Fermi National Accelerator Laboratory /3oY5-

FERMI LAB-Pub- 8 9/214 -A

October 19 8 9_/3_

THE GRAND UNIFIED PHOTON SPECTRUM

A Coherent View of the Diffuse Extragalactic Background Radiation

M. TED RESSELL I'3

and

MICHAEL S. TURNER I'2'3

1 Department of Astronomy and AArophysics

The University of Chicago

Chicago, IL 60637-1433

:Department of Physics and The Enrico Fermi Institute

The University of Chicago

Chicago, IL 60637-1433

a NASA/FermiIab Astrophysics Center

Fermi National Acceleragor Laboratory

Balavia, IL 60510-0500

Abstract. We present in a coherent fashion the spectrum of diffuse extragalactic background radiation (DEBRA) at wavelengths from 10_Gm to 10-24cm. Each wavelength

region, from the radio to ultra-hlgh energy photons and cosmic rays, is treated both separately and as part of the grand unified photon spectrum (GUPS). A discussion of, and

references to, the relevant literature for each wavelength region is included. This review

should provide a useful tool for those interested in diffuse backgrounds, the epoch of galaxy

formation, astrophysical/cosmological constraints to particle properties, exotic early Universe processes, and many other astrophysical and cosmological enterprises. As a worked

example, we derive the cosmological constraints to an unstable-neutrino species (with arbitrary branching ratio to a radiative decay mode) that follow from the GUPS.

To appear in Comments on Astrophysics.

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INTRODUCTION

Observation of the diffuse extragalactic background radiation (DEBRA) at various

wavelengths provides a unique window on various astrophysical, cosmological, and particle

physics phenomena. The existence of the cosmic microwave background radiation (CMBR)

with a temperature of 2.74K is well established and, perhaps, provides the strongest evidence for the hot big bang cosmology. Deviations of this radiation from a thermal spectrum

and from spatial anisotropy are expected to provide a wealth of information concerning

a variety of cosmological problems, including galaxy formation, star formation, and the

properties of relic elementary particles. Some theories of structure formation predict the

existence of a diffuse radiation at the infrared and optical wavelengths from the first burst

of star formation as primeval galaxies formed. 1 In the x-ray and "),-ray regions there is

an, as yet, unexplained diffuse background. Any relic particle species that has a radiative

decay mode should contribute to the diffuse background, and hence measurements of the

diffuse background can be used to discover or to set useful limits to the masses and couplings of such a particle species. Included in the list of relic particles whose existence or

properties can be so probed are axions, neutrinos, photinos, and gravitinos. As a worked

example we will consider the constraint_s that apply to a relic neutrino species with an

arbitrary branching ratio to a radiative decay mode. Finally, numerous exotic sources for

high energy photons--including superconducting cosmic strings--have been and continue

to be suggested.

Since there are a number of uses for a compilation of the various diffuse background

measurements we have attempted to review and present all the relevant data in the most

simple, coherent, and useful manner. Each spectra] region is treated separately, the reliability of various measurements are commented upon, and an annotated guide to the

literature is provided. Whenever there is, as yet, no definitive data we have attempted to

place the best upper limits to the flux provided by other existing data. Finally, we have

presented all the data in a consistent set of units: energy flux per unit area per unit time

per unit energy per unit solid angle (in cgs units). This corresponds to

dgVE (erg cm-2s-1 erg-1 sr-1) . (1)

IE =-----dAdtdEdgt

It is a simple matter to convert to two other forms of the differential flux often found in

the literature I,_ and I_:

d,_" E hc

I_ = = -C-_IE

dAdtd)_df_ A _

I_- = hiE.

dAdtdudf2

In addition, the differential particle number flux

d_'_ (cm_Zs_aerg_asr_l)

dAdtdEdO

(2)

2
is related to IE by

dAdtdEdgt

IE ,I 1

= -K = = -iNz..

Finally, integral fluxes (either number or energy) are sometimes of use:

dY(> E) dY(E')

dAdtd_2 - JE dAdtdEd_ dE"

Supposing that

it follows that

d5r

dAdtdEd_ -- cE -n,

d.T" (n- 1) d.T'(> E)

dAdtdEdf_ E dAdtdgt '

valid for n > 1. The following is a brief list of useful conversion factors:

1 Jansky = 10-2aergcm-2s-aHz -a

h -a (1 Watt m-2Hz-lsr -1) = 1.509 x 1029erg cm-2s-aerg -1

_cc lergcm = \E ]

sr -1

5.034 x 107erg cm-2s-lerg-lsr -a

1.986 x 10-Sergcm-2s-lerg-asr -1.

