Download using a cepheid variable to determine distance

USING A CEPHEID VARIABLE TO DETERMINE DISTANCE
In this exercise you will use data taken from observations of a Cepheid variable star over a period of 80
days. On each day, the apparent visual magnitude was recorded. Using this data you will be able to plot
a light-curve for this Cepheid, and from this light curve, determine the period of the light curve. The
mean apparent magnitude mv is the average magnitude from the graph. Using the Period-Luminosity
Relation for Type II Cepheids (given below in equation form), find the Absolute Magnitude of the
Cepheid (M). These items allow one to calculate the distance modulus ( m - M ) for the star, and from
that modulus, calculate the distance to the star. The relevant formulas are given at the bottom of the
exercise sheet. You will need a scientific calculator to do the required calculations.
DATA FOR CEPHEID LIGHT CURVE
Day
0
5
10
15
20
25
30
35
40
mv
Day
5.45
45
5.10
50
4.50
55
4.79
60
5.02
65
5.18
70
5.31
75
5.40
80
5.47
mv
5.50
5.45
5.10
4.50
4.79
5.02
5.18
5.31
1. Period of the Cepheid variable (P) = _____ days
2. Mean apparent magnitude (mv) = ______
3. Absolute magnitude of the Cepheid (M) = _____
4. Distance modulus ( m - M ) = _________
5. Distance to the Cepheid ( r ) = _______ parsecs
Distance to the Cepheid ( r ) = _______light years
The Calculation of Absolute Magnitude
The period-luminosity relation for classical (Pop.I) Cepheid can be expressed by the following
equation
L = 354 T1.152
where L is luminosity in solar units
T is the period in days
To find the absolute magnitude M once the luminosity is known, use the equation
M = 4.8 - 2.5 log(L)
where +4.8 is the absolute magnitude of the sun
The distance-magnitude relationship
The inverse square law leads to a fairly simple relationship between the apparent magnitude (m)
of a star as seen from earth, with the absolute magnitude (M), and the distance (d) from the star to the
earth.
M = m - 5 log( d/10 )
where log stands for the common logarithm
This equation can be expressed in a somewhat simpler form for computational purposes
m - M = 5 log(d) - 5
You can plot the light curve data on the attached graph sheet (next page). Remember that a light-curve
is a smooth curve, so draw a smooth curve connecting together the data points on the graph. Identify on
the graph where you make your period measurement.
Light Curve for a Cepheid Variable
4.5
4.6
apparent visual magnitude
4.7
4.8
4.9
5
5.1
5.2
5.3
5.4
5.5
5.6
0
5
10
15
20
25
30
35
40
Time (days)
45
50
55
60
65
70
75
80