Download Still Lost in Space

Still Lost in Space
Assignment 6
Model answer to Assignment Five plus the
new data you’ve been asking for.
Conclusions from the first Data
Release
 What could you conclude from the first set of data?
 This universe looks superficially like our own, but
on closer examination is actually quite different.
 Perhaps the biggest surprise was the enormous
parallaxes of the stars.
 Taken at face value, this would imply that they are
only a few AU away! A few are almost as close to us
as the Sun is to the Earth.
Really Close?
 If they really were this close, they could not
possibly be stars. As they appear as bright as stars
but are 104 times closer, by the inverse square law,
they would have to be 108 times fainter. No such
stars exist in our universe
 Also any star that was so close (down to 1.5 AU)
would be clearly visible as a disk, even with the
naked eye, let alone a telescope.
Two Possibilities
So we are left with two possibilities:
 1: They are not stars, but some different and weird
type of object.
 2: They are stars, but the universe has a strongly
saddle-shaped geometry that warps the angles and
causes our parallax measurements to give
spuriously high values.
Which is true?
If they are stars?
 If they are stars (and the universe is very curved), then they
should have stellar spectra. They do not.
 Also, only a few of them should pulse, and any pulsations
should take hours to months.
 Instead they all pulse, some with periods as short as a quarter
of a second! No stars do this.
 Could the pulsation be due to something orbiting each of
them very quickly? Even if the orbiting thing was travelling at
the speed of light (very unlikely) it could only travel less than
75,000 km in 0.25 seconds, which means the radius of its
orbit must be less than (probably MUCH less than) 12,000 km
- which is smaller than virtually any type of star.
Oscillating Universe?
 Is there any way to save the “star” hypothesis?
 The pulsations could be caused by an extremely
rapidly oscillating universe.
 But then all stars should have the same period,
which they do not.
 Perhaps different bits of the universe are pulsing at
different rates?
 General Relativity says this could only happen if the
mass distribution is also pulsing by vast amounts
on comparable timescales, which seems unlikely.
 And anyway, this wouldn’t explain the weird
spectra.
Not Stars
 So the simplest conclusion is that these things are
not stars, or at least not stars as we know them.
 They are something strange and different.
 We thus no longer need the “saddle shaped
universe” hypothesis. Which is not to say that it
isn’t true - just that we have no evidence for it.
 Let’s tentatively assume (as a starting point) that
the geometry of space is not radically curved.
 Then these “stars” really are far fainter than real
stars, and really are only a few AU away from us.
What are these “Stars”?
 What then can we learn about these “stars” that
aren’t stars.
 They must be pretty small, otherwise we’d see
disks, given their close distance. Much smaller even
than planets (Mars and Jupiter are both further from
the Earth than many of these things, but easily
show disks with even small telescopes).
 The data show some striking patterns.
 The pulse period, wavelength and pulse amplitude
are all strongly correlated.
All the same?
 Could all these “stars” be basically the same type of object,
only lying at different distances?
 Perhaps they are extremely compact emission-line nebulae.
Normally any nebula would emit multiple lines, but perhaps
these nebulae contain only one element, and very unusual
excitation mechanisms, so that only one line is produced?
 In this case, the different wavelengths would be explained by
an expanding or contracting universe. The expansion or
contraction rate would have to be enormous to give such big
red/blueshifts for objects so close.
 Unfortunately there is no correlation between wavelength and
distance.
Lumpy Matter
 It is, I suppose, just possible that different bits of the
universe are expanding and contracting, and thus
explaining different redshifts for “stars” at the same
distance.
 But even that would not explain why the amplitude of
the pulsations correlates with the wavelength.
 And it would require a very strange distribution of vast
moving quantities of dark matter on very small length
scales (remember, the metric isn’t arbitrary - it is
controlled by the distribution of matter).
Doppler Effect?
 Could the different wavelengths be caused by the
Doppler effect - different objects moving at different
speeds?
 That would’t explain the correlation between pulse
amplitude and wavelength.
 And the necessary speeds would be a good fraction
of the speed of light.
 Given that the objects are only a few AU away, we
should easily see them moving at these huge
speeds, and we do not.
