Cuesta College Eclipsing Binary Project Briefing In support of an ongoing Eclipsing Binary Star Project Conducted by Thomas C. Smith (Dark Ridge Observatory)

Cuesta College Eclipsing Binary Project Briefing

In support of an ongoing Eclipsing Binary Star ProjectConducted by Thomas C. Smith (Dark Ridge Observatory)

And Russ M. Genet (Orion Observatory)

Eclipsing Binary Project Briefing

Briefing overview:This briefing is being presented to the North County Cuesta College Astronomy 10 class and as such needed to be presented at a level appropriate to the audience. An will attempt to first present some basic concepts including eclipsing binary (EB) star types, viewing an EB from earth, differential photometry overview, and light curve concepts. Next will be a description the science that our project is intended to accomplish at a high level. In conclusion, a list of equipment that we use, including pictures of the project observatories and telescopes, and what is consider to be the minimum hardware and software requirements needed to conduct similar projects to that of Dark Ridge Observatory (Thomas C. Smith) and Orion Observatory (Russ M. Genet) current works.


Basic concepts:Angle of inclination

The angle of inclinations of a binary star system is, of course, relative to our line of sight. Here is a graphic that shows this concept.

Ref: (1)


Points or phases of the eclipsing binary

•At point 1 the eclipse starts and the light begins to decrease. •At point 2 the eclipse becomes total and the light output is constant until •Point 3 where the smaller star begins to emerge and the light output begins to grow until •Finally at point 4 the eclipse is complete.

Ref: (1)


Here is a graphic showing the way the cycle repeats for a generic eclipsing binary star

Ref: (1)


Multiple and binary stars in general It is believed that over 50% of all star systems in the universe exist

with multiple stars making up a gravitationally bound system. Eclipsing Binary star systems exist in various configurations.

Three basic types of eclipsing binary stars exist. They are “detached”, “semi-detached”, and “contact”. These terms are used to discuss not only the physical separation of the stars but their gravitational separation using the term Roche Lobe to describe this.

Detached, relatively long orbital period where the two stars are separated by a very significant distance where often times vary different star types being involved. One good example of this is Algol in the constellation Perseus. This eclipsing binary star is made up of a blue spectral class B8 star of about 3 solar diameters and is accompanied by a yellow spectral class K2 of about 3.5 solar masses. These stars orbit around each other in about 68 hours and eclipse each other for a period of about 3 hours.


Ref: (1)


On the other end of the type listing, and of most interest to our project are the “contact” binaries. These systems typically have mass ratios of about 0.40. Their Roche lobes are filled and surrounded in a common envelope. These stars are in contact and joined by a neck around the Lagrange point (L1). These are W-UMa type binary stars and they have an orbital size of about 2 solar radii.

Here is an artist rendition of a contact W-UMa eclipsing binary system


Photometry discussed Photometry is the measurement of apparent magnitudes of astronomical objects, like

stars. It is derived from the word Photon which is a quantum, or discrete amount of electro-magnetic energy.

To “do” photometry one simply measures the amount of this energy using devices that are made to collect photons (or electrons once converted) and subsequently reading out the measured quantity.

Hipparcose, in 250 BC, and using only his unaided eye, classified all the visible stars into 6 categories. With the invention of the telescope much later, astronomers found that they could improve on this classification by measuring the size of the star and several means were devised, including using an aperture mask, to make these determinations.

Photometry, as we know it today, began in the early 1900’s with Edward Pickering at Harvard University, whose concept was to use photographic film plates, measuring the density of the silver that was accumulated at the point of photon interaction by measuring the amount of light that could pass through the exposed and developed plate. A year later the first thermopile photometer was built by Harland Stetson at Dartmouth University to measure this phenomenon. This method was improved as technology progressed to the point we are currently at using charged coupled devices (CCD) to convert the incoming photons into electrons that are “stored” in the CCD photosite until read out by accompanying electronics.


Differential photometry The concept of differential photometry involves

measuring the target star’s light as well as a non-varying star’s light that is located fairly near the target star. The point of differential photometry is to determine the amount of change of the target star’s light over time and this is done by taking the difference between the target star’s light value and the non-varying star’s light value over the course of the session. When these variations are plotted against an axis of time, adjusted as though observed from the center of our sun (heliocentric time) the resulting plot is called a “light curve”.


Here are a couple of light curves that I have generated from different configurations of eclipsing binary stars. Notice the different shapes of the light curves.

Ref: (2)


Kepler’s Laws and masses of the binary systemThe determination of masses in binary systems generally uses Kepler’s third

law:(m1 + m2) P2 = (d1 + d2)3 = R3,

where P is the orbital period, m1 and m2 are the respective masses, and R = r1 + r2, and the "seesaw equation" for the center of mass:m1d1 = m2d2 andd1 + d2 = R

where R is the total separation between the centers of the two objects.

