M5 Cluster’s Overall Spectral Type by means of a H-R Diagram


M5 Cluster Image captured from Skynet


The purpose of this project is to investigate the absolute magnitudes and surface temperature of stars in the cluster M5 and create an H-R Diagram. The information that will be extracted from our project will help uncover important information about the stars plotted in our H-R Diagram. For this specific diagram, we are focusing on extracting the temperatures, magnitudes and spectral types as our variables in consideration for our plot.

Although, it is most unlikely for the M5 to have any direct effect on our Solar System, still the study of it will help us further understand the behavior of stars in the manners of their wavelengths emitted, temperature, shifts, mass, etc. With the outcomes, we aim to achieve a better understanding of the aging M5 globular cluster. Similarly, we hope to gather more understanding of the behaviors of stars and their evolutionary process throughout the years.


An H-R diagram was constructed by Ejnar Hertzsprung and Henry Norris Russell in the early 1900s, it plots the temperature of stars against their luminosity or the colour of stars against their absolute magnitude [8]. The H-R diagram is a key tool in tracing the evolution of stars. Stars begin their life in the main sequence, but then evolve off into the red giant phase and supergiant phase before dying as white dwarfs or some more violent endpoint [9]. We used the absolute magnitudes and temperatures of the stars in the cluster to create an H-R diagram.

The H-R diagram has 3 main regions, each for a different group of stars. Main sequence stars (Region 1): They stretch from the upper left to the bottom right of the diagram. Red Giants and Supergiants (Region 2): These stars are mostly 6,000K or cooler yet more luminous than main-sequence stars of the same temperature. They are much larger than main-sequence stars. Red Supergiants have stars that are even more luminous than giants. They contain extremely high luminosities. Therefore they are located on the top right side of the diagram. White Dwarfs (Region 3): These stars are very hot yet very dim. They have low luminosity, therefore they are very small. This is why they are located on the bottom left side of the diagram.

An HR diagram showing stars in the Milky Way galaxy

M5 Cluster

Globular clusters are densely packed collections of ancient stars. Roughly spherical in shape, they contain hundreds of thousands of stars [1]. Globular cluster Messier 5 (M5, NGC 5904) was first seen by Gottfried Kirch and his wife Maria Margarethe on May 5, 1702, when they observed a comet, and described it as a nebulous star [2]. It is thought to be one of the oldest globular clusters, with a computed age of 13 billion years [3]. The cluster is also one of the largest known, measuring 165 light-years in diameter and exerting a gravitational influence over a radius of 200 light-years [4]. Its apparent magnitude is 6.7 and its location is 25,000 light-years away in the Serpens constellation [5]. Its Declination is 02:04:51.7 and Right Ascension is 15:18:33.2 [6].



Spectral types are basically stellar classifications of stars. The stars spectra differs depending on its temperature and composition. There are a total of 7 categories to distinguish the different types of spectral types. A fun mnemonic for the sequence is Oh, Be, A Fine Girl/Guy, Kiss Me!


The importance of spectral types comes from how much information astronomers can use to their advantage.Each element in the periodic table can appear in gaseous form and will produce a series of bright lines unique to that element. Hydrogen will not look like helium which will not look like carbon which will not look like iron… and so on. Thus, astronomers can identify what kinds of stuff are in stars from the lines they find in the star’s spectrum.



Skynet was used to take pictures of the M5 cluster. We scheduled two batches of observations, one for the B-filter and one for the V-filter, each batch consisting of 250 pictures with 10 seconds of exposure time each.

Maxim DL was used to help identify the stars in the cluster and to calculate apparent magnitudes for each star for its respective filter. First, we carefully picked images that were of good quality out of the 250 pictures for each batch; and then we stacked them. Second, we calibrated the final images with the apparent magnitudes that we had obtained from Afterglow, in order to proceed to take the apparent magnitude of each star. Lastly, we observed each star and took their apparent magnitudes according to their respective filters. The number of stars that we observed was around 800 stars.


Based on the data we collected, we built a Python program to create an H-R diagram. When the data was collected and written in the observation document, one of the functions reads the file and converts the data to the format that Python understands. The function passes the converted data to the other function which is shown below. The function reads the converted data and processes it in such a way it represents a line graph with accurate representation. Furthermore, the code gives colour based on the star’s temperature, for example very hot stars over 20,000 K are shown in blue and the less hot stars in red or other colors. We used a built-in python module (matplotlib) which is a block of organized reusable code that can basically plot graphs with the data it is presented with. The methods and for-loop result in the formation of this H-R diagram.


To calculate for temperatures, we used the apparent magnitudes from the B and V filtered stars. Then, from those values, we used Ballestero’s Formula to calculate for temperature.

The M5 Cluster H-R Diagram made by the group

To calculate for absolute magnitude, we used the Magnitude Formula. For the values of m, we used the apparent visual magnitude value of the V-filter; and for the distance, we used the known value of 7,500 parsecs which is the average distance from Earth to the M5 cluster [7].

Lastly, our team wrote a program in order to take all the values that we had obtained previously, and create an H-R Diagram. By looking at the H-R diagram, we can see that most of the stars are red giants, with some dimmer main sequence stars being detected. It is the reasonable result since older clusters tend to have more red giants.


By observing the rendered H-R diagram of our collected data, there appears to be a noticeable density of stars present within the 7500-2500 degrees kelvin range, with a significant variance in magnitude ranging from +7-0 on average. Based on comparisons to pre-existing H-R diagrams[10] this dense cluster of recorded stars fall into either the main sequence or red giant category of stars. Those recorded with a magnitude of 4 or greater are likely to be a part of the main sequence, while stars of a lesser magnitude correlate with red giants. Based on this information our H-R diagram shows that there are a significant number of red giants recorded in the cluster. According to additional data Cluster M5 is known to be one of the oldest clusters[3], which would result in a large volume of red giants present within the system. From this we can conclude from our method of data collection to have consistency with previous documentation. For future developments, further data can be collected on dimmer stars in the cluster to develop a better understanding of the cluster. Additionally, further optimisations can be made to the python script to improve data alongside additional means of automating the data collection process.










[9] Paust, Nathaniel E. Q.; et al. (February 2010), “The ACS Survey of Galactic Globular Clusters. VIII. Effects of Environment on Globular Cluster Global Mass Functions”, The Astronomical Journal, 139 (2): 476–491, Bibcode:2010AJ….139..476P, doi:10.1088/0004-6256/139/2/476.