Lab 9: Double Stars

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

Objectives (AKA Purpose)
Preparation
Tasks and Criteria for Success
Task Master
Double Stars: What are They?
Observations
Angular Resolution
Rayleigh Criterion
Binaries
Naked-Eye Observations (RMI only)
Finale
Post Mortem
Lab Exercise
Report Form: RMI Qualification: If you do NOT have a printer or do NOT want to waste paper, you will have to hand print the Report Form in sufficient detail for your own use.
General Instructor Prep
Lab Key: Access to lab instructors only.
Instructor Notes: Access to lab instructors only.
Prep Task: None.
Quiz Preparation: General Instructions
Prep Quizzes and Prep Quiz Keys
Quiz Keys: Access to lab instructors only.

Objectives (AKA Purpose)

Lab 9: Double Stars

double stars

We touch on the following topics:

Preparation

instructor

Prep Items:
1. Read this lab exercise itself: Lab 9: Double Stars.
  Some of the Tasks can be completed ahead of the lab period. Doing some of them ahead of lab period would be helpful.
2. It is probably best to print out a copy of Report Form on the lab room printer when you get to the lab room since updates to the report forms are ongoing.
  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.
3. Do the prep for quiz (if there is one) suggested by your instructor.
  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.
4. This is an observing lab. So you should review Telescope Operation and List of Tricks for the Telescope as needed.
  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.
5. There are are many keywords that you need to know for this lab. Many of these you will learn sufficiently well by reading over the Lab Exercise itself.
  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.
  A further list of keywords which you are NOT required to look at---but it would be useful to do so---is:
Prep Items for Instructors:
1. From the General Instructor Prep, review as needed:
2. This is an observational lab. The observations are essential.
  Therefore you should check the weather well in advance (e.g., using National Weather Service (NWS) 7-day forecast, Las Vegas, NV) and on the night of by visual inspection.
  The weather and seeing have to be pretty good.
  If they are NOT good enough, you should choose another lab preferably one from some other date in lab schedule. If nothing the lab schedule is suitable, then check the catalog of Introductory Astronomy Laboratory Exercises.
3. You will have to make sure the telescopes are set out and taken down.
4. You will have agree with other instructors about observing times.
5. The sky alignment on the telescopes must be set.
  This is mostly because the students will need the clock drive on to observe the double stars adequately particularly when they switch eyepiece to increase telescope magnification.
  The sky alignment is also good because it helps them find the double stars and gives them practice using the menus on the LCD keypad.
Task Master
Double Stars: What are They?

A double star is any pair of stars that are close together in angle in the eye of the beholder as viewed through a telescope and also any binary system.
A double star is often considered just as a single star when NOT resolved into two stars in naked-eye astronomy or telescopic visual astronomy.
1. The Two Main Classes of Double Stars:
  There are two main classes of double stars:
  1. Optical doubles: These any two stars that are NOT gravitationally bound to each other and are close together in angle. They may be very far from each other in space and usually have no physical connection at all.
    However, optical doubles are observationally interesting: they are fun to look at and they can be used to test one's angular resolution and the astronomical seeing (usually abbreviated to seeing).
  2. Binary systems: These are two gravitationally bound stars orbiting their barycenter (i.e., mutual center of mass).
    Actually, 2 gravitationally-bound stars that are labeled a double star may be part of multiple star system of more than 2 stars. The 2 stars labeled a double star are just the most prominent members of the multiple star system.
    One shouldn't get too finicky in terminology.
2. An Example of a Double Star:
  An example of a famous pair of stars that are NOT considered a double star is Castor and Pollux.
  But Castor, in fact, is itself a well known double star. For an explication, see the sky map in the figure below (local link / general link: iau_gemini.html).
  An example of another famous
  double star is Albireo which is illustrated in the figure below (local link / general link: star_double_star_albireo.html).
3. Measuring Angles Using Your Hand:
  You can roughly measure angles using your hand.
  Explication is given in the figure below (local link / general link: alien_angular.html).
4. Task 1: Angular Separation of Castor and Pollux:
  What is the angular separation of Castor and Pollux in fists? Explain how you got your answer.
  Answer:
  End of Task
Observations

