Download Physics 1025: Lecture 17 Sun (cont.), Stellar Distances, Parallax

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Physics 1025: Lecture 17 Sun (cont.), Stellar Distances, Parallax, Stellar Motions
Announcements
Sun (continued)
How do we look at the sun? DON’T ever look at the sun, especially with any sort of optical aid or you will
do permanent damage to your retina! Even so-called “safe” eyepieces may have been dropped, cracked,
etc. and now let in damaging infra-red rays.
One last thing about the sun is the sunspot cycle – sometimes you see lots of sunspots and other times
few. Once there was an amateur astronomer in Germany about 150 years ago who was a druggist and
worked nights. He wanted to do astronomy during the daytime and a friend advised him to look at
sunspots which he did. If you plot the number of sunspots seen verses year you will see that the curve
oscillates up and down with a period of roughly 11 years between maximum number of sunspots. If you
look at the spots in detail, during one cycle the leading spot in the northern hemisphere might be a N
pole (and a S pole in the southern hemisphere), yet 11 years later in the next cycle the leading spot in
the northern hemisphere will be a S pole (and a N pole in southern hemisphere), namely the polarity of
the leading poles has switched. Hence the true period is 22 years for a complete sunspot cycle to repeat
itself. There is also an overall modulation of the peak sizes themselves, the e.g. during the 1600’s there
was a period of practically no sun spots at all, the Maunder minimum, associated with the Little Ice Age.
We now go on to examining the stars: their distances and motions. One of the most fundamental
astronomical questions is the distance to the stars; every class from now on will introduce at least one
means for this determination – astronomers are very clever in finding indirect means, since there is only
one direct method and the stars are very far away.
Parallax is the only direct way to measure stellar distances. Since the stars are so far away you need a
huge baseline for this technique of measuring the apparent shift in position of a nearby star against the
background stars due to the earth’s motion around its orbit. Tycho Brahe knew about parallax, but even
with his careful measurements he could not find it, so used this to argue that the earth was stationary.
In 1727 the aberration of starlight (about 20” due to the finite motion of earth) was found – this shifts all
stars together.
E
θ
star
R
↓
↓
s
We define the parallax angle θ for a baseline s= 1 AU and calculate R using θ = s/R, where θ is in radians
(1 rad=57.3˚, i.e. 2πrad=360˚) Hence we have
R = s/θ(rad) = 57.3/θ(deg) = 57.3 x 60/θ(min)
= 206,000/θ(sec)
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Suppose a star is so far out that θ= 1” for a baseline of 1 AU = 93,000,000 miles. Then R = 206,000s/θ.
(Remember that the total motion is only 2” of arc.) Then R = 19 x 10 12 miles.
We define 1 parsec as a new unit of length, a distance such that a star has a parallax of 1 second of arc
with a baseline of 1 AU. Hence the star’s distance in parsecs R(parsecs)= 1/θ”
It’s hard to realize how big this is: if you draw a 1 inch circle for the earth’s orbit, than 200 inches = 17
feet and 206,000 inches is about 5 miles, out past Kathy Johns to the Holiday Mall – then you’d see a
total shift of 1” arc across the baseline of 1 inch.
Another distance used in astronomy is the light year, the distance light travels in one year.
1 light year = 180,000 miles/ sec x 3600 sec/hr x 24 hr/day x 365.25 days/year = 5.88 x 1012 miles, not
too dissimilar to a parsec (pc).
Therefore 1 parsec = 3.26 lt years.
If a star is 3¼ light years away, you’d see a 1” parallax around earth’s orbit. NO star is this close to the
sun: the maximum parallax is for Proxima Centauri (the nearest star) whose θ= .75” so R = 4/3 pc = 1.33
pc or 4.3 lt years.
But remember diffraction dims star images and blurs them – with the best seeing you’d see 1” circles on
the roof, so the maximum parallax shifts are a fraction of the stellar ‘diameter’ seen.
The first accurate determination of parallax was in 1838 when Bessel of Konigsberg measured 61Cygni.
The measurements are so difficult only a few 100 stars have their parallaxes determined (i.e., their
distances measured directly).
What you actually see is the parallax wobble superimposed on top of the so-called ‘proper motion’, or
angular motion along the celestial sphere perpendicular to the line of sight to the star. (Proper motion
was discovered by E. Halley of comet fame, who compared Ptolemy’s ancient star catalogue with star
positions determined early in the 1700’s.)
May
Oct
Oct
μ
How do astronomers pick out the nearby stars to measure?
Answer: stars with large proper motions have large parallax (because they are nearby!) Think of people
moving randomly in a park: those near to you will zoom across your field of view with large ‘proper
motion’ (and being near to you will also have large ‘parallax’), although if you select on this basis you will
also miss some nearby stars which happen to be heading directly towards you (hence have zero proper
motion). Again the blink microscope comes in handy, comparing two photographic plates taken, e.g. 30
years apart, then you can easily pick out the 1 out of 1000 stars which ‘jumps’ back and forth indicating
large proper motion (and a nearby star).
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This is a good place to discuss the motions of stars in space. Stars have a general Space velocity which
can be broken into perpendicular components: radial velocity (along the line of sight) and tangential
velocity (along the celestial sphere perpendicular to the line of sight).
VT
Vs
S
R
VR
There is a relation between these components given by the Pythagorean Theorem: VS2 = VT2 + VR2. Hence
given VT you can say nothing about VR,but VS must be greater than or equal to VT. Now VT is related to
the proper motion μ and distance to the star by VT (km/sec) = R(pc) x μ (“/yr) x 4.74 where the factor
4.74 is from a conversion of units. We measure VR from the Doppler effect, the apparent wavelength
shift of a line due to motion along the line of sight: ∆λ/ λ = VR/c, where c is the velocity of light and ∆λ is
the wavelength shift from the unshifted line λ. The star’s light will be blue-shifted if the star approaches
earth. (Note in the case of an expanding nebula like the Crab Nebula, we assume it expands equally in all
directions (i.e. spherically) and set VR= VT and can solve for the distance R to the nebula.)
Is the sun moving? You’d assume so, as most stars move and why should the sun stand still? If you plot
proper motions on the celestial sphere, there will be one particular place from which the proper
motions more or less diverge: this point is called the ‘Apex of the sun’s Way’ and is really a perspective
effect. It’s like walking through the forest – the trees appear to open out in front of you in angular
positions from the point directly ahead of you, and so it is with stars. The divergence of their proper
motions is only a reflection of the sun’s motion through space. Similarly, the trees appear to close in
behind you, and also the proper motions appear to converge to a point directly opposite to the Apex on
the Celestial sphere: this point is called the Antapex, the point from which the sun appears to be
headed.
Apex
Antapex