## Redshift and Distance in Cosmology

Posted in The Universe and Stuff with tags , , , , , on April 29, 2019 by telescoper

I was looking for a copy of this this picture this morning and when I found it I thought I’d share it here. It was made by Andy Hamilton and appears in this paper. I used it (with permission) in the textbook I wrote with Francesco Lucchin which was published in 2003.

I think this is a nice simple illustration of the effect of the density parameter Ω and the cosmological constant Λ on the relationship between redshift and (comoving) distance in the standard cosmological models based on the Friedman Equations.

On the left there is the old standard model (from when I was a lad) in which space is Euclidean and there is a critical density of matter; this is called the Einstein de Sitter model in which Λ=0. On the right you can see something much closer to the current standard model of cosmology, with a lower density of matter but with the addition of a cosmological constant. Notice that in the latter case the distance to an object at a given redshift is far larger than in the former. This is, for example, why supernovae at high redshift look much fainter in the latter model than in the former, and why these measurements are so sensitive to the presence of a cosmological constant.

In the middle there is a model with no cosmological constant but a low density of matter; this is an open Universe. Because it decelerates much more slowly than in the Einstein de Sitter model, the distance out to a given redshift is larger (but not quite as large as the case on the right, which is an accelerating model), but the main property of interest in the open model is that the space is not Euclidean, but curved. The effect of this is that an object of fixed physical size at a given redshift subtends a much smaller angle than in the cases either side. That shows why observations of the pattern of variations in the temperature of the cosmic microwave background across the sky yield so much information about the spatial geometry.

It’s a very instructive picture, I think!

## Subaru and Cosmic Shear

Posted in The Universe and Stuff with tags , , , , , , on February 15, 2019 by telescoper

Up with the lark this morning I suddenly remembered I was going to do a post about a paper which actually appeared on the arXiv some time ago. Apart from the fact that it’s a very nice piece of work, the first author is Chiaki Hikage who worked with me as a postdoc about a decade ago. This paper is extremely careful and thorough, which is typical of Chiaki’s work. Its abstract is here:

The work described uses the Hyper-Suprime-Cam Subaru Telescope to probe how the large-scale structure of the Universe has evolved by looking at the statistical effect of gravitational lensing – specifically cosmic shear – as a function of redshift (which relates to look-back time). The use of redshift binning as demonstrated in this paper is often called tomography. Gravitational lensing is sensitive to all the gravitating material along the line of sight to the observer so probes dark, as well as luminous, matter.

Here’s a related graphic:

The article that reminded me of this paper is entitled New Map of Dark Matter Spanning 10 Million Galaxies Hints at a Flaw in Our Physics. Well, no it doesn’t really. Read the abstract, where you will find a clear statement that these results do not show significant evidence for discordance’. Just a glance at the figures in the paper will convince you that is the case. Of course, that’s not to say that the full survey (which will be very much bigger; the current paper is based on just 11% of the full data set) may not reveal such discrepancies, just that analysis does not. Sadly this is yet another example of misleadingly exaggerated science reporting. There’s a lot of it about.

Incidentally, the parameter S8 is a (slightly) rescaled version of the more familiar parameter σ8  – which quantifies the matter-density fluctuations on a scale of 8 h-1 Mpc – as defined in the abstract; cosmic shear is particularly sensitive to this parameter.

Anyway, if this is what can be done with just 11%, the full survey should be a doozy!

## Ongoing Hubble Constant Poll

Posted in The Universe and Stuff with tags , , , , on July 18, 2018 by telescoper

Here are two interesting plots that I got via Renée Hložek on Twitter from the recent swathe of papers from Planck The first shows the tension’ between Planck’s parameter estimates direct’ measurements of the Hubble Constant (as exemplified by Riess et al. 2018); see my recent post for a discussion of the latter. Planck actually produces joint estimates for a set of half-a-dozen basic parameters from which estimates of others, including the Hubble constant, can be derived. The plot  below shows the two-dimensional region that is allowed by Planck if both the Hubble constant (H0) and the matter density parameter (ΩM) are allowed to vary within the limits allowed by various observations. The tightest contours come from Planck but other cosmological probes provide useful constraints that are looser but consistent; BAO’ refers to Baryon Acoustic Oscillations‘, and Pantheon’ is a sample of Type Ia supernovae.

You can see that the Planck measurements (blue) mean that a high value of the Hubble constant requires a low matter density but the allowed contour does not really overlap with the grey shaded horizontal regions. For those of you who like such things, the discrepancy is about 3.5σ..