In this section, we do pre-observation work (for both IPI and RMI). and then observations (but only for IPI).
1. Task 2: Sky Map:
  Sub Tasks:
  1. Print out the sky map shown in the figure below (local link / general link: sky_map_current_time_las_vegas.html) following the instructions given in the figure caption.
    RMI qualification: If you do NOT have access to a printer, you will have to hand-draw the sky map.
  2. You should update the time on the Your Sky control panel to your approximate observing time (e.g., 8:00 pm, 9:00 pm, etc.) if needed.
    You will have to do a conversion from local time to Universal Time (UT) to update the time. How to do the conversion is explicated in the figure below (local link / general link: sky_map_current_time_las_vegas.html).
  3. Find and highlight on the sky map all the double stars for your season shown below in the Observing Working Table for Double Stars (local link / general link: star_double_star_table.html).
    NOT all the double stars in the Observing Working Table for Double Stars are labeled on the printed-out sky map. You will have to click on the names of the unlabeled ones (on the printed-out sky map) in Observing Working Table for Double Stars to get a sky map with them located. Label the unlabeled double stars on your printed-out sky map.
  4. Only one sky map is needed per group and it should be appended to the favorite report form---unless your instructor asks for each group member to make a sky map.
    RMI qualification: Whether you report your sky map in any way depends on the instructions for your particular semester of the Remote Instruction Course.
  End of Task
2. Task 3: Observations (IPI only):
  Sub Tasks:
  1. When your instructor directs, go up to the roof and start observations.
  2. You observe the double stars in the Observing Working Table for Double Stars below (local link / general link: star_double_star_table.html) for your season.
    Generally, you go down the list in order since the generally the double stars get harder to resolve going down the list, and so you gain experience as you go.
    However, if a double star is getting close to the horizon or being threatened to be clouded-out, you may have to observe it early. Double stars that may need to be observed early are marked with OE for "observe early".
  3. Remember the steps in locating an astronomical object:
    1. Use the LCD keypad location tool to get to the vicinity of the double star. There is a menu for double stars.
      Of course, if you can locate the double star by eye using your sky map, you can just slew the C8 to the vicinity of the double star without using the LCD keypad location tool.
    2. Center the red laser dot of the star pointer on the double star.
    3. Then center of the finderscope on the double star.
    4. The double star should then be in the C8's field of view (FOV).
    5. If you are looking at some dim star that can't be seen with the naked eye, you are looking at the WRONG star.
      All the double stars in the Observing Working Table for Double Stars are bright enough to be seen with the naked eye even in Las Vegas though some barely.
      You could ask your instructor if you are doubtful.
  4. Record in the Observing Working Table for Double Stars if a double star is observed and if it is resolved.
    Add a comment if needed: e.g., clouded-out, too close the horizon, the secondary star in the double star too faint to be seen compared to the primay star, awesome.
  End of Task
Angular Resolution

