Credit/Permission: For text, © David Jeffery. For figures etc., as specified with the figure etc. / Only for reading and use by the instructors and students of the UNLV astronomy laboratory course.
This is a lab exercise with observations which are essential: see Sky map: Las Vegas, current time and weather.
Sections
We will learn about stars as astronomical objects.
We touch on the following topics:
Some of the
Tasks can be completed ahead of the lab period.
Doing some of them ahead of lab period would be helpful.
However, you can print a copy ahead of time if you like especially if
want to do some parts ahead of time.
You might have to compensate for updates in this case.
The Lab Exercise itself is NOT printed in the lab ever.
That would be killing forests
and the Lab Exercise is designed to be an active web document.
General remarks about quiz prep are given at
Quiz Preparation: General Instructions.
For DavidJ's lab sections, the quiz prep is doing all the items listed here and self-testing with the
Prep Quizzes and Prep Quiz Keys
if they exist.
Review the parts of the
Celestron C8 telescope
in the figure below (local link /
general link: telescope_c8_diagram.html).
You should also review the
Observation Safety Rules.
However to complement and/or supplement the reading, you should at least
read the intro of a sample of the articles
linked
to the following keywords etc.
so that you can define and/or understand some keywords etc. at the level of our class.
Patchy cloud cover might NOT stop the lab. The
instructor
will have to make an executive decision, possibly at the last moment.
If the sky is going to be too cloudy, then
an alternative lab from the
Introductory Astronomy Laboratory Exercises
should be chosen.
Usually you should choose the alternative lab from
this semester's
Lab Schedule: one without
observations or one with observations which is sufficiently challenging with observations omitted
(e.g., Lab 5: Planets).
I'd usually recommend doing
Lab 10: Stellar Spectra as the alternative lab.
The same instructions as in the last item apply.
In this section, we prepare to observe stars,
observe stars,
and do just little post-observation analysis of
stars.
Since we may be going outside early or late, it may be that we will have to
delay the observation part until later sections are completed.
But we should to the preparation fast to be ready for observing within 20 minutes!!!
Sub Tasks:
Below is the
Table: Bright Stars to be Observed
with separate lists for
summer and fall
and
winter
and spring.
There is some overlap between the two seasonal lists.
You will try to observe the
bright stars from
seasonal list chosen by the
instructor---which will usually be the
summer and fall list
for the summer semester and
fall semester
and the
winter
and spring list
for the spring semester.
This task is done with the
telescope
for IPI, but
with NO telescope
for RMI.
In fact, using the telescope
is primarily for practice using
the telescope since
the observations for actual results are done best by
naked-eye astronomy.
So RMI students
should just ignore any directions to use the
telescope
in this task.
Sub Tasks:
You have to fill in the star names TWICE since there are two panels in the
Observing Working Table.
Only one filled-in
Observing Working Table
is needed per group and it should be appended to the
favorite report form---unless your
instructor
asks for each group member to make fill-in
an Observing Working Table.
Have you done this?
Y / N
If stars look like
donuts and NOT
a bright points of light,
the C8 is out
of focus.
Do this while you observe using
naked eye---the
telescope does NOT help in
comparing brightnesses of stars
when doing visual astronomy.
The human eye perception of
brightness correlates with
apparent V magnitude.
Decreasing brightness approximates INCREASING
apparent V magnitude.
Do this while you observe using both
the naked eye
and the telescope---the
telescope may NOT really help much
in this job, but it's good practice to use it.
Redness decreases going red, orange, yellow, white, blue.
The human eye perception of
redness correlates with (color index) B-V.
Decreasing redness approximates DECREASING
B-V.
The KNOWN
data can be obtained from Wikipedia
by clicking on the star name in the
Table: Bright Stars to be Observed above
(local link /
general link)
Stars approximate
blackbody radiators which
motivates our interest in blackbody radiation
in this lab exercise.
The shape of the blackbody spectrum
of blackbody radiation
is determined by a single parameter the
temperature.
Blackbody spectra
are described in the figure below
(local link /
general link: blackbody_spectra.html).
Humans
can only see light in the
visible band (fiducial range 0.400--0.700 μm)---the
fact that we only see in this band is why we call it the
visible band.
Much of the visible-band light,
we see is or approximates
blackbody radiation:
e.g., sunlight,
light and
incandescent light bulbs.
In fact, humans prefer
visible-band
light for ordinary illumination that
is or mimics blackbody radiation.
Fluorescent lamps
and light-emitting diodes (LEDs)
do NOT emit blackbody radiation, but
for ordinary illumination they are adjusted to make the
psychophysical response
similar to that of blackbody radiation.
