How do we determine the ##H_0## from standard rulers and standard candle?

[Arman777]

I am doing a research project about Hubble tension. Even if I have some ideas about how we measure the $$H_0$$ by using the standard candles, i don't have much knowledge about it.

I suppose we are measuring the luminosity distance and then by dividing it (1+z) to get the proper distance and the using hubble's law we can find the Hubble parameter ?

But I have no idea about the standard ruler case. Can someone give me detailed explanation or some sources that gives detailed explanation to calculate these things ? (Standard rulers and standard candles)

 

[jedishrfu]

Scientific American published an article on it here:

https://www.scientificamerican.com/...-the-universes-expansion-a-lingering-mystery/

and here's a related article:

https://www.skyandtelescope.com/astronomy-news/tension-continues-hubble-constant/

 

[kimbyd]

I am doing a research project about Hubble tension. Even if I have some ideas about how we measure the $$H_0$$ by using the standard candles, i don't have much knowledge about it.

I suppose we are measuring the luminosity distance and then by dividing it (1+z) to get the proper distance and the using hubble's law we can find the Hubble parameter ?

But I have no idea about the standard ruler case. Can someone give me detailed explanation or some sources that gives detailed explanation to calculate these things ? (Standard rulers and standard candles)

In practice it's done through multi-parameter fits. You throw a bunch of parameters into one of a number of algorithms which estimates them all at the same time.

To understand a little bit of why standard candles constrain $H_0$, in addition to the links that jedishrfu provided, you could check out this paper:
https://arxiv.org/abs/astro-ph/9905116

One side thing, though: the measurement of $H_0$ is exactly degenerate with the intrinsic brightness. So it turns out that the accuracy of the $H_0$ measure is basically just the accuracy of the average brightness of the standard candles. Which we get by using independent distance measures to calibrate the brightness.

There's also the issue that $H_0$ and the curvature $\Omega_k$ behave very similarly, so you need to either assume a curvature or use standard candles across a very wide range of redshift in order to get any reasonable constraint on $H_0$.

 

[Arman777]

In practice it's done through multi-parameter fits. You throw a bunch of parameters into one of a number of algorithms which estimates them all at the same time.

I think that's for standard rulers.

To understand a little bit of why standard candles constrain H0H0H_0, in addition to the links that jedishrfu provided, you could check out this paper:

It does not say much, If i did not look wrong..

There's also the issue that H0H0H_0 and the curvature ΩkΩk\Omega_k behave very similarly, so you need to either assume a curvature or use standard candles across a very wide range of redshift in order to get any reasonable constraint on H0H0H_0.

How so ?

I kind of figure it out how to use standard candles to measure the Hubble constant. But I did not understand the standart rulers idea.

 

[kimbyd]

I apologize for misreading. Standard rulers are much the same, however. Just different astrophysical phenomena. The only significant difference is you use the angular diameter distance instead of the luminosity distance.

In either case, there are two things you need to get $H_0$. First, you need the observed lengths at different redshifts. Then you need a baseline estimate of the "true" length. The most common standard ruler comes from baryon acoustic oscillations, which is a ruler that expands with the universe. The "true" length comes from CMB observations, and at each redshift they compare the observed size to the "true" size to get the angular diameter distance. And once you have a distance estimate, you use one of the aforementioned fitting methods to obtain $H_0$ (and other parameters).

 

[Arman777]

I see. I ll try to look it into the more detail. But currently I am kind of stuck at something. So can we measure distances to nearby cepheids by parallax method ?. Then we can calibrate the luminosity-period relation. But then in the article that I am reading its said that we are calibrating the SN Ia supernovas as well.

For that we are looking for cepheids that are near to SN Ia. We can calculate the distance to the cepheid using Leavitt's law. So to the SN Ia. But what does it mean calibrates the SN Ia ? Is that mean that we can measure the luminosit of SN Ia's that does not have cepheids stars nearby ? Its kind of not clear to me.

copying

"For Hubble constant determinations, the challenge in using SNe Ia remains that few galaxies in which SN Ia events have been observed are also close enough for Cepheid distances to be measured. Hence, the calibration of the SN Ia distance scale is still subject to small-number statistical uncertainties. At present, the numbers of galaxies for which there are high-quality 692 Freedman·Madore
Annu. Rev. Astro. Astrophys. 2010.48:673-710. Downloaded from www.annualreviews.org by California Institute of Technology on 04/03/11. For personal use only.
CepheidandSNIameasurements(inmostcasesmadewiththesametelescopesandinstruments as the Hubble flow set) is limited to six objects (Riess et al. 2009b)."

