In this thread the question was touched upon as to whether or not the Hubble constant (H0)could be as high as 84 km s-1 Mpc-1 rather than the currently preferred value of ~72 km s-1 Mpc-1 as determined by the Hubble Key Project .

The purpose of this thread is to look at some of the reasons why it is still possible that the value of H0 could in fact be as large the mid 80's.

The HKP final report has been cited ~1100 times since being published in May 2001 so it is an extremely influential paper and important reason why most researchers have accepted H0=~72. This acceptance has been bolstered by the WMAP results.

However, the extragalactic distance scale has numerous pieces (or rungs on the ladder) and there are a number of ways that the HKP final result could be incorrect. First it should be noted that the difference between H0=72 and H0=84 only requires a systematic 0.33 mag shift in the distance scale. For most distance indicators we're talking about a 1-2 sigma shift.

The HKP determined that H0=72 from 5 methods: The I-band Tully-Fisher relation (I-TFR -->spirals), surface brightness fluctuation method (SBF -->ellipticals - mostly), Fundamental plane (FP-->ellipticals), Type Ia Sn, Type II SN. The value of H0 was determined for each of these methods independently and then combined for a final value of H0. One of the reasons for the acceptance of their final result is that 5 methods were used.

One of the rungs underlying these distance methods is the Cepheid variable distance scale - which must be used to fix the zero point of the relations used for the 5 secondary distance indicators listed above.

The Cepheid distance scale is then one place where a systematic shift in the zero points of all 5 distance indicators could take place. Sandage has long argued for a lower value of H0 and recently recalibrated the Cepheid distance scale and concluded H0=62 . However, more recently van Leeuwen et al showed problems with the Sandage et al Cepheid PL relation slope and also showed that the HKP Cepheid scale should be revised so that distances are closer and the value of H0 would then shift to 76.

Looking at the HKP final analysis reveals some other avenues for caution in accepting H0=72 as the final word:

• One of the methods they used (the FP) actually gave a Hubble constant of 82.
• Only 4 galaxies were used for the Type II SN H0 estimate and only 3 calibrators with Cepheid distances were available for calibration of the zero point.
• Only 6 galaxies in 6 clusters were used for the SBF analysis - and the number of cepheid calibrators was the same size - 6.
• While there were 36 Type Ia SN in the analysis, there were only 6 galaxies for calibrating the zero point.
• The I-TFR distances tend to overestimate distances relative to other methods - including methods presented in their own paper for some clusters. For example, the FP distance to Abell 3574 (Table 9) is 51.6 Mpc while the I-TFR distance in Table 7 is 62.2 Mpc. The Centaurus 30 cluster I-TFR distance is 43.2 Mpc (Table 7) whereas a Cepheid distance to NGC 4603 in the same cluster is 33.3 Mpc and the SBF method from the large study of Tonry et al (2001) gives a distance of ~33 Mpc (same as the Cepheid distance). For Antlia the HKP I-TFR distance is 45.1 Mpc whereas the Tonry et al SBF distance is ~33 Mpc.

Tully&Pierce (2000) found H0=77 from the I-band TFR, but they note that it might be more appropriate to use the maser distance to NGC 4258 to fix the zero point of the Cepheid distance scale rather than the traditionally used Large Magellanic Cloud distance. If the maser distance is used, then they would find H0=86 rather than 77. Using the maser distance would ripple through the distance indicators used by the HKP as well raising H0 above 80.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

I think that the Cepheid distances are about as accurate as our knowledge about the distance to the LMC. We have observed and studies a very large number of Cepheids there, and so the statistics about their brightness is pretty solid. Our distance measurement to the LMC is not so far off as to allow the kind of error bars you are asking about.

In about ten years when the Gaia data is in, we'll have very accurate direct trigonometric measurements of the distances of quite a few local Cepheids. This will also help nail things down.

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Forming opinions as we speak

In looking at the HKP paper linked to in the OP, the quoted uncertainty range is from H_o = 64 to 80. I didn't look at the paper in detail, so I'm wondering if that range is intended to be so-called "1 sigma" errors, or if they are "3 sigma". If the former, that allows H_o in the mid 80s without even contradicting the HKP. Also note that the error is almost entirely systematic, because their statistical errors would seem to average to a lower value, perhaps +/-3 or less, so the +/-8 they quote must be largely due to exactly the effects dgruss23 is talking about. As it is much easier to have a significant systematic error than a significant statistical error (statistics are much better understood than systematics-- the latter change with every major new discovery), it seems that H_o =80 is completely plausible, and even 85 would seem to be pretty hard to completely rule out. Even the HKP authors might well agree with that, I would expect.

