How is Cosmic Microwave Background's temperature measured?

How is Cosmic Microwave Background's temperature measured?

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How do Cosmic Microwave Background missions/telescopes measure CMB temperatures? I understand that CMB has Planck's spectrum. So I was thinking one strategy could be to measure the spectral radiance corresponding to different frequencies coming from a certain direction and then compared these data points with theoretical Planck's law. Is this technique practically feasible?

That is what is done. This is shown in an old xkcd comic

The curve shows the distribution of frequencies in the CMB, and by using the marked value of the maximum you can determine the value of T, the apparent (red-shifted) temperature of the CMB

How is Cosmic Microwave Background's temperature measured? - Astronomy

Detailed analysis of the microwave background radiation gives practically our only direct evidence of conditions before galaxy formation. The spectral shape and departures from perfect isotropies give (temporal and angular) evidence on the existence of structures at the epoch of recombination, which is the last view we currently have until galaxies and AGN begin to take shape at some epoch like z=10 (or whatever it is. ). Two very useful references for much of the material in these final lectures are Peacock's Cosmological Physics (Cambridge 1999) and Galaxy Formation by Longair (Springer 1998). The existence of a recombination epoch happens because the densities of matter and radiation have different dependences on the cosmic scale factor (1/R³ versus 1/R 4 ).

The best-known maps of fluctuations in the background are from the COBE Differential Microwave Radiometer (DMR). These images illustrate the four-year data products as measured at 53 GHz, in galactic coordinates with the galactic center in the middle. At the top is the overall background temperature (blank to an excellent approximation), then in the middle we see the result at a magnified stretch with the mean value removed. This shows the dipole interpreted as a Doppler shift due to motion of the Milky Way with respect to the sphere of matter now seen radiating in the background, and some of the residual contamination from the Galactic foreground. Finally at the bottom we see the all-sky fluctuations with the dipole removed (note, by the way, that we cannot separate any intrinsic dipole structure in the CMBR from effects of our relative motion). The individual fluctuations at high galactic latitudes are now significant (which was an improvement over the initial announcements based on 2-year maps from the data). The Tenerife and South Pole experiments also confirmed individual structures. A further advance and unification of structures on various scales came with the first maps from the Wilkinson Microwave Anisotropy Probe (WMAP), shown below the COBE results.

The horizon size at the last-scattering surface, important not only for big questions of causal connectivity but in the growth of perturbations, is 184 (&Omega h²) -1/2 Mpc. The spectrum of fluctuations (usually considered as a power spectrum in wavenember l of, for example, Bessel functions on the sphere) is highly diagnostic of processes in the early Universe, which has driven much of the work on improving maps of structure in the CMBR. We expect a Sachs-Wolfe "plateau" for small values of l, leading to an acoustic (or Doppler) peak. The location of this peak is sensitive to both &Omega and &Lambda, while its amplitude is sensitive almost purely to &Omega. Models also predict that harmonics of this peak should be seen to higher values of l. These may be explored with the publicly released CMBFAST code (see Seljak and Zaldarriaga 1996 ApJ 469, 437, more recently updated to include both closed and open geometries, with the interesting difference that only spatially wrapped spherical wavenumbers are allowed in the closed case). This typical prediction was taken from the MAP WWW site, which includes further versions showing the effects of varying cosmological parameters:

The really new aspect of the WMAP results is in covering a wide range of angualar scales at high sgnal-to-noise ratio in a single experiment, dramatically reducing the potential role of systematic errors. (In fact, for low values of l, one becvomes limited now by cosmic variance - the fact that we have only one slice of the early Universer to observe, and we must work with whatever it happens to present). In deriving cosmological quantities, one usually niormalizes the power to what we see locally (say on 100-Mpc scales). The total density parameter &Omega tot shifts the location of the first (strongest) peak to smaller l for higher values this is a curvature measurement giving the relative scales between then and now. The baryon density by itself changes the peak ratios of odd and even peaks (through dissipation in compressive phases of the acoustic motions). Large values of the cosmological constant &Lambda move the first peak to higher l and lower amplitude, while both baryon density and H0 affect the height of the peaks. A helpful way to see why such effects happen is to note that the Universe at recombination was pervaded by a field of velocity perturbations transmitted acoustically (now that was different). We see this field slices with the redshift width of the time it took to complete recombination, so smaller-scale fluctuations will be damped out. The peaks and valleys tell what scales had the right timing to constructively or destructively interfere, since for a given wavnumber k the phase follows e i s k t where s is the sound speed.

