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Rivers of Gas Flow Around Stars

Sunday, December 28, 2008

NASA - Rivers of Gas Flow Around Stars in New Space Image (12/8/08)
A new image from NASA's Spitzer Space Telescope shows a turbulent star-forming region, where rivers of gas and stellar winds are eroding thickets of dusty material.

The picture provides some of the best examples yet of the ripples of gas, or bow shocks, that can form around stars in choppy cosmic waters.

"The stars are like rocks in a rushing river," said Matt Povich of the University of Wisconsin, Madison. "Powerful winds from the most massive stars at the center of the cloud produce a large flow of expanding gas. This gas then piles up with dust in front of winds from other massive stars that are pushing back against the flow."

Swan nebula (M17) – click for 516×420 image

More: here

Zooming in on an early galaxy

Monday, December 22, 2008

One of the key questions about galaxies concerns the process in which they form. Galaxies are made up of stars, but in general stars do not form in isolation – except for the very first stars in the universe, which we discussed here.

More normally, stars form simultaneously in close proximity to each other as part of the larger process of galaxy formation. But galaxy formation can happen in one of at least two different ways. In the first case, the baryonic matter that will eventually form stars gradually contracts under gravitational force along with the larger mass of dark matter in which it is "trapped". This is a gradual process in which the entire galaxy is formed as the baryonic matter eventually collapses to a state that is dense enough for individual stars to form, much as stars form even today, albeit quite slowly, as in the Milky Way of the present time. (The present rate is only 2 or 3 per year on average.)

Alternatively, in the second case, relatively small groups of stars form within irregular protogalaxies, which then over long periods of time (billions of years) merge with each other to form galaxies as we are familiar with them today.

The first scenario is typically called "monolithic collapse" or formation by "gas accretion". The second is called the "hierarchical" or "merger" scenario.

Of course, both processes can occur. Conceivably some of the large galaxies we can see today were built up from the merger of many smaller galaxies, while others formed more or less in isolation. But the interesting question is whether one or the other of these scenarios was more common in the early days of the universe. (Since at the present time most matter available to feed galaxy growth is already part of a galaxy, most galaxy growth now is by merger.)

In the very early universe, that is for the first 2 or 3 billion years after the big bang (which was about 13.7 billion years ago), there would have been less opportunity for galaxy mergers, so one might expect that more of the galaxies back then formed in isolation rather than in a hierarchical process of mergers.

As explained in this article on redshift, galaxies that formed within the first 3 billion years after the big bang all have redshifts of about 2.2 or more.

Unfortunately, at such redshifts, the objects are at distances of 10.7 billion to more than 13 billion light-years, so it's nearly impossible to make out any details, even with the most powerful existing telescopes, and even using sophisticated technology like adaptive optics. Therefore, there's very little reliable information about the actual morphology of early galaxies, making it impossible at present to obtain enough evidence to decide between the two scenarios.

In particular, it's certainly not possible to discern the overall shape of such a distant galaxy, to determine whether it's an ordinary spiral, a more shapeless elliptical galaxy, or something else, such as a pair of merging galaxies. Morphological information is what one needs in order to discriminate between nice orderly spiral galaxies and galaxies that are distorted due to mergers.

Even though situating a telescope in space, such as the HST, or on the Moon solves the problem of atmospheric distortions, the only way to get better resolution is by using a larger mirror. Telescopes with larger optics are being planned, but fortunately nature itself provides some help even today, albeit in very rare circumstances, as we'll explain in a moment.

Although we can't easily determine the properties of such early galaxies, at least it's possible to find them relatively easily in surveys, without even having to study them spectroscopically. We just discussed the technique for finding these early galaxies by the Lyman break techniques.

It turns out that even though we cannot see the structure of these Lyman-break galaxies directly, we can do spectroscopic measurements that tell us a surprising amount of information about these galaxies. This information can tell us about galaxy rotation, whether there are strong outflows of gas (due to stellar winds or supernova ejecta), and even the approximate rate of star formation in the galaxy.