See the webpage The Hubble Constant, maintained by John Huchra, at the Harvard-Smisthonian Center for Astrophysics. He has compiled all reported values of the Hubble Constant (H0), from 1924 to 2004. You can download the text data file, or just look at his plots. Most notably, see the two plots near the bottom of the page, which show H0 from 1970-2001, and again from 1996-2005.

We can see from the data that a value of 84 km/sec/Mpc would lie significantly outside the indicated range of reported values (the lines drawn on the plot are clearly not 1-sigma uncertainties, and look more like 3-sigma uncertainties, but are probably neither). It certainly appears, based on these plotted data, that 84 km/sec/Mpc is an unreasonably high value, and significantly unlikely.

Also keep in mind that all published values of H0 are here, not just those determined by the Cepheid P-L relationship. I think it is significant that the several methods used all agree in more or less ruling out a value of H0 that high.

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The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it. -- Bertrand Russell

The Cepheid distances provide zero point calibration for the other distance indicators. There are now ~30-40 galaxies with Cepheid distances ... but only a handful of those can be used to calibrate any given secondary distance indicator as I noted in the bullets in the OP. It doesn't take a very large systematic error in the calibration of the zero point of the Cepheid distances in combination with a systematic error intrinsic to the calibration of the secondary distance indicator and small numbers of Cepheid calibrators (3 for the Type II SN, 6 for the SBF and Type Ia SN) to push H0 to 85.

I derived H0=84 using the TFR and 2MASS Ks-band photometry for a sample of 318 spirals that met very strict selection criteria designed to eliminate galaxies that were likely to have large distance errors. The calibrator sample was 26 galaxies with distances based upon the same Cepheid distance scale the HKP used.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

Each research group will target a certain approach as a test of H0. The fact that multiple teams find H0 values ~ 70 doesn't rule out higher values. Tully&Pierce discussed this in their paper. They found H0=77 and asked why their lonely value on the higher side should be trusted and then went on to present their reasons why they believe their value is better. And they noted that if the Cepheid distance scale was calibrated to the geometric maser distance to NGC 4258 that they would get H0=86.

If you look at the approaches used it becomes a question of whose assumptions are better. The Sandage et al team assumes a significant impact from Malmquist, cluster population incompleteness and other biases throughout their analysis - and apply their correction methods they find H0 ~60.

Other research groups don't agree that the large bias corrections are needed and they find a "shorter" distance scale and thus larger H0 values.

Other methods such as time delays of gravitational lenses require assumptions about the distribution of dark matter in order to derive H0. For example, Kochanek and Schechter find H0=48 for isothermal mass distributions, but the same lenses give H0=71 if they eliminate the DM halo and assume constant M/L ratios.

So it is very difficult to look at a list of H0 values and derive any conclusion other than the conclusion that the various methods utilized in the last 20 years give H0 values in the range of 40-90 km s-1 Mpc-1. Which methods are the best and lead to the most reliable values? That requires scrutiny of each study.

But - for example, if the geometric maser distance is adopted for NGC 4258, the distance scale shifts such that Tully&Pierce would get H0=86. In fact Tully&Pierce said there were arguments to be made for preferring the maser distance, but they kept their calibration based upon the LMC distance because that is what everyone else does and it would therefore be easier to compare their results with other studies.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

Yes, I think there is a potential pitfall in just looking at previously published values. There's a kind of "blind leading the blind" element to systematic errors-- one person makes a plausible assumption, and in the absence of any contrary evidence, everyone else follows along. At some point along the way, the nature of that assumption kind of gets lost to history, replaced by a source of systematic error that is easy to overlook. Perhaps one single systematic error would cause us to go back and recreate all of those same plotted results, changing nothing but that one assumption, and we would find they were all higher as a result. That's the concept of "systematic" error taken to the logical conclusion of being systematically applied by everyone. Perhaps Tim is saying there is no error source that is really that systematic over such a wide array of methods, I can't really speak to that-- I merely point out that such would be an essential piece of that type of argument.