Different Objects
 So the most plausible explanation is that the
objects emitting at different wavelengths really are
different types of object, and not just the same
class of object seen at different redshifts.
 So what are they? Could they all be compact
nebulae, but each with a different element and
hence a different wavelength?
 You’d need a whole lot of elements, it would still be
puzzling that you only see one line, and the
correlations with pulse period or amplitude would
not be explained.
One family
 It rather seems as if we are looking at one family of
object, with somewhat variable properties.
 The more distant ones appear fainter.
 If you use the inverse square law to compute the
real luminosities of these objects, they all come out
roughly the same.
 Furthermore, this luminosity correlates with the
frequency - redder objects are brighter.
Like Nothing We’ve Seen Before
 So - these “stars” are like nothing we’ve ever seen
in our own universe.
 They are extremely small, much fainter than stars,
and emit all their light at one wavelength.
 Their luminosity, wavelength, pulse period and
pulse amplitude all correlate nicely together,
suggesting that they are one family of object.
 So what are they? Nobody has any idea.
Suggestions being bandied around are white holes,
worm holes, strange neutron stars and much more.
 Clearly more data are needed.
More Data
 You have now been stranded through the wormhole for a day.
 You’ve put together some new equipment and made lots of
new observations, guided by the initial data.
 A bigger telescope was built, and pointed at the nearest of the
“stars”, only 1.5 AU away, if you believe the parallax data.
 Even with a resolution of 0.03 arcseconds, it looked like a dot.
 You’ve been tracking several of the nearer stars, looking for
signs of motion. No transverse motion was seen - the angle to
each star from your ship remains constant.
Triangle!
 In an attempt to measure the geometry of space,
you sent out a second probe, at right-angles to you
and the first probe.
 Laser beams were exchanged between both probes
and you, forming an equilateral triangle, 10,000 km
on a side.
 The interior angles of this triangle added up to
179.99996 degrees, with an error estimate of
0.00005 degrees.
Microwave Background
 No microwave background was detected. Any
emission warmed than 1K would have been pixed
up with your equipment.
 A puzzle - measurements from the probes indicate
that the vacuum outside the ship is much emptier
than even typical intergalactic space in our
universe.
 They are picking up no atoms at all that hadn’t
leaked out from the USS Drongo or the probes.
 Also, no cosmic rays are being detected.
Wider Wavelength Coverage
 You’ve managed to put together a spectrograph that
can observe UV light in the wavelength range 10400nm, and IR light in the range 800-2500 nm.
 You pointed this spectrograph at dozens of stars
and saw nothing in any of them. They do not appear
to emit any radiation in these bands.
Radio Array
 While you’ve continued with your observations, the
sensor division have been rigging up some pretty
nice equipment.
 They’ve built a radio array that allows them to
pinpoint exactly where in the sky the mysterious
radio bursts are coming from.
 They then provide you with the coordinates, and
you then point your big new telescope in that
direction.
Imaging the Bursts
 Remarkably, each burst appears to be coming from
a star.
 Most of these stars are much fainter than the ones
you’ve been studying so far - that’s why you needed
the bigger telescope.
 The stars appear quite normal. They have spectra
much like the other stars, and they too pulse in
brightness.
Different Colours
 These “radio emitting” stars have spectra peaking
at a wide range of wavelengths, though they
perhaps are more concentrated at longer
wavelengths.
 Indeed, several were not initially detected at optical
wavelengths, and were only found when you
hooked up your infra-red spectrograph to your new
telescope.
Data Table
 Once again, I’ve provided an Excel file containing
the data on these sources.
 It includes both the radio data on the bursts and the
subsequent optical data.
 You tried to measure parallaxes for these sources,
using the small space-probe exactly as before.
Assignment
 The details of this assignment (ie. word limit, group
work etc, how to submit) are identical to the last
one.
 The deadline is 10am on Thursday 12th June.
 Once again, you should try and deduce as much as
you can about the strange universe in which you
find yourselves.
 Top priority is determining the large scale
cosmology of this universe, as this is what will help
you generate a wormhole to get you back home.