While brief, the epoch of recombination did have a nonzero duration, which translates into a finite thickness in redshift. As set out by Jones and Wyse (1985 A&A 149, 144), the cosmological dependences cancel almost perfectly giving an optical-depth function &tau(z) = 0.37 (z/1000) 14.25 . Thus the distribution of last-scattering redshift (specifically e -&tau d&tau/dz) is strongly peaked, almost Gaussian with mean of z=1065 and standard deviation &sigmaz = 80. (WMAP data give zrec = 1089 ± 97). This will modify the spectrum slightly with respect to a perfect single-temperature blackbody, and will be manifested by damping out irregularities due to structure which is smaller than the comoving depth of this apparent shell. Details of the recombination process have been recently re-examined by Seager, Sasselov, and Scott (2000, ApJS 128, 431) using full radiative transfer codes and sophisticated models for all the relevant ions, who found that Peebles (1968 ApJ 153, 1) and Zel'dovich et al. (1968 JETP Lett. 28, 146) did remarkably well in reducing the problem to approximate differental equations. Further details exist, but at about the level of uncertainty in some of the relevant reaction rates. In evaluating the spectrum of the background radiation, it is noteworthy (see the treatment by Peacock, for example) that the thermal form of the radiation spectrum was established when brehmsstrahlung was active at redshift of order 10 6 and no major additional input between then and recombination is allowed by the existing limits on departures from a Planck form.

Further developments should come fast, with NASA's Wilkinson Microwave Anisotropy Probe (WMAP) still operating in the L2 region and and ESA's Planck in the pipeline. These should yield significant measurements of high-order harmonics in the fluctuation spectrum sufficient to measure the basic cosmological parameters by themselves.

Fluctuations in the Cosmic Microwave Background

The cosmic microwave background is the afterglow radiation left over from the hot Big Bang. Its temperature is extremely uniform all over the sky. However, tiny temperature variations or fluctuations (at the part per million level) can offer great insight into the origin, evolution, and content of the universe.

If you were approaching the Earth on a spaceship, the first thing you would notice is that the planet is spherical. As you drew closer to the Earth, you would see the surface divide into continents and oceans. You would need to study the Earth's surface very carefully to see the mountains, cities, forests and deserts that cover the continents.

Similarly, when cosmologists first looked at the microwave sky, thirty years ago, they noticed it was nearly uniform. As observations improved, they detected the dipole anisotropy. Finally, in 1992, the Cosmic Background Explorer (COBE) satellite made the first detection analogous to seeing "mountains on the surface of the Earth": it detected cosmological fluctuations in the microwave background temperature. Several members of the WMAP science team help lead the COBE program and build the spacecraft. COBE's detection was confirmed by the Far InfraRed Survey (FIRS) balloon-borne experiment.

Comparison of COBE and WMAP sky images
Fluctuations seen by COBE Fluctuations seen by WMAP (Simulated)

In the comparison of the images above, images on the left produced by the COBE science team, show three false color images of the sky as seen at microwave frequencies. The images on the right show one of our computer simulations of what the WMAP experiment detects. Note that WMAP detects much finer features than are visible in the COBE maps of the sky. This additional angular resolution allows scientists to infer a great deal of additional information, beyond that supplied by COBE, about conditions in the early universe.

The orientation of the maps are such that the plane of the Milky Way runs horizontally across the center of each image. The top pair of figures show the temperature of the microwave sky in a scale in which blue is 0 Kelvin (absolute zero) and red is 4 Kelvin. Note that the temperature appears completely uniform on this scale. The actual temperature of the cosmic microwave background is 2.725 Kelvin. The middle image pair show the same map displayed in a scale such that blue corresponds to 2.721 Kelvin and red is 2.729 Kelvin. The "yin-yang" pattern is the dipole anisotropy that results from the motion of the Sun relative to the rest frame of the cosmic microwave background. The bottom figure pair shows the microwave sky after the dipole anisotropy has been subtracted from the map. This removal eliminates most of the fluctuations in the map: the ones that remain are thirty times smaller. On this map, the hot regions, shown in red, are 0.0002 Kelvin hotter than the cold regions, shown in blue.

There are two main sources for the fluctuations seen in the last figure:

  • Emission from the Milky Way dominates the equator of the map but is quite small away from the equator.
  • Fluctuating emission from the edge of the visible universe dominates the regions away from the equator.
  • There is also residual noise in the maps from the instruments themselves, but this noise is quite small compared to the signals in these maps.

These cosmic microwave temperature fluctuations are believed to trace fluctuations in the density of matter in the early universe, as they were imprinted shortly after the Big Bang. This being the case, they reveal a great deal about the early universe and the origin of galaxies and large scale structure in the universe.

