Anisotropy StudiesAnisotropy StudiesWhat We Can LearnWhat We Can Learn

Paul SommersLeeds

July 23, 2004

Auger has good sensitivity to discrete sourcesAuger has good sensitivity to discrete sources

1/E2 source spectrum equal energy flux per decade.

Source sensitivity better than 1 ev/cm2s is \good.\

One TeV Crab unit is 17 eV/cm2s.

Mrk 501 in 1997, mean energy flux was 60 eV/cm2s.

In lower state (1998-199), Mrk 501 was 4 eV/cm2s.

For Auger, 1 eV/cm2s per decade produces

2.5 showers/year above 1020 eV

25 showers/year above 1019 eV

[Valid at very southern declinations for Auger South.

Uniformly valid for full-sky Auger.]

What should we conclude if we detect 10 or more showers What should we conclude if we detect 10 or more showers above 10above 102020 eV with uncorrelated arrival directions? eV with uncorrelated arrival directions?

F := expected number for each contributing source.

Probably:

Fmax <~ 1

N(>F) ~ F-3/2

N(>Fmin ) ~ hundreds, not tens

Too many sources to be AGNs within GZK radius

(unless B-fields are so strong that arrival directions are scrambled and Fmax > 1).

What about sub-GZK charged particle astronomy?What about sub-GZK charged particle astronomy?

Super-GZK charged particle astronomy is plausible because: (1) High magnetic rigidity small deflection from source

(whose distance cannot be greater than ~50 Mpc).

(2) No background from sources at larger distances.

It would be a coincidence if the “\small deflection\ energy threshold were the same as the GZK \no background\ energy threshold. Assuming them to be different, there are two possibilities

(1) Super-GZK arrival directions are also magnetically scrambled or

(2) There is a sub-GZK regime of small magnetic deflection --

for sources out to some (energy-dependent) distance.

Super-GZK astronomy is signal-limited.

Sub-GZK particle astronomy has signal-to-noise limitation.

S/N AnalysisS/N Analysis

Noise N = b1/2, where background b = I(>E) A T ~ D Z2B2/E2

I(>E) ~ 1/E2

N ~ ZB(ATD)1/2 / E2

S = F A T

F(>E) ~ 1/E

S ~ AT/E

S/N ~ (A T)1/2 E/ (Z B)

Example:

Take I(>1019) = .5 / km2sr yr; A=3000 km; and

Suppose = (5 deg)2 ; T=1 yr N=6

Then S = 30 (1 eV/cm2s for 1 yr) S/N = 5

Blobs or Arcs?Blobs or Arcs?

Is there (generally) a unique minimum-action path connecting the Earth to the source for each energy?

Should we expect a curve of arrival directions parametrized by magnetic rigidity?

Or are the intervening B-field directions chaotic in the sense of causing 2-dimensional dispersion?

Is the time spread relevant? That is, would you get an arc of arrival directions if they all arrived at the same instant?

What if we detect no discrete source?What if we detect no discrete source?

Look for statistical evidence for clumpiness that suggests many low-flux sources:

Power in high-l part of the angular power spectrum?

[cf. GAP notes by J-C Hamilton et al.]

A peak in the 2-point correlation function at small

separations?

Search for correlation with AGNs and other source catalogues, with the overall mass distribution, etc.

IRAS PSCz Catalogue

This image shows the PSCz density field in the Supergalactic Plane out to a radius of 150 Mpc/h.

The smoothing length varies from 3 Mpc/h locally to 11.5 Mpc/h at the edge (by Enzo Branchini, Durham) .

The following animation shows the 2-dimensional celestial distribution of matter as a function of radius (recession speed).

The GZK radius is roughly 4000 km/s.

Matter Distribution 7 Mpc < D < 21 Mpc

Cronin astro-ph/0402487 [Kravtsov]

No test for isotropyNo test for isotropy

There are two problems with trying to prove isotropy:

With finite statistics you can only get upper limits on some types of anisotropy.

More importantly:

There are an infinite number of possible anisotropy patterns. No finite number of arrival directions can exclude them all. Any random sampling from a uniform distribution will have clumps. If you look at the sky map, you might recognize Angela`s grandmother`s face, for example.

Fighting Fighting a posterioria posteriori anisotropy analyses anisotropy analyses

The face of Angela`s grandmother would be a remarkable discovery, but only if predicted.

Without a targeted search for that pattern, it must be regarded as just one of an unbounded number of possible trials.

It is impossible to assess a fair statistical penalty for any pattern that is recognized after examining the data.

The Auger Collaboration has approved the concept of anisotropy analysis prescriptions to fix the number of trials.

[This does not limit sky mapping, publishing upper limits, or any other result that does not claim a positive detection of some quantified statistical significance. Nor does it discourage exhaustive exploration of arrival direction data for the purpose of identifying interesting prescribed searches for future data sets.]

