Photo electic Photometry Lab
1 Ob jectives
To learn how to make precise measurements of stellar brightnesses, and how the Earth's atmo-
sphere a ects our ability to measure brightness.
1. Learn how to measure stellar brightness with a photo electric photometer
2. Get go o d familiarity with the celestial sphere
3. Analysis of data, estimation of errors
4. Learn ab out Standards in measurement and calibration
5. Learn how the atmosphere e ects starlight that passes through it
2 Skills Required
This is an advanced lab b ecause 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 telescop e, 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 quantitativeway to measure the brightness of a star. Photometry is imp ortant
in photography, astronomy, and illumination engineering. Instruments used for photometry are
called photometers. Lightwaves stimulate the human eye in di erent degrees, dep ending on the
wavelength of the light. Because it is dicult to make an instrument with the same sensitivity
for di erent wavelengths as the human eye, photometers need sp ecial colored lters to make
them resp ond like the human eye.
Photometry is very imp ortant in astronomy b ecause it gives the astronomer a direct measure
of the energy output of stars, or of the amount of light re ected or scattered by surfaces of
planets and other small b o dies. Colors, or measurements of the amount of light through lters
centered at di erentwavelengths can give information on the temp eratures of stars. 1
3.1 The Photomultiplier
The key to the op eration of the photomultiplier is called the photoelectric e ect, discovered in
1887 by H. Hertz. When light strikes a metal surface, electrons are released, the numb er released
b eing prop ortional to the intensity of the light. Electrons are b ound to the metal by electric
forces, and light with sucient energy can lib erate the electrons. The way a photometer works
is that light enters the instrument and strikes the photo catho de made of a metal chosen so
that optical light exceeds the threshold for release of the electrons . For typical materials the
quantum eciency is ab out 10, meaning for every 100 incident photons, only 10 electrons
are released. In order to get enough electrons to measure as a current, the photo catho de is places
in a multiplier tub e. A series of dyno des are kept at electric p otentials less negative than the
photo catho de, thus the released electrons are accelerated and travel toward the dyno de. The
impacts of the electrons on the dyno de release ab out 4-5 times as many electrons, and these
are accelerated to another dyno de at an even less negative p otential. This pro cess is rep eased
many times until there is a large cascade of electrons which can b e measured at the last dyno de
called the ano de. At the end of the multiplication chain, 1 initial electron can deliver ab out 4
10
10 electrons at the ano de!
Figure 1: Diagram of a photomultiplier, from N. Gin
4 Exp eriment
In this lab you will measure the brightness of some variable stars, and fully calibrate them.
Figure 2 shows an example of an unusual typ e of variable star, called an R Coronis Borealis
star. It varies irregularly in brightness { usually b eing very bright, but o ccasionally growning
faint. For this typ e of star, dust in the star's atmosphere condenses out o ccasionally and blo cks
the starlight. The star gets bright again when the star heats up and vap orizes the dust or blows
it o .
We will rep ort our brightnesses in the standard V visual and R red astronomical mag-
nitude system. Magnitudes arose historically from the ancient greeks who listed the brightest
stars in the sky as having \ rst imp ortance" or rst magnitude. The next brightest as having
\second imp ortance" or second magnitude. The eye is actually a logarithmic detector, and this
system as b een formalized such that each magnitude di erence is a factor of 2.5 in brightness.
We will b e measuring an electric current or counts photons p er second, C , from the star, and
this has to b e 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 typ e 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 b e 2 eclipses
each p erio d, and the eclipse with the greatest light loss will b e called the primary eclipse. This
o ccurs when the hotter, brighter star is blo cked from view. The light curves are imp ortant to
study b ecuase they contain information ab out the star's sizes, their shap es, mass exchange, and
star sp ots.
Information ab out sp eci c eclipsing binary systems in Table 1 are listed b elow:
The AW UMa system is probably either a triple or quadruple star system. The masses of
the primary stars are M = 1.790.14 M , and M = 0.1430.011 M . The third star
1 2
has an apparent mass of M = 0.850.13 M .
1
Lib is a chemically p eculiar close contact binary star system.
The star 68 Herculis u Herculis, HD 156633, SAO 65913 is a Beta Lyrae typ e 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 ab out 4.7
and the minima alternate b etween ab out 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. . 3
Figure 3: Lightcurve of eclipsing binary 68 u Her.
4.2 Intrinsic Variable Stars
Intrinsic variables are stars whichvary in brightness b ecause of internal changes which can cause
pulsations. Some of the pulsations can b e very long overayear while others can b e short. For
this lab we will select only short-p erio d variables of the following typ es:
Scuti stars {low amplitude, sinusoidal b ehavior with p erio ds < 0.3 dy.