If they are NOT so adjusted, people tend NOT to like them---some do NOT
like them anyway.
The
visible band is described in
figure below
(local link /
general link: visible_band.html).
Sub Tasks:
Have you done this?
Y / N
Note: The Libretexts image is from Libretexts: Blackbody Radiation.
There is a way to find the exact peak of a
blackbody spectrum:
Wien's law
which is explicated in the figure below
(local link /
general link: wien_law.html).
For T = 4500 K using Wien's law
(see the figure above:
local link /
general link: wien_law.html),
calculate the peak wavelength λ
and by-eye determine its color band
(see the figure above:
local link: visible_band.html /
general link: visible_band.html).
Show your calculation and give the units
of the final wavelength answer.
Stars have what is called a
photosphere.
The stellar photosphere and
other things are elucidated in the figure below
(local link /
general link: star_g2_v.html).
The probability of a radially-traveling photon
(a particle of light) escaping from
a stellar photosphere
to infinity is about:
Blame Ptolemy (c.100--c.170 CE).
The Ptolemaic magnitude system
is explicated in the figure below
(local link /
general link: ptolemy_magnitude.html).
What are, respectively, the brightest and dimmest star classes in the
Ptolemaic magnitude system?
In the 19th century,
Norman Pogson (1829--1891)
noted that
Ptolemaic magnitude system
was roughly logarithmic in
radiant flux (AKA flux)
(energy per unit time per unit area)
and that 5 magnitudes (5 mag) was approximately a factor of
100 in
flux.
So Pogson---good old
Pogson---regularized the
magnitude system
as a logarithmic system
with 5 magnitudes (5 mag) defined to be exactly a factor of 100
in flux.
This means that 1 mag corresponds to a factor of
100**(1/5) = 10**(2/5) = 2.51188643 ... ≅ 2.512 in change in
flux.
So an INCREASE of 1 mag corresponds to a DECREASE in flux by a factor of ∼ 2.512.
The formula relating
magnitude to
flux is
The 2.5 factor is an infernal nuisance too---but there's nothing to be done about it---blame
Pogson.
Note that magnitudes
are rarely
integers within
uncertainty:
they usually have a
decimal fraction part.
Also note that magnitudes
can be negative---which are
magnitudes brighter than
positive magnitudes
do the wrong-wayness of the
magnitude system.
A passband is just a filter
that absorbs electromagnetic radiation
over some wavelength band
according to some
transmission function
(which can also be called a passband).
The zero-point
magnitude for
a passband is assigned by some authority
for darn good reasons---which are usually unmentioned---if you are in
the inner circle, you just know.
Order the following magnitudes
from brightest to dimmest: 0.0, -1.7, 4.5, 6.1, -3.2, 10.0, 22.5, -0.5.
The
Ptolemaic magnitude system
was based on visual astronomy,
first with the
naked eye and then telescopic.
Now the actual psychophysical sensitivity of
the human eye to
flux is very complex
(see
telescopeoptics.net: Eye intensity response, contrast sensitivity).
So Pogson's choice of
a logarithmic
magnitude system
is NOT obviously optimum for correlating
visual astronomy
with device-measured observations.
But there is NO reason for wanting an optimum choice now since
there is NO need to try to make
visual astronomy quantitatively accurate.
The measurement of electromagnetic radiation
in broad wavelength bands
from astronomical objects
is called photometry.
Photometry is almost always
reported in magnitudes.
Why do photometry?
One can learn a lot about astronomical objects
from what electromagnetic radiation
is emitted in various
wavelength bands.
This ideal CANNOT be realized for real
filters.
One overwhelming reason why NOT for ground-based astronomy
is that the Earth's atmosphere
is ineluctably part of the filters.
Real filters
have a transmission function
that varies from zero to a peak (which is always less than 100 %) back to zero with
increasing wavelength.
There are
many systems of photometric filters
that are used or have been used in
photometry
(see Wikipedia: Photometric System: Filters).
Usually, the name for a passband
and the symbol for its magnitude
is letter which is called
a photmetric letter.
Here we will only look at the most standard
system of photometric filters,
the UBVRI passband system.
The symbols for the individual passbands
are---you guessed it---U,
B,
V,
R,
I.
The UBVRI passband system
is illustrated in the figure below
(local link /
general link: photometry_ubvri.html).
To which passbands does
flux at
wavelength λ
= 5000 angstroms (Å)
= 0.5 microns (μm)
contribute according to
the figure above
(local link /
general link: photometry_ubvri.html)?
Apparent magnitude
is magnitude
as measured from Earth.