Angular resolution is the ability of an optical system to distinguish small details of an image.
A second meaning of angular resolution is the smallest angle that allows two point light sources to be resolved.
Context decides which meaning applies as usual.
Actually, there is almost never a hard limit to angular resolution (in both the first and second meanings).
However there usually a characteristic angular resolution limit (in the second meaning) that defines an angular size scale of marginal angular resolution (in the first meaning).
Below we consider three characteristic angular resolution limits that occur in astronomy
1. Seeing:
  A first meaning of seeing is qualitatively "the amount of apparent blurring and twinkling of astronomical objects like stars due to turbulence in the Earth's atmosphere, causing variations of the optical refractive index of the Earth's atmosphere" (Wikipedia: Astronomical seeing: slightly edited).
  If stars or other astronomical point light sources are too close together, you CANNOT resolve them because of the seeing: i.e., you do NOT have angular resolution (in the first meaning of the term) to resolve them.
  The seeing in a second meaning is the smallest resolvable angular separation on the sky set by seeing in its first meaning: i.e., it is an angular resolution (in its second meaning).
  Context decides which meaning of seeing applies as usual.
  Seeing θ_S (in its second meaning) is usually determined empirically. You measure what it is when you observe.
  Fiducial excellent seeing has θ_SE = 0.4'' (which is available at high-altitude mountaintop observatories) and fiducial good seeing has θ_SG = 1'' (see Wikipedia: Astronomical Seeing: The full width at half maximum (FWHM) of the seeing disc).
  In cities, seeing is often much poorer (i.e., larger) than ∼ 1''.
  It has been claimed---by Diane Pyper Smith?---that θ_S ≅ 4'' is possible near the Las Vegas Strip. Yours truly will believe it when yours truly resolves the angular separation of Castor A and Castor B which currently is ∼ 5'': to be more precise, 4.87'' in 2013 (see Observer's Handbook, Royal Astronomical Society of Canada).
  Believe it or NOT, let's write fiducial Las Vegas Strip value as θ_SL = 4''.
2. The Rayleigh Criterion:
  There is an intrinsic angular resolution limit due to the wave nature of light.
  As foreshadowed above in the preamble of this section (i.e., section Angular Resolution), the limit is NOT sharp. But there is a formula giving a fiducial angular resolution limit that for useful for most cases called the Rayleigh criterion. The Rayleigh criterion is
```
  θ_R = (4.952'')*[(λ_μ/0.5 μm)/D_in]  , 
```
  where θ_R is the Rayleigh criterion angular resolution limit itself, λ_μ is wavelength in microns (μm), and D_in is the diameter of the primary in inches.
  Recall the visible band has fiducial range 0.4--0.7 μm.
  So for visible band, a human-fiducial Rayleigh-criterion limit is
```
  θ_RV ≅ 5''/D_in  .  
```
3. Human Eye Angular Resolution:
  The human-eye angular resolution naturally varies significantly with person.
  However, the typical and fiducial value is θ_H = 1 arcminute (') = 60 '' (see Wikipedia: Naked-eye astronomy). Some sharp-eyed people may be able to do better.
  In visual astronomy, this human-eye angular resolution limit is enhanced via telescope magnification.
  Recall the magnification formula:
```
  M = f_p/f_e , 
```
  where M is angular magification, f_p is primary focal length, and f_e is eyepiece focal length. There is sometimes a minus which just indicates the magnification involves a point inversion, but the minus sign is usually suppressed since inversions are finicky details which are often altered by other optical devices (e.g., star diagonals) anyway.
  Since magnification magnifies angles by M, it effectively enhances (i.e., reduces) the human-eye angular resolution limit θ_H by 1/M to θ_HT. One can see this from by solving
```
  M*θ_HT = θ_H  to get θ_HT = θ_H/M  .  
```
  Thus, the fiducial telescopic human-eye angular resolution limit is
```
  θ_HT = θ_H/M = 60''/M .  
```
  So M = 60 gives θ_TH = 1'' which is the same as θ_SG = 1'' (i.e., fiducial good seeing: see subsection Seeing above).
  For the magnifications available to our labs, see Table: C8 Telescope Magnification and Field of View below (local link / general link: telescope_c8_mag_fov_table.html):
4. The Dominant Angular Resolution Limit:
  In general, all three angular resolution limits discussed above (see subsections Seeing, The Rayleigh Criterion, and Human Eye Angular Resolution) are active.
  There must be some valid way of combining them to get an overall angular resolution limit.
  However, usually one angular resolution limit is dominant---the largest one.
  Thus,
```
  θ_dominant = max( θ_S , θ_RV , θ_HT )  .
```
  If the dominant angular resolution limit is overwhelmingly the largest, then it is essentially the angular resolution limit.
  If there is an overwhelmingly angular resolution limit, there is little point in trying to reduce the non-dominant angular resolution limits since that will NOT significantly improve the angular resolution.
  But if you can reduce the dominant angular resolution limit, that will improve the angular resolution.
5. Task 4: Angular Resolution:
  Sub Tasks:
  1. Read the above section Angular Resolution preamble and the above subsections Seeing, The Rayleigh Criterion, Human Eye Angular Resolution, The Dominant Angular Resolution Limit. Have you read them? Y / N
  2. For the C8 telescope, what is the Rayleigh criterion limit θ_RV and the fiducial telescopic human-eye angular resolution limit θ_HT in two cases: 1) for the standard 40-mm eyepiece magnification; 2) the largest possible magnification? Give the first value to 3-digit precision and the others to 2-digit precision.
    Answer:
  3. Which of θ_RV or the BEST θ_HT is the dominant limit? Why?
    Answer:
  4. Given the last answer, how good does the seeing limit have to be before (θ_RV / the best θ_HT) becomes dominant? Are we ever likely to be limited by (θ_RV / the best θ_HT) in Las Vegas, Nevada? Why or why NOT?
    Answer:
  5. Complete Table: Parameters to Equal/Surpass the Seeing Limit below.
  6. What does the table show how to do?
    Answer: seeing limits.
```
_________________________________________________________________________________

Table:  Parameters to Equal/Surpass the Seeing Limit
_________________________________________________________________________________


Seeing   θ_S   D_in = 5''/θ_RV   D_in = 5''/θ_RV   M = 60''/θ_HT   M = 60''/θ_HT
                  (θ_RV=θ_S)       (θ_RV=θ_S/3)      (θ_HT=θ_S)     (θ_HT=θ_S/3)
         ('')       (in)               (in)             (X)             (X)
_________________________________________________________________________________

Poor      10
LV Strip   4
Good       1
Excellent  0.4
_________________________________________________________________________________ 
```
  7. Read the below subsection An Example of Seeing. Have you read it? Y / N
  End of Task
6. An Example of Seeing:
  As an example of seeing, consider the film in the figure below (local link / general link: star_seeing.html).
Rayleigh Criterion