One thing that spectroscopic data allows astronomers to do is to map "velocity fields" in different parts of a galaxy. That is, we can determine how fast specific parts of the galaxy are moving relative to the galaxy as a whole. For example, in a rotating spiral galaxy, we should detect that the half of the galaxy rotating away from us has an additional redshift beyond the overall redshift of the galaxy, while the other half has a slightly lower redshift. If this pattern varies in a regular way from one end of the galaxy to the other, we can be fairly sure the galaxy is a spiral. On the other hand, if the relative velocities of different parts of the galaxy are irregular or "chaotic", we probably have a galaxy without much regular structure.

However, even this velocity field information we have is at a rather low resolution compared to the size of the galaxy. For historical reasons, astronomers customarily use a length scale called a parsec, or "parallax arcsecond", which is about 3.26 light-years. The resolution, for spectroscopic purposes, of an object at redshift z≳2.2 is about 1300 pc (parsecs), or 4000 light-years, and this is more than half the size of the visible part of a typical Lyman-break galaxy. (Our Milky Way is a lot larger, roughly 100,000 light-years in diameter.)

What can be done about this? Not a whole lot, actually, until we have telescopes with much better resolution – except in certain very special circumstances. Those circumstances exist when another large galaxy or galaxy cluster lies directly in the line of sight between us and the very distant galaxy we're interested in. Then we have what is called a gravitational lens. This works pretty much like an ordinary optical lens, because according to general relativity massive objects are capable of bending light.

A group of astronomers have now examined one example of exactly this circumstance. The distant galaxy in question is named J2135-0102 (a catalog number). It lies at z=3.075. So we see it as it was 2.13 billion years after the big bang. We know that there were already galaxies much less than a billion years after the big bang, so this one isn't that unusual.

Because of this gravitational lens, it has been possible to map the velocity field of J2135-0102 with a resolution of ~120 pc, about 5 times better than possible without the gravitational lens. The abstract of the research paper reveals what can be learned from this:

The formation and assembly of a typical star-forming galaxy at redshift z ≈ 3
Recent studies of galaxies ~2–3 Gyr after the Big Bang have revealed large, rotating disks, similar to those of galaxies today. The existence of well-ordered rotation in galaxies during this peak epoch of cosmic star formation indicates that gas accretion is likely to be the dominant mode by which galaxies grow, because major mergers of galaxies would completely disrupt the observed velocity fields. But poor spatial resolution and sensitivity have hampered this interpretation; such studies have been limited to the largest and most luminous galaxies, which may have fundamentally different modes of assembly from those of more typical galaxies (which are thought to grow into the spheroidal components at the centres of galaxies similar to the Milky Way). Here we report observations of a typical star-forming galaxy at z = 3.07, with a linear resolution of ~100 parsecs. We find a well-ordered compact source in which molecular gas is being converted efficiently into stars, likely to be assembling a spheroidal bulge similar to those seen in spiral galaxies at the present day. The presence of undisrupted rotation may indicate that galaxies such as the Milky Way gain much of their mass by accretion rather than major mergers.

So, the researchers have concluded that in the case of this small, but typical, Lyman-break galaxy, a fairly regular structure is present, and it is more likely due to gas accretion rather than hierarchical assembly.

That's the big news, but the researchers were able to deduce a few other things as well.

For example, from the rotation curve, J2135-0102 appears to have a mass of ~2×109 M (solar masses) within a radius of 1800 pc. (The Milky Way, by comparison, is about 5.8×1011 M.) The galaxy's rate of star formation has also been estimated at 40±5 M per year – much higher (per unit volume) than the Milky Way's rate of only 2 or 3 M per year. This high rate, however, does seem to be typical of the rate in other Lyman-break galaxies that have been studied.