Another plot you might find interesting is this one:

The solid line shows how the Hubble constant’ varies with redshift in the standard cosmological model; H0 is the present value of a redshift-dependent parameter H(z) that measures the rate at which the Universe is expanding. You will see that the Hubble parameter is larger at high redshift, but decreases as the expansion of the Universe slows down, until a redshift of around 0.5 and then it increases, indicating that the expansion of the Universe is accelerating.  Direct determinations of the expansion rate at high redshift are difficult, hence the large error bars, but the important feature is the gap between the direct determination at z=0 and what the standard model predicts. If the Riess et al. 2018 measurements are right, the expansion of the Universe seems to have been accelerating more rapidly than the standard model predicts.

So after that little update here’s a little poll I’ve been running for a while on whether people think this apparent discrepancy is serious or not. I’m interested to see whether these latest findings change the voting!

## Celebrating the Sloan Telescope

Posted in The Universe and Stuff with tags , , , , , , , , on May 9, 2018 by telescoper

A little bird tweeted at me this morning that today is the 20th anniversary of first light through the Sloan Telescope (funded by the Alfred P. Sloan Foundation) which has, for the past two decades, been surveying as much of the sky as it can from its location in New Mexico (about 25% altogether): the Sloan Digital Sky Survey is now on its 14th data release.

Here’s a picture of the telescope:

For those of you who want the optical details, the Sloan Telescope is a 2.5-m f/5 modified Ritchey-Chrétien altitude-azimuth telescope located at Apache Point Observatory, in south east New Mexico (Latitude 32° 46′ 49.30″ N, Longitude 105° 49′ 13.50″ W, Elevation 2788m). A 1.08 m secondary mirror and two corrector lenses result in a 3° distortion-free field of view. The telescope is described in detail in a paper by Gunn et al. (2006).

A 2.5m telescope of modest size by the standards of modern astronomical research, but the real assets of the Sloan telescope is a giant mosaic camera, highly efficient instruments and a big investment in the software required to generate and curate the huge data sets it creates. A key feature of SDSS is that its data sets are publicly available and, as such, they have been used in countless studies by a huge fraction of the astronomical community.

The Sloan Digital Sky Survey’s original legacy’ survey was basically a huge spectroscopic redshift survey, mapping the positions of galaxies and quasars in three dimensions to reveal the `cosmic web’ in unprecedented detail:

As it has been updated and modernised, the Sloan Telescope has been involved in a range of other surveys aimed at uncovering different aspects of the universe around us, including several programmes still ongoing.

## A Galaxy at Record Redshift?

Posted in The Universe and Stuff with tags , , , , , on July 13, 2015 by telescoper

Skimming through the arXiv this morning I discovered a paper by Zitrin et al. with the following abstract:

I’m not sure if the figures are all significant, but a redshift of z=8.68 makes this the most distant spectroscopically confirmed galaxy on record with a present proper distance of about 9.3 Gpc according to the standard cosmological model, just pipping the previous record holder (whose redshift was in any case disputed). Light from this galaxy has taken about 13.1 Gyr to reach us; that means light set out from it when the Universe was only about 4% of its current age, only about 600 million years after the Big Bang. (Those figures were obtained using the inestimable Ned Wright’s cosmology calculator.)

We are presumably seeing a very young object, in which stars are forming at a considerable rate to account for its brightness. We don’t know exactly when the first stars formed and began to ionize the intergalactic medium, but every time the cosmic distance record is broken we push that time back closer to the Big Bang.

Mind you, I can’t say I’m overwhelmingly convinced by the identification of the redshifted Lyman-α line:

But what do I know? I’m a theorist whose suspicious of data. Any observers care to comment?

## That Big Black Hole Story

Posted in The Universe and Stuff with tags , , , , , , , , on February 28, 2015 by telescoper

There’s been a lot of news coverage this week about a very big black hole, so I thought I’d post a little bit of background.  The paper describing the discovery of the object concerned appeared in Nature this week, but basically it’s a quasar at a redshift z=6.30. That’s not the record for such an object. Not long ago I posted an item about the discovery of a quasar at redshift 7.085, for example. But what’s interesting about this beastie is that it’s a very big beastie, with a central black hole estimated to have a mass of around 12 billion times the mass of the Sun, which is a factor of ten or more larger than other objects found at high redshift.