From the first of these equations, if the period P and the average separation R are known, we can solve for the total mass M = m1 + m2 of the binary system. Then, if we know enough about the orbits to determine the distances d1 and d2 separately, the second equation can be used to determine the individual masses m1 and m2. (The above equations assume that the orbits are circular. If they are more elliptical, the analysis is similar but becomes more complicated.)

Ref: (1)


In practical applications of mass determination we are often faced with insufficient information to apply the preceding method. This is typically because of some combination of two problems:

We may not be able to map the orbits exactly (obviously true if the binary is astrometric and we see only one star).

Even if the orbits can be mapped, they correspond to the 2-dimensional projections on the celestial sphere of the true 3-dimensional orbit and further information is required to construct the true orbit.

In these instances, we often can only determine only the sum of the masses rather than the individual masses, or we may only be able to place limits on the masses rather than actually determine them.


Extending the barycenter concept to a third body

In our project, one of our initial goals was to determine if we could detect the presence of a third body, such as a planet, in orbit around a W-UMa eclipsing binary system using fairly inexpensive and off-the-shelf equipment and software. In order to do this using only our photometry we needed to determine, with high precision, the time of minimum light of the primary eclipse of the system. Additionally we needed to make repeated measurements of the system over an extended period of time.

Eclipsing Binary Project Briefing Why? If we look at our own solar system as a model we see that our planets orbit around our star, the Sun. During this process, the larger planets exert a significant gravitational tug on the Sun to the point where our Sun changes its position, dominated by the affect of Jupiter, relative to Earth by about 5 seconds, light-travel time, over the course of Jupiter’s orbital period of 12 years. From an observer’s point of view outside of our solar system, this would appear as a wobble in the Suns position over that 12 year period. The maximum changes in the light-travel time effect are apparent when the Sun and Jupiter are in direct alignment with the observer; the trick here is to somehow measure this change in light-travel time. This is where our eclipsing binary stars comes into play. With no significant outside influences on the system, and ignoring small changes in the system that happen over a very long period of time (mass transfers between the two stars), the primary eclipse time of minimum or TOM can be used as an accurate and consistent “tick” of a clock. With the geometrical configuration of the binary stars a potential third body, a minimum distance for the third body, can be calculated such that the system can remain stable and not eject the third body from the system. It turns out that this distance is about the distance required for a 3 day orbital period. As a significantly influential third body affects the barycenter of the system the effect manifests itself as either a retarding or an advancement of the time of minimum of the binary stars. If we observe the system over a long enough period of time we should be able to detect at least a Jupiter sized planet orbiting at a Jupiter distance from the eclipsing binary star system.


A small fly in the ointment…

Since we occupy a position in our solar system that sees the effect of our Jupiter-Sun barycenter shift, we need to carefully remove this effect in order to not get a false indication that the binary system contains a third body. This is done by making our time recording for the binaries primary time of minimum relative to the barycenter of our solar system and not just the center of our Sun.


In short, this is where our current project is heading.

With the new season of observing nearly complete we are going to be analyzing all the images and digital data from our season and adding the results with the 2004 season. With two years of data and time having elapsed we may be able to mine through our data and see if we might have caught any possible third-body candidates. We are working on papers that are to be presented to the astronomical community through various organizations that deal with our project and new hardware we are developing. Two of the big tasks ahead are to reduce and analyze the data using an ensemble of comparison stars and also to archive all the digital data we have amassed to date into a format that can be shared with the rest of the scientific community.


Equipment of the modern photometrist on a shoestring

In order to make accurate photometric observations of an eclipsing binary star system it is necessary to have certain minimum equipment:

A telescope that is of sufficient aperture and rigidly mounted capable of being controlled from a computer.

A CCD camera that is capable of maintaining a fairly constant detector temperature over the course of the imaging session.

A means to automatically guide the telescope on a chosen star in or near the field of view of the telescope/CCD combination.

A computer that both corrects the pointing of the telescope over the night and to store the images taken by the CCD camera.

A software program to manipulate the images taken as well as to measure the intensity of the light from the objects that were recorded.


Here is a description and photos of the equipment that is used in our project.