Further reading:

Cosmic Eye Sheds Light On Early Galaxy Formation, Just Two Billion Years After Big Bang (10/8/08) – press release

Cosmic eye telescope used to spot distant galaxy (10/8/08) - news article in the Telegraph (UK)

Daniel P. Stark, A. Mark Swinbank, Richard S. Ellis, Simon Dye, Ian R. Smail, Johan Richard (2008). The formation and assembly of a typical star-forming galaxy at redshift z ≈ 3 Nature, 455 (7214), 775-777 DOI: 10.1038/nature07294


Lyman-break galaxies

Sunday, December 14, 2008

Now that we have a good foundation regarding the concept of redshift (see here), we can turn to a particular type of galaxy that is especially easily identified by redshift.

There's a class of very distant galaxies (like, around 12 billion light-years distant) that have been the subject of a fair amount of research in the past decade or so – because the technology to even find them in the first place is not much older than that.

The class is called "Lyman-break galaxies". The reason for the name will emerge from the following, so just accept it for now.

The first thing we need to consider is how such very distant galaxies can be detected out of everything that's out there, most of which is considerably closer. It isn't actually so hard to get an image of a galaxy that far away. The so-called Hubble Deep Field survey, conducted in 1995, captured some objects as far away as 12.7 billion light years – as they existed only about a billion years after the big bang.

How do we know, roughly, what the distance is to these objects? That, too, isn't so hard. Astronomers just measure the redshift in the light spectrum from the object. This is, roughly, the amount by which well-known emission/absorption spectral lines have been shifted to longer wavelengths.

Because of the redshift-distance relationship discovered by Edwin Hubble, the redshift is a very good indication of the distance of the object. An accurate calculation of distance for a given redshift depends on the values of certain additional parameters. But these values have now been pretty well determined independently. You can experiment with the relationship yourself at this page.

The Hubble Deep Field survey was able to identify objects with a redshift as high as 6. That corresponds to a distance of about 12.7 billion light-years. Of course, objects at that distance are quite faint, so the only ones we can detect were extremely bright when the light we see was emitted. Essentially all we can see at that distance are quasars, which are galaxies with an extremely active, bright nucleus. Ordinary galaxies, especially smaller ones, are generally undetectable at that distance.

However, the Hubble telescope, and a few newer ground-based telescopes, can detect fairly small galaxies at a distance corresponding to z=3 or a little more. These are the Lyman-break galaxies. z=3 corresponds to an object that is about 11.5 billion light-years away. So we are now seeing the object as it was 11.5 billion years ago, about 2.2 billion years after the big bang – about 16% of the present age of the universe.

Now, even though it is possible and relatively straightforward to measure spectra of objects at z=3, it's still tedious and time-consuming. One would like to have an easier way to identify such objects in a survey of thousands of objects in something like the Hubble Deep Field.

As it turns out, there is a clever trick for finding objects with z=3 without even measuring spectra. The trick depends on the fact that even the brightest stars do not emit much light beyond a certain point in the extreme ultraviolet region of the spectrum. The cutoff is around a wavelength of 91 nm (billions of a meter). This is the so-called Lyman limit, which corresponds to the most energetic photons that can be emitted by very hot hydrogen.

The reason for this cutoff lies in the details of the Lyman series of lines in the emission spectrum of atomic hydrogen. Each line in that series corresponds to the energy of a photon which can be emitted when an electron moves to the lowest possible energy level from a higher level. There is a line at the same place in the absorption spectrum, due to an electron being boosted by a photon of the right energy from a lower to a higher level.

Because energy is quantized, the spectrum is not continuous and consists of discrete lines. However, at shorter wavelengths the lines come closer and closer together, until they reach a limit at 91.1267 nm. This is the Lyman limit. It represents the energy required to remove an electron completely from a hydrogen atom, starting at the lowest energy level. A hydrogen atom cannot emit a photon of higher energy, no matter how hot the gas is.

Since stars consist mostly of hydrogen gas, even the hottest stars cannot emit light with photons much more energetic (shorter wavelengths) than the Lyman limit. Since stars do contain other elements, especially helium, very hot stars are capable of radiating photons that are somewhat more energetic, but in general very little of the total energy output is from even farther into the ultraviolet. (Remember that shorter wavelength means higher energy.)

