Which redshift is used to determine the Hubbleconstant?

Which redshift is used to determine the Hubbleconstant?

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I think they measure cosmological redshift to use in the Law of Hubble-Lemaître together with the distance to calculate $H_0$. Is this correct, or do they use Doppler shift (too)?

$H_0$ indicates how fast the universe is expanding, so I find it logical that we measure cosmological redshift. But the galaxies are receding (due to the Hubble Flow) away from us, so do they gain an additional Doppler shift?

The term "Hubble flow" refers to the homologous expansion of space and the resulting recession of all galaxies from each other (if they're not close enough to be gravitationally bound). This effect causes the "cosmological redshift", i.e. the redshift that light from distant galaxies attain as it travels through space.

In addition to this motion away from each other, galaxies have a so-called peculiar velocity, i.e. a motion through space. This motion adds an additional Doppler shift to the cosmological redshift, either to larger or smaller wavelengths, depending on the direction.

Whether or not you see these two types of redshift as fundamentally different, is not trivial I think. In most textbooks, they are described as two different things, the former having to do with the dynamics of the fabric of space, and the latter having to do with motions of emitters and observers. But in fact it may not be so different. For instance the Welsh cosmologist Geraint Lewis argues that, in some sense, the cosmological redshift can be interpreted as the sum of infinitely many infinitesimally small Doppler shift (Lewis 2016). On the other hand, the American physicist Sean Carroll argues that the notion of expanding space is nevertheless an extremely useful concept (Carroll 2008).

Ep. 279 Hubble Constant

When Edwin Hubble observed that distant galaxies are speeding away from us in all directions, he discovered the reality that we live in an expanding Universe. Hubble worked to calculate exactly how fast this expansion is happening, creating the Hubble constant – which astronomers continue to refine and reference in their research.

Show Notes

Transcript: The Hubble Constant

Fraser: Welcome to Astronomy Cast, our weekly facts-based journey through the Cosmos, where we help you understand not only what we know, but how we know what we know. My name is Fraser Cain I’m the publisher of Universe Today, and with me is Dr. Pamela Gay, a professor at Southern Illinois University-Edwardsville. Hi, Pamela. How are you doing?

Pamela: I’m doing well. How are you doing, Fraser?

Fraser: Good. Global warming is treating us really well here on the west coast today. It’s beautiful! I’m wearing like shorts and a t-shirt in the middle of November. We’re recording this episode a little late, so it’s almost December and the weather is beautiful. So yeah, it’s great!

Pamela: We have the exact same thing here. I was riding my horse outside in short sleeves yesterday and me and the horse were both sweaty, and that doesn’t normally happen outside this…yeah, we’re destroying the environment in ways that allow t-shirts in November.

Fraser: Yeah. Thanks, global warming! So as always we’re recording this episode of Astronomy Cast as a live Google plus hang-out, and if you want to watch us record live (trust me it’s so much better!),then what you do is you circle Astronomy Cast on Google plus, and then you’ll get an event notification in your stream, in your calendar of when we’re going to record our next episode and then you can just watch us live and ask your questions and stick around and interact with the fans and it’s super-fun. So it’s a really great way — if you really enjoy Astronomy Cast, this is a great way to take it to the next level. Alright, let’s rock!

Fraser: So when Edwin Hubble observed that distant galaxies are speeding away from us in all directions, he discovered the reality that we live in an expanding universe. Hubble worked to calculate exactly how fast this expansion is happening creating the Hubble constant, which astronomers continue to refine and reference in their research today. So, Pamela, I guess the first step is to go back…now we’ve talked about Hubble and we’ve talked about the Big Bang, but I think it would be great to go back for a second and talk about that discovery that Hubble made as part of his research. So what was he looking for?

Pamela: Well, so the interesting thing is I need to take you back a step, actually, because it wasn’t just his discovery. It all started with a guy with an awesome name who’s been forgotten largely by history, whose name is Vesto Slipher. He was working at Lowell Observatory in Arizona, and he was a spectrometrist. He took images of galaxies that were not the type of pretty spiral or elliptical images that you see on astrophotography websites, but rather he took the light, put it through a thin slit, and I believe a prism, and spread that light out into a rainbow that he imaged, called a spectrum, and we’ve talked about those in other episodes, and when he looked at these spectrums, he was able to use Doppler shifting to measure the velocity of the galaxies, and the expectation was that the galaxies would have a random distribution of motions — that some would be moving towards us, some would be moving away from us, and what he found was the majority of the nearby galaxies, while there are a couple moving toward us like Andromeda, the majority of them are moving away, and that just completely blew his mind, and this was back in a time when we didn’t know galaxies were galaxies, we just called them spiral nebula. And this was like all kinds of confusing.

Fraser: I mentioned this, that I’ve got an old astronomy book that’s like from the 1920s and if you look through it, it has the Andromeda nebula, and it has these other nebulae, and it’s just so cool to see in fairly recent history that this was still their idea. Now one thing you mentioned the Doppler shifting, the red-shifting the blue-shifting…so what exactly was going on there with the light from these galaxies?

Pamela: So when an object is moving away from you, its light will get shifted toward the red. If it’s sound, the sound will get shifted to longer, deeper wavelength noises, so it will go from sounding like a trumpet to sounding like a tuba basically. We’re used to experiencing this with fire trucks. We hear them the pitch gets more high-pitched as it’s coming towards us, as it moves away, we hear this low-pitched noise. Well, light does the exact same thing, more or less, and so when we see galaxies moving away from us, light from specific spectra lines that we know the exact color they should be, it gets shifted, so if we were to use…like we use Gary Gonella’s h-alpha filter every virtual star parties on Sunday nights and we see these beautiful nebula. Well, these beautiful nebulae that show up so nicely through his h-alpha filter that only allows the light from that one transition from hydrogen to pass through, well, if those nebulae were moving away from us at great velocities, their light would be a completely different color, and they’d disappear from the images.

