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 10-400nm, 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.