Transcript Cuesta College Eclipsing Binary Project Briefing

Cuesta College Eclipsing Binary Project Briefing
In support of an ongoing Eclipsing Binary Star Project
Conducted 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.
Eclipsing Binary Project Briefing
Basic concepts:
Angle of inclination
Ref: (1)
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.
Eclipsing Binary Project Briefing
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
Ref: (1)
Eclipsing Binary Project Briefing
Here is a graphic showing the way the cycle
repeats for a generic eclipsing binary star
Ref: (1)
Eclipsing Binary Project Briefing
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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.
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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.
Eclipsing Binary Project Briefing
Ref: (1)
Eclipsing Binary Project Briefing
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 WUMa 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
Eclipsing Binary Project Briefing
Photometry discussed
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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.
Eclipsing Binary Project Briefing
Differential photometry
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The concept of differential photometry involves
measuring the target star’s light as well as a nonvarying 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 nonvarying 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”.
Eclipsing Binary Project Briefing
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)
Eclipsing Binary Project Briefing
Kepler’s Laws and masses of the binary system
The 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 and
d1 + 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)
Eclipsing Binary Project Briefing
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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 2dimensional projections on the celestial sphere of the true 3dimensional 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.
Eclipsing Binary Project Briefing
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.
Eclipsing Binary Project Briefing
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.
Eclipsing Binary Project Briefing
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.
Eclipsing Binary Project Briefing
Equipment of the modern photometrist on a shoestring
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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.
Eclipsing Binary Project Briefing
Here is a description and photos of the equipment that is used in our
project.
Dark Ridge Observatory (DRO) http://www.darkridgeobservatory.org :
Meade 14” LX200GPS
Telescope
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 planetarium
Software Bisque’s CCDSoft V5 for image capture and image processing
Microsoft Excel for evaluating image digital data and generating light
curves
Microsoft Access 2003 for front end of image object storage system
Microsoft SQL Server 2000 acting as the backend database for storing
the digital information from all the observations
Eclipsing Binary Project Briefing
Orion Observatory (OO) http://www.orionobservatory.org :
Meade 10” LX200 Classic
Telescope
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 planetarium
Software Bisque’s CCDSoft V5 for image capture and image processing
Microsoft Excel for evaluating image digital data and generating light
curves
Eclipsing Binary Project Briefing
Photos of our observatories and equipment:
DRO
OO
Eclipsing Binary Project Briefing
DRO
OO
Eclipsing Binary Project Briefing
New high-speed dual-channel dichroic photometric equipment
Eclipsing Binary Project Briefing
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.
Data
Time
Instrumental
Magnitude
Time
Instrumental
Magnitude
Time
Instrumental
Magnitude
Time
Instrumental
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
Eclipsing Binary Project Briefing
Plot:
Eclipsing Binary Star Light Curve
0.00
Instrumental Magnitude
0.10
0.20
0.30
0.40
0.50
0.60
0.00
0.10
0.20
0.30
0.40
0.50
Time
0.60
0.70
0.80
0.90
1.00
Eclipsing Binary Project Briefing
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
0.00
Instrumental Magnitude
0.10
0.20
0.30
0.40
0.50
0.60
0.00
0.10
0.20
0.30
0.40
0.50
Time
0.60
0.70
0.80
0.90
1.00