How Does The Cosmic Microwave Background Show That The Universe is Expanding?

Summary:: I've been searching for weeks and still with the doubt.
I just know scientist look the content of the CMB and with general relativity calculates the expansion rate today that is 73 km/s/Mpc, but nowhere does it say how exactly. Please help.

I've been searching for weeks and still with the doubt.
I just know scientist look the content of the CMB and with general relativity calculates the expansion rate today that is 73 km/s/Mpc, but nowhere does it say how exactly. What does the contents of the universe have to do with the expansion speed of the universe today? Please help.

The CMB isn't completely uniform. There are tiny fluctuations in it, evidence of non-uniformity that eventually developed into stars, galaxies and clusters.

My limited understanding is that the power spectrum of these fluctuations is predicted to depend on the mix of matter, radiation, dark matter and dark energy present in the universe. Thus if you measure the power spectrum you can invert the prediction and get an estimate of the amounts of each type in the universe. Then you feed those into the Friedmann equations to get the scale factor and its derivatives at any time, and hence ##H_0##.

Summary:: I've been searching for weeks and still with the doubt.
I just know scientist look the content of the CMB and with general relativity calculates the expansion rate today that is 73 km/s/Mpc, but nowhere does it say how exactly. Please help.

I've been searching for weeks and still with the doubt.
I just know scientist look the content of the CMB and with general relativity calculates the expansion rate today that is 73 km/s/Mpc, but nowhere does it say how exactly. What does the contents of the universe have to do with the expansion speed of the universe today? Please help.

The CMB is generally regarded as evidence of the big bang model because it apparently verifies the expansion of space due to the redshifting of the perfect blackbody spectrum measured, but we don't actually know what its temperature (or wavelength) was at recombination via observation. The temperature of recombination can be estimated using equilibrium theory but as far as I'm aware this process is not independent of the current CMB temperature.

The way I see it, the existence of the CMB at microwave wavelengths is enough in most people's eyes to confirm the big bang model, because it would be required by that model. However there is other independent evidence of expanding space such as Hubble and Lemaitre's work on galaxy redshift correlations.

On another note, the CMB also offers indication of inflation as well as evidence of dark energy (accelerated expansion, see "late-time integrated Sachs Wolfe effect", both of which allude to expanding universe.

My issue is just that the CMB redshift estimate is itself dependent on the temperature today (Saha equation). So we are using the observed temperature today to calculate the redshift of recombination, which is then used to calculate the temperature of the CMB at recombination. Which is fine as long as we don't rely on that as evidence of expansion. Maybe it is irrelevant, but it seems a bit self-referential to me. I would say the CMB fits nicely into the current model, but evidence of expansion comes from direct measurements, e.g. galaxy redshift correlations.

Not entirely. We can detect spectral lines in the CMB, though not with very high precision. So we have at least a rough independent check on calculations involving temperature.

Also, we can measure the temperature of the CMB today very precisely, since we have its spectrum over a very wide range of frequencies. So I don't see why it's an issue that the temperature today is one of the inputs we need to use.

No, you have this backwards. The method of estimating the CMB redshift this way involves first knowing both temperatures--the temperature today, which we measure directly, and the temperature at recombination, which we calculate based on the known properties of hydrogen. The ratio of those two temperatures then gives the redshift of the CMB from then to now.

The redshift, calculated as above, is direct evidence of expansion, since the redshift directly gives the factor by which the universe expanded from recombination to now. (To be precise, that expansion factor is ##1 + z##.) The only possible confounding factor, which is present in observations of galaxies, namely that individual galaxies are not in general exactly comoving with the Hubble flow, is not there with the CMB since it is exactly comoving with the Hubble flow.

Yes, I agree. The Saha equation features in equilibrium calculation and the temperature of recombination is related to the current temperature via redshift (i.e. model-dependent).

It's possible I miss understand the process, true, but this is not really what I meant or what is causing confusion/consternation, and just to add, my initial post was intended to sympathise with OP's lack of satisfaction with the nature of the evidence.

I think the issue here is my (and maybe other people's) understanding of what constitutes observational evidence. If we measure that the background radiation is in the microwave range, there is nothing except our cosmological model that tells us this is due to a redshift. Therefore such a conclusion is not model independent, so can this measurement really be strong evidence of the same model's validity? Of course it confirms some predictions of the model, if and only if the radiation has actually redshifted. (Yes, a static universe might have trouble explaining it, true, but still it is no smoking gun imo.)