So it is NOT in itself a measure of intrinsic
brightness, but just of apparent brightness.
Absolute magnitude
CANNOT be measured directly.
If you know the distance to an
astronomical object,
then you can determine what is called
the distance modulus
μ = 5*log(d_pc)-5.
Then absolute magnitude M_absolute
is determined from the formula
M_absolute = M - μ = M - (5*log(d_pc)-5).
If you know M_absolute and M, then the
distance modulus
can be calculated from
μ = M - M_absolute.
The
absolute magnitude in
V is given the
symbol M_V.
Thus, we have
Now M_V is often
given as a proxy for
luminosity, the total energy
output per unit time emitted by an
astronomical object.
But it is only a proxy.
There is NOT a one-to-one relationship
between M_V
and luminosity.
To get luminosity,
you first need
bolometric magnitude M_bol
which is a logarithmic measure
of luminosity.
Bolometric magnitude M_bol
is given by the formula
Bolometric corrections
are, in fact, always negative since M_bol < M_V since M_bol corresponds to more energy than M_V.
The old
wrong-wayness of magnitudes
turns up again.
Finally, to relate
Bolometric magnitude
to luminosity, we have---without
derivation---the formula
In
the HR diagram
(which we discuss below in section The HR Diagram),
either absolute V magnitude M_V
or logarithmic
luminosity is used as the
vertical axis.
B-V
can be used to calculate a star's
photospheric temperature
and it can be used as proxy for
photospheric temperature
when that quantity CANNOT be calculated for whatever reason.
A color index
(AKA color) is
a measure of the shape of a
spectrum
and can be related to the
photospheric temperature.
It is is the difference
between two different
magnitudes
measured for one spectrum.
The most commonly used
color index
for stars is
B-V which is
the difference between the
B and
V
magnitudes.
If you invert the
magnitude for
B-V
you get
As B-V increases,
(a) the ratio F_V / F_B increases and thus (b) reddish light increases relative to bluish light.
Yours truly sometimes calls
B-V redness because of point (b).
As B-V increases,
photospheric temperature
decreases
for stars which approximate
blackbody radiators as discussed
in section Blackbody Spectra.
Decreasing
photospheric temperature
shifts the peak of the blackbody spectrum redward.
It seems weird that
temperature decreases as B-V increases,
but that's the wrong-wayness of
magnitude system for you.
The range of B-V for
main sequence stars
is about -0.33 to 1.4
(see Wikipedia: Color index).
B-V can be used to
calculate photospheric temperature
in several ways.
If stars were exactly
blackbody radiators,
B-V would give you exactly
their photospheric temperature
from a simple calculation or a lookup table.
But stars are NOT exactly
blackbody radiators and NO
simple formula
relates B-V
to photospheric temperature
exactly.
What is done is a set of stellar models are calculated and you look
for the model with the B-V
and other observable characteristics of the star
you are studying and the model tells you the
photospheric temperature
(usually the
effective temperature version)
and other stellar parameters that CANNOT be directly observed.
The accuracy of the values obtained from the model depend on how accurate the model is.
People are always trying to improve stellar models.
For one non-extensive set of model results
see Wikipedia: Color index.
There are several ways of approximately calculating
photospheric temperature which we briefly
review below.
A very crude approximate formula
for photospheric temperature
that works reasonably well for
B-V from 0 to 1.4
for main-sequence stars is
This crude approximate
photospheric temperature
is really neither effective temperature
nor a color temperature.
It just crudely approximately either.
A color temperature
for a star
can be obtained using Wien's law
as discussed in the figure above
(local link /
general link: wien_law.html).
But using Wien's law accurately
requires an accurate
stellar spectrum.
An easy approach is to use
B-V which just requires
photometry which is easier
to obtain to high accuracy than
a stellar spectrum.
All one does is adjust the temperature
of a blackbody spectrum
until the B-V
calculated from the
blackbody spectrum matches
the observed
B-V of a
star: i.e., one fits the
blackbody spectrum to an observed
B-V value.
The temperature
of the fitted blackbody spectrum
is a color temperature
for a star.
Sub Tasks:
Have you done this?
Y / N
You vary the
temperature
slider until
the panel B-V value equals
the B-V for the
main-sequence-stars
in the table below.
You are NOT matching the
temperature in the table which
CANNOT be done actually for T ≥ 25000 K anyway since that is the upper limit of
the applet.
Enter the fitted color temperatures
in the table below.
Extinction
is the wavelength
absorption or scattering of
electromagnetic radiation
by interstellar dust
along the line of sight
from an astronomical object
to the Earth.