 

[kimbyd]

Essentially, yes. They use multiple "rungs" to calibrate the distance ladder appropriately, with each step calibrating the next. Sometimes we get lucky and there are local effects that allow far more accurate measurements of the distances to particular galaxies.

Note that some measurements, such as the Cosmic Microwave Background or Baryon Acoustic Oscillation measurements, do not rely upon the distance ladder at all.

I believe the current mismatch in measurements of the Hubble expansion rate came about precisely because a number of astrophysicists attempted to reduce the error bars on the various rungs of the distance ladder. Making those calibrations more precise brought the discrepancy to the foreground.

Oh, and as a side note, you don't necessarily need to use the distance ladder to use supernovae for cosmology. You can, for example, leave the intrinsic brightness of supernovae as a free parameter. This requires combining supernovae with some other data set to get any results (such as the CMB), but it is very much doable.

 

[Arman777]

Note that some measurements, such as the Cosmic Microwave Background or Baryon Acoustic Oscillation measurements, do not rely upon the distance ladder at all.

Yes they based on standart rulers which is completely dark for me ...

Essentially, yes.

I see, thanks

 

[kimbyd]

Yes they based on standart rulers which is completely dark for me ...

The CMB observations use neither standard rulers nor standard candles. The potential systematic errors for at least the temperature data are very, very small. The polarization data is trickier (in part because of the design of the Planck and WMAP satellites, in part because the signal is so much dimmer). But still, the CMB data remains incredibly solid with very few input assumptions required.

This is just because of the nature of the CMB, where the physics of the early universe make the primary signal just so much brighter than the main systematic errors that might creep in. That and the physics of the early universe behaved in such a way that we can use approximations that make accurate calculations easy. This isn't possible with a lot of other things.

That said, naturally baryon acoustic oscillation measurements use standard rulers, but the standard ruler they use is measured from the CMB, which is already one of the cleanest cosmological measurements there is.

 

[Arman777]

The CMB observations use neither standard rulers nor standard candles

Then how are they calculating it ? Any sources that can share ?

 

[timmdeeg]

That said, naturally baryon acoustic oscillation measurements use standard rulers, but the standard ruler they use is measured from the CMB, which is already one of the cleanest cosmological measurements there is.

As an aside I wonder, why do we know the length of the sound horizon with such high precision? The Planck data are very accurate, so from this we know the subtended angle by the sound horizon. And it is clear that its length is a function of this angle. It seems that an accurate value of the angle corresponds to a value of the length equal in accuracy. Why are we sure about that?

 

[kimbyd]

Then how are they calculating it ? Any sources that can share ?

Max Tegmark has a mostly readable but very detailed description on his website:
https://space.mit.edu/home/tegmark/cmb/pipeline.html

He's got a lot of other resources there as well. Wayne Hu also has a detailed introduction to CMB science:
http://background.uchicago.edu/~whu/beginners/introduction.html

 

[kimbyd]

As an aside I wonder, why do we know the length of the sound horizon with such high precision? The Planck data are very accurate, so from this we know the subtended angle by the sound horizon. And it is clear that its length is a function of this angle. It seems that an accurate value of the angle corresponds to a value of the length equal in accuracy. Why are we sure about that?

I was going to go into a long explanation of how we know this value so precisely from theory, but then I realized it's much, much simpler than that. The relationship between the angular diameter distance of the sound horizon (which is directly measured) and the comoving distance (which is also the proper distance at the time of emission) is simply a factor of the redshift. The redshift is estimated by combining the observed CMB temperature (known to 0.02% accuracy) with the results of Earth-based experiments on the behavior of Hydrogen-Helium plasmas. Those Earth experiments (and theoretical analysis via quantum electrodynamics) show at what temperature the plasma condenses to a neutral gas, such that the ratio between that temperature and the observed temperature gives us the redshift.