The Freedman et al. final HKP paper does a good job, IMHO, of laying out the case for the value they conclude with.

Maybe it's worth going over it, and looking at certain sections in some detail?

For example, we could clarify what the +/- numbers refer to (1 sigma? 3 sigma? something else??); the extent to which the secondary methods are independent; dive into the various chains of observations that lead to the stated systematics; consider the importance (or not) of the stated good agreement and consistency; examine the (statistical) approaches to combining different kinds of estimates; and discuss the two quite independent methods (lensing and the SZE).

I think it would also be of considerable interest to compare this paper with the Spergel et al. WMAP 3-year paper ("Implications for Cosmology" - link is to the WMAP site, click on the appropriate link there to get the paper), and the extent to which a value of 84 is consistent with what's reported in this WMAP team paper.

That's the general idea. This thread is devoted to only one measurement, singled out for special treatment. But how does one go about the task of figuring the probability that any one particular measurement is "right"? It can only be done by comparing the one measurement to a population of like measurements. In this case, the population of measurements given by Huchra serves that purpose. Because they are all derived from different methods, they don't all share the same systematics. So the spread of measurements is a fair representation not only of random uncertainties, but systematic uncertainties.

It only needs to be shown that the given value (84) is significantly high compared to the population, to argue that it is unlikely. Note that I am only saying that it is improbable, not impossible. Just consider the inverse argument. If you are going to claim that this one measurement must be likely correct, then how do you explain all the others being unlikely? It seems unreasonable to me that they would be.

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The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it. -- Bertrand Russell

Not true, this thread is devoted to the question of whether the Hubble Constant is actually a resolved matter or whether it is possible that H0 could be as high as 85. It makes sense to focus first on the HKP final report because it has been so influential.


But you have to look at the methods utilized by the different research groups, not just their final result. For example, Ekholm et al 1999 find H0=53 from the TFR whereas Tully&Pierce 2000 find H0=77 from the TFR. Their methods are different.

It is not good enough to compare the final H0 values, you must compare the distance estimates for clusters that are in common. You must look at the calibration procedures, sample sizes and other factors. Ekholm et al use large bias corrections whereas Tully&Pierce find bias corrections are small.

As noted above and in previous posts, even utilizing the same distance indicator the studies will show a wide range of H0 values. I just noted such a case with the TFR. As another example, using Type II Sn Hamuy 2003 find H0=81 but Leonard et al 2003 find H0=57.

Examples of the types of things that must be looked at are mentioned throughout my posts on this thread - starting with the bullets in the OP. The HKP used four Type II SN with 3 cepheid calibrators. They used 6 SBF distances to find H0. Their I-band TFR to A3574 is 62 Mpc whereas their Fundamental plane distance to the same cluster is 51 Mpc. They find a SBF distance to Coma of 102 Mpc whereas their I-TFR and FP distances are 86 Mpc to Coma.

You can dissect each study this way if you want. You'll find many studies or distance estimates are based upon small numbers of calibrators. Many studies have small sample sizes such as the HKP Type II SN and SBF estimates, this paper , the type II SN papers I linked to above, and the estimates from lensing studies. Many studies are based upon assumptions that have not been resolved among the specialists (again the lensing studies). Many studies are basically a repeat of an earlier analysis with small changes by the same group of researchers. For example I linked to the TFR study of Ekholm et al who found H0=53 in 1999. The same group found H0=53-57 in 1997 using largely the same methods and data sets. So these are not two completely independent H0 estimates.

And finally it should not be forgotten that most of the H0 values are based upon the same Cepheid distance scale - so a systematic error in the zero point of the Cepheid distances is going to affect every one of those studies. As simple a change as adopting the maser distance to NGC 4258 would make Dr. Huchra's list look very different and H0=84 would no longer be on the high end but closer to the middle.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

Apparently, the simple answer is no. According to Harvard's Water Maser Cosmology Project....

Today, the best estimate of the Hubble constant is uncertain by perhaps 10% when all things are considered.

Of course, in traditional astronomical terms, "uncertain by 10%" is astoundingly accurate.

