The CMB dipole

The CMB dipole

the largest anisotropy in the sky

The dipole, mapped by COBE. One half of the sky is warmer than the other by about three thousandths of a kelvin, and the entire pattern is a statement about which way the observer is going. The band across the middle is the Milky Way, which is a statement about something else.

Amplitude	3.3621 ± 0.0010 mK
Against a background of	2.7255 K
Cause	The observer's motion. Nothing else
Implied speed	369.82 ± 0.11 km s−1
Direction	Towards Crater, at the border of Leo
Annual modulation	≈0.27 mK, from the Earth's orbit
Used for	Absolute calibration
Calibrated against	The Earth going round the Sun

The CMB dipole is the largest structure in the cosmic microwave background: one half of the sky is warmer than the other by about 3.4 millikelvin, in a smooth pattern with a single hot pole and a single cold one.^[1] It is larger than every other feature of the background put together by a factor of about a hundred.

It is also the only feature of the background that says nothing whatever about the universe. It is a Doppler shift, produced by the observer moving through a radiation field that is otherwise very nearly the same in all directions, and everything it encodes is a fact about the observer's velocity.^[2]

The effect

The background radiation has a temperature of 2.7255 K and, corrected for our motion, is isotropic to a few parts in a hundred thousand. An observer moving through it sees the radiation ahead blue-shifted and slightly hotter, and the radiation behind red-shifted and slightly cooler, in a pattern proportional to the cosine of the angle from the direction of travel:

The measured amplitude gives $v = 369.82 \pm 0.11$ km s⁻¹ for the Sun, towards a point in Crater near the boundary of Leo. This is not a velocity with respect to any object. It is a velocity with respect to the radiation, which is as near to a rest frame as the universe provides and is not one in the sense that would trouble relativity: no experiment done in a closed box detects it, and it is measured by looking out of the window.^[3]

Detection

Penzias and Wilson made the first clear measurement of the background itself on 20 May 1964, and were given the Nobel Prize for it in 1978. The dipole took longer, being small against an already faint signal and hard to separate from the instrument.

Conklin reported the first hints in 1969, Henry had a three-sigma detection by 1971, and Smoot, Gorenstein and Muller settled it in 1977, each using a differential radiometer comparing two widely separated patches of sky rather than attempting an absolute temperature.^[4] COBE, WMAP and Planck have since measured it to four figures.

The annual modulation

The velocity in the dipole is the Sun's, and the Earth does not share it. The Earth is also going round the Sun at 29.78 km s⁻¹, in a direction that turns through a full circle once a year, and that velocity adds to the solar one.

The dipole therefore breathes. Its amplitude and direction shift over the year by the ratio of the two speeds:

This is a small quantity and it is not in dispute. It has been observed since COBE, its period is one year, its phase is that of the Earth's orbital velocity, and it matches the prediction because the Earth's orbital velocity is known from planetary ranging to better than a centimetre per second.^[5]

The calibration

The interesting part is what is done with it.

An instrument measuring temperature differences of a few microkelvin needs an absolute scale, and there is no laboratory source good enough to supply one in orbit. What the missions use instead is the orbital dipole: a signal of known amplitude, known direction, and known period, generated by a motion that has been measured to nine significant figures by other means entirely.

So the calibration runs the other way from what one might expect. WMAP and Planck do not check the Earth's orbit against cosmology. They assume the Earth's orbit, of which they are certain, and use it to fix the scale of the cosmology, of which they are not.^[6] Working cosmologists calibrate their instruments against the Earth going round the Sun, every year, and publish the residuals.

The use made of it

The background is cited on the other side of the question, though not usually this part of it. The claim concerns the quadrupole and octopole – the next two terms after the dipole – which some analyses find preferentially aligned with the ecliptic plane, a coincidence given the name the axis of evil.^[7]

Whether the alignment is real is a live question: it is a small effect in a sample of one sky, the statistical significance depends on how the question is posed after the data has been seen, and foreground subtraction near the galactic plane is difficult. It is a reasonable thing to be interested in.

It is not, however, the dipole, and the two are regularly run together. The dipole is a hundred times larger, is not in dispute by anyone, has a known cause, and says that the Solar System is moving at 370 kilometres a second. An argument which cites the microwave background as evidence for a stationary Earth is obliged to pass over its single largest feature, which is a measurement of how fast we are going.

See also

• Stellar parallax – the annual effect that tracks the Earth's position
• Stellar aberration – the annual effect that tracks its velocity
• Kinematic and dynamic equivalence – where all three are set against what each account must supply
• Heliocentrism – the arrangement all three agree on
• Geocentrism – the account that must produce them another way
• Luminiferous aether – an earlier attempt at a frame you could measure against

References

1. ^ Planck gives 3.3621 ± 0.0010 mK. The background's mean temperature is 2.7255 K, so the dipole is a departure of about one part in eight hundred.
2. ^ This is worth stating carefully. The dipole is a genuine measurement and an entirely real feature of the observed sky; what it is not is a feature of the universe. Subtract the observer's motion and it goes away, which is not true of any other structure in the map.
3. ^ The distinction is the one Mach and Newton disputed and the one relativity settled: there is no preferred frame for the laws, and there is nonetheless a frame in which the radiation is isotropic. See Mach and Newton's bucket.
4. ^ The differential method is the same trick as Michelson and Morley's: comparing two directions is enormously easier than measuring either one, and it is how nearly every anisotropy has been found since.
5. ^ 0.27 mK against a 3.36 mK dipole, which is a ten-thousandth of the background temperature. It is measured routinely.
6. ^ The orbital dipole is used as a calibrator precisely because it is the best-known signal in the sky, and it is the best known because it comes from a motion measured by radar and spacecraft tracking rather than by cosmology.
7. ^ The name is Land and Magueijo's, from 2005, and was meant more lightly than it has since been taken.

External links

• Planck 2018 results I: overview and cosmological legacy – Astronomy & Astrophysics
• Penzias & Wilson, "A Measurement of Excess Antenna Temperature at 4080 Mc/s" – Astrophysical Journal (1965)
• COBE DMR dipole map – Wikimedia Commons
• Cosmic microwave background – general reference