Fraser: And so is that one of the filters that astronomers use is to look at this at that wavelength?

Pamela: So what we actually do with galaxies is we don’t constrain ourselves to just one wavelength generally. First of all galaxies are kind of faint, doing that you’re not going to get very much light in, so what we do…and we also don’t know what velocity they’re at, so if you don’t know what velocity they’re at, using a narrow gun filter isn’t useful, so we take all the light and spread all the light out, and we’ll look at as much of the wavelength as our individual instrument allows. Some of the best instruments out there allow you to get all the way from infrared to low ultraviolet spread out in this continual spectrum where you can see dips created from magnesium, you can see dips created from the different hydrogen lines. We see all sorts of different things as we look at these galaxies – calcium lines… And we use all these different lines to figure out the shift created by the velocity of the galaxies.

Fraser: So Slipher, which is the best name ever I think, had sort of laid the groundwork for this next discovery by Hubble, right?

Pamela: Right, so the thing with what Vesto Slipher did was he couldn’t actually measure the distances to the galaxies, so all he knew was a bunch — a statistically improbable number — of the galaxies that he looked at were shifted so that they were moving away from us they were red-shifted. Well, what Hubble was able to do was he took deep, deep images, ones that allowed him to see individual stars, that allowed him to carefully resolve faint objects in many of these galaxies, and he took a time series of them so that he was able to identify individual stars called Cepheid variables. They change in brightness over time, and as they change in brightness, they do it in a very systematic way, so that one that changes over one period of time…we know it gives off one amount of light. One that changes over a very different period of time, we know it gives a different amount of light, and so he was able to use this beating of the pulsating variable stars to say, “I know how much light this star is actually giving off, more or less.” That was part of the confusion, but I know, more or less, how much light is actually given off. I can measure how much light I see, and this allows me to calculate the distance the same way when we see a motorcycle headlight, we know roughly how bright that should be and we can gauge the distance to the motorcycle based on how bright the headlight appears.

Fraser: And what did he discover? He was able to find these stars, these standard candles in all these galaxies around him? He’s able to accurately measure the distance, which is great.

Pamela: Accurately is a stretch.

Fraser: He was able to in order of magnitude…

Pamela: I’ll go with that — with large error bars.

Fraser: He was able to “measure-ish” the distance to these galaxies, and what did he discover?

Pamela: Well, what he found… and the problem with his accuracy, he could tell the relative distances, but he couldn’t tell the actual distances, so he was able to say, “This system’s farther away than this system,” and when he made those measurements, he realized those systems that are further away are moving significantly faster than the ones that are nearby, and that is consistent with looking at an expanding universe. If you imagine yourself in a theater and all the chairs in the theater are moving apart from one another a centimeter per movie, well, at the end of one movie, the chair next to you is one centimeter away, the chair next to it is two additional centimeters away, and each movie, well, that one that’s two chairs away, two movies later it’s going to be four centimeters away, three movies later…this just keeps increasing as you see that more distant chair appears to be moving faster. Well, it’s not that it’s moving faster, it’s that the spaces between the chairs is increasing at a constant rate that makes things that are further away appear to be moving faster.

Fraser: Right. Right. OK. And so he makes this amazing discovery, you know, to calculate these distances and this velocity, and sort of stumbles upon one of the most important discoveries in all of science.

Pamela: And there had been people who predicted this might be the case. Einstein’s theories of General Relativity and Special Relativity, when he chewed through all the numbers, when he examined our universe in detail, one of the things that came out of relativity is the idea that when you do the calculus of space/time, there can be a constant involved that makes our universe Steady State, but at the same time if that constant doesn’t have the exact right value, our universe is either expanding apart or collapsing in on itself. It’s not a static place, so Einstein originally tried to use his cosmological constant to stay the universe, but there were folks like Lamantre who said, “No, no, no! Our universe could be expanding!” and put these ideas forward, and so the theories were there that when Hubble put together the pieces of Vesto Slipher’s spectra and his own photometry of the variable stars, when all those pieces came together, there was a complete picture in one very special moment in history.

Fraser: And so they had…he came to this…I mean, did he actually come to this conclusion and say, “OK, so we live in an expanding universe therefore, the universe had to have come from a single point in the ancient past?”

Pamela: That wasn’t in the original paper. Now, I clearly was not alive when this was happening, so I can’t say what people were arguing at the conferences, I can’t say what letters were getting floated back and forth, but in the literature, that original plot of distance vs. velocity lays out the case for an expanding universe. Now, the two theories that emerged over time was the notion of a Big Bang, but also what’s called the Steady State model of the universe. This is a model that we now know isn’t true, that observational data doesn’t support it, but it took a while for us to realize that, and the Steady State model basically says that there’s new stuff coming into existence that’s pushing the universe apart, so this is the idea of that movie theater that has stuff coming into it vs. the stuff in the theater expanding, so you can imagine ooze pushing the chairs apart vs. just what already exists pushing the chair apart.

Fraser: New chairs…new chairs pushing the chairs apart.

Fraser: So specifically what did he calculate this expansion to be? How did he describe this?

Pamela: It’s just a plot! That’s the awesome thing is this is a very clean, simple-to-look-at result with a lot of error bars in the initial stuff. It was just a plot of distance vs. velocity showing as distance increases, velocity increases. Now, it was noisy, it was ugly, we were still…we only had fairly small telescopes by today’s standards, we couldn’t see very great distances, he ran into problems when he started observing galaxies in the Virgo cluster because that’s a gravitationally-bound system. Galaxies in an individual cluster — that cluster isn’t expanding, it’s the separation between the clusters is expanding.

Fraser: Right. We get that question a lot, right? Which is, “Is the actual galaxies expanding? Are the solar systems expanding? Are we expanding?” I know you guys have Thanksgiving shortly, so…so you might be expanding.

Pamela: I’m not going to answer the question “Are we expanding?” in general. In the specific case of the cosmological constant, no, it bears no effect on the human body.