In this section, we go into a bit more depth on the Rayleigh criterion discussed above in subsection The Rayleigh Criterion.
1. Task 5: Geometrical Optics and Diffraction:
  Sub Tasks:
  1. Read the figure below (local link / general link: optics_airy_disk.html). Have you read it? Y / N
  2. Given that λ is wavelength and L is a characteristic size for aperatures and obstacles, λ/L → 0 implies you:
    1. are in the EXACT limit of geometrical optics.
    2. are in the INEXACT limit of geometrical optics.
    3. HAVE to consider the wave nature of light.
    4. do NOT have to consider the wave nature of light.
  3. The diffraction pattern for plane waves perpendiculary incident on a circular aperture is the:
    1. Airy diffraction pattern which is a diffraction pattern with square symmetry.
    2. Airy diffraction pattern which is a diffraction pattern with circular symmetry.
    3. powder diffraction pattern which is a diffraction pattern with square symmetry.
    4. powder diffraction pattern which is a diffraction pattern with circular symmetry.
  End of Task
2. Task 6: Using the Rayleigh Criterion:
  Sub Tasks:
  1. Read the figure below (local link / general link: optics_rayleigh_criterion.html). Have you read it? Y / N
  2. Evaluate the Rayleigh criterion coefficient (4.952'')*(λ/0.5 μm) for wavelengths 0.4 μm, 0.5 μm, 0.6 μm, and 0.7 μm.
    Answer:
  3. Now evaluate the Rayleigh criterion itself for these wavelengths and D_in = 8.
    Answer:
  End of Task
Binaries

