Can top rungs replace bottom ones in cosmic distance ladder?

[geoduck]

For example, can spectroscopy replace measurements of stars made by parallax?

And ultimately can Hubble's law replace every rung of the ladder - just measure the redshift of the object you want to know about to get the distance?

Or do the higher rungs really only work good for great distances?

 

[Drakkith]

The issue is that each rung only works under certain conditions which usually make that particular rung work only within a certain distance. Some rungs could theoretically work for any distance, where others can't.

For example, parallax could theoretically work for ANY distance. It's just that we'd need orders of magnitude more precision to be able to measure the parallax of extra-galactic objects.

Conversely, Hubble's law only works for multi-megaparsec distance because everything within a few million light years of us is too tightly bound by gravity to be pulled away by expansion. There is nothing we can do about this, so this rung is set.

Spectroscopy only measures the redshift or blueshift of an object, so it by itself can't be used to determine distance. Instead it has to be used with something else, such as Hubble's Law. Within our local group, a redshift or blueshift measurement only tells us how fast something is moving relative to us, not how far away it is since Hubble's law doesn't apply at distances this small.

 

[geoduck]

Spectroscopy only measures the redshift or blueshift of an object, so it by itself can't be used to determine distance. Instead it has to be used with something else, such as Hubble's Law. Within our local group, a redshift or blueshift measurement only tells us how fast something is moving relative to us, not how far away it is since Hubble's law doesn't apply at distances this small.

Spectroscopy also encompasses a technique whereby you measure the apparent brightness of a star, and note its wavelength or color. With these two pieces of information, presumably you can calculate distance using an HR diagram.

But does the HR diagram assume stars are a certain size? From Boltzmann's law, P=σT⁴A, that is power equals stefan constant σ times temperature (to the fourth) times surface area of star. The brightness measured on Earth is P/(4*pi*distance^2). Knowing the color of the star gives you T.

So σT⁴A/(4*pi*distance^2)=apparent brightness

It seems you need to know the area of the star A to get the distance. Is there an assumption that all stars are the size of the sun?

 

[ianchristie]

No there is no assumption that all stars are the same size. The two measurements you mention, apparent brightness and colour/temperature are not sufficient to place a star on the HR diagram. We need size or distance as well. Size will give us distance as you noted. (Conversely distance can give us size.) In fact we measure the distance using methods such as parallax and main sequence fitting and then calculate the size from the temperature and absolute magnitude. For example white dwarfs like Sirius B are extremely hot, (from their colour), and would be extremely bright if they were Sun-sized. We can even see that stars vary in size dramatically without knowing their actual size or absolute magnitude. Sirius B is extremely faint compared to Sirius A even though it is much hotter. They are both at exactly the same distance, hence Sirius B must be tiny compared to Sirius A.

 

[geoduck]

I was under the impression that measuring color and brightness was used to determine the distance.

It seems instead that color and brightness is used to determine size once distance is known, so it's parallax that determines distance, and size is determined by HR diagrams?

 

[ianchristie]

The HR diagram is not used to determine anything. It is just a very distinctive plot of absolute magnitude/luminosity versus colour/temperature/spectral class. (These things are closely connected and are effectively proxies for each other.) Determination of this data requires knowledge of the distance to the star from some technique independent of the HR Diagram. The value of the HR Diagram is that it is so distinctive that any ideas about the nature or life cycle of stars can be tested by applying them to a large number of stars and then plotting the resulting data. If the plot does not resemble the HR diagram then the ideas are not good.

In simple terms:-
Distances are determined using the "Cosmic Distance Ladder". For "nearby" stars parallax is used, it's the first rung on the ladder. It currently works at distances out to a few hundred parsecs, roughly a thousand light years. (The Gaia mission will extend this out to most of our galaxy, about 100,000 ly.) For more distant stars in clusters (open or globular) there are two main possibilities: "Main sequence fitting" or "Cepheid Variables" so these are equal second rungs. Main sequence fitting works to about 100,000 ly, Cepheid variables are visible in galaxies at tens of millions of light years so this techniques spans both intra and inter galactic distances. After that there are various techniques which are applied to whole galaxies such as the Tully-Fisher Relationship, and techniques such as that using Type 1A supernovae. At the extreme of distance and time astronomers use Hubble's Law.
This is a simplification and omits much of the fine detail and lots of slightly less significant rungs. The Wikipedia page on the Cosmic Distance Ladder is good for many reasons. It has the detail if you want it but also has enough plain English to give you a good overview if that is all you need.
Cheers.