Fraser: Right, it’s about the…I guess before the concept of dark energy, it’s really this, you know, you have two cars driving away from each other, and those two cars are going to be driving away from each other, and they’re going to be moving apart, they’re not going to be…the cars themselves aren’t going to be expanding as well.

Pamela: But you have to be careful. It’s not the objects that are moving it’s the space that’s expanding.

Fraser: Right. The road is growing with the cars on top of it.

Pamela: The road is growing, and they have their emergency brakes on. They have no velocity.

Fraser: Yeah. They’re stopped. But how did he actually describe this? I mean, you say it’s a plot over time, but like, I know there’s like a certain number of megaparsecs per…

Pamela: Well, back then we were still trying to figure all that stuff out. So the poor guy in his initial measurements…we had problems we didn’t exactly know how to calibrate the distance to Cepheid variable stars, so when your meter stick is severely broken, you end up with the wrong number. So he originally ended up with the universe expanding at roughly 500 km/second/megaparsec, and what that says is every million parsecs of space…

Fraser: How big is a million parsecs of space?

Pamela: So there’s roughly three-ish light years per parsec, so…

Fraser: Like 3 million light years, so distance kind of here to Andromeda-ish because Andromeda’s like 2 million light years away from here.

Pamela: Something…Yeah, but then we’re going to mix our units and add km/second in there just to throw everything off, so it’s not that huge an expansion given the size of our universe, but the thing is it can be measured. Now, the problem is that in order to measure it accurately, you need to be able to measure distances accurately, and that’s where everything falls apart. There we’re trying…none of the variable stars are close enough that we can use parallax to measure them, so we’ve had to use all sorts of broken ladders to build our way out to the nearby universe, and we did an entire episode on distance scales, but…

Fraser: Yeah. So 500 km/sec/megaparsec, and so that means that if…

Fraser: He was wrong, but that was his initial calculation. So in other words if an object is one megaparsec away, then it’s going to be moving at 500 km/second.

Fraser: And if it’s 2 megaparsecs away, then it’s moving away from us at 1000 km/second.

Pamela: The space between us is expanding at…

Fraser: Yes, at a rate to make that other object appear as if it is moving by 1000 km/sec, and if we’re 3 megaparsecs, 5 megaparsecs, 10 megaparsecs away…OK. Great, so he did these initial calculations and they were mind-bending, but not super-accurate, right? But I know that astronomers have been working on this number like crazy, and in fact, we still report on it, we still write articles, astronomers refine…

Pamela: Between 66 and 74…

Fraser: 66 and 74 km/sec/megaparsec. Right, which is sort of almost like a factor of 10 less than he originally anticipated.

Pamela: And what’s kind of awesome about this number is for decades there was this horrible cat-and-dog argument between Allan Sandage and Gérard de Vaucouleurs about whether or not it was 50 km/sec/megaparsec, or 100 km/sec/megaparsec, and it was just this entire community — people picked sides, and they mocked each other, and it was ugly, and I remember as an undergrad one of my professors he was not going to pick sides, he simply said use 100 it’s easier. Move on.

Fraser: Right, because it doesn’t really matter because they’re big numbers and chances are everybody’s wrong, so it doesn’t matter.

Pamela: And it was only after Gérard de Vaucouleurs died that people were finally able to start settling down on the answer. The kind of crazy thing is the answer turned out to be roughly 70 – midway between 50 and 100, so both dudes were wrong, and unfortunately, like so many arguments in astronomy, the real work was only done after one of the people who made it a heated, contentious ordeal had passed away, and now we know the Hubble key project has done awesome work trying to refine our distance scale with Cepheids, trying to figure out the supernovae problem, and we’re getting there. And what’s awesome (and we’ve talked about this in other episodes) is there are so many different lines of evidence that we’re able to look at — from using the Wilkinson Microwave and Isotropy Probe (WMAP) to look at cosmological values to measuring supernovae to…we still use Cepheids to ground us.

Fraser: Now, I know – and this has always baffled me, and I tend to sort of avoid it when I write articles, which is that astronomers reference especially in their research papers the distance to objects using a “zed” value, a redshift value, zed=5 or something like that. What on earth does that mean?

Pamela: When we started this conversation, we talked about how Vesto Slipher had measured the Doppler shifting, the red-shifting of the galaxies, and the mathematical way of translating this is if you take the wavelength of the light that you observe, and you subtract off the wavelength of where you expected the light to be, and then divide all of that by where you expected the light to be, this gives you a fractional offset, basically, and that value mathematically is called “zed,” “z” — pick a term.

Fraser: For you Americans out there you could say “z” sure.

Pamela: Redshift is probably the best way to confuse fewer people.

Pamela: And so this redshift value is just the fractional shifting of the wavelength of the light. It’s what you can observe. To get beyond this fractional shifting of the light requires you to make assumptions about space and time. It requires you to make assumption about how the universe is expanding, so when we work to translate that fractional observed shift in the color, we have to say, “OK, so what value of h [missing audio] are we going to accept? What mathematical value for the density of mass in the universe are we going to accept?” The omega value…and it’s only once you make assumptions about those values that you can translate that redshift into a distance. Now, the easy way to think of it is anything greater than 1 is really far away. What’s kind of amusing to me is when I started grad school, I observed the high redshift universe, I looked at things that are redshift of 1.2, 1.3, and a galaxy at a redshift of 1 has a look-back time of roughly 7.5 to 8 billion years…

Pamela: …depending on how you look at it, so you’re looking back to more than half the age of our universe.

Fraser: Right. I mean, compare that, as I mentioned, to Andromeda at 2½ million light years away, you’re only looking back 2½ million years ago. Other objects in our supercluster, 10 to 50 million years old, so you’re seeing galaxies that are 6 billion, 8 billion light years away, and that’s just…that’s considered a low redshift?