SomeSome anisotropy is expected, even if discrete sources are anisotropy is expected, even if discrete sources are

not detectablenot detectable

Diffusion from a dominant source produces a strong dipole moment.

Galactic disk sources should give a quadrupole.

Supergalactic disk sources would give a different quadrupole

Diffusion from a small number of sources would give some other

low-l multipole moments.

Decay of relic particles in the galactic halo would produce a dipole moment.

Dark matter is not distributed isotropically in our neighborhood, and that anisotropy should produce a multipole signature.

Some non-zero multipoles are expected in almost any fingerprint.

The spectrum and composition only limit the theories for cosmic ray production. An anisotropy fingerprint is needed to identify their origin with confidence.

There will always be a need for more anisotropy data -- either to study sources in detail or to find subtle deviations from isotropy.

Full sky exposure is crucialFull sky exposure is crucial

Data from Auger South can and should be used to search for discrete sources and large-scale anisotropy patterns.

Without Auger North, however, there is an important hole in the observed sky (which includes the Virgo Cluster and much of the other nearby matter concentrations).

The steep exposure gradient of Auger South means vastly different sensitivity to discrete sources in different parts of the sky.

No multipole moment can be measured rigorously without integrating the density function over the entire celestial sphere.

5-year Auger Full-Sky Simulation

of isotropy

( E > 1019 eV and < 60o )

36000 arrival directions

Relative exposure as function of

sin(declination)

Auger North + Auger South

Auger is an Observatory!Auger is an Observatory!

Auger is not an experiment to answer a few specific questions.

It is an observatory to study all aspects of high energy cosmic rays -- EeV cosmic rays, ankle cosmic rays, sub-GZK cosmic rays, and perhaps super-GZK cosmic rays.

In each energy regime, the arrival directions are key to discovering where they come from and properties of the sources.

Incomplete sky coverage impairs every anisotropy study and precludes mapping large-scale patterns.

Results from the Auger Obervatory will generate interest and suggest follow-on studies. Even each absence of a predicted pattern is an important result that stimulates re-thinking and new model predictions. Whatever we see (or don`t see) will be important observations that advance our understanding of the universe`s highest energy particles.

SummarySummary

Auger has good sensitivity to discrete sources.

SummarySummary

Auger has good sensitivity to discrete sources.

Numerous uncorrelated super-GZK arrival directions would imply a large number of contributing sources.

SummarySummary

Auger has good sensitivity to discrete sources.

Numerous uncorrelated super-GZK arrival directions would

imply a large number of contributing sources.

Sub-GZK charged particle astronomy is also a possibility.

SummarySummary

Auger has good sensitivity to discrete sources.

Numerous uncorrelated super-GZK arrival directions would

imply a large number of contributing sources.

Sub-GZK charged particle astronomy is also a possibility.

Statistical analyses can probe for discrete sources that are not individually detectable.

SummarySummary

Auger has good sensitivity to discrete sources.

Numerous uncorrelated super-GZK arrival directions would

imply a large number of contributing sources.

Sub-GZK charged particle astronomy is also a possibility.

Statistical analyses can probe for discrete sources that are not individually detectable.

Matter in the nearby universe is not isotropic; there is an important concentration in Auger South`s blind spot.

SummarySummary

Auger has good sensitivity to discrete sources.

Numerous uncorrelated super-GZK arrival directions would

imply a large number of contributing sources.

Sub-GZK charged particle astronomy is also a possibility.

Statistical analyses can probe for discrete sources that are not individually detectable.

Matter in the nearby universe is not isotropic; there is an important concentration in Auger South`s blind spot.

There is no test for isotropy.

SummarySummary

Auger has good sensitivity to discrete sources.

Numerous uncorrelated super-GZK arrival directions would

imply a large number of contributing sources.

Sub-GZK charged particle astronomy is also a possibility.

Statistical analyses can probe for discrete sources that are not individually detectable.

Matter in the nearby universe is not isotropic; there is an important concentration in Auger South`s blind spot.

There is no test for isotropy.

Analysis prescriptions are needed to guard against finding spurious patterns in the noise.

SummarySummary

Auger has good sensitivity to discrete sources.

Numerous uncorrelated super-GZK arrival directions would

imply a large number of contributing sources.

Sub-GZK charged particle astronomy is also a possibility.

Statistical analyses can probe for discrete sources that are not individually detectable.

Matter in the nearby universe is not isotropic; there is an important concentration in Auger South`s blind spot.

There is no test for isotropy.

Analysis prescriptions are needed to guard against finding spurious patterns in the noise.

Anisotropy is expected at some level in almost any model.

Auger is an observatory and requires full-sky exposure.