Even for stars that do radiate more energetic photons, such photons can ionize neutral hydrogen atoms, hence they will be absorbed by interstellar or intergalactic clouds of hydrogen. In fact, any photon more energetic than the Lyman limit is likely to be absorbed quickly by a hydrogen atom, because it can completely eject the only electron, with perhaps some energy left over (emitted as a longer wavelength photon).

The result is that there is a rather sharp cutoff (or "break") in a stellar emission spectrum at 91 nm. So normal galaxies whose light comes mostly from stars have the same cutoff. (In a quasar, where much of the radiation is due to matter falling into a supermassive black hole, it's possible for a large proportion of the energy output to consist of photons more energetic than the Lyman limit. Such photons are created, for example, in particle collisions between massive particles accelerated to near the speed of light.)

Bottom line: light from normal galaxies has a sharp cutoff at the 91 nm wavelength, when viewed from a great distance.

Now recall from our redshift discussion that if the redshift is z, then the factor by which wavelength is lengthened is z+1. Therefore, at a redshift of 3, 91 nm photons are shifted to a wavelength of 364 nm, in the near ultraviolet part of the spectrum. A normal star like the sun radiates a lot at this wavelength, in the range often called UV-A. So does a common "black light".

Simple filters are easily made that allow light to pass only in a narrow range of wavelengths. A blue filter, for example, passes photons only around 440-490 nm. If you have a filter that passes only ultraviolet light in a band of wavelengths less than 364 nm, no light at all will get through from objects with z≥3. Objects with z<3 may still be visible through such a filter, since there will still be some shifted photons with wavelengths somewhat less than 364 nm. But some light from a z=3 object could pass through a filter that admits light with wavelengths greater than 364 nm, including a filter for light in the visible range.

Objects with z>3 will have their Lyman limit shifted all the way into the visible part of the spectrum, so they might not be visible even through a blue filter. In fact, if the criterion is objects that don't make it through a blue filter, one can estimate that 3.5≲z≲4.5. At z=6, Lyman limit photons are shifted to 637 nm – red light. A red filter would therefore pass visible light from a z=6 object, but blue or green filters would not.

Astronomers take advantage of this situation by using an ultraviolet filter, together with filters in the visible range (e. g. red, green, and blue). Any object which is visible through all the filters must have z<3, but an object visible through red and blue filters, and not the ultraviolet filter, should have z≈3. By adjusting the short wavelength filter, it's possible to select for objects at higher z in the same way.

The technique isn't foolproof. For example, a galaxy that has few hot stars with strong emission near 91 nm will have most of its light shifted so it doesn't pass through the UV filter, even if z≈2. Indeed, even an ordinary star in our galaxy could pass the test if it has little emission at UV wavelengths. Of course, such a star would be a lot cooler than our sun, and have a negligible redshift besides. So the actual redshift has to be confirmed by spectrometer measurement. However, the procedure is pretty efficient – around 75% of candidate objects actually have z≈3.

Thus it's relatively simple to do a survey for objects around specific redshift values, without going to the trouble of doing a spectroscopic measurement. Galaxies discovered in this way are, naturally enough, called Lyman-break galaxies (LBG for short) .

OK, that's all well and good, but what have we actually discovered about LBGs? There are some things we can learn just by counting them. However, ideally we could image them through telescopes in enough detail to learn something about their size, morphology, rate of star formation, evolution, and so on.

Such questions are easiest to deal with for the galaxies near z=3, because we can detect more of them than at higher redshifts (the more distant ones may be too small or dim to see at all), and because we can see more detail in them than more distant ones.

The first thing to note is that most LBGs will have fairly active star formation going on, because only young, newly-formed stars are hot enough to emit light near 91 nm.

The distribution of such galaxies is somewhat interesting. When the filters are arranged to be able to identify galaxies with 2.4≤z≤3.6, surveys find upwards of 400 candidates. The redshifts of these can then be measured with a spectrometer. There are several peaks in the distribution, around z=2.95, 3.15, and 3.35. By combining the redshift data with spatial direction of each object, actual clusters of galaxies can be identified.