Water masers do appear to have potential for modifying and giving us a more accurate distance scale. One interesting article I haven't seen mentioned is: A Revised Cepheid Distance to NGC 4258 and a Test of the Distance Scale by Jeffrey A. Newman, et al.

[Edit: Hmm. If that article link doesn't work for you, try this one.]

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Everyone is entitled to his own opinion, but not his own facts.

Thanks for the link cougar!

One thing to keep in mind when they quote the 10% accuracy is that it really applies to the uncertainty of the individual H0 estimates given the assumptions and methods applied in each study. The actual value of H0 could still be more than 10% different from any of the individual studies that have attempted to estimate H0. For example, Tully&Pierce noted the potential for a 12% change in H0 with the maser distance to NGC 4258.

Ekholm et al find H0=53 in one study. So 10% sets an upper limit of 58 from their methods - consistent with their reported uncertainty. Tully&Pierce find H0=77 and 10% sets a lower limit of 69 - again consistent with their reported uncertainty. So the 10% accuracy doesn't lead to an overlap in the results of the two studies.

My point is just that while the data and calibrators now in principle allow a determination of H0 to 10% accuracy. That H0 value is only accurate to within 10% of the true value of H0 if the assumptions and methods of the study are in fact valid.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

On significant source of error worth revisiting is the distance at which the 'Hubble flow' dominates the observed motion - in 2001, there was considerable debate on this.

It would also be of value to 'penciling in' the magnitudes of distant supernova Ia observed since 2001 to the Hubble Key Project graph. In 2001 the magnitudes fell roughly into line. Is that still true?

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jwj

It's a big universe out there...is it really unwinding, really burning out?

From another BAUT Q&A thread: this 2007 paper [...]: Cepheid parallaxes and the Hubble constant:

You've been ToSeek'd since I linked to that paper in the OP of this thread and post #131 of the thread you linked to.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

Oops!

So do you think it's worth going over the Freedman et al. HKP paper in some detail? And/or the Spergel et al. one?

Not all of either, but the parts which lead to the final estimate and the estimated systematic uncertainties.

More generally, maybe it's worth looking at what's known about the stated systematic uncertainties in the main independent methods used to get to an estimate of H₀?

And probably the related papers. The HKP final report doesn't present all the details of the calibration of the secondary distance indicators. Other papers were devoted to that.

Perhaps at some point.

And cross comparisons between methods reveal some inconsistenties as I noted in the OP.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

Measure the Hubble Constant (aka Freedman et al. (2000)).

From the Introduction (section 1):For our purposes, the Mould et al. (2000a) paper is (very likely) worth reading; but let's start with §2 and §3, a summary of the method and determination of Cepheid distances. After that, we could consider the van Leeuwen et al (2007) paper as it relates to Cepheid distances, before moving on to §4 and §5 (where Freedman et al. apply a nearby flow field correction and "compare the value of H0 obtained locally with that determined at greater distances").

Then we could take a look at the secondary methods (§6 and §7, plus Mould et al. (2000a), van Leeuwen et al (2007) again, and some of the other papers mentioned in the OP). If we're still on track after that, or perhaps in conjunction, §8 should become highly pertinent ("The remaining sources of uncertainty in the extragalactic distance scale and determination of H0").

OK?

Nereid is very probably referring to a paper published in 2001, "Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant", ApJ 553, 47.

http://adsabs.harvard.edu/abs/2001ApJ...553...47F

Go to this URL and click on the "arXiv e-print" link, then click again on the "PDF link in the upper right to grab a copy of the text in PDF (unless you have access to electronic ApJ).

I suspect that section 2 (mostly details of observations and reductions) will be of less interest to most readers here than section 3.

Any discussion relevant to the topic of this thread is fine with me. My primary point is that this general belief that the value of the Hubble Constant has been largely finalized (at a value of ~70) by the HKP final results is incorrect. It is still possible that the value of H0 could be into the 80's - even if the HKP cepheid calibration was unchanged by newer results such as that of van Leeuwen. In fact the van Leeuwen study only increases the possibility that H0 is actually in the 90's.

So anything you want to comment on is fine. I pointed to a few items of interest in the OP.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

I tried to fix this typo but the save function on changes has not been working for me the last few days. That is supposed to be 80's, not 90's.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

Greetings everyone!