As a result, we know the redshift of the CMB to an accuracy of 0.04%. The increase in the error bars comes from, I believe, uncertainty in the normal matter density at the time of emission, and the CMB measurement of the normal matter density has an accuracy around 0.7%.

Knowing the redshift and angular diameter distance accurately, then, provides an accurate estimate of the proper distance.

 

[Arman777]

Max Tegmark has a mostly readable but very detailed description on his website:
https://space.mit.edu/home/tegmark/cmb/pipeline.html

He's got a lot of other resources there as well. Wayne Hu also has a detailed introduction to CMB science:
http://background.uchicago.edu/~whu/beginners/introduction.html

I ll look into it in detail but it seems nice. Thanks for the info

 

[timmdeeg]

Knowing the redshift and angular diameter distance accurately, then, provides an accurate estimate of the proper distance.

At the time of recombination the sound wave is "frozen", so we measure its angular size precisely. But how do we know its the proper length expressed in light years at that time (according to Wikipedia 480 million LJ)? Doesn't this require the physics of the propagation of sound waves through the plasma?

EDIT
https://researchportal.port.ac.uk/p...coustic_oscillations_A_cosmological_ruler.pdf
In brief, the matter correlation function quantifies the excess probability of finding a pair of mass concentrations at separation r compared with the case in which concentrations are placed completely at random.
...
That BAO feature is on a large enough scale that it participates in the expansion of the universe. It remains approximately fixed in units of comoving length, a scale that grows with cosmological expansion: At present, the BAO scale is approximately 150 megaparsecs (480 million light-years; a cluster of galaxies is 2–10 Mpc across). The width of the cover image corresponds to 2.5 BAO scale lengths
...
Positions of galaxies in the angular and radial directions are obtained in different ways. For that reason, testing the consistency of the BAO scale across the line of sight requires different cosmological quantities than testing the scale along the line of sight. Across the line of sight, we determine the BAO scale from the increase in the number of pairs with a given angular separation and use the cosmological model to relate angular separation to distance.

Is this just another approach to determine the BAO length? I must confess I don't yet grasp how one can deduce with high accuracy the proper length of the CMB sound waves from clusters of galaxies. Eventually by averaging the size of the clusters?Then it would be clear. I've just been skimming through this article though.

 

[PeterDonis]

how do we know its the proper length expressed in light years at that time

Because if you know redshift and angular size, you can calculate proper length.

according to Wikipedia 480 million LJ

If by "LJ" you mean "light years", that is the estimated proper length of a typical BAO now, not at the time of recombination. More precisely, it's the estimated proper length now between comoving observers who, at the time of recombination, were located one BAO wavelength apart.

Doesn't this require the physics of the propagation of sound waves through the plasma?

Not to just know the proper length, no; as above, knowing the redshift and the angular size are enough to calculate that.

If you want to explain why acoustic oscillations of particular proper lengths are present at recombination, that's where the physics of propagation of sound waves in plasma become useful.

 

[timmdeeg]

Because if you know redshift and angular size, you can calculate proper length.

Ah, understand. I have been thinking too complicated.

If you want to explain why acoustic oscillations of particular proper lengths are present at recombination, that's where the physics of propagation of sound waves in plasma become useful.

Does the physics of propagation of sound waves in plasma yield said proper length at recombination consistent with the redshift - angular size calculation? Perhaps a possibility to compare prediction vs. observation (whereby I am not sure whether plasma physics predicts a certain sound wave length)?

 

[PeterDonis]

I am not sure whether plasma physics predicts a certain sound wave length

Any such prediction would depend on the initial conditions, and those are going to be model dependent. So I would say plasma physics would be used to test various models and their predictions (do the initial conditions that this model requires for the very early universe predict sound waves that are consistent with what we observe at recombination?), not to try to make a prediction independent of any specific model.

 

[timmdeeg]

Any such prediction would depend on the initial conditions

So could our knowledge of the sound wave length at recombination then provide some constraints regarding the initial conditions?

 

[PeterDonis]

could our knowledge of the sound wave length at recombination then provide some constraints regarding the initial conditions?

In a sense, yes, since that knowledge can be used to test models. But "retrodicting" properties of the early universe from data at recombination is model-dependent, so I don't know if the data could be used to provide any model-independent constraints by itself.

 

[timmdeeg]

Thanks for some new insights.