The existence of distinct clustering at less than 2 billion years after the big bang is an indication that the spatial distribution of matter, including dark matter, at that time was already fairly lumpy.

Now, about the galaxies themselves. What are we able to say about them? Well, in terms of the spectra we can measure, the LBGs seem to be much like galaxies near us that have a lot of star-forming activity. (Such galaxies are called starburst galaxies.) The spectra indicate the presence of many very large, hot stars, of spectral class O and B. Such stars are normally rare, because they have very short lives. So if we can detect that there are many such stars, relatively speaking, it means that the rate of forming new stars of this type (and, presumably other types) is fairly high – much higher (in terms of stars per unit volume) than in our galaxy or most nearby galaxies today.

Another example of what can be inferred from the spectra is that the LBGs seem to have a lot of interstellar gas and dust, compared to nearby galaxies with rapid star formation. Uncertainties about just how much dust is there complicates estimation of how many stars might be present. The spectra also suggest that there are large outflows of gas and dust from the LBGs. These outflows are typically driven by very hot, massive stars' stellar winds and supernovae (which are the terminal stages of massive stars). Such characteristics indicate that rapid star formation in LBGs and nearby star-forming galaxies may have different causes.

The most interesting and most fundamental question about galaxy evolution is that of whether a typical galaxy grows in a "monolithic" way, in which most news stars are formed as the mass of baryonic matter gradually contracts gravitationally. Or, on the other hand, whether some stars form in small proto-galaxies, which go on to merge with each other, assembling large galaxies like our own, in the process undergoing bursts of new star formation. It's also possible that both processes occur to significant degrees.

This question is difficult to answer with spectroscopic data. We really need to have direct optical information about the shape ("morphology") of early and evolving galaxies. The problem is that, in most cases, galaxies with z≳2 are too small and faint to image optically with adequate resolution, even with the current generation of sophisticated ground-based telescopes using adaptive optics. That is, we can't see directly whether the early galaxies are amorphous blobs, regular ellipsoids, or picturesque spirals. However, there seem to be relatively few examples with highly elongated shapes, corresponding to a spiral galaxy seen mostly edge-on.

But it's hard to discern morphology reliably even using a space telescope like Hubble. The resolution is such that a single pixel may cover a large part of the object – a few percent of the area, or much more. In a subsequent article I'll discuss an interesting case where we've gotten lucky.

In general, the Hubble finds that LBGs at z≈3 seem to be fairly compact and regular. We still can't necessarily distinguish ellipsoids from spirals. But with z≳4, objects appear to be more diffuse and irregular.

The size of the objects, at least in terms of the parts not too faint to be detectable, seem to be on the order of 50,000 light-years or less – smaller than half the size of our galaxy. But this represents emissions in the ultraviolet part of the spectrum (which we see shifted to the visible part), so the extent of the objects in terms of emitted visible light could well be larger.

Much of our knowledge of LBGs at z≈3 was established over 10 years ago. Since then we have learned somewhat more about the issues of clustering, stellar types and gas/dust content in early galaxies, and galaxy morphology, by a variety of means. We will look at some recent studies about such topics before too long (hopefully).

It's worth noting that the Lyman-break technique can be also be used at smaller and larger values of z. At values of z>3 the Lyman-break will be shifted all the way into the visible part of the spectrum, while for z<3, the Lyman-break will occur at shorter UV wavelengths. All these can be handled by proper choice of filters.

For example, for z up to about 6, around 1 billion years after the big bang, we have, from 2003, a study that shows relatively few bright galaxies. Since this was in the period of reionization, which required many hot, bright stars, there must have been many more galaxies around that were just too small to be detected.

New insight into the cosmic renaissance epoch (8/21/03)
In particular, the astronomers conclude on the basis of their unique data that there were considerably fewer luminous galaxies in the Universe at this early stage than 500 million years later.

There must therefore be many less luminous galaxies in the region of space that they studied, too faint to be detected in this study. It must be those still unidentified galaxies that emit the majority of the energetic photons needed to ionise the hydrogen in the Universe at that particularly epoch.

