Investigation 4-4:
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Materials
- Image Processing software
- Images:
Plotting the Light Curve for a Cepheid
A Cepheid was monitored for a 15-day time span,
but on only eight of those nights were the skies clear enough to get
good images. You are to measure the brightness of the star on each image
and create a light curve for the star. A light curve is a plot with
brightness on the vertical axis and time (days) on the horizontal
axis.
Perform the following procedure on each of the images
listed below.
The name of the file gives you the date of
observation.
may06cepheid, may08cepheid, may10cepheid,
may11cepheid, may14cepheid, may15cepheid,
may18cepheid, may21cepheid
Each file contains an image of the
Cepheid star and a reference star observed on a given night. The Cepheid
is the star on the left and the reference star is on the right.
4.26.
Use the photometry tool to measure the brightness in counts of each Cepheid
and reference stars. With the photometry tool selected, click on the center of each of the star images in turn. Record the data that appears in the "Photometry" window in a table like the one below.
Sample chart:
4.27. Find the brightness (intensity) value ratio, Bc / Br,, where Bc = the intensity value of the Cepheid and Br = the intensity value of the reference star.
4.28.
Plot your series of intensity ratios and corresponding dates on a graph
with axes like the blank graph shown below. Be careful to skip
nights when dates are missing from the observations.
Sample graph:
4.29. What is
the period of this Cepheid?
II. Find the Luminosity of a Cepheid
4.30.
Use the Period-Luminosity diagram to estimate Luminosity (V) of the
Cepheid measured in Activity I. Note: Both axes are logarithmic scales
and luminosity is given in solar units; e.g., 1000 means 1000 times the
luminosity of the Sun.
4.31. Use the value for the luminosity of
the sun through a V filter to calculate L(V) of your Cepheid in Watts.
L(V) of the Sun = 5.7 x 1025 Watts.
III. Find the Distance to a Cepheid
The apparent magnitude in V of the reference star is 8.0.
From the Brightness Conversion Table, this is equivalent to an apparent
brightness in V of 2.28 x 10 -12 Watts/m 2.
4.32. Calculate the
apparent brightness of the Cepheid.
4.33. Use the luminosity in V
for the Cepheid and the equation for apparent brightness to determine
the distance, d, to the Cepheid in meters. (For the equation go to the
Cepheid Variable Stars As Distance Indicators Discussion Sheet.)
4.34.
Convert the distance to light years. (1 light year = 9.5 x 1015
m)
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