature due to their very small size.

Depending on the observed star cluster, these same groups of stars may be visible on CMDs and their properties can be interpreted in a similar way to an H-R Diagram.

Stars in a star cluster are all roughly the same age and the same distance from Earth. Astronomers can determine the cluster distance an age by fitting a set of model curves called isochrones to the CMD of a star cluster.

OpenStax Astronomy textbook links:

The Stars: A Celestial Census
The H-R Diagram

Teacher Notes

1. Our investigations are designed so that students cannot proceed to the next page without answering each question. If you would like to quickly preview the entire investigation, you can create an educator account and log in.
   
2. Each investigation includes some questions that invite students to share their world views and life experiences to make connections between science and the real-world. In this investigation, the question is on page 14. This may be an opportunity for a small group or class discussion, or if in an asynchronous setting, students can contribute to a discussion forum.
3. The H-R Diagram portrayed in textbooks or webpages is an idealized diagram created to show a representative sample of all types of stars. Astronomers do not really use H-R Diagrams to analyze data because temperatures and luminosities of stars are derived values and not directly collected by instruments. Instead, star brightnesses through different filters are measured and color-magnitude diagrams (CMDs) are constructed, typically for star clusters, since all the stars in a cluster are at about the same distance from Earth, and thus the relative brightness es of stars in a cluster can be comparable to their relative luminosities.

4. Star cluster data on a CMD do not match the classic distribution of stars shown on an H-R Diagram. A very young cluster will display few giants and no white dwarfs. A very old cluster will lack the uppermost parts of the main sequence where the hottest blue-white stars would typically be located. Because of this, no single cluster can display all of the star characteristics portrayed on an H-R Diagram.

5. Proxy data from Gaia Data Release 3 were used in this investigation. Measurements through three filters, G, BP, and RP were used to create the CMDs. The Color Index scale is derived from BP - RP. Gaia filters transmit over a broad range of wavelengths and are not single color filters. For instance, BP does not mean only blue and RP does not mean only red. In fact, all three filters transmit wavelengths beyond the range of human vision. The BP filter transmits the shortest wavelengths of light, the RP filter transmits the longest wavelengths, and the G filter is in between these two. More information about Gaia filters may be found here.

6. It is important to emphasize that the relationships between stellar masses and lifetimes apply only to stars on the main sequence, since they are based on equations for hydrogen-fusing stars in hydrostatic equilibrium.
7. Red dwarfs (at the lower end of the main sequence) are predicted to make up about 85% of all main sequence stars, according to a theoretical relationship called the initial mass function. But H-R Diagrams and color-magnitude diagrams of star clusters do not reflect this distribution, since red dwarfs are very difficult to detect due to their extreme dimness.

8. The Sun’s position on an H-R Diagram may visually suggest that the Sun is an average star in terms of its characteristics. The scales of on an H-R Diagram create this illusion. First, the horizontal axis is neither linear nor logarithmic. Second, the y axis is logarithmic. The Sun’s characteristics are not at the midpoint in the range of values for main sequence star properties, such as temperature, size, lifetime, luminosity or mass.

9. Hertzsprung and Russell are credited with the original publications of color-luminosity plots that evolved into modern day versions of the H-R Diagram. However, Hans Rosenberg published the first such diagram in 1910.

10. Isochrones are model curves generated from stellar evolution models for stars of various masses and chemical compositions. In this investigation, the sets of isochrones available for each cluster have been customized to account for the cluster’s metallicity and reddening. This has been done to keep the length and complexity of the data reduction process in line with the time constraints and learning outcomes for this investigation.