Pamela: Well, so z of 1 is now considered a moderate to low redshift. It all depends on whom you’re talking to. Supernovae people…they’re starting to push out further than that, but the majority of what we see is in that z=1, but it’s kind of crazy the way we can never get all the way back to the beginning. So the high redshift things that we look at, they’re at a redshift of order of 4. Some of the highest things that we’ve looked at are estimated to have redshifts of 6, and this is where we start looking at light that came from more than 12 billion years ago.

Fraser: Yeah, I mean, galaxies are being turned up now using, like, gravity lensing that are only 500 million years after the Big Bang.

Pamela: Right. And so > 4 means that you’re looking at the first one to two billion years of our universe, and it’s been amazing to me to see how our definition of high redshift observing has changed from z > 1 is high redshift to z > 4 is high redshift, and 1 is nearby. As our technology has increased, as we’ve pushed out further, it’s like with racecars. The definition of a high speed racecar has changed since the 1920s. Well, now our definition of observing the high redshift universe has changed as well.

Fraser: And there are some calculators out there, I know [missing audio] that can convert that sort of thing, so you can put in the z ratio and you’ll get a …

Pamela: The best one out there is Ned Wright’s. He’s at UCLA — just type in cosmological calculator, it will take you to his javascript page, it has perfectly reasonable default values. I know lots of scientists who…I remember the first time I had to calculate this stuff, I sat there and I wanted to cry after they discovered what we’re talking about in our next episode, which is the cosmological constant, and Ned Wright just programmed all of it so no grad student ever needs to cry over doing this again.

Fraser: Right. You do it once, and then you use his calculator.

Pamela: Yes. Yes. You prove you can do it, and then you move on with life. It’s like long division.

Fraser: So as I mentioned, you know we’re still reporting on stories and we did one, like, must have been like six months ago about “Astronomers Narrow In, Decide, Calculate the Most Accurate Measurement for the Expansion of the Universe Ever,” and then, you know that number you just quoted, so you know… how big are the error bars now? How much farther do they have to go to really get to the bottom of this?

Pamela: It depends on which way that you look. So some of them have 15% error, some of them have 5% error, but what’s awesome is that all of these overlapping error bars are, in fact, overlapping, so when you put all of the pieces together, it looks like we’re probably good to +/- three km/sec/megaparsec, which is kind of awesome.

Fraser: It’s pretty amazing. Hubble would really appreciate that precision.

Fraser: Since he was probably off by a factor of 10, but…cool! Alright, cool! And so as you mentioned, next up we’re going to talk about the cosmological constant, which is Einstein’s biggest blunder. Way to go, Einstein.

Pamela: Blunder and discovery.

Fraser: Blunder and discovery. Well, thank you very much, Pamela.

Pamela: OK, I’ll talk to you later.

Fraser: Talk to you next week. Bye.

This transcript is not an exact match to the audio file. It has been edited for clarity.

Distance and Red Shift of stars

Hi PhilJ,
Welcome to these Forums and keep asking questions.

The "tables for the distance against red shift of stars" is in fact the Hubble parameter H, which for nearby galaxies is H = v.d .

A modern evaluation of H is 71 km/sec/Megaparsec.

The stars concerned are in other galaxies because those in our own galaxy have their own velocities as they orbit around the galactic centre and it is generally thought that our galaxy does not expand with the universe.

Galaxies also have their own peculiar motions and so there is a variation around the value of H which becomes less significant at greater distances.

The Hubble relationship is one of the last rungs in what is known as the Distance Ladder, which you can find more about here.

300 light years). Beyond that, the parallax angle becomes too small for our instruments to resolve. However, the upcoming Space Interferometry Mission (SIM) is going to be able to do microarcsecond astrometry, which means that it could, in principle, measure the distance to anything in the galaxy (within its limiting magnitude, of course).

Beyond the distances that can be measured by parallax, we must use "secondary" methods. This includes the standard candles that Chronos mentioned. The reason they should be thought of as secondary (or, in some cases, tertiary or higher) is that they must be calibrated by some other distance-finding method. That is, we don't know the intrinsic brightness of a standard candle unless we can measure the distance and flux to one nearby. This means, unfortunately, that higher-order distance-finding methods carry with them the systematic errors of the lower-order ones.

The standard candle that can take us furthest (so far) is the Type Ia supernova. In principle, this can be used to measure the Hubble constant and normalize the distance-redshift relationship that is the subject of this thread. However, it turns out that Cepheids are actually better for this job. Why? Well, the basic reason is that we can get better statistics with Cepheids -- there aren't enough supernovae occurring nearby. However, supernovae are much brighter than Cepheids, so they can take us to much larger distance and are much better for measuring the higher-order changes in the distance-redshift relationship. This is why we were able to detect the acceleration of the universe with them.

To expand upon SpaceTiger's excellent post .

The best trigonometric parallaxes, to date, have been determined by the HIPPARCOS mission, whose" says the "Median precision of parallaxes (Hp < 9 mag)" is 0.97mas.

In addition to SIM," [Broken] will provide a substantially increased 'parallax' view of most of the Milky Way galaxy, at least for stars which are bright enough for it to 'see' (which will be an awful lot, down to Vmag

There are a number of means by which distance can be measured, circumventing the 'distance ladder', with all its attendant cascading of standards (and uncertainties). For example, gravitational lensing. Unfortunately, these methods all have their own challenges (and errors), limitations, etc. To date, the ladder built on standard candles remains pretty much the most accurate.


So far we have looked at evidence for the expanding Universe. Not until the early 20th century did scientists realise that 'spiral nebula' were actually different galaxies and not part of ours. Georges Lemaître was one of the most prominent of 20th century astronomers and Edwin Hubble developed his theories.

Hubble proposed there was a relationship between the distance to galaxies to their redshift (or receding velocity). In other words how fast a galaxy moved was in proportion to its distance.