In order to understand the intrinsic
flux of
an astronomical object,
extinction
has to be corrected for.
Sometimes the correction is easy, sometimes NOT.
We will NOT worry about
extinction
further in this lab.
The HR diagram
is explicated in the figure below
(local link /
general link: star_hr_lum.html).
Sub Tasks:
Then go File/print preview/scale 100% or whatever fills the page/print.
Only one HR diagram is needed per group
and it should be appended to the
favorite report form---unless your
instructor
asks for each group member to make an
HR diagram.
RMI qualification: If you
do NOT have a printer,
hand draw the
HR diagram below
(local link /
general link: star_hr_lum_3.html)
as best you can
faute de mieux.
If there are multiple values for star,
the star is actually a
multiple star system
and we only want the first value.
You will have to interpolate as best you can for the
spectral subtype:
Note these are stars
of high apparent brightness and NOT necessarily of high
luminosity
(i.e., small absolute V magnitude).
Except use small X's
instead of small circles.
Stars on both lists
will have both a circle
and an X.
Do the preparation required by your lab
instructor.
Keywords:
Celestron C8 telescope,
blackbody radiation,
blackbody spectrum,
brightest stars,
B-V,
color index
(AKA color),
color temperature,
effective temperature,
giant star,
Hertzsprung-Russell (HR) diagram,
luminosity,
luminosity class,
luminosity distance,
luminosity function (astronomy),
magnitude
(absolute magnitude,
apparent magnitude),
main sequence,
OBAFGKM spectral classification,
passband
(AKA transmission function),
photometry,
photospheric temperature,
spectral type,
star,
stellar classification,
supergiant,
TheSky
(TheSky6,
TheSkyX,
List of Tricks for TheSky,
TheSky Orientation),
white dwarf,
Wien's law,
Wikipedia: List of Brightest Stars,
zero-age main sequence (ZAMS).
A further list of keywords which you are NOT required to look at---but it would be useful to do so---is:
Task Master:
EOF
End of Task
RMI qualification:
If you do NOT have access to a
printer you will have to
hand sketch the
sky map or use
Google Sky.
__________________________________________________________________________________
Table: Bright Stars to be Observed
__________________________________________________________________________________
Summer and Fall Stars
__________________________________________________________________________________
No. Common Name Bayer De. SAO No. Comment
__________________________________________________________________________________
1 Altair α AQL 125122
2 Antares α SCO 184415
3 Arcturus α BOO 64589
4 Capella α AUR 40186
5 Caph β CAS 21133
6 Deneb α CYG 49941
7 Mizar ζ UMA 28737
8 Polaris α UMI 308
9 Rasalgethi α HER 102680 ∼ 5° west of the brighter Rasalhague.
10 Rasalhague α OPH 102932
11 Sadr γ CYG 49528
12 Sheliak β LYR 67451
13 Tarazed γ AQL 105223
14 Tsih γ CAS 11482
15 Vega α LYR 67174
__________________________________________________________________________________
Winter and Spring Stars
__________________________________________________________________________________
No. Common Name Bayer De. SAO No. Comment
__________________________________________________________________________________
1 Aldebaran α TAU 94027 Late fall too.
2 Betelgeuse α ORI 113271
3 Capella α AUR 40186
4 Caph β CAS 21133
5 Castor α GEM 60198
6 Polaris α UMI 308
7 Pollux β GEM 79666
8 Procyon α CMI 115756
9 Rigel β ORI 131907
10 Sirius α CMA 151881
Below are stars in Pleiades (an open star cluster)
in order of apparent magnitude in V.
The Pleiades are good for late fall too.
You probably need the sky alignment on the telescopes to find the Pleiades.
The Pleiades are in Taurus ∼ 10° north, ∼10° west of Aldebaran
using the astronomical NSEW: 10° ≅ a fist.
The Pleiades
should be ranked only among themselves and this ranking
is optional at the discretion of the
instructor.
The instructor
may ask you to ONLY find them and NOT rank them.
1 Alcyone η TAU
2 Atlas 27 TAU
3 Electra 17 TAU
4 Maia 20 TAU
5 Merope 23 TAU
__________________________________________________________________________________
_______________________________________________________________________________________
Table: Observing Working Table
_______________________________________________________________________________________
Brightness
_______________________________________________________________________________________
No. Common V Magni- Observed Brightness Observed Relative Actual Relative
Name tude (VB = very bright Brightness Brightness
(filled B = bright (1 = brightest (filled in
in post- M = middling 2 = 2nd brightest post-observation
observat- F = faint etc.) ranking by
ion) VF = very faint decreasing
U = unobserved) V magnitude,
1, 2, 3, etc.)