Recall binaries (AKA binary stars, binary systems) are gravitationally bound pairs of stars.
In isolation from all other sources of gravity, a a binary forms an exact two-body system in the limit of Newtonian physics.
Of course, in reality there are is NO complete isolation. There are always perturbations. Also, general relativity changes the behavior of the two-body system from Newtonian physics with the change increasing with the mass of the bodies and decreasing with their separation. Nevertheless, many binaries approximate exact two-body systems in the limit of Newtonian physics to high accuracy.
The more luminous member of a binary is called the primary star and the less luminous member, the secondary star.
1. Examples of Exact Two-Body Systems:
  Animations in the 2 figures below (local link / general link: orbit_elliptical_equal_mass.html; local link / general link: orbit_circular_large_mass_difference.html) illustrate exact two-body systems.
2. Classes of Binaries:
  There are several common classes of binaries.
  The classes do overlap since one binary can fall into more than one class.
  The classes are:
  1. Close binary: The component stars are close together in some sense.
    The sense is often that component stars interact significantly by processes other than the gravitational force between spherically symmetric objects.
  2. Eclipsing binary: The component stars eclipse each other as observed from the Earth.
    This means the binary systems has edge-on inclination (i.e., are at nearly 90° inclination).
    Eclipsing binaries are usually NOT visual binaries. Their eclipsing nature is known from dips in their light curve as illustrated in the animation in the figure below (local link / general link: star_binary_eclipsing.html) of a close eclipsing binary.
  3. Spectroscopic binary: One or both of the component stars are observed via spectroscopy which shows their stellar spectral lines shifting due to the Doppler effect caused by the orbital motion of the said component stars.
    Visual binaries are often NOT classed as spectroscopic binaries even though they usually have observed spectra---but one can always adapt the terminology to one's needs.
    There are two sub-classes spectroscopic binaries (wouldn't you know it):
    1. double-lined spectroscopic binary: Both component stars have observable spectra if the stars are NOT separately resolved, then their spectra will be added together to make an observed spectrum.
      The periodic Doppler shifts of the two spectra make the system an obvious binary.
    2. single-lined spectroscopic binary: Only one component star has an observable spectrum. The other component star is too dim.
      The periodic Doppler shifts of the one spectrum make the system an obvious binary.
  4. Visual binary: The component stars can be resolved with a telescope.
    Of course, whether binary is a visual binary or NOT depends on what telescope you are referencing. Often one references the highest angular resolution telescope that has looked at the binary.
  5. Wide binary: The component stars are far apart in some sense.
    The sense is often that component stars do NOT interact significantly by processes other than the gravitational force between spherically symmetric objects.
    Wide binaries are the opposites of close binaries.
  Note that a gravitationally-bound companion object to a star need NOT be an ordinary star.
  It could be a compact object: a white dwarf, neutron star, or black hole. We still call the system a binary in this case. In fact, self-gravitating systems of two compact objects are also usually called binaries.
  If the companion object is a brown dwarf then yours truly thinks??? the system is called a binary.
  A two-body system consisting of 2 brown dwarfs is probably also called a binary???.
  However, star and one or more gravitationally-bound planets is called a planetary system.
3. Sirius AB: A Visual Binary:
  Sirius AB is an example of a visual binary.
  The figure below (local link / general link: star_sirius.html) shows the orbit of Sirius AB.
4. An Animation of an Eclipsing Binary:
  The animation in the figure below (local link / general link: star_binary_eclipsing.html) illuatrates an eclipsing binary which is also a close binary.
5. Task 7: Binaries:
  Sub Tasks:
  1. Read the all of section Binaries above (local link / general link: Binaries). Have you read it? Y / N
  2. Binary stars orbit their mutual ______________________ (AKA barycenter) in ______________________ in general with the barycenter at a focus. The other focus of each orbit is just an empty point in space.
    1. center of mass; circular orbits
    2. center of mass; ellitptical orbits
    3. enter of mass; hyperbolic orbits
    4. center of radiation; circular orbits
    5. center of radiation; ellitptical orbits
  3. Which of the following is NOT a kind of binary:
  End of Task
Naked-Eye Observations (RMI only)
1. Task 8: Naked-Eye Observations (RMI only):
  Modifications to the sub tasks in General Task: Naked-Eye Observations below:
  1. Since you already have sky map printed/drawn in Task 2: Sky Map, you do NOT print/draw another one.
  2. You should try to find all the double stars for your season shown above in the Observing Working Table for Double Stars (local link / general link: star_double_star_table.html) and located on your sky map. You CANNOT, of course, resolve the double stars into 2 stars with the naked eye.
    However, you should be able to find in the winter and spring not-too-late night sky Castor (α GEM) and Pollux (β GEM) which are "twin" stars even though NOT collectively a double star in the usual meaning. Their angular separation is 4°30'19.53'' at some epoch, maybe the J2000 epoch (see Distance between Pollux and Castor?). This angular separation is about half a fist at arm's length.
  EOF
  End of Task
Finale

Goodnight all.
Post Mortem
Post mortem comments that may often apply specifically to Lab 9: Double Stars:
1. Nothing yet.

Naked-Eye Observations (RMI only)