This is Hubble's Law - v=H0D

v = recession velocity
H0 = Hubble constant
D = distance to galaxy (mega parsec - Mpc)

Velocity is taken by measuring the galaxy over a period of time

We can calculate the distance to nearby galaxies by knowing their apparent and absolute luminosity.

To do this Hubble needed a constant of proportionality - the Hubble constant.

This is a special measurement to astronomers, as it means they can measure the age of the Universe.

Different measurements have been made, notably by the Hubble Space Telescope (HST) and Wilkinson Microwave Anisotropy Probe (WMAP). Most past measurements have been values between 50 and 100 Mpc. HST measured 74.2 ± 3.6 (km/s)/Mpc in 2009.

If the number is too high we find stars older than the Universe, and if it is too low there is not enough matter in the Universe to account for it. The constant therefore supports the Big Bang theory.

There are two areas on which scientists cannot yet agree:

  1. An accurate measurement everyone can agree on
  2. Knowing if the constant is constant and always has been that value.

The implication for the Law is that the Universe is expanding. Remember however that groups of galaxies can be gravitationally bound (like ours), so this does not necessarily apply.

New name for the constant

In 2018 the law was renamed as the Hubble-Lemaître to recognise the work of Belgian astronomer Georges Lemaître who derived the law and estimated the constant before Hubble.

Which redshift is used to determine the Hubbleconstant? - Astronomy

At the controls of a simulated telescope, students view distant clusters of galaxies and obtain their spectra with a photon counting spectrometer. The telescope offers two fields of view, a wide field view of 2.5 degrees, and a magnified field ("instrument view") of 15 arc-minutes. Stars are represented by realistic point spread functions scaled to magnitude, and galaxies by images from actual CCD frames. In the instrument mode, students can position the slit of a spectrograph on the galaxy and take spectra. The photon counting spectrograph simulates actual Poisson statistics and contains both a sky background and a galaxy spectrum. The relative contribution of the galaxy depends on how much "light" from the image is included in the slit, so that the highest signal-to- noise is obtained when the slit is positioned on the brightest part of the galaxy, just as with a real spectrograph. Students are advised to obtain spectra with signal-to-noise of about 10, so that they can see and measure the Ca H and K lines, which are used to determine the redshift of the galaxy.

Wavelengths can be measured using the mouse cursor, and recorded for further analysis. The spectrometer also records the integrated apparent V magnitude of the galaxy, which is used, along with an assumed absolute magnitude, to determine the distance of the galaxy. With this information for five or six galaxies at various distances, students can plot out a Hubble diagram, determine the Hubble parameter, and estimate the age of the universe.

A wide variety of instructor-settable options are available. Instructors can construct their own galaxy fields using GENSTAR, a utility supplied by CLEA, and can even install their own image files to represent galaxies. The integration time to reach a given signal- to-noise can be set to conform to the needs of the class and the speed of the computer. Even the value of the Hubble parameter can be specified by the instructor the default is 75 km/sec/Mpc.

Hubble's law

Edwin Hubble first proposed this law in 1929 based on a study of the light received from the distant galaxies. He observed that the characteristic colors, or spectral lines (see spectrum spectrum,
arrangement or display of light or other form of radiation separated according to wavelength, frequency, energy, or some other property. Beams of charged particles can be separated into a spectrum according to mass in a mass spectrometer (see mass spectrograph).
. Click the link for more information. ), emitted by the stars in the galaxies do not have exactly the same wavelengths observed in the laboratory rather they are systematically shifted to longer wavelengths, toward the red end of the spectrum.

Such "red shifts" could occur because other galaxies are moving away from our own galaxy, the Milky Way. The change in the wavelength of light that results from the relative motion of the source and the receiver of the light is an example of the Doppler effect Doppler effect,
change in the wavelength (or frequency) of energy in the form of waves, e.g., sound or light, as a result of motion of either the source or the receiver of the waves the effect is named for the Austrian scientist Christian Doppler, who demonstrated the effect
. Click the link for more information. . The precise definition of the red shift is the increase in the wavelength divided by the original wavelength for a given relative velocity, this quantity is the same for all wavelengths or colors. For example, a red shift of 0.05 means that all wavelengths are increased by 5% because of the recessional velocity. Thus the velocity of any given galaxy is measured by its red shift.

Subsequent work has confirmed the general features of Hubble's law, but one specific part&mdashHubble's constant&mdashhas been drastically corrected. This value suggests the relative rate at which the scale of the universe changes with time. The value is currently estimated at about 45 to 46 mi (72 to 74 km) per second per megaparsec, based on studies of type 1a supernovas, which have a known brightness, using Cepheid variable stars to determine the supernovas distances. There is still some uncertainty in the value of this constant&mdasha more recent estimate based on data from the Planck space observatory was about 42 mi (67 km) per second per megaparsec, and a third, more recent method that was based on type 1a supernovas but used red giants to determine distances resulted in an estimate of about 43 mi (70 km) per second per megaparsec&mdashalthough the difference much less what it was in 1990. Hubble's original value for the expansion rate was between five and ten times too large because he underestimated the distances to the galaxies. The Hubble constant has received much attention because its reciprocal can be thought of as a time that represents the age of the universe. A low Hubble's constant implies that the universe is expanding slowly and therefore must be very old to have reached its current size. Conversely, a high estimate implies a rapid expansion and a relatively young universe. Current estimates place the age of the universe at around 13.799 billion years.

Relative Motion of the Galaxies

Hubble's law applies to all galaxies or clusters sufficiently distant from one another that gravitational forces are negligible. According to the law, these galaxies are flying away from each other at tremendous speeds as the fabric of space they occupy stretches, such that the greater the distance between any two galaxies, the greater their relative speed of separation. In other words, the expansion of the universe is roughly uniform. This empirical finding strongly supports the theory that the universe began with an explosive big bang (see cosmology cosmology,
area of science that aims at a comprehensive theory of the structure and evolution of the entire physical universe. Modern Cosmological Theories
. Click the link for more information. ).