1 GeV = 1.602 x 10-3erg

h = 6.626 x 10-2VergHz -I

hc = 1.986 x 10-a6ergcm = 1.986 x 10-Serg/_

tic = 1.973 x 10 -14 GeV cm.

1 sr = 3.283 x 103 sq deg = 4.255 × 101° sq arcsec

Finally, "diffuse background" means different things in different circumstances. For

example, it can refer to a background of unresolved, discrete sources, e.g., the contribution

of QSO's to the x-ray background or the extragalactic cosmic rays, or to an intrinsically

diffuse background produced by relic-particle decays or radiation scattered and thermalized

by dust. In all instances DEBRA refers to extragalactic, rather than galactic, radiation.

RADIO (102cm- 10%m)

The radio region for which there is data spans the wavelengths from 10%m to 102cm.

At wavelengths longer than about 1 km the opacity of the ISM is very large due to free-free

absorption by electrons. Therefore, there are no measurements of the diffuse extragalactic

radiation at wavelengths significantly longer than this. Accordingly, X ,,_ 1 km constitutes

the long wavelength limit to our spectrum. Unlike most other spectral regions that we will
discussthere have not been measurementsin the radio recently. The data we discussis

quite firm as it has stood the test of time. In the region from 6.5 x 104cmto 3.7 x 102cm

we haveusedthe data of Clark, Brown, and Alexander,2 and for wavelengthsshorter than

this we have chosenthe data of Bridle. 3

The diffuse background in the radio is thought to be comprised of three components:

synchrotron radiation from the galactic disk; similar radiation from the halo; and the

diffuse extragalactic background radiation due to the integrated emission of all unresolved

extragalactic radio sources. It is difficult to separate the three components from one

another, and so we have chosen to present the total flux observed in this region as opposed

to various authors' estimates of the purely extragalactic component. The data we display

is taken from the region near the north galactic pole, and thus it should have the least

amount of contamination from the disk component of the diffuse radiation. It should,

however, be considered as a combination of galactic and extragalactic radiations, and thus

as a very firm limit to the DEBRA. The radio data are summarized in Figure 1.

MICROWAVE and SUBMILLIMETER (10-2cm- 102cm)

Unlike the radio, the microwave and submiUimeter portion of the DEBRA has been

the subject of intense, ongoing research. This is due, of course, to the presence of the

relic radiation from the hot big bang which dominates this region of the spectrum. Since

the surface of last scattering for the CMBR is the Universe at a red shift of about 1100

and an age of a few-hundred-thousand years, this radiation provides valuable information

about the early history of the Universe. The ongoing research is of two types: study of

the spatial anisotropy; and study of the spectral shape. Here we are concerned with the

spectral measurements. For a review of the anisotropy data we refer the reader to the

excellent reviews by Partridge 4 or Wilkinson. 5

The microwave and submillimeter region of the spectrum extends from wavelengths of

102cm to 10-2cm. Measurements of the spectrum of the CMBR are generally reported as

an equivalent black body temperature. The energy flux received from a black body that

fills the aperture of the antenna is

21/3

IE(BB) = -_ [exp(hv/kT) - 1]-_; (3)

it follows directly that the equivalent thermodynamic temperature of a source with flux

IE is

(hvll_)

T,q,,i,,- ln(1 -_ 2v3]C2IE)" (4)

A useful review that details the general methods used in spectral measurements, as well as

containing most of the recent measurements, is that of Richards. 6 Before the recent rocket

flight of Matsumoto, et al.,7 Smoot and collaborators s found that all measurements of the

CMBR in the wavelength range of 0.1 cm to 50 cm were consistent with that of a black

body spectrum at temperature TCMBR -- 2.74 + 0.02K. For completeness, we have also

4
included a somewhat older result at _ - 75 cm; see Weiss 9 for details. At wavelengths

longer than 100 cm the galactic background overwhelms the CMBR (see Figure 1). For

purposes of comparison we have plotted a black body spectrum of this temperature along

with the observational data. Because of the great importance of the CMBR there is a

wealth of experimental data for this region of the spectrum; the above mentioned reviews

by Richards 6 arid Smoot, et al.s contain most of the recent data and a rather complete

survey of the literature. The experimentalists working in this spectral region are generally

very careful in estimating their errors and so the data is generally quite trustworthy. We

have summarized the existing data in Figure 2.

A great deal of excitement has recently been generated by the submillimeter measurements of Matsumoto, et a17 