Homework 07
Please answer at least 4 of the following 5 questions correctly for full
credit:
Question 1
For main sequence stars: How do we use the Hertzsprung-Russell diagram to
get the distance of a star that does not show any parallax?
Answer
The main sequence in the Hertzsprung-Russell diagram is a line that relates
surface temperature to intrinsic luminosity of the star. So if we know that
a star is on the main sequence, we can use the measurement of its surface
temperature (e.g. by V-B filters) to know its intrinsic luminosity, and in
the sky we can measure its apparent luminosity. The difference between
apparent and intrinsic luminosity then allows us to calculate the distance.
This is called spectroscopic parallax. The problem of course is that there
might be dust along the way that we do not know about and that changes the
apparent magnitude we measure and/or the temperature we derive (reddening).
If there is dust we do know about we can take that into account in our
calculations.
So the short (and correct) answer is: We get the intrinic magnitude from the
diagram after measuring the surface temperature of our main sequence star.
Question 2
What is the difference between a spectroscopic or an eclipsing binary star
system and a visual binary star system?
Answer
Nothing much except that with respect to a visual binary system the resolution
of our observation instrument is good enough so that we can see the proper
motion of the indiviual components of the binary system and thus directly
measure the orbits. For the spectroscopic or eclipsing binary system we cannot
resolve the individual stars in the binary system.
Question 3
In terms of redshift and blueshift: What do we expect to observe in a
spectroscopic binary star system? Do we expect to make this observation on
the blackbody radiation for the stars in the system or for lines in their
spectra?
Answer
Redshift or blueshift are always observed on spectral lines, not on continuous
spectra like e.g. a blackbody radiation spectrum. We can see Doppler shifts
only if things move away from us or towards us; not if they move in a plane
perpendicular to our line-of-sight. So if two objects that we can not resolve
individually but that present themselves to our telescopes as a single point
of light orbit each other AND orbit each other in a plane that is not simply
perpendicular to our line-of-sight to them, we will see at least one of the
objects move alternatingly towards us and then away from us as it orbits around
the other much heavier star. If they are of similar mass, they will move around
a common center of gravity, and that means that while one moves away the other
moves towards us, and they exchange these roles regularly as they orbit that
common center of gravity. Either way, the pattern is alternately moving away
from or towards us, and so the shift will oscillate between red- and blueshift.
That is the pattern we identify binary star sytems by spectroscopically.
Question 4
What kind of radiation was used to discover the spiral structure of our own
Milky Way galaxy? Describe the changes in the hydrogen atom that lead to its
emission, and tell us why that radiation can get to receivers here on Earth,
i.e. why it can penetrate the obscuring dust throughout the galaxy as well
as the atmosphere around the Earth itself.
Answer
The 21cm radio emission of cold atomic hydrogen was used. As hydrogen
accumulates where the mass is (gravitation), it follows the spiral structure
of the mass in the galaxy (stars) and revealed for the first time that our own
galaxy is a spiral one.
Question 5 (the quantitative one...)
When we talk about the lifetime of a main sequence star, we mean the time it
stays on the main sequence part of the Hertzsprung-Russel diagram.
What is the exponent in the mass-lifetime relationship for main sequence stars?
(Look at my lectures, not the book!) Who lives longer, the more or the less
massive stars? When you write down the proportionality between lifetime
L and mass M with the correct exponent, make sure the sign of
your exponent reflects the correct order of who lives longer. In other words:
think about what a negative or a positive exponent mean. Remember that
an expression with a negative exponent is the same as one over that same
expression with a positive exponent.
Answer
Lifetime is roughly proportional to the mass to the power of -2.5 (see
Lecture 21, page 5).
The deadline for submitting solutions to this homework has passed.
Last modified: Fri Mar 14 13:04:21 MDT 2008