Hubble's law was deduced from observations that indicate that the more distant a galaxy, the greater its red shift and hence the greater its velocity relative to the Milky Way. The fact that all other galaxies (with the exception of M31, the Andromeda Galaxy Andromeda Galaxy,
cataloged as M31 and NGC 224, the closest large galaxy to the Milky Way and the only one visible to the naked eye in the Northern Hemisphere. It is also known as the Great Nebula in Andromeda. It is 2.
. Click the link for more information. ) seem to be receding from the Milky Way does not imply that there is anything special about our position in space. Because the expansion of the universe is approximately uniform, it would appear to an observer in any galaxy that all other galaxies, including the Milky Way, were receding from the observer's galaxy.


See E. Harrison, Cosmology (1981).

Which redshift is used to determine the Hubbleconstant? - Astronomy

Hubble's Law and the Distance Scale

Hubble's Law and the Distance Scale

  • Copernicus and Kepler -- scale and dynamics of the solar system
  • Bessel -- parallax of stars, and placement of stars at vast distances
  • Hubble -- use of Cepheid variables to determine distance to galaxies
  • Hubble's Law
    • Henrietta Leavitt discovered a relationship in apparent magnitude and period for Cepheids in the Small Magellenic Cloud (SMC). Since they are all at about the same distance, she recognized that this was a period-luminosity relation.
    • Harlow Shapley set about calibrating the scale and applied it to Cepheids in the Milky Way, determining the size and scale of our galaxy. (Unfortunately, he calibrated using Pop II Cepheids in globular clusters, and so made an error.)
    • Edwin Hubble determined the distance to the Andromeda galaxy in 1924, thus proving that these "spiral nebulae" were external galaxies.
    In 1912, even before Hubble showed that galaxies are external island universes , Slipher observed the red-shifted spectral lines from galaxies. From this it had already been argued that spiral nebulae were external galaxies based on their unusual velocities.

    In 1929, Hubble published his paper announcing what is now called Hubble's Law . Recall that for v << c, redshift is given by ( Dl/l o ) = v/c

      In astrophysics, we use z = ( Dl/l o ) as the redshift , so velocities are related
      to redshift simply by

        v = cz .

      where H o is a constant of proportionality, now called the Hubble Constant . Hubble's finding implies that the more distant a galaxy, the larger the recession velocity. This leads directly to the expansion of the universe , which we will discuss in some detail.

      Before this discovery, the prevailing view was that the universe was static (in a steady state). This led Einstein, just a few years before (1915) to choose a value for an integration constant in his General Theory of Relativity that gave a static universe. He called this the biggest blunder of his life after Hubble's announcement, but his second biggest blunder was to set it to zero, thus giving a uniform expansion. We now suspect that it has some other value, such that the universe is accelerating its expansion!

      72 +/- 8 km s - 1 Mpc - 1 .

      The Astrophysical Journal, 553:47-72, 2001 May 20
      © 2001. The American Astronomical Society. All rights reserved. Printed in U.S.A.

      Final Results from theHubbleSpace Telescope KeyProject to Measure the Hubble Constant

      Wendy L. Freedman , Barry F. Madore , Brad K. Gibson , Laura Ferrarese , Daniel D. Kelson , Shoko Sakai , Jeremy R. Mould , Robert C. Kennicutt, Jr. , Holland C. Ford , John A. Graham , John P. Huchra , Shaun M. G. Hughes , Garth D. Illingworth , Lucas M. Macri , and Peter B. Stetson

      Received 2000 July 30 accepted 2000 December 19

      We present here the final results of the Hubble Space Telescope (HST) Key Project to measure the Hubble constant. We summarize our method, the results, and the uncertainties, tabulate our revised distances, and give the implications of these results for cosmology. Our results are based on a Cepheid calibration ofseveral secondary distance methods applied over the rangeof about 60400 Mpc.The analysis presented here benefits from a numberof recent improvements and refinements, including (1) a larger LMC Cepheid sample to define the fiducialperiod-luminosity (PL) relations, (2) a more recent HSTWide Field and PlanetaryCamera 2 (WFPC2) photometriccalibration, (3) a correction for Cepheid metallicity, and (4) a correction for incompleteness bias in theobserved Cepheid PL samples. We adopt a distancemodulus to the LMC (relative to which the more distant galaxies are measured) of m 0(LMC)= 18.50 ± 0.10 mag, or 50 kpc. New, revised distances are given for the 18 spiral galaxies for which Cepheids have been discovered as part of theKey Project, as well as for 13 additionalgalaxies with published Cepheid data. The new calibrationresults in a Cepheiddistance to NGC 4258 in better agreement with the maser distance to this galaxy. Based on these revised Cepheid distances, we find values (in km s -1 Mpc -1 ) ofH0 = 71 ± 2 (random) ± 6 (systematic) (Type Ia supernovae), H0 = 71 ± 3 ± 7 (Tully-Fisher relation), H0 = 70 ± 5 ± 6 (surface brightness fluctuations), H0 = 72 ± 9 ± 7 (Type II supernovae), and H0 = 82 ± 6 ± 9 (fundamental plane). Wecombine these results forthe different methods withthree different weighting schemes,and find good agreementand consistency with H0= 72 ± 8 km s -1 Mpc -1 . Finally,we compare these results with other, global methodsfor measuring H0.

      • between distances determined by trigonometric parallax and Cepheids,
      • and between Cepheid distances and the Redshift scale.

      The observed velocities of galaxies are due to both peculiar velocities , and to the recession velocity due to expansion of space (recessional motion is called the Hubble flow ). Since the latter grows with distance, the motions of nearby galaxies are dominated by their peculiar velocities.