I've been away from the BABB since before it became the BAUT. When I was last here, I was working for the Ion/Neutral Mass Spectrometer on the Cassini mission to Saturn. Now I'm an astrophysics grad student, studying low-luminosity AGN.

I started lurking again a couple weeks ago, and decided to jump in after noticing something on astro-ph that ya'll might find interesting: "A comprehensive study of Cepheid variables in the Andromeda galaxy. Period distribution, blending and distance determination" by F. Vilardell, C. Jordi and I. Ribas

http://arxiv.org/abs/0707.2965

The examine 281 Fundamental Mode Cepheids in Andromeda and look at some of the systematics of the sample. Rather an interesting paper in its own right, but also relevant, I think, to the discussion at hand.

I'll be in and out... Hopefully my own ignorance won't drag things down too much here!

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"What do you care what other people think?" -- Richard Feynman
"For a successful technology, reality must take precedence over public relations, for nature cannot be fooled." -- Feynman, at the conclusion of his Challenger report

Welcome back. If you've read it, can you summarize it's salient features for the lazier ones among us, present company included?

The most interesting portion of the paper to me was the authors' analysis of the degree to which crowding (light from fainter stars near the target Cepheids) contaminated the Cepheid measurements, and how they decided to address it (they used the period-amplitude relationship to pick samples with less crowding).

No really big news in it, I would say. The abstract does a good job of explaining their results.

For the purposes of this thread, here are the parts of this section of the HKP Final Results paper that have particular relevance (IMHO):Which tells us what random uncertainty the team was aiming at.So what is the equivalent (Sandage team) "Final Results HKP" paper re calibration of Type 1a supernovae?Which doesn't seem to be many galaxies, even if there are many Cepheids in each galaxy.

An interesting exercise might be to duplicate a subset of the HKP team's work, using new observations of Cepheids in galaxies other than those 31 ... if there are, in fact, any such observations.
And the team did find it very difficult to beat down the uncertainties in the absolute photometric calibration (see Section 2.5) ... so the value of the Hubble constant cannot be locked down tighter than these absolute photometric calibration uncertainties ...

Here . But it is difficult to directly compare their result with the HKP result because they also use a different Cepheid calibration. The van Leeuwen paper pointed out that the Sandage group uses a steeper slope for the Cepheid P-L relation which van Leeuwen et al was not able to confirm. Rather they found a slope almost unchanged from that used by the HKP>



Yes, that was one of my points in the OP. Several of the secondary indicators have 6 or less zero point calibrators which increases the chances of a systematic error in the zero point.

There have been a couple of papers that have come out since the HKP final report that have looked at the Cepheid's in other galaxies. The Cepheid sample hasn't been significantly enlarged beyond the HKP sample though.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

An, Terndrup, & Pinsonneault have used open clusters to derive the Galactic Cepheid P-L. Applying their P-L relation to NGC 4258 they find distance modulus of 29.28 +/-0.10 which agrees with the maser distance. For the LMC they find a distance modulus of 18.34 +/- 0.06. The LMC distance modulus is 0.16 mag smaller than the distance modulus adopted by the HKP and results in a larger value of the Hubble constant.

With the new LMC distance the HKP value of H0 would be revised to 77.5 and the Tully&Pierce value of H0 would be revised to 83.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

These numbers are very important for establishing the zero point of the hubble flow. I don't have a feel for how much effect a ~0.1 magnituded error in Cepheid distance scaling would have. The 'Cepheid' slope to nearby galaxies is critical. Anybody want to weigh-in on this before I work out an estimate?

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jwj

It's a big universe out there...is it really unwinding, really burning out?

A 0.10 mag error in the Cepheid scale would change H0 by ~3.3 km s-1 Mpc-1.

In this particular case the value of H0 would be reduced rather than increased, because the effects of blending cause Cepheid distances to be less than the actual distance. However, as the authors note - other studies have demonstrated that the blending effect us only important for very local galaxies.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

Could you provide the exact quotation from the paper to support your last sentence, please? I just re-read sections of the paper and could not find such a statement. Moreover, it doesn't seem to make sense: the most distant a galaxy, the larger the area (and volume) covered by a seeing disk, so the LARGER the number of stars which are blended together with any particular Cepheid. The blending problem should become _worse_ with distance, it seems, not less important, as you imply.