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PHYS 110L Lab #11: Distance to M100 as Determined by Cepheid Variable Stars, Summaries of Astronomy

This lab assignment guides students through the process of measuring the distance to the galaxy m100 using cepheid variable stars. It involves analyzing light curves of cepheid variables, applying the period-luminosity relation, and calculating distances using the distance modulus equation. Students compare their results with published values and analyze the factors that contribute to variations in distance measurements.

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2023/2024

Uploaded on 02/23/2025

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Name:__________________________________________ Date:_________________
PHYS 110L Lab # 11 Distance to M100 as Determined by Cepheid Variable Stars
1
Instructions: Please read and follow the steps described below and answer all questions. Feel
free to use Excel for your calculations.
Introduction:
Part #1 Using Cepheids as Distance Estimators
Measuring the distance to an astronomical object is very difficult and is one of the greatest
challenges facing astronomers. Over the years different distance estimators have been found.
One of these is a class of stars known as Cepheid variables that change in brightness.
Cepheids are rare and very luminous stars that have a very regularly varying luminosity. They
are named after the star Delta-Cephei in the constellation Cepheus, which was the first known
example of this particular type of variable star.
In 1912 the astronomer Henrietta Leavitt observed 20 Cepheid variable stars in the Small
Magellanic Cloud (SMC), a dwarf galaxy orbiting the Milky Way. The small variation in
distance to individual Cepheid variables in the SMC are negligible compared with the much
larger distance to the galaxy. Henrietta Leavitt uncovered a relation between the intrinsic
brightness (luminosity) and the pulsation period (time between peak brightness) of Cepheids and
showed that more luminous Cepheids have a longer period
(known as the Period-Luminosity relation). By observing
the period of a Cepheid, one can deduce its luminosity and
so, by observing its apparent brightness, calculate its
distance. This is done by recalling that brightness decreases
with the square of the distance (e.g., if the distance to a star
were to double, it would look only ¼ as bright). In this way
Cepheids can be used as a “standard candle” to measure
distance. Cepheid stars can be distinguished from other
variable stars by their characteristic light curves (a plot of
brightness versus time; see Figure 1).
1
Modified from The Distance to M100 as Determined by Cepheid Variable Stars, from The ESA/ESO Astronomy
Exercise Series Exercise 2.
Learning Objectives:
In this lab assignment you will use observations of Cepheid variable stars to measure the
distance to the galaxy M100. You will then compare your result with the published value.
Figure 1: The light curve of a
Cepheid has a shape with brightness
rising sharply, followed by a gentle
decline.
period
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Name:__________________________________________ Date:_________________ PHYS 1 10 L Lab # 11 Distance to M100 as Determined by Cepheid Variable Stars^1 Instructions: Please read and follow the steps described below and answer all questions. Feel free to use Excel for your calculations. Introduction: Part #1 Using Cepheids as Distance Estimators Measuring the distance to an astronomical object is very difficult and is one of the greatest challenges facing astronomers. Over the years different distance estimators have been found. One of these is a class of stars known as Cepheid variables that change in brightness. Cepheids are rare and very luminous stars that have a very regularly varying luminosity. They are named after the star Delta-Cephei in the constellation Cepheus, which was the first known example of this particular type of variable star. In 1912 the astronomer Henrietta Leavitt observed 20 Cepheid variable stars in the Small Magellanic Cloud (SMC), a dwarf galaxy orbiting the Milky Way. The small variation in distance to individual Cepheid variables in the SMC are negligible compared with the much larger distance to the galaxy. Henrietta Leavitt uncovered a relation between the intrinsic brightness (luminosity) and the pulsation period (time between peak brightness) of Cepheids and showed that more luminous Cepheids have a longer period (known as the Period-Luminosity relation). By observing the period of a Cepheid, one can deduce its luminosity and so, by observing its apparent brightness, calculate its distance. This is done by recalling that brightness decreases with the square of the distance ( e.g., if the distance to a star were to double, it would look only ¼ as bright). In this way Cepheids can be used as a “standard candle” to measure distance. Cepheid stars can be distinguished from other variable stars by their characteristic light curves (a plot of brightness versus time; see Figure 1). (^1) Modified from The Distance to M100 as Determined by Cepheid Variable Stars , from The ESA/ESO Astronomy Exercise Series Exercise 2. Learning Objectives: In this lab assignment you will use observations of Cepheid variable stars to measure the distance to the galaxy M100. You will then compare your result with the published value. Figure 1: The light curve of a Cepheid has a shape with brightness rising sharply, followed by a gentle decline. period

Part #2 The Spiral Galaxy M M100 is a magnificent spiral galaxy in the large Virgo cluster of galaxies. The Virgo cluster contains approximately 2,500 galaxies. M100 is a rotating system of gas, dust, and stars similar to the Milky Way, and is viewed face on. M100 is one of the more distant galaxies where accurate measurements of Cepheid variables have been made. This lab is based on Hubble Space Telescope images and data for this galaxy. Measurements and Calculations: The Period-Luminosity relation for Cepheid variable stars has been revised many times since Henrietta Leavitt’s first measurements. Today the best estimate of the relation is: 𝑀 = − 2. 78 log 10 (𝑃) − 1. 35 where 𝑀 is the absolute magnitude of the star and 𝑃 is the period measured in days. Light curves for a sample of 12 Cepheids in M100 that have been measured by the Hubble Space Telescope are shown in Figures 3 and 4. Table 1 Cepheid Star Number Period (days) Absolute Magnitude (M) Average Apparent Magnitude Distance (Mpc) 1 52 6.1204893 24.95 16. 2 47 - 5.998432 25.35 18.6074306 5 3 42 - 5.862633 25.75 21. 4 39 5.7731596 25.45 17. 5 31 5.4959855 26.45 24. 6 29 5.4154664 26. 45 23. 7 29 5.4154664 2 6.5 24. 8 26 5.2836259 25.75 16. 9 26 5.2836259 26.5 22. 10 25 5.2362732 2 5.55 14. 11 24 5.1869873 26.25 19. 12 22 5.0819351 26.3 18. 89674535 Figure 2 : The M100 spiral galaxy located in the Virgo cluster of galaxies.

Question 2: Could the fact that the 12 Cepheid stars have different positions within M100, which has a diameter of 33 kpc (33,000 pc), be the reason why the distances vary? No because distances vary from 16 to 25 MP. There is a lot of distance so would likely not be a reason. Question 3: What is the average value of the distance for the 12 Cepheid variable stars? Please include the unit for your distance. 19.77539595 MPC Question 4: In the original scientific paper using Hubble Space Telescope measurements, the distance to M100 was calculated as 17.1 ± 1.8 Mpc (where 1.8 Mpc is the uncertainty in the distance). How does your average distance for M100 from Question 3 compare with this published value? 12.8, not within the uncertainty.

Figure 3 : Light curves for Cepheid variables in M100 that have been observed with the Hubble Space Telescope. The absolute magnitude, M , is determined from the period of the Cepheids.