      Example: The quasar PC 1247+3406 is moving away from us at over 94% of the speed of light. What is its redshift? What is its distance (parametrized with h )?

      z = ( Dl/l o ) = ( l-l o )/ l o = < [ (1+ v/c)/ (1 - v /c)] 1/2 - 1> = 2.48

      d = (c/100 h) [(z + 1) 2 - 1]/[(z + 1) 2 + 1]
      = (3 x 10 5 /100 h) (0.847) = 2.54/h Gpc

      Which redshift is used to determine the Hubbleconstant? - Astronomy

      Simultaneous measurements of distance and redshift can be used to constrain the expansion history of the universe and associated cosmological parameters. Merging binary black hole (BBH) systems are standard sirens—their gravitational waveform provides direct information about the luminosity distance to the source. There is, however, a perfect degeneracy between the source masses and redshift some nongravitational information is necessary to break the degeneracy and determine the redshift of the source. Here we suggest that the pair instability supernova (PISN) process, thought to be the source of the observed upper limit on the black hole mass in merging BBH systems at ∼ 45 ⊙ , imprints a mass scale in the population of BBH mergers and permits a measurement of the redshift-luminosity-distance relation with these sources. We simulate five years of BBH detections in the Advanced LIGO and Virgo detectors with a realistic BBH merger rate, mass distribution with smooth PISN cutoff, and measurement uncertainty. We show that after one year of operation at design sensitivity the BBH population can constrain H(z) to 6.1 % at a pivot redshift z≃ 0.8. After five years the constraint improves to 2.9 % . If the PISN cutoff is sharp, the uncertainty is smaller by about a factor of two. This measurement relies only on general relativity and the presence of a mass scale that is approximately fixed or calibrated across cosmic time it is independent of any distance ladder. Observations by future “third-generation” gravitational wave detectors, which can see BBH mergers throughout the universe, would permit subpercent cosmographical measurements to z ≳ 4 within one month of observation.

      Observations in astronomy

      The redshift observed in astronomy can be measured because the emission and absorption spectra for atoms are distinctive and well known, calibrated from spectroscopic experiments in laboratories on Earth. When the redshift of various absorption and emission lines from a single astronomical object is measured, z is found to be remarkably constant. Although distant objects may be slightly blurred and lines broadened, it is by no more than can be explained by thermal or mechanical motion of the source. For these reasons and others, the consensus among astronomers is that the redshifts they observe are due to some combination of the three established forms of Doppler-like redshifts. Alternative hypotheses and explanations for redshift such as tired light are not generally considered plausible. ⎽]

      Spectroscopy, as a measurement, is considerably more difficult than simple photometry, which measures the brightness of astronomical objects through certain filters. ⎾] When photometric data is all that is available (for example, the Hubble Deep Field and the Hubble Ultra Deep Field), astronomers rely on a technique for measuring photometric redshifts. ⎿] Due to the broad wavelength ranges in photometric filters and the necessary assumptions about the nature of the spectrum at the light-source, errors for these sorts of measurements can range up to δz = 0.5 , and are much less reliable than spectroscopic determinations. ⏀] However, photometry does at least allow a qualitative characterization of a redshift. For example, if a sun-like spectrum had a redshift of z = 1 , it would be brightest in the infrared rather than at the yellow-green color associated with the peak of its blackbody spectrum, and the light intensity will be reduced in the filter by a factor of four, (1 + z) 2 . Both the photon count rate and the photon energy are redshifted. (See K correction for more details on the photometric consequences of redshift.) ⏁]

      Local observations

      In nearby objects (within our Milky Way galaxy) observed redshifts are almost always related to the line-of-sight velocities associated with the objects being observed. Observations of such redshifts and blueshifts have enabled astronomers to measure velocities and parametrize the masses of the orbiting stars in spectroscopic binaries, a method first employed in 1868 by British astronomer William Huggins. Ε] Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to diagnose and measure the presence and characteristics of planetary systems around other stars and have even made very detailed differential measurements of redshifts during planetary transits to determine precise orbital parameters. ⏂] Finely detailed measurements of redshifts are used in helioseismology to determine the precise movements of the photosphere of the Sun. ⏃] Redshifts have also been used to make the first measurements of the rotation rates of planets, ⏄] velocities of interstellar clouds, ⏅] the rotation of galaxies, ΐ] and the dynamics of accretion onto neutron stars and black holes which exhibit both Doppler and gravitational redshifts. ⏆] Additionally, the temperatures of various emitting and absorbing objects can be obtained by measuring Doppler broadening – effectively redshifts and blueshifts over a single emission or absorption line. ⏇] By measuring the broadening and shifts of the 21-centimeter hydrogen line in different directions, astronomers have been able to measure the recessional velocities of interstellar gas, which in turn reveals the rotation curve of our Milky Way. ΐ] Similar measurements have been performed on other galaxies, such as Andromeda. ΐ] As a diagnostic tool, redshift measurements are one of the most important spectroscopic measurements made in astronomy.

      Extragalactic observations

      The most distant objects exhibit larger redshifts corresponding to the Hubble flow of the universe. The largest observed redshift, corresponding to the greatest distance and furthest back in time, is that of the cosmic microwave background radiation the numerical value of its redshift is about z = 1089 ( z = 0 corresponds to present time), and it shows the state of the Universe about 13.8 billion years ago, ⏈] and 379,000 years after the initial moments of the Big Bang. ⏉]

      The luminous point-like cores of quasars were the first "high-redshift" ( z > 0.1 ) objects discovered before the improvement of telescopes allowed for the discovery of other high-redshift galaxies.

      For galaxies more distant than the Local Group and the nearby Virgo Cluster, but within a thousand megaparsecs or so, the redshift is approximately proportional to the galaxy's distance. This correlation was first observed by Edwin Hubble and has come to be known as Hubble's law. Vesto Slipher was the first to discover galactic redshifts, in about the year 1912, while Hubble correlated Slipher's measurements with distances he measured by other means to formulate his Law. In the widely accepted cosmological model based on general relativity, redshift is mainly a result of the expansion of space: this means that the farther away a galaxy is from us, the more the space has expanded in the time since the light left that galaxy, so the more the light has been stretched, the more redshifted the light is, and so the faster it appears to be moving away from us. Hubble's law follows in part from the Copernican principle. ⏊] Because it is usually not known how luminous objects are, measuring the redshift is easier than more direct distance measurements, so redshift is sometimes in practice converted to a crude distance measurement using Hubble's law.