Look at spectroscopic redshift measurements. These are actual measurements of motion and are model independent (whatever the actual nature of the motion). We don't need to resort to distance-redshift relations to know that the distance between us and the source is changing somehow, we can actually see it! When we observe that there is also a relationship between the rate of change and distance, and this applies everywhere in the sky, we can conclude really only one of two things: 1) either we are the at the centre of everything, 2) everything is moving away from everything else. In either model we choose we have expansion: provided we believe Einstein's second postulate it can't be peculiar motion.

This is why I say expansion is not immediately evident by measuring a Planck curve with a temperature of 2.7K.

The Cosmic Microwave Background: A plausible (but different) explanation.

Most people here seem to be familiar with the CMB. What is it?

The cosmic microwave background, in Big Bang cosmology, is electromagnetic radiation which is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all space. Wikipedia

So the conventional idea is that the CMB is like a leftover flash from the Big Bang. Is there another way to explain the CMB?

One possibility involves Entropy.

Entropy is what balances Energy out. Entropy is why like charges repel, opposites attract and why energy goes from a high concentration to a low one.

Turn on a light and it's Energy radiates away into space because of Entropic dispersal. Now just extend the same idea to the entire Universe.

If the Universe had a beginning, and if it is not infinite (since it is seen as expanding) then Entropy will disperse a certain amount of Energy into the existing volume of space (ie. the Universe)

Since the Universe is not infinite , and since there's a non zero amount of Energy within it, there must be a non zero base energy level for the Universe.

This Energy would be radiative in nature (ie low energy photons or very low energy wavelengths of Light).

The actual temperature of the cosmic microwave background is 2.725 Kelvin. And at just 2.75 degrees about absolute zero, the CMB may represent the Entropic Energy basement of the Universe.

Energy spreading out over time takes time. You might be able to use the CMB temperature as a different way to figure out the age of the Universe.

New cosmic recipe

Beyond the anomalies, however, the Planck data conform spectacularly well to the expectations of a rather simple model of the Universe, allowing scientists to extract the most refined values yet for its ingredients.

Normal matter that makes up stars and galaxies contributes just 4.9% of the mass/energy density of the Universe. Dark matter, which has thus far only been detected indirectly by its gravitational influence, makes up 26.8%, nearly a fifth more than the previous estimate.

Conversely, dark energy, a mysterious force thought to be responsible for accelerating the expansion of the Universe, accounts for less than previously thought.

Finally, the Planck data also set a new value for the rate at which the Universe is expanding today, known as the Hubble constant. At 67.15 kilometres per second per megaparsec, this is significantly less than the current standard value in astronomy. The data imply that the age of the Universe is 13.82 billion years.

“With the most accurate and detailed maps of the microwave sky ever made, Planck is painting a new picture of the Universe that is pushing us to the limits of understanding current cosmological theories,” says Jan Tauber, ESA’s Planck Project Scientist.

“We see an almost perfect fit to the standard model of cosmology, but with intriguing features that force us to rethink some of our basic assumptions.

“This is the beginning of a new journey and we expect that our continued analysis of Planck data will help shed light on this conundrum.”


We present an internal consistency test of South Pole Telescope (SPT) measurements of the cosmic microwave background (CMB) temperature anisotropy using three-band data from the SPT-SZ survey. These measurements are made from observations of ∼ 2500 ° 2 of sky in three frequency bands centered at 95, 150, and 220 GHz. We combine the information from these three bands into six semi-independent estimates of the CMB power spectrum (three single-frequency power spectra and three cross-frequency spectra) over the multipole range 650<ℓ<3000. We subtract an estimate of foreground power from each power spectrum and evaluate the consistency among the resulting CMB-only spectra. We determine that the six foreground-cleaned power spectra are consistent with the null hypothesis, in which the six cleaned spectra contain only CMB power and noise. A fit of the data to this model results in a χ 2 value of 236.3 for 235 degrees of freedom, and the probability to exceed this χ 2 value is 46%.

Bibliographical note

What is cosmic microwave background in physical science?

Click to read full answer. Simply so, what does the cosmic microwave background tell us?

The CMB radiation tells us the age and composition of the universe and raises new questions that must be answered. The Cosmic Microwave Background, or CMB, is radiation that fills the universe and can be detected in every direction. Microwaves are invisible to the naked eye so they cannot be seen without instruments.

what is the temperature of the cosmic microwave background? 2.725 K

Likewise, what is meant by cosmic background radiation?

Cosmic background radiation is an electromagnetic radiation from the Big Bang. The origin of this radiation depends on the region of the spectrum that is observed. One component is the cosmic microwave background.