Dwarf Cepheids { Amplitudes < 1 mag, p erio ds < 0.3 day and can have asymmetric light
curves.
RR Lyrae stars { Similar the Dwarf Cepheids, with p erio ds b etween 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 Bo otes variable star is a rapidly rotating A-typ e dwarf star which has avery small
p erio dicity 38 min and probable low amplitude variation thus is not our rst choice for
a target . This star p ossesses a circumstellar dust disk.
V703 Sco is a p ost-main sequence red giant star, adwarf Cepheid.
X Sgr is a sp ectroscopic binary system with a cepheid variable star. The orbital p erio d of
the companion star is 507.25 days.
Note: the columns with 7UT, 8UT and 9UT show the airmass and altitude of the ob jects
as a function of time. 4
Table 1: Candidate Variable Stars
Name 2000 2000 V Typ e Per Epoch 7UT 8UT 9UT
AW UMa 11:30:04 +29:57:53 WUMa 6.8-7.1 0.43 38044.782 1.4/46 1.8/33 2.9/20
Bo o 14:16:10 +51:22:02 Sct 6.5-7.1 0.267 39370.422 1.2/58 1.2/54 1.4/47
Lib 15:00:58 {08:31:08 EA/SD 4.9-5.9 2.33 22852.360 1.1/61 1.1/61 1.2/53
68 u Her 17:17:20 +33:06:00 Lyr 4.7-5.4 2.05 27640.654 1.3/52 1.1/64 1.0/73
V703 Sco 17:42:17 {32:31:23 RRLyr 7.8-8.6 0.115 37186.365 2.4/24 1.8/33 1.6/40
X Sgr 17:47:34 {27:49:50 Cep 4.2-4.9 7.01 35643.31 1.8/32 1.4/44 1.2/52
W Sgr 18:05:01 {29:34:48 Cep 1.58-3.98 7.59 34587.26 2.0/30.2 1.5/42 1.3/52
4.3 Op en Clusters
Op en 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 di erence between the stars will b e their
masses. Stars are gaseous balls, and would collapse under their own self gravity,ifitwere 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 temp erature 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 typ e of plot,
called a Hetzspring-Russell diagram, to determine the age of the cluster of stars. This typ e
of plot was rst develop ed indep endently 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 o ccurs.
As a star runs out of fuel in its core, it b egins 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 b eginning of H-burning, while the star is still forming, it will move 5
toward the main sequence as the core heats up. Star clusters will have stars of di erent masses,
hence stars at di erent 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.
Table 2: Candidate Op en Clusters
0
Name Constell 2000 2000 Mag Size [ ] 7UT 8UT 9UT
NGC 6231 Sco 16:54.0 {41:48 2.6 14 2.6/23 2.1/28 1.9/31
M6 Sco 17:40.4 {32:14 4.2 33 2.4/25 1.8/34 1.6/40
NGC 6475 Sco 17:53.9 {34:49 2.4/24 1.8/33 1.6/40
4.4 Standard Stars
While we can accurately measure the brightness of celestial ob jects with our photometer, to b e
useful scienti cally,we have to put our measurements on a standard scale. Not all devices will
pro duce the same C for the same ob jects b ecause of di erences 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
pro ject 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 Pro cedure
Follow the pro cedure outlined b elow to obtain calibrated data on your ob ject.
Set up telescop e, and align the nder
As so on as Polaris is visible, p olar align the telescop e 6
Table 3: Standard Stars
Cat Name Name2 Sp ec 2000 2000 V R Comment
3982 Leo Regulus B8V 10:08:22 +11:58:02 1.36 1.38 Var?
4033 UMa HD89021 A2IV 10:17:06 +42:54:52 3.45 {
4534 Leo HD102647 A3V 11:49:04 +14:34:19 2.14 2.08 Var Scuti
4983 43 Com 13:11:52 +27:52:41 4.26 3.77
4662 Crv HD106625 B8III 12:15:48 {17:32:31 2.60 2.64 Var
5072 70 Vir HD117176 G5V 13:28:26 +13:46:44 4.98 {
5056 Vir Spica B1V 13:25:12 {11:09:41 0.96 { Var
SA 92-336 13:45:21 +00:47:23 8.05 7.53
5340 16 Bo o 14:15:40 +19:10:56 -0.05 -1.04
6175 13 Oph 16:37:09 {10:34:01 2.56 2.46
Find one of the bright stars in the standards list using a nding chart Norton's and set
the telescop e setting circles and turn on tracking
mount the photometer, and nd your ob ject and center in the photometry ap erture and
fo cus the telescop e.
