Thread by @geodesicvoyager

I've been reading some cosmology papers lately and I'm just in awe at how clever an idea the cosmic distance ladder is. And I need to share that feeling!

So how do we know how fast the universe is expanding? Here is a thread on that. Sorry about the length

Usually when doing science we use tools and equipment we understand and control to study things we don't. This broadly true whether you are measuring things with a ruler or studying particle physics with an accelerator.

Cosmology is a bit different, its tools are stars and galaxies (besides telescopes ofc) and its laboratory the entire universe. Equipment we don't control and don't perfectly understand. Nevertheless scientists have come up with clever ways to use these astronomical tools to ...

... to study the universe at large. The cosmic distance ladder is one of my favorite examples.

The rate of expansion of the universe is captured in the Hubble–Lemaître law

v = H0 x d

d : distance to a galaxy
v : speed at which it is moving away
H0 : local Hubble constant

So how do we measure the speed? By spectrography

All atoms and molecules have distinct spectral lines which show up when you split their light into a rainbow. By studying these molecular fingerprints, astronomers can figure out what stuff far away stars and galaxies are made of

But when a star or galaxy is moving with respect to us, the lines in its spectrum shift. They shift to the blue end when moving towards us, and to the red end when they moving away. The larger the speed the larger the shift. So measure the red shift and we can calculate the speed

But speeds are easy to measure, distances which are much harder. That is because farther an object the dimmer it appears as its light spread out more. This is as true in astronomy as in daily life. A galaxy can be far and bright or close and dim. Usually we have no way to tell

This is where the cosmic distance ladder comes in. Using a variety of 'standard candles' one can measure distances at several 'rungs', with the lower one calibrating the next

This lets us to go farther than parallax alone, which is the one direct way we have to measure distance

Lets start with parallax. Hold out your thumb and close one eye, and then the other. Your thumb will appear to shift from one place to other as you do. Thats parallax!

Knowing the distance between the eyes and the shift of your thumb, you can calculate how far your thumb is

We replicate this in astronomy by measuring a stars position at different points in Earth's orbit. Knowing how big our orbit we can calculate the distance to the star.

Parallax is mostly just geometry. It's a direct measurement of distance and is the lowest rung in the ladder

But farther an object, the smaller its parallax (that mark on the wall didn't change)

Even modern precise telescopes like Gaia telescope can only measure parallax of stars within our galaxy. So how do we get distances to other galaxies? That is where the next rung comes in

On the next rung are (usually) Cepheids. These are fascinating variable stars whose luminosity/brightness fluctuates with time. Henrietta Swan Leavit discovered in 1908 that the time period of the fluctuation depends on the true luminosity of the star; now known as Leavitt's law

Leavitt's law needs to be calibrated for it to give us the true luminosity which we do by parallax measurements of Cepheids in our galaxy. With the the calibrated relation we can measure the distance to Cepheids much farther away or to their galaxies containing them.

Cepheids are an example of standard candles, a term also coined by Leavitt to mean an astronomical source whose true luminosity we know because of its properties (fluctuations in this case).

We will come upon another example in a few tweets below.

Once calibrated by a lower rung (like parallax for Cepheids) we can measure the distances to far away galaxies by measuring using standard candles from those galaxies! This is the idea behind the distance ladder.

Cepheids are only visible to < 150 million light years away. At these small distances peculiar velocities - random gravitational motion of the galaxies - are comparable to the recession speed from the expansion of Universe, and create significant uncertainty in the H0 measurement

Precisely estimating H0 requires galaxies much farther away where peculiar velocity is negligible. Enter the next rung, type 1a supernova.

Type 1a supernova occur in binary systems with one normal star and one white dwarf, which pulls matter from the former & grows more massive

White dwarf are zombie stars supported against gravity by a quantum 'force' called the electron degeneracy. But there is a limit, a pressure valve so to speak for the degeneracy called the Chandrasekhar limit. If the white dwarf grows beyond ~1.44 solar masses it just explodes!

And thats precisely what the type 1a supernova is. The white dwarfs eats from the other star until it explodes. While the science is complicated, the gist is the because they all happen at ~ 1.44 solar masses type 1a supernovae are standard candles too.

And one can tell their true luminosity from their light curves. Since they are literally explosions of stars they are visible from much farther away, where peculiar velocities are not much of a bother.

Type 1a are the final rung in the cosmic distance ladder to measure H0.

The lower rung of Cepheids calibrates type 1a similar to how parallax calibrated them. For this one needs a type 1a to occur in a nearby galaxy containing a cepheid.

I skipped over some details and more calibration options but this is more or less how the distance ladder works

The best measurement for Hubble constant this way is by the SH0ES team

H0 = 74.03 ± 1.42 km/s/Mpc

(arxiv.org/abs/1903.07603)

Thats precise upto 2%! How amazing that we can do that by looking at things across the universe!

But that is not the end of the story. There are other measurements of H0, some through the 'local universe' like SHOES and some early universe CMB ones like Planck. And these measurements seem to disagree by a small but significant amount.

This Hubble constant tension is one ..

.. the most important open questions in modern cosmology. Perhaps we don't understand something about the type 1a supernovas or perhaps the CMB. Or it could be an indicator of entirely new physics we don't understand.

Keep an eye out on the Hubble constant tension in the future!

Image credits:

Distance ladder : NASA, ESA, A. Feild (STScI), and A. Riess (STScI/JHU)

Astronomical parallax : Alexandra Angelich (NRAO/AUI/NSF)

type 1a process : NASA, ESA and A. Feild (STScI)

H0 tension: Aiola et al, 2007.07288