Why is the cosmic microwave background radiation so uniform?

The cosmic microwave background is the afterglow radiation left over from the hot Big Bang. Its temperature is extremely uniform all over the sky. However, tiny temperature variations or fluctuations (at the part per million level) can offer great insight into the origin, evolution, and content of the universe.

The Inflatable Universe

A 12 inch inflatable globe (beach ball) can be used as a model of the observable universe. The ball's surface represents the furthest we can see in microwave light, the oldest visible light in the universe. The ball presents the baby picture created just 378,000 years after the Big Bang,

13.8 billion years ago, before planets, stars or galaxies existed! The patterns imply a universe dominated by a mysterious "dark energy" and an exotic "dark matter." This full sky image of microwave light was captured by the Wilkinson Microwave Anisotropy Probe (WMAP). The WMAP team created a special inflatable beach ball with a representation of the microwave light pattern on it to help the public understand where this light comes from. This project is now 10 years old and the ball supply is exhausted, unfortunately. In place of the now defunct beach ball, here is a paper ball that can be cut out and assembled:

Hot and Cold Spots

The colors indicate temperature variations of light within the young universe, red for hotter, blue for cooler. These slight variations of temperature were caused by slight variations in the density of the matter from which the light was last scattered. But the red stripe along the globe's equator is a much more recent/closer/stronger foreground microwave signal from our Milky Way Galaxy.

The sizes of the hot and cold spots let scientists calculate fundamental values for the shape, size, age, rate of expansion (and more) of our universe.

If the microwave light were shifted up to the visible spectrum and amplified, our eye would see a colorful rainbow of spots across the whole sky. 2.7251 kelvins

2.7249 kelvins

12-inch Model of the Universe

The 12 inch ball (with a 6 inch radius) can represent the distance light has been able to travel in the nearly 13.7 billion years since the matter of the universe cooled to less than 3000 kelvins. We are at the center of this bubble of light, but many more times this volume of space exists outside this bubble, we just can not yet see its light. Every year the bubble of the observable universe grows a little larger as new light reaches our eyes. The bubble expands as the fabric of space itself stretches. Light stretches and cools (akin to distributing the same amount of energy within a continually expanding oven) toward the ultimate chilly "absolute zero" temperature (0 kelvins).

The light from the first stars appeared roughly 400 million years after the Big Bang. Yet in the model above it is a much larger distance in from the edge of the ball (about 10 billion light years). This is the result of the expanding fabric of space. The universe was more compressed, but expanding more rapidly than it is today.

What WMAP Sees

The temperature difference measured now between the coldest and hottest spots is extremely small, but the early universe was very hot. When the average density of matter in the universe was comparable to air at sea level, its temperature was 2.73 billion degrees! (The average density today is the equivalent of about one proton per cubic meter.) At these temperatures, protons and electrons could not bind together to form neutral atoms. The free electrons scattered the cosmic background radiation much as water drops scatter visible light in clouds, so the early universe would appear as a dense fog. As the universe expanded, it cooled. 378,000 years after the Big Bang, it was cool enough for protons and electrons to combine into neutral hydrogen. Neutral hydrogen is transparent, so the cosmic background radiation has traveled freely through the universe since that time.

On a cloudy day, we can look through the air to see the surface of the clouds. Similarly, we can see through the universe out to where it was filled with free electrons and see the “dense fog” that filled the early universe. The reason we can “see” the early universe is that we see objects as they were in the past due to the time it takes light to travel across space. For example, we see the Sun as it existed 8 minutes earlier. We see the “cloud surface” from which the cosmic background radiation was last scattered as it existed 13.7 billion years ago.

You can find out more about the WMAP mission and the solutions to some of the mysteries of our cosmos, starting on the WMAP Home page.

Notes: The presentation of the image on the beach ball above has been set to be viewed in the same fashion as an inflatable constellation guide. Hold it up to the sky and you can match the patterns on the ball to the patterns on the sky. So technically the image is inverted if you were positioned outside the bubble of light we can see. But this is of no importance in the scientific analysis of the image.


The calibration methods for the FIRAS have been described and the accuracy estimated. All of the recent precision estimates of the CMB temperature agree within 2.5 times their uncertainties. These estimates were made with a variety of methods from different platforms and different frequencies. Combining all of the estimates results in a very modestly elevated χ 2 and an improved absolute temperature estimation of 2.72548 ± 0.00057 K.

I thank the WMAP team for providing the smoothed sky maps in velocity units. A special thanks to J. Weiland and G. Hinshaw.