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 b e
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 exp osure time and gain for b oth on logsheets provided.
Go to your program ob ject and do a set of measurements.
Try to get at least 3 measurements of your standard star at di erent times - i.e. telescop e
p ositions at di erent elevations a low and high elevation . The standard star will b e 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 exp ect 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 di erent from the rst, but also approximately equal
to the brightness of the star. With a large number of observations, we exp ect that on average
the measurements will be distributed around the correct value. The standard deviation is a
measure of howmuch scatter there is in the data, and gives us an estimate of howwell we know
the numb er. The formal de titions of mean and standard deviation, , are: 7
X
1
x = x 2
i
N
X
1
2 2
= x x 3
i
N 1
where N is the number of data p oints.
5.1.1 Spherical Trigonometry
When we are considering co ordinate systems in the night sky, on the celestial sphere, we need
to explore a new mathematical area called spherical trigonometry, b ecause 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 lab eled a, b, and c, and the opp osite angles A, B , and C , then we have 2
imp ortant rules which are relevantto astronomical co ordinate systems: the law of sines:
sin s sin c sin s
2 1
= = 4
sin A sin A sin A
1 2 3
and the law of cosines:
cos s = cos s cos s + sin s sin s cos A 5
1 2 3 2 3 1
Figure 6: Spherical Traingle.
5.2 Calculating Airmass
The starlight that reaches our telescop e has passed through the Earth's atmosphere, and as
it do es so some of the light is lost due to scattering and absorbtion. The more atmosphere it
passes through, the more lightis 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 dep end up on
where in the sky the star is. The measure of howmuch atmosphere the light is passing through
is called the airmass, . Airmass is given by the following formula:
1
= sec z = [sin sin + cos cos cos HA ] 6
Here, is the latitude of the observing site, is the declination of the ob ject and HA is the
hour angle of the ob ject. This formula derives from the law of cosines in spherical trigonometry. 8
5.2.1 Hour Angle and Sidereal Time
The rst step to computing howmuch 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 p oint directly overhead and the North Celestial Pole NCP . The star will
b e at it's highest elevation ab ove 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 ob ject on the celestial meridian, HA=0. For an ob ject
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 ob ject 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 typ e of day is called the sidereal day, and
this is the time b etween two successive passages of a star overhead. The solar day is 24 hours,
h m
but the sidereal day will be slightly shorter, 23 56 . This is why the stars rise 4 min earlier
each day. There are ab out 365.25 solar dyas in a year, and during this time the Earth makes
366.25 rotations ab out its axis. Greenwich mean time nad Greenwich sidereal time agree at one
instantevery year at the autumnal equinox 9/22 . The formal de nition 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 Co ecients { Least Squares Fits
For small to mo derate airmasses, there is a simple linear relationship b etween the brightness or
apparent magnitude m of an ob ject and its airmass. If you plot mag versus airmss, the slop e
obs
of the line will equal the extinction co ecient, k :
m = m k 8
i obs
Because of random errors, all the p oints won't fall exactly on a straight line. Ideally wewant
to have the b est straight line that represents the data. This is computed by computing the sum
of the di erences b etween 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 pap er by hand and do an \eyeball" t. If you
are interested, the equations for tting a set of data, x, y , for the slop e, k and intercept b
are:
!
X X X X
1 x y x y 1
i i i i
9 k =
2 2 2 2
i i i i
!
2
X X X X
1 x y x x y
i i i i
i
b = 10
2 2 2 2
i i i i 9
where
!
2
2
X X X
1 x x
i
i
= 11
2 2 2
i i i
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
do es not give us a calibrated numb er. We use the standard star measurements to convert our
instrumental magnitudes, m to a true magnitude. The true magnitude is given by:
i
m = m k + V R +z 12
i
Here is called the color term and z is a calibration zero p oint. If we rearrange this equation
to:
y = m m + k = V R +z 13
i
we see that this is just the equation of a straight line with a slop e 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 p oint. Once we know k , , and z we can plug these
into our equation ab ove to compute the true magnitudes from our instrumental magnitudes for
our ob jects of unknown brightness.
At this p oint, for variable stars, we will plot magnitude versus time, and for the clusters we
will plot magnitude versus color as our nal data pro duct.
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 scho ol, the photo electric 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 go o d guide on how to do photometry for amateurs:
Photoelectric Photometry of Variable Stars { A Practical Guide for the Smal ler Observa-
tory 2nd Ed., Ed. by Hall and Genet available from Willman Bell, Inc.,
http://www.willb ell.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 scienti c
contribution. The AAVSO http://www.aavso.org/ab out/ collects amateur photometry on
variable stars for use by professional astronomers. 10