Dark Ridge Observatory (DRO) http://www.darkridgeobservatory.org :

TelescopeMeade 14” LX200GPS

CCD camera SBIG ST7XE

Optical System f/3.3 focal reducer and field flattener resulting in an overall system f/ratio of approximately f/4

Mounting Permanent pier on a polar aligned wedge

Observatory Semi-automated roll-off roof

Computer 2.4 GHz Intel P4 in observatory for telescope, camera and environmental recording.3.4 GHz Intel P4 in house for processing images and generating light curves

Software Software Bisque’s TheSky6 Professional planetariumSoftware Bisque’s CCDSoft V5 for image capture and image processingMicrosoft Excel for evaluating image digital data and generating light curvesMicrosoft Access 2003 for front end of image object storage systemMicrosoft SQL Server 2000 acting as the backend database for storing the digital information from all the observations


Orion Observatory (OO) http://www.orionobservatory.org :

TelescopeMeade 10” LX200 Classic

CCD camera SBIG ST8XE

Optical System f/3.3 focal reducer and field flattener resulting in an overall system f/ratio of approximately f/4

Mounting Permanent pier on a polar aligned wedge

Observatory Manual tilt-off roof

Computer 1.6 GHz Intel P4 in observatory for telescope, camera and environmental recording.3.2 GHz Intel P4 in house for processing images and generating light curves

Software Software Bisque’s TheSky6 Professional planetariumSoftware Bisque’s CCDSoft V5 for image capture and image processingMicrosoft Excel for evaluating image digital data and generating light curves


Photos of our observatories and equipment:

DRO OO


DRO OO


New high-speed dual-channel dichroic photometric equipment


Photometry Exercise In this exercise we will generate a light curve from some

simulated eclipsing binary data. Plot the points into the provided graph using the values of

instrumental magnitude on the Y-axis and the time of the data point collection on the X-axis.

Draw an estimated best-fit curve that represents the trends of the data provided.

Identify the primary and secondary times of minimum light.

TimeInstrumental

Magnitude TimeInstrumental



Magnitude

0.00 0.24 0.25 0.44 0.50 0.24 0.75 0.50

0.01 0.24 0.26 0.43 0.51 0.24 0.76 0.50

0.02 0.24 0.27 0.39 0.52 0.24 0.77 0.49

0.03 0.24 0.28 0.35 0.53 0.24 0.78 0.49

0.04 0.24 0.29 0.32 0.54 0.24 0.79 0.48

0.05 0.25 0.30 0.30 0.55 0.24 0.80 0.46

0.06 0.25 0.31 0.29 0.56 0.24 0.81 0.43

0.07 0.25 0.32 0.27 0.57 0.25 0.82 0.38

0.08 0.25 0.33 0.27 0.58 0.25 0.83 0.35

0.09 0.26 0.34 0.26 0.59 0.26 0.84 0.32

0.10 0.26 0.35 0.26 0.60 0.26 0.85 0.30

0.11 0.27 0.36 0.25 0.61 0.27 0.86 0.29

0.12 0.27 0.37 0.25 0.62 0.27 0.87 0.28

0.13 0.29 0.38 0.25 0.63 0.28 0.88 0.27

0.14 0.30 0.39 0.25 0.64 0.29 0.89 0.27

0.15 0.32 0.40 0.25 0.65 0.30 0.90 0.26

0.16 0.35 0.41 0.24 0.66 0.32 0.91 0.25

0.17 0.39 0.42 0.24 0.67 0.35 0.92 0.25

0.18 0.43 0.43 0.24 0.68 0.38 0.93 0.24

0.19 0.44 0.44 0.24 0.69 0.43 0.94 0.24

0.20 0.45 0.45 0.24 0.70 0.46 0.95 0.24

0.21 0.45 0.46 0.24 0.71 0.48 0.96 0.24

0.22 0.45 0.47 0.24 0.72 0.49 0.97 0.24

0.23 0.45 0.48 0.24 0.73 0.49 0.98 0.24

0.24 0.45 0.49 0.24 0.74 0.50 0.99 0.24

1.00 0.24

Data


Eclipsing Binary Star Light Curve

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0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

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Plot:


References

(1) Some instructional images were from a lecture series “Astronomy 162 Stars, Galaxies, and Cosmology” http://csep10.phys.utk.edu/astr162/lect WEB SYLLABUS Dept. Physics & Astronomy, University of Tennessee http://csep10.phys.utk.edu/astr162/index.html

(2) Light curves were taken from data and plot generated by the author/presenter, Smith T.C., Director of Dark Ridge Observatory

(3) Photographs of equipment and observatories were from the author/presenter, Smith T.C. , Director of Dark Ridge Observatory

(4) High-speed dual-channel dichroic images were from proposed paper “Low Cost Multi-channel Photometer”, Smith T.C., Genet R.M, 2005

Eclipsing Binary Project Briefing Plot Answer

Eclipsing Binary Star Light Curve

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0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

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Cuesta College Eclipsing Binary Project Briefing In support of an ongoing Eclipsing Binary Star Project Conducted by Thomas C. Smith (Dark Ridge Observatory)

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