Anyway, I thought perhaps it might be useful to explain a little bit about what difficulties this observation might pose for the standard “Big Bang” cosmological model. Our general understanding of galaxies form is that gravity gathers cold non-baryonic matter into clumps  into which “ordinary” baryonic material subsequently falls, eventually forming a luminous galaxy forms surrounded by a “halo” of (invisible) dark matter.  Quasars are galaxies in which enough baryonic matter has collected in the centre of the halo to build a supermassive black hole, which powers a short-lived phase of extremely high luminosity.

The key idea behind this picture is that the haloes form by hierarchical clustering: the first to form are small but  merge rapidly  into objects of increasing mass as time goes on. We have a fairly well-established theory of what happens with these haloes – called the Press-Schechter formalism – which allows us to calculate the number-density $N(M,z)$ of objects of a given mass $M$ as a function of redshift $z$. As an aside, it’s interesting to remark that the paper largely responsible for establishing the efficacy of this theory was written by George Efstathiou and Martin Rees in 1988, on the topic of high redshift quasars.

Anyway, this is how the mass function of haloes is predicted to evolve in the standard cosmological model; the different lines show the distribution as a function of redshift for redshifts from 0 (red) to 9 (violet):

Note   that the typical size of a halo increases with decreasing redshift, but it’s only at really high masses where you see a really dramatic effect. The plot is logarithmic, so the number density large mass haloes falls off by several orders of magnitude over the range of redshifts shown. The mass of the black hole responsible for the recently-detected high-redshift quasar is estimated to be about $1.2 \times 10^{10} M_{\odot}$. But how does that relate to the mass of the halo within which it resides? Clearly the dark matter halo has to be more massive than the baryonic material it collects, and therefore more massive than the central black hole, but by how much?

This question is very difficult to answer, as it depends on how luminous the quasar is, how long it lives, what fraction of the baryons in the halo fall into the centre, what efficiency is involved in generating the quasar luminosity, etc.   Efstathiou and Rees argued that to power a quasar with luminosity of order $10^{13} L_{\odot}$ for a time order $10^{8}$ years requires a parent halo of mass about $2\times 10^{11} M_{\odot}$.  Generally, i’s a reasonable back-of-an-envelope estimate that the halo mass would be about a hundred times larger than that of the central black hole so the halo housing this one could be around $10^{12} M_{\odot}$.

You can see from the abundance of such haloes is down by quite a factor at redshift 7 compared to redshift 0 (the present epoch), but the fall-off is even more precipitous for haloes of larger mass than this. We really need to know how abundant such objects are before drawing definitive conclusions, and one object isn’t enough to put a reliable estimate on the general abundance, but with the discovery of this object  it’s certainly getting interesting. Haloes the size of a galaxy cluster, i.e.  $10^{14} M_{\odot}$, are rarer by many orders of magnitude at redshift 7 than at redshift 0 so if anyone ever finds one at this redshift that would really be a shock to many a cosmologist’s  system, as would be the discovery of quasars with such a high mass  at  redshifts significantly higher than seven.

Another thing worth mentioning is that, although there might be a sufficient number of potential haloes to serve as hosts for a quasar, there remains the difficult issue of understanding precisely how the black hole forms and especially how long it takes to do so. This aspect of the process of quasar formation is much more complicated than the halo distribution, so it’s probably on detailed models of  black-hole  growth that this discovery will have the greatest impact in the short term.

## A Grand Design Challenge

Posted in Astrohype, The Universe and Stuff with tags , , , , , on July 20, 2012 by telescoper

While I’m incarcerated at home I thought I might as well make myself useful by passing on an interesting news item I found on the BBC website. This relates to a paper in the latest edition of Nature that reports the discovery of what appears to be a classic “Grand Design” spiral galaxy at a redshift of 2.18. According to the standard big bang cosmology this means that the light we are seeing set out from this object over 10 billion years ago, so the object formed about 3 billion years after the big bang.

I found this image of the object – known to its friends as BX442 – and was blown away by it..

..until I saw the dreaded words “artist’s rendering”. The actual image is somewhat less impressive.

But what’s really interesting about the study reported in Nature are the questions it asks about how this object first into our understanding of spiral galaxy formation. According to the prevailing paradigm, galaxies form hierarchically by progressively merging smaller clumps into bigger ones. The general expectation is that at high redshift – corresponding to earlier stages of the formation process – galaxies are rather clumpy and disturbed; the spiral structure we see in nearby galaxies is rather flimsy and easily disturbed, so it’s quite surprising to see this one. Does BX442 live in an especially quiet environment? Have we seen few high-redshift spirals because they are rare, or because they are hard to find? Answers to these and other questions will only be found by doing systematic surveys to establish the frequency and distribution of objects like this, as well as the details of their internal kinematics.

Quite Interesting.