Desperately Seeking Distances

One of the most shocking things about astronomy is that when we take a
picture of celestial objects in the night sky, we have very little
idea how far away they are.  This is utterly different from everyday
life, where our brain automatically processes distance-related clues
and instantly supplies us with correct judgements.  The brain knows
the true sizes of everyday objects, so it can use the apparent size
of, say, a car to infer its distance: the smaller the car appears, the
further away it must be.  The same can be done with the apparent
brightness of lights: if we see headlights but they appear faint, we
know the car is still far away.

But in astronomy, we can only figure out the true sizes and distances
of things with a lot of effort.  One difficulty is simply that
everything is so far away: apart from the Sun, no star is close enough
to ever appear larger than a point, so we can't judge their distances
by their apparent sizes.  Another difficulty is that the universe is
far less standardized than our man-made world: most cars have more or
less the same true size, but stars and galaxies come in a vast range
of intrinsic sizes, preventing us from forming a rule of thumb about
"if it appears this big, it must be about that far away."  Imagine if
some trickster built a 50-foot iPad, faithful in every detail.  If you
mistook it for a real iPad, you would guess that it's much closer to
you than it really is.  The universe is full of the equivalents of
50-foot iPads---stars 100 to 1000 times bigger in diameter and
millions of times bigger in volume than our Sun---as well a
50-millimeter iPads---dwarf galaxies containing thousands of times
fewer stars than does our own Milky Way galaxy.

Astronomers have painstakingly built up a vast store of knowledge
regarding the sizes and distances of things, which I won't attempt to
describe here (but at the end of this post I provide a few links to
sites which help you visualize these things).  The point is that when
a new technique to estimate distances comes along, it's a potentially
powerful tool for astronomers.  Today's episode describing a recent
paper of mine shows how I explored a new idea for determining
distances and showed that it was interesting, but ultimately less
powerful than other ideas that have already been developed.

The new idea is actually an old problem turned on its head, which is
often a useful way to make progress in science.  Imagine that you're
the assistant to a seventeenth-century scientist, put in charge of
monitoring his inventory of chemicals.  You get really frustrated
because you can't tell how much alcohol is in the narrow-necked
bottle---it keeps expanding during the day and contracting at night.
You could continue to view this as a problem, or you could turn the
problem on its head and invent the thermometer.  In science, we often
approach relationships between two or more variables (in this case,
temperature and volume) with a predetermined notion of which variable
is important or worth measuring.  But when measuring that variable
gets frustrating, brainstorming a new goal often results in a valuable
new tool.  That's easy to point out in retrospect but difficult to
apply in practice because on an everyday basis we are often too caught
up in reaching our immediate goals.

In this case, the original "problem" arises from using an effect
called gravitational lensing in which light from background
galaxies is bent by the gravity of an intervening mass concentration
such as a cluster of galaxies.  We can use this effect to determine
the mass of the cluster, if we know the distance to the background
galaxies.  In certain contexts, it's very difficult to know the
distance to the background galaxies accurately enough, and overcoming
this difficulty is an ongoing area of research for major gravitational
lensing projects now in the planning phase. 

At some point my colleague Tony Tyson suggested to my graduate student
Will Dawson that he look into how well the distances to background
galaxies could be pinned down by studying the lensing effect around a
few well-studied mass concentrations.  At the least, it might be
possible to distinguish between sets of galaxies which are more or
less in the foreground (and thus are not lensed) and sets of galaxies
which are more or less in the background (and thus are lensed).  With
different lenses at different distances, it might be possible to infer
something more specific about how galaxies are distributed in terms of
distance from us.

We tried different ways of pulling this information out of the data,
but none of them worked very well.  So I suggested something nearly as
good, at least as a first step: assuming that some solution exists,
let us compute how precise the solution could be in a best-case
scenario.  This would tell us whether continued searching for the
solution would even be worth it.  Now, the ability to compute the
precision of an experiment which has not even been performed yet seems
like magic, but in my previous post I explained how it works.
For me, the best thing about this whole project was that I did a
calculation like this for the first time (they don't teach you this
stuff in school) and therefore really understood it for the first
time.  It's really a pleasure to come to understand something which
previously seemed like a bit of a black box.

The result: lensing can be used to infer how galaxies are distributed
in terms of distance from us, but only roughly.  The precision gets
better and better as you add more data, but to do as well as other
methods which have already been developed requires a very large amount
of data indeed.  For a given amount of telescope time, the other
methods are more precise.  That doesn't mean this method will never be
used: because it piggybacks on a lot of data which will be taken
anyway for other purposes, it may someday be used to double-check that
the other methods are not way off due to faulty assumptions or other
"systematic errors."  It's always good to have multiple different ways
to check something as important as the distances of galaxies.  It may
be somewhat disappointing that this method won't be the primary method
people use, but we can take some satisfaction in definitively
answering the question "how good will this method ever be?" rather
than getting bogged down searching for marginal improvements. 

A few resources about the sizes of things in the universe:

• Scale of the Universe is a neat visualization which lets you zoom smoothly from very small things like atoms all the way to the size of the observable universe, and has nice accompanying music.  But it doesn't show you the distances between celestial objects.  Most tools don't, because the distances are so large that 99% of your screen would be empty space!  Scale of the Universe 2 is by the same people and honestly I can't see much difference between the two. 
• Nikon's Universcale is a similar approach, but with more accompanying text information so you can learn more.  The presentation is a little weak on the astronomical end of the scale, but strong on the micro end of the scale.
• Powers of 10 is a classic documentary which does the same zoom trick and does show you the distances between things.  A much more slick attempt at the same thing called Cosmic Voyage was made decades later, but I still prefer the classic.

This work was supported by the University of California (and therefore to some extent by the State of California) through my salary.  I thank California for investing in research.  It ultimately pays off because research apprenticeships are how we train the next generation to become independent thinkers.