Download Binary Star Par 1802 Word Document

An unusual binary star system in the Orion nebula
(Translated from Sterne und Weltraum 12/08 by G S Kelly)
For many years astronomers have assumed that the stars in binary or multiple systems form at the same
time. Now, however, a research team headed by Keivan Stassun at the Vanderbilt University in
Tennessee, have come across a binary star system, Par 1802 in the 1500 light-year distant Orion Nebula,
which throws up questions. It consists of two young stars which have not yet reached the main sequence
(i.e. they haven’t settled down into a stable hydrogen-burning state) and each have about 40% of the
Sun’s mass. They apparently formed together about 1 million years ago. Their radii are approximately
1.75 times that of the Sun.
Par 1802 is an eclipsing variable – both stars orbit about their common centre of mass, so that from our
point of view each star regularly obscures the other. That causes the total brightness of the system to drop.
In Par 1802’s case the period is 4.7 days. From the light curve and spectroscopic investigations we can
deduce the size, brightness and temperature of both stars as well as orbital information. By doing that, the
research team has discovered that, in spite of having the same mass, the stars are clearly different.
One is about 300 degrees hotter than its partner and gives out about twice as much light. It apparently has
a 10% greater diameter.
The simplest explanation for this is that one of the stars formed about half a million years later than its
partner and is therefore behind in its development. This is not possible according to current understanding
of stellar development. Keivan Stassun and his colleagues acknowledge that it might be necessary to
modify the model of stellar production.
Data from Keivan Stassun’s paper:
Period of orbit = 4.673845 ± 0.000068 days
Orbital speed of component A = 59.5 ± 1.0 km s1
Orbital speed of component B = 57.9 ± 1.1 km s1
Brightness
(arbitrary units)
Idealised light curve showing the eclipses (for the authors’ actual graph, follow the link above):
0.2
Note: “Orbital phase” relates to 1 cycle of the
orbit. Notice that that the authors have taken the
zero time to be the main minimum. To convert to
actual times, multiply by the orbital period.
0.0
0.2
0.4
0.6
0.8
Orbital Phase (1.0 = 4.038  105 s)
Other Data: G = 6.67  1011N m2 kg2 ;Solar mass , M = 1.989  1030kg; Solar radius, R= 695 000 km
Equations: Period of mutual orbit: T  2
M2
d3
d
; Centre of mass: r1 
G(M1  M 2 )
M1  M 2
In the questions that follow, we’ll assume that the system is viewed edge on and that the orbits of the two
stars (A and B) in the system are circular.
Questions.
1. Find the distance between the two stars in this system. [Use the period and speed of the orbit of each
star to find its orbital radius. How is the separation of the stars found from these orbital radii?]
2.
Determine star A’s fraction of the total mass of the system. [Hint: Use the equation for centre of
mass]
3.
By calculating the total mass of the system, shows that the 40% figure for both stellar masses, given
in the passage, is approximately correct.
4.
Use the graph of brightness to estimate the radii of the two stars. Assume that the radii are
approximately equal. You will need to estimate the total eclipse time from the brightness graph.
Hint: The dip in brightness happens when one star passes behind the other.
vA
A
B
vB
You could imagine that star A were stationary and
calculate the time for star B to go past it. How fast
would star B appear to be going from the point of
view of star A?
Express your radii in terms of R and compare your answer with that given in the passage.
5.
Explain how the brightness graph supports the following statements:
(a) We see the system edge-on.
(b) One component is brighter than the other.
(c) [More difficult] The orbit is circular – or close to it.
6.
The paper by Stassun gives the overall effective temperature of the star system as 3500 K. Taking
this as the temperature of the brighter component, use the 10% figure in the passage and the factor of
2 in the brightness, estimate the temperature of the fainter component and compare your figure with
the information in the passage.
More advanced work involving uncertainties:
Notice that the uncertainties are given to two significant figures, which is not expected for GCE Physics
of the WJEC. This is acceptable here because of the very large number of readings involved and the
statistical analysis performed by Stassun et. al.
7.
Determine the uncertainties in each of the answers to questions 1, 2 and 3.
G S Kelly
2 December 2008