_______________________________________________________________________________________
1 | | | | |
2 | | | | |
3 | | | | |
4 | | | | |
5 | | | | |
6 | | | | |
7 | | | | |
8 | | | | |
9 | | | | |
10 | | | | |
11 | | | | |
12 | | | | |
13 | | | | |
14 | | | | |
15 | | | | |
_______________________________________________________________________________________
Color Index B-V or Redness
_______________________________________________________________________________________
No. Common B-V Observed Color Observed Relative Actual Relative
Name (filled (R = red B-V (i.e., Redness) B-V
in post- O = orange (1 = reddest (filled in
observat- Y = yellow 2 = 2nd reddest post-observation
ion W = white etc.) ranking by
B = blue decreasing B-V,
U = unobserved) 1, 2, 3, etc.)
_______________________________________________________________________________________
1 | | | | |
2 | | | | |
3 | | | | |
4 | | | | |
5 | | | | |
6 | | | | |
7 | | | | |
8 | | | | |
9 | | | | |
10 | | | | |
11 | | | | |
12 | | | | |
13 | | | | |
14 | | | | |
15 | | | | |
_______________________________________________________________________________________
Dense bodies all at one temperature
radiate blackbody radiation.
The magnitude system
goes back to
ancient Greek astronomy.
M = -2.5*log(F) + M_zero ,
where M is magnitude,
F is a flux in a passband,
and M_zero is the zero-point for the passband.
The minus sign makes the magnitude system
run the wrong way---brighter is lower, dimmer is higher.
This is an endless source of confusion---blame
Ptolemy.
One can learn a lot more from
spectroscopy
(i.e., measuring spectra),
but accurate spectroscopy
if often a lot harder to obtain than
accurate photometry
and is sometimes impossible.
The ideal passbands for
photometry would
have 100 % transmission in a specified
wavelength bands and zero outside.
Recall that in astro-jargon,
"apparent" means as seen from Earth.
Absolute magnitude
is magnitude
as measured from a fiducial distance to the
astronomical object
of 10 parsecs (pc)
= 32.6156377 ... light-years (ly)
M_V = V - μ .
M_bol = M_V + BC ,
where BC is the
bolometric correction which
must be calculated from
modeling in general and is different
for every stellar class and,
speaking generally, every
kind of astronomical object.
L/L_☉ = 10**[(M_bol - M_bol_☉)/(-2.5)]
where ☉ is the
astronomical Sun symbol,
L_☉ is solar luminosity,
and M_bol_☉ is solar
bolometric magnitude.
In this section, we consider the
color index
B-V
which is a direct observable for a
star
and a useful characterizing parameter just by itself.
F_V / F_B = 10**[(B-V)/2.5] ,
F_V is flux in
V
and F_B is the flux in
B.
In astro jargon,
redward/blueward means to longer/shorter
wavelength.
In shorthand: B-V ↑ reddness ↑
photospheric temperature ↓.
T = (10**4 K)/ [(B-V) + 1] = (104 K) / [(B-V) + 1] .
As B-V decreases below 0,
the formula underestimates T.
For B-V = 0.33, the
underestimation is by a factor of ∼ 3.
T = (10**4 K)/ [(B-V) + 1] = (104 K) / [(B-V) + 1] .
to evaluate temperatures
for the B-V values and enter them in the
appropriate column in the table below.
_______________________________________________________________________________
Table: Characteristic Temperatures for Main-Sequence Stars
_______________________________________________________________________________
Stellar Class B-V Model Effective Blackbody Fit Crude Approximate
Temperature Color Temperature Formula Temperature
(K) (K) (K)
_______________________________________________________________________________
O5 V -0.33 42000
B0 V -0.30 30000
A0 V -0.02 9790
F0 V 0.30 7300
G0 V 0.58 5940
K0 V 0.81 5150
M0 V 1.40 3840
_______________________________________________________________________________
Note: The B-V and
effective temperature data are taken from
Wikipedia: Color index.
_______________________________________________________________________________
In this section, we learn a little about the
Hertzsprung-Russell (HR) diagram.
In fact, only use the brightest star of a
multiple star system even if the
stars are somehow listed separately
in Wikipedia: List of Brightest Stars.
For example, a G0 star is at the left edge of the G range, a G5 star in the middle,
and a G9 star at the right edge.
You do NOT have to be too precise, just get the points approximately correctly.
There might be something here,
sine die---maybe
on the Greek kalends.
Goodnight all.
Post mortem comments that may often apply specifically to
Lab 8: Stars:
