Photoelectic Photometry Lab
1 Objectives
To learn how to make precise measurements of stellar brightnesses, and how the Earth's atmosphere aects our ability to measure brightness.
1.
2.
3.
4.
5.
Learn how to measure stellar brightness with a photoelectric photometer
Get good familiarity with the celestial sphere
Analysis of data, estimation of errors
Learn about Standards in measurement and calibration
Learn how the atmosphere eects starlight that passes through it
2 Skills Required
This is an advanced lab because it requires some knowledge of observing (so that the team is
ecient enough to get all the required data), and will require extensive data analysis. The
equipment used in this lab is very easy to use. Skills used:
Polar Alignment of telescope, use of setting circles
Ability to nd things using star charts
Statistical Analysis
Spherical Trigonometry
Understanding Sidereal time, Hour Angle, Airmass
Linear Least Squares ts
3 Background
Photometry is a quantitative way to measure the brightness of a star. Photometry is important
in photography, astronomy, and illumination engineering. Instruments used for photometry are
called photometers. Light waves stimulate the human eye in dierent degrees, depending on the
wavelength of the light. Because it is dicult to make an instrument with the same sensitivity
for dierent wavelengths as the human eye, photometers need special colored lters to make
them respond like the human eye.
Photometry is very important in astronomy because it gives the astronomer a direct measure
of the energy output of stars, or of the amount of light reected (or scattered) by surfaces of
planets and other small bodies. Colors, or measurements of the amount of light through lters
centered at dierent wavelengths can give information on the temperatures of stars.
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3.1 The Photomultiplier
The key to the operation of the photomultiplier is called the photoelectric eect, discovered in
1887 by H. Hertz. When light strikes a metal surface, electrons are released, the number released
being proportional to the intensity of the light. Electrons are bound to the metal by electric
forces, and light with sucient energy can liberate the electrons. The way a photometer works
is that light enters the instrument and strikes the photocathode (made of a metal chosen so
that optical light exceeds the threshold for release of the electrons). For typical materials the
quantum eciency is about 10%, meaning for every 100 incident photons, only 10 electrons
are released. In order to get enough electrons to measure as a current, the photocathode is places
in a multiplier tube. A series of dynodes are kept at electric potentials less negative than the
photocathode, thus the released electrons are accelerated and travel toward the dynode. The
impacts of the electrons on the dynode release about 4-5 times as many electrons, and these
are accelerated to another dynode at an even less negative potential. This process is repeased
many times until there is a large cascade of electrons which can be measured at the last dynode
called the anode. At the end of the multiplication chain, 1 initial electron can deliver about 4
1010 electrons at the anode!
Figure 1: Diagram of a photomultiplier, from N. Gin
4 Experiment
In this lab you will measure the brightness of some variable stars, and fully calibrate them.
Figure 2 shows an example of an unusual type of variable star, called an R Coronis Borealis
star. It varies irregularly in brightness { usually being very bright, but occasionally growning
faint. For this type of star, dust in the star's atmosphere condenses out occasionally and blocks
the starlight. The star gets bright again when the star heats up and vaporizes the dust or blows
it o.
We will report our brightnesses in the standard V (visual) and R (red) astronomical magnitude system. Magnitudes arose historically from the ancient greeks who listed the brightest
stars in the sky as having \rst importance" or rst magnitude. The next brightest as having
\second importance" or second magnitude. The eye is actually a logarithmic detector, and this
system as been formalized such that each magnitude dierence is a factor of 2.5 in brightness.
We will be measuring an electric current or counts (photons) per second, C , from the star, and
this has to be converted into a magnitude (m) system. This is done with the following equation:
2
Figure 2: Data on R Coronis Borealis from mid 1966 through mid 1996.
m = ,2:5 log(C )
(1)
4.1 Eclipsing Binaries
Eclipsing Binaries are a type of variable star system which is not varying intrinsically. Instead
the apparent brightness variation is caused by the geometry (as viewed from earth) of a pair of
orbiting stars. As one star passes in front of another the starlight dims. There will be 2 eclipses
each period, and the eclipse with the greatest light loss will be called the primary eclipse. This
occurs when the hotter, brighter star is blocked from view. The light curves are important to
study becuase they contain information about the star's sizes, their shapes, mass exchange, and
star spots.
Information about specic eclipsing binary systems in Table 1 are listed below:
The AW UMa system is probably either a triple or quadruple star system. The masses of
the primary stars are M1 = (1.790.14)M, and M2 = (0.1430.011)M. The third star
has an apparent mass of M1 = (0.850.13)M.
Lib is a chemically peculiar close contact binary star system.
The star 68 Herculis (u Herculis, HD 156633, SAO 65913) is a Beta Lyrae type eclipsing
binary. It was discovered to be variable by J. Schmidt in 1869, and was found to be an
eclipsing binary in 1909 by Baker. The maximum magnitude of the system is about 4.7
and the minima alternate between about 5.0 and 5.4. Figure 3 shows a set of observations
made by Phil McJunkins (Texas A&M Univ.) and Dan Bruton (Austin State Univ.).
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Figure 3: Lightcurve of eclipsing binary 68 u Her.
4.2 Intrinsic Variable Stars
Intrinsic variables are stars which vary in brightness because of internal changes which can cause
pulsations. Some of the pulsations can be very long (over a year) while others can be short. For
this lab we will select only short-period variables of the following types:
Scuti stars { low amplitude, sinusoidal behavior with periods < 0.3 dy.
Dwarf Cepheids { Amplitudes < 1 mag, periods < 0.3 day and can have asymmetric light
curves.
RR Lyrae stars { Similar the Dwarf Cepheids, with periods between 0.3 to 1.0 day.
Below is a description of the intrinsic variable stars which might be observed during the
lab.
Below are some brief descriptions of the intrinsic variable stars included in this lab.
The Bootes variable star is a rapidly rotating A-type dwarf star which has a very small
periodicity (38 min) and probable low amplitude variation (thus is not our rst choice for
a target). This star possesses a circumstellar dust disk.
V703 Sco is a post-main sequence red giant star, a dwarf Cepheid.
X Sgr is a spectroscopic binary system with a cepheid variable star. The orbital period of
the companion star is 507.25 days.
Note: the columns with 7UT, 8UT and 9UT show the airmass and altitude of the objects
as a function of time.
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Table 1: Candidate Variable Stars
Name
AW UMa
Boo
Lib
68 u Her
V703 Sco
X Sgr
W Sgr
(2000)
11:30:04
14:16:10
15:00:58
17:17:20
17:42:17
17:47:34
18:05:01
(2000) V
Type
+29:57:53 WUMa 6.8-7.1
+51:22:02 Sct
6.5-7.1
{08:31:08 EA/SD 4.9-5.9
+33:06:00 Lyr 4.7-5.4
{32:31:23 RRLyr 7.8-8.6
{27:49:50 Cep 4.2-4.9
{29:34:48 Cep 1.58-3.98
Per
0.43
0.267
2.33
2.05
0.115
7.01
7.59
Epoch
38044.782
39370.422
22852.360
27640.654
37186.365
35643.31
34587.26
7UT
1.4/46
1.2/58
1.1/61
1.3/52
2.4/24
1.8/32
2.0/30.2
8UT
1.8/33
1.2/54
1.1/61
1.1/64
1.8/33
1.4/44
1.5/42
4.3 Open Clusters
Open clusters are groupings of stars which physically reside in the same place in space (i.e.
they are all at approximately the same distance from the earth), and formed at the same time.
Because they are at the same distance from us, their apparent relative brightnesses are the same
as their absolute relative brightnesses. The one main dierence between the stars will be their
masses. Stars are gaseous balls, and would collapse under their own self gravity, if it were not for
the outward pressure from the hot interior gases where the thermonuclear reactions are taking
place. The more massive stars burn their fuel faster, in order to keep high enough pressure to
counteract gravity. We learned in the lecture on light and radiation that hotter stars are also
bluer stars. If we plot a diagram of temperature (or color) versus the brightness of a star in a
cluster, we will see that the stars do not fall randomly on the plot. We can use this type of plot,
called a Hetzspring-Russell diagram, to determine the age of the cluster of stars. This type
of plot was rst developed independently in 1911-1913 by E. Hertzsprung and H. N. Russell.
Figure 4: Schematic HR Diagram. The diagonal line of stars is called the main sequence, where
stable H-fusion occurs.
As a star runs out of fuel in its core, it begins to collapse and will eventually heat up enough
to start the fusion of He. At the end of the H-burning stage, the star moves o the Main
Sequence. Also, prior to the beginning of H-burning, while the star is still forming, it will move
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9UT
2.9/20
1.4/47
1.2/53
1.0/73
1.6/40
1.2/52
1.3/52
toward the main sequence as the core heats up. Star clusters will have stars of dierent masses,
hence stars at dierent stages of evolution, and by making a HR diagram, we can estimate the
age of the cluster.
Figure 5: Schematic HR Diagram for clusters of ages 1 million years, 100 million years and a
globular cluster 10-16 billion years old.
Name
NGC 6231
M6
NGC 6475
Table 2: Candidate Open Clusters
Constell (2000) (2000) Mag Size [0 ] 7UT
Sco
Sco
Sco
16:54.0
17:40.4
17:53.9
{41:48
{32:14
{34:49
2.6
4.2
14
33
8UT 9UT
2.6/23 2.1/28 1.9/31
2.4/25 1.8/34 1.6/40
2.4/24 1.8/33 1.6/40
4.4 Standard Stars
While we can accurately measure the brightness of celestial objects with our photometer, to be
useful scientically, we have to put our measurements on a standard scale. Not all devices will
produce the same C for the same objects because of dierences in quantum eciency of the
detector, etc. In order to put things into a standard scale, we measure stars of known brightness,
called standars. Below are some stars we will use as standards.
Note: Some of the \Standard" stars are actually listed as variables(!). These are ok for our
project since the magnitude of variation is so small that we will not detect it ( Leo: V =
0.07 mag; Vir: V = 0.05 mag).
4.5 Procedure
Follow the procedure outlined below to obtain calibrated data on your object.
Set up telescope, and align the nder
As soon as Polaris is visible, polar align the telescope
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Cat #
3982
4033
4534
4983
4662
5072
5056
5340
6175
Table 3: Standard Stars
Spec (2000) (2000)
Leo Regulus
B8V 10:08:22 +11:58:02
UMa HD89021 A2IV 10:17:06 +42:54:52
Leo HD102647 A3V 11:49:04 +14:34:19
43 Com
13:11:52 +27:52:41
Crv HD106625 B8III 12:15:48 {17:32:31
70 Vir HD117176 G5V 13:28:26 +13:46:44
Vir Spica
B1V 13:25:12 {11:09:41
SA 92-336
13:45:21 +00:47:23
16 Boo
14:15:40 +19:10:56
13 Oph
16:37:09 {10:34:01
Name
Name2
V
1.36
3.45
2.14
4.26
2.60
4.98
0.96
8.05
-0.05
2.56
R
1.38
{
2.08
3.77
2.64
{
{
7.53
-1.04
2.46
Comment
Var?
Var Scuti
Var
Var
Find one of the bright stars in the standards list using a nding chart (Norton's) and set
the telescope setting circles and turn on tracking
mount the photometer, and nd your object and center in the photometry aperture and
focus the telescope.
Take 10 sets of measurements of the standard star you select and record the time (Universal
Time, UT { which is the time in Greenwich = HST + 10 hr). Each measurement will be
a reading of the count rate of the star, followed by a measurement of the blank sky next
to the star. Be sure to note the exposure time and gain for both on logsheets provided.
Go to your program object and do a set of measurements.
Try to get at least 3 measurements of your standard star at dierent times - i.e. telescope
positions at dierent elevations (a low and high elevation). The standard star will be used
to measure the amount of atmospheric extinction.
If you are observing a cluster, you must get observations in two lters.
5 Data Reduction
5.1 Means and Errors
If we make a measurement of the brightness of a star, we expect our measurement will be
approximately equal to its brightness, but not exactly equal. Because of random errors, if we
make a second measurement, it will be dierent from the rst, but also approximately equal
to the brightness of the star. With a large number of observations, we expect that on average
the measurements will be distributed around the correct value. The standard deviation is a
measure of how much scatter there is in the data, and gives us an estimate of how well we know
the number. The formal detitions of mean and standard deviation, , are:
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X
x = N1 xi
X
2 = N 1, 1 (xi , x)2
where N is the number of data points.
(2)
(3)
5.1.1 Spherical Trigonometry
When we are considering coordinate systems in the night sky, on the celestial sphere, we need
to explore a new mathematical area called spherical trigonometry, because we are dealing with
angles on a spherical surface. A spherical triangle is the intersection of 3 arcs. If the sides of a
spherical triangle are labeled a, b, and c, and the opposite angles A, B , and C , then we have 2
important rules which are relevant to astronomical coordinate systems: the law of sines:
sin(s1 ) = sin(s2) = sin(c)
(4)
sin(A1) sin(A2 ) sin(A3)
and the law of cosines:
cos(s1 ) = cos(s2 ) cos(s3) + sin(s2) sin(s3) cos(A1 )
(5)
Figure 6: Spherical Traingle.
5.2 Calculating Airmass
The starlight that reaches our telescope has passed through the Earth's atmosphere, and as
it does so some of the light is lost due to scattering and absorbtion. The more atmosphere it
passes through, the more light is lost. When a star is at our zenith, or on the meridian, it will
pass through the least amount of atmosphere, but on the horizon it will pass through more
atmosphere, and more light is lost. If we are going to make precise measurements of stellar
brightness, we need to correct for the amount of light which is lost, and this will depend upon
where in the sky the star is. The measure of how much atmosphere the light is passing through
is called the airmass, . Airmass is given by the following formula:
= sec(z) = [sin() sin() + cos()cos() cos(HA)],1
(6)
Here, is the latitude of the observing site, is the declination of the object and HA is the
hour angle of the object. This formula derives from the law of cosines in spherical trigonometry.
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5.2.1 Hour Angle and Sidereal Time
The rst step to computing how much atmosphere the starlight has passed through is to calculate
what is called the hour angle, HA. The observer's meridian is an imaginary great circle passing
through the zenith (point directly overhead) and the North Celestial Pole (NCP). The star will
be at it's highest elevation above the horizon when it crosses the meridian. The HA is an angular
measure from the intersection of the celestial meridian and the celestial equator westward along
the celestial equator. The units of measure are in hours rather than degrees. There are 24 hours
in a circle of 360. For example, for an object on the celestial meridian, HA=0. For an object
on the W horizon HA=6 and on the E horizon HA=-6. We don't have to measure this angle,
we can calculate it.
HA = ST , (7)
where is the right ascension of the object and ST is the sidereal time.
Greenwich mean time is regulated by the motion of the Sun. One solar day is the time
between two successive passages of the sun overhead. However, during the day the sun is
moving along its orbit around the sun, so to reach the same place in the sky, the earth has to
rotate a little bit farther than 1 full rotation. Another type of day is called the sidereal day, and
this is the time between two successive passages of a star overhead. The solar day is 24 hours,
but the sidereal day will be slightly shorter, 23h56m. This is why the stars rise 4 min earlier
each day. There are about 365.25 solar dyas in a year, and during this time the Earth makes
366.25 rotations about its axis. Greenwich mean time nad Greenwich sidereal time agree at one
instant every year at the autumnal equinox (9/22). The formal denition of Sidereal time, ST,
is that it is the Hour Angle of the Vernal Equinox. Attached to the back of the lab is a table of
sidereal times for Greenwich England at 0UT on each day for the TOPS workshop.
5.3 Extinction Coecients { Least Squares Fits
For small to moderate airmasses, there is a simple linear relationship between the brightness or
apparent magnitude mobs of an object and its airmass. If you plot mag versus airmss, the slope
of the line will equal the extinction coecient, k:
mi = mobs , k
(8)
Because of random errors, all the points won't fall exactly on a straight line. Ideally we want
to have the best straight line that represents the data. This is computed by computing the sum
of the dierences between the t line and the data and minimizing this. This technique is called
least squares tting. This is easy to do with a computer, but tedious with a calculator, so
for the lab, we could just plot things on graph paper by hand and do an \eyeball" t. If you
are interested, the equations for tting a set of data, (x, y, ) for the slope, k and intercept b
are:
X 1 X xi yi X xi X yi !
1
(9)
k=
i2 i2 , i2 i2
X x2i X yi X xi X xi yi !
1
b= (10)
i2 i2 , i2 i2
9
where
=
X 1 X x2i
i2
i2 ,
X xi !2
i2
(11)
5.4 Color Terms and Zero Points
Finally, the last step in our data reduction is to take account of the fact that our instrument
does not give us a calibrated number. We use the standard star measurements to convert our
instrumental magnitudes, mi to a true magnitude. The true magnitude is given by:
to:
m = mi , k + (V , R) + z
(12)
Here is called the color term and z is a calibration zero point. If we rearrange this equation
y = m , mi + k = (V , R) + z
(13)
we see that this is just the equation of a straight line with a slope of and intercept z for
x-values of \V-R". We know the colors and magnitudes of our standard stars, so we plot them
and do another t to get and z, our zero point. Once we know k, , and z we can plug these
into our equation above to compute the true magnitudes from our instrumental magnitudes for
our objects of unknown brightness.
At this point, for variable stars, we will plot magnitude versus time, and for the clusters we
will plot magnitude versus color as our nal data product.
6 Follow-up and Further work
If you would like to go the HOA sessions during rotation later you can use this software to help
analyze the data.
If you are really interested in pursuing this for your school, the photoelectric photometer is
available from Optec, Inc., 199 Smith Street, Lowell, MI, 49331, (616) 897-9351, FAX: (616)
897-8229, http://www.optecinc.com/. At the TOPS workshop, you used the SSP-3, which costs
$895.00 (lters and carrying case are extra).
There are several good guide on how to do photometry for amateurs:
Photoelectric Photometry of Variable Stars { A Practical Guide for the Smaller Observatory 2nd Ed., Ed. by Hall and Genet (available from Willman Bell, Inc.,
http://www.willbell.com/photo/photo3.htm, $24.95).
Astronomical Photometry, Henden & Kaitchuck, $24.95.
Software for Photometric Astornomy, Henden & Kaitchuck, $69.95.
There are numerous organizations where your data might be sent to make a real scientic
contribution. The AAVSO (http://www.aavso.org/about/) collects amateur photometry on
variable stars for use by professional astronomers.
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