      Gravitational interactions of galaxies with each other and clusters cause a significant scatter in the normal plot of the Hubble diagram. The peculiar velocities associated with galaxies superimpose a rough trace of the mass of virialized objects in the universe. This effect leads to such phenomena as nearby galaxies (such as the Andromeda Galaxy) exhibiting blueshifts as we fall towards a common barycenter, and redshift maps of clusters showing a Fingers of God effect due to the scatter of peculiar velocities in a roughly spherical distribution. ⏊] This added component gives cosmologists a chance to measure the masses of objects independent of the mass to light ratio (the ratio of a galaxy's mass in solar masses to its brightness in solar luminosities), an important tool for measuring dark matter. ⏋]

      The Hubble law's linear relationship between distance and redshift assumes that the rate of expansion of the universe is constant. However, when the universe was much younger, the expansion rate, and thus the Hubble "constant", was larger than it is today. For more distant galaxies, then, whose light has been travelling to us for much longer times, the approximation of constant expansion rate fails, and the Hubble law becomes a non-linear integral relationship and dependent on the history of the expansion rate since the emission of the light from the galaxy in question. Observations of the redshift-distance relationship can be used, then, to determine the expansion history of the universe and thus the matter and energy content.

      While it was long believed that the expansion rate has been continuously decreasing since the Big Bang, recent observations of the redshift-distance relationship using Type Ia supernovae have suggested that in comparatively recent times the expansion rate of the universe has begun to accelerate.

      Highest redshifts

      <<#invoke:see also|seealso>> Currently, the objects with the highest known redshifts are galaxies and the objects producing gamma ray bursts. The most reliable redshifts are from spectroscopic data, and the highest confirmed spectroscopic redshift of a galaxy is that of UDFy-38135539 ⏌] at a redshift of z = 8.6 , corresponding to just 600 million years after the Big Bang. The previous record was held by IOK-1, ⏍] at a redshift z = 6.96 , corresponding to just 750 million years after the Big Bang. Slightly less reliable are Lyman-break redshifts, the highest of which is the lensed galaxy A1689-zD1 at a redshift z = 7.6 ⏎] and the next highest being z = 7.0 . ⏏] The most distant observed gamma ray burst was GRB 090423, which had a redshift of z = 8.2 . ⏐] The most distant known quasar, ULAS J1120+0641, is at z = 7.1 . ⏑] ⏒] The highest known redshift radio galaxy (TN J0924-2201) is at a redshift z = 5.2 ⏓] and the highest known redshift molecular material is the detection of emission from the CO molecule from the quasar SDSS J1148+5251 at z = 6.42 ⏔]

      Extremely red objects (EROs) are astronomical sources of radiation that radiate energy in the red and near infrared part of the electromagnetic spectrum. These may be starburst galaxies that have a high redshift accompanied by reddening from intervening dust, or they could be highly redshifted elliptical galaxies with an older (and therefore redder) stellar population. ⏕] Objects that are even redder than EROs are termed hyper extremely red objects (HEROs). ⏖]

      The cosmic microwave background has a redshift of z = 1089 , corresponding to an age of approximately 379,000 years after the Big Bang and a comoving distance of more than 46 billion light years. ⏗] The yet-to-be-observed first light from the oldest Population III stars, not long after atoms first formed and the CMB ceased to be absorbed almost completely, may have redshifts in the range of 20 < z < 100 . ⏘] Other high-redshift events predicted by physics but not presently observable are the cosmic neutrino background from about two seconds after the Big Bang (and a redshift in excess of z > 10 10 ) ⏙] and the cosmic gravitational wave background emitted directly from inflation at a redshift in excess of z > 10 25 . ⏚]

      Redshift surveys

      <<#invoke:main|main>> With advent of automated telescopes and improvements in spectroscopes, a number of collaborations have been made to map the universe in redshift space. By combining redshift with angular position data, a redshift survey maps the 3D distribution of matter within a field of the sky. These observations are used to measure properties of the large-scale structure of the universe. The Great Wall, a vast supercluster of galaxies over 500 million light-years wide, provides a dramatic example of a large-scale structure that redshift surveys can detect. ⏛]

      The first redshift survey was the CfA Redshift Survey, started in 1977 with the initial data collection completed in 1982. ⏜] More recently, the 2dF Galaxy Redshift Survey determined the large-scale structure of one section of the Universe, measuring redshifts for over 220,000 galaxies data collection was completed in 2002, and the final data set was released 30 June 2003. ⏝] The Sloan Digital Sky Survey (SDSS), is ongoing as of 2013 and aims to measure the redshifts of around 3 million objects. ⏞] SDSS has recorded redshifts for galaxies as high as 0.8, and has been involved in the detection of quasars beyond z = 6 . The DEEP2 Redshift Survey uses the Keck telescopes with the new "DEIMOS" spectrograph a follow-up to the pilot program DEEP1, DEEP2 is designed to measure faint galaxies with redshifts 0.7 and above, and it is therefore planned to provide a high redshift complement to SDSS and 2dF. ⏟]

      Age of the Universe

      The discovery that the universe is expanding led to the proposal of the big bang theory. This theory suggests that, at some point in the distant past, all of space-time itself was concentrated at a single point.

      Obtaining a value for the Hubble constant therefore allowed the first rough estimates of the age of the universe to be made.

      It was discovered in 1998, through observations of type Ia supernovae in extremely distant galaxies, that the rate of expansion of the universe is increasing. Prior to this discovery, it had been assumed that the expansion of the universe was slowing down. Taking this into account led to our current estimate for the age of the universe of around 13.8 billion years.


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