Ironically, it was a little later that the Lyman-break technique was applied to closer objects, z≈1. In 2006 we have:

Ubiquitous Galaxies Discovered In The Early Universe (3/9/06)
For the first time, Denis Burgarella and his team have been able to detect less distant galaxies via the Lyman-break technique. The team collected data from various origins: UV data from the NASA GALEX satellite, infrared data from the SPITZER satellite, and data in the visible range at ESO telescopes. From these data, they selected about 300 galaxies showing a far-UV disappearance. These galaxies have a redshift ranging from 0.9 to 1.3, that is, they are observed at a moment when the Universe had less than half of its current age. ...

From their observations of this sample, the team also inferred various information about these galaxies. Combining UV and infrared measurements makes it possible to determine the formation rate for stars in these distant galaxies for the first time. Stars form there very actively, at a rate of a few hundred to one thousand stars per year (only a few stars currently form in our Galaxy each year). The team also studied their morphology, and show that most of them are spiral galaxies. Up to now, distant galaxies were believed to be mainly interacting galaxies, with irregular and complex shapes. Denis Burgarella and his colleagues have now shown that the galaxies in their sample, seen when the Universe had about 40% of its current age, have regular shapes, similar to present-day galaxies like ours.

Further reading:

Lyman-Break Galaxies

Mapping the Distant Universe

The Properties of Lyman-Break Galazies at z∼3 – excellent article

Searches for high-redshift galaxies


Warning of nut allergy 'hysteria'

Saturday, December 13, 2008

Warning of nut allergy 'hysteria'
Measures to protect children with nut allergies are becoming increasingly absurd and hysterical, say experts.

A peanut on the floor of a US school bus recently led to evacuation and decontamination for fear it might have affected the 10-year-old passengers.

Such extreme steps to reduce exposure to nuts are not isolated and are fuelling fear and anxiety, reports the British Medical Journal Online.

A UK allergy expert said a similar "epidemic" was present in Britain. ...

[Professor Nicolas Christakis, a professor of medical sociology at Harvard Medical School] said these responses were extreme and had many of the hallmarks of mass psychogenic illness (MPI), previously known as epidemic hysteria.

Often seen occurring in small towns, schools and other institutions, outbreaks of MPI involve healthy people in a flow of anxiety, most often triggered by a fear of contamination.

I think Professor Christakis is so right about this. And I think his observation applies to the way some people react to many things they don't understand, such as the use of pheromones to control destructive insect infestations. See here.

It's very sad, too, that this kind of ignorance is often spread by "journalists" who seem to deliberately ignore important distinctions they ought to understand, to say nothing of the underlying science. As I discussed in my item linked above.

Further reading:

Fear of nuts creating hysteria of epidemic proportions (12/10/08) – press release

Why are U. S. politicians so corrupt?

Wednesday, December 10, 2008

Because voters elect them based on their looks rather than their ethics. See here for more.


Saturday, December 6, 2008

There are some recent very interesting research results about very distant early galaxies that I want to discuss. Understanding these results depends on knowing a few basic concepts that one learns in any modern introduction to astronomy. I expect that most readers here know these concepts very well. But just to make sure that the necessary details are understood by anyone who happens along, I want to provide a tutorial for those who might need a refresher on the ideas.

Readers who are confident about these basics won't find anything new here except, perhaps, for the precise mathematical definition of redshift stated at the very end.

Fundamental to almost any science is the process of measurement. In astronomy, perhaps the most important quantity that can be measured through an optical telescope is brightness. But observed, measurable brightness all by itself is not too useful, because what's more important for an object such as a distant star or galaxy is not the observed brightness, but instead the intrinsic brightness – the amount of light actually emitted by the object, not what we are able to observe.

Since observed brightness falls off as the square of the distance, we can compute the intrinsic brightness from the observed brightness if we know the distance. Unfortunately, for most astronomical objects outside the solar system, there's no simple way to determine the distance. We can't just do it with a yardstick. There are a few indirect techniques for measuring astronomical distance, but most of these fail for things that are really distant, like most galaxies.

There is, however, one thing that's relatively easy to measure with a telescope, whether it's of the optical kind or one that works in some other part of the electromagnetic spectrum, like a radio telescope. And that is the relative strength of the electromagnetic signal at different wavelengths in the spectrum. This is what a spectrometer (literally, an instrument for measuring a spectrum) does in the optical part of the spectrum.

In a type of luminous object called (paradoxically) a "black body", the signal strength of electromagnetic radiation varies continuously across the spectrum in a known way, without sharp peaks or dips. But normally the signal strength from a star or a cloud of interstellar gas does not vary smoothly. Instead, there are usually particular wavelengths at which the signal is especially stronger or weaker than at most adjacent wavelengths. This is because of the way a hot gas of atoms or molecules emits or absorbs radiation unusually strongly at certain particular wavelengths.

These special wavelengths are the emission or absorption lines in the spectrum. When we know the kind of atom or molecule involved, these wavelengths can be measured in a laboratory, and each type of atom or molecule has its own characteristic "signature" of lines. If a gas of these atoms or molecules is emitting light, we get emission lines as peaks in the spectrum. And if a continuous spectrum of light passes through the gas (when it is cool enough not to emit light), we find absorption lines at the same wavelengths.

The most abundant elements in the universe are hydrogen and helium. The spectral signatures from these two gases are quite well known. But when we measure spectra from (for example) distant stars, we find slight shifts in where the lines are from where they "ought" to be. This shift is known as the Doppler shift, and it tells us precisely how fast the object is moving towards or away from us. (For very distant objects, the same shift occurs, but not for the usual reason, as we will explain later.) In most cases, especially for distant objects like galaxies, the shift is towards longer wavelengths. For visible light, that shift is in the direction of the red end of the visible spectrum, so it's called a "redshift".

The remarkable thing, which has been known for less than 100 years, is that light from very distant objects like galaxies is almost always shifted in the red direction, meaning that most such objects are moving away from us. The amount of the shift is easily computed to be proportional to the speed of the object along the line of sight. And what has been found that is even more remarkable than the existence of the shift in (usually) the red direction is that the amount of the shift (and hence the speed of the movement) varies directly with the actual distance to the object for most remote objects.

Because of the existence of this velocity-distance relationship, it becomes possible to infer the distance of an object from a measurement of its spectrum. This is why redshift is so important in astronomy. So let's have a look at the history of how this surprising, unexpected relationship was discovered.

Edwin Hubble, in the early 1920s, was the astronomer most responsible for the discovery of the velocity-distance relationship, and hence the first to understand that the universe as a whole is expanding.

Several other astronomers around 1920 recognized that shift of spectral lines from a galaxy might be interpreted as being the result of relative motion between the Earth and the galaxy. A blue shift would mean the object was moving in Earth's direction, while a red shift would mean it was moving away. Other interpretations of the red shift are possible. Indeed, some astronomers around 1920 (and even today) preferred other interpretations. But the interpretation of the red shift of spectra as a result of relative velocity has become accepted as the best way to interpret vast amounts of observational data.

In 1920 galaxies were not known to be enormous collections of stars like the Milky Way, and lying outside it. They were then just thought of as fuzzy stars – nebulae (from the Latin for "clouds"). But the interpretation of spectral redshift as due to relative velocity, followed by Hubble's discovery of a correlation between this redshift and actual distance, showed convincingly that galaxies had to be so remote that they could not be part of the Milky Way.

Naturally, the correlation between redshift (hence apparent velocity) and distance, which at the time could be stated as a simple proportion, became known as Hubble's Law. And the constant of proportionality became known as the "Hubble constant". (The relationship was actually a little more complicated, as we'll explain shortly.)

Hubble was able to derive an independent estimate of distance from Earth to relatively nearby galaxies by identifying stars in those galaxies whose intrinsic brightness could be accurately estimated. These stars are known as Cepheid variables. In this type of variable star, it was known that the regular period in which the brightness changes is directly related to the maximum brightness of the star. Thus a measurement of the period of such a star in any galaxy where the star could be identified indicates what its actual brightness is, and from its apparent brightness as seen from Earth, the actual distance can be determined.

Because Hubble could estimate in this way how far away a few galaxies were, he was able to determine that they were much too far away to actually lie within the Milky Way – contrary to what had been generally assumed up to that time. Indeed, the general supposition then was that the Milky Way comprised the entire universe, so Hubble's discovery was a big deal.

Hubble's Law simply states that the amount of redshift of a galaxy was proportional to its distance. The constant of proportionality, usually denoted by H (guess why) is called the "Hubble constant".

As it turns out, Hubble underestimated the actual distance of the galaxies he studied by nearly a factor of 10, due to errors in measuring the brightness of distant Cepheids. Consequently, the initial value figured for the Hubble constant was also off by the same factor.

This numerical problem was corrected soon enough. But it turns out that there are a couple of conceptual problems as well with the law. These became apparent before long when cosmologists tried to apply the equations of Einstein's general relativity theory to describing the expansion of the universe. Surprisingly enough, a fairly simple equation, called the Friedmann equation, first proposed by Alexander Friedmann in 1922, does a very good job.

The story of the Friedmann equation itself is quite interesting, but a little off topic right now. However, as cosmologists now understand the equation and use it to model the universe, a couple things in the conceptual understanding of Hubble's law are changed from Hubble's original idea. In the first place, Hubble's constant isn't in fact a constant at all, so cosmologists now prefer to call it "Hubble's parameter". It varies in a known way for objects that are very far apart, like billions of light years. But for relatively nearby galaxies it is pretty close to constant (the value is about 71, in case you're wondering).

The second conceptual point is that cosmological redshift is now understood to be due to the actual expansion of space itself, rather than the Doppler shift it was originally presumed to be. A classical Doppler shift results because the peak-to-peak distance of a periodic wave emitted by an object moving away from the observer is slightly longer than it would be if there were no relative motion, precisely because of the relative motion. The distance is increased by how far the source of the wave moves in the time between two peaks.

Now that cosmologists conceive of space itself as actually expanding with time, the redshift that a photon undergoes in traveling a long distance between points A and B results from the expansion of space that occurs in the time it takes for the photon to travel from A to B. The wavelength itself is stretched along with space.

Nevertheless, there is still a relatively simple, monotonic, though nonlinear, relationship between the distance of a remote galaxy and its observed redshift. Converting from a redshift to distance involves a variety of assumptions about certain parameters, such as the Hubble parameter and the curvature (if any) of space on a large scale. But these parameters have been measured in a variety of independent ways so that we now have fairly reliable estimates of their values. (You can go here if you want to play with this relationship yourself.)

The actual distances of remote objects are rather difficult (if not impossible) to determine with any accuracy, while redshift is pretty easy to measure with spectrometers. Consequently, astronomers customarily think of distance, which isn't directly observable, in terms of spectral redshift, which is. In fact, standard operating procedure is to report the redshift rather than the inferred distance.

The formal definition of redshift, denoted by z, is
z = (λ0 - λe) / λe
Here λ0 is the measured wavelength of a photon, while λe is the original wavelength of the photo when it was emitted.

For example, if the wavelength is exactly doubled, λ0 = 2λe, so z=1. If you rearrange terms in the definition of z, you get λ0 = (z+1)λe. That is, z+1 is the actual factor by which the wavelength is increased for any given z. (If this seems confusing, just remember that z=0 means no shift at all, so the factor of expansion is simply 1.)

In subsequent articles where I will discuss recent research results, there will be a lot of talk of redshift. The simple equation just shown can then be used to compare the change in photon wavelengths. A table or calculation such as noted above can be used to infer the distance of the object in question. And from this distance, one then knows how long ago the object emitted the light we see now, hence how long this time was after the big bang occurred (which is now estimated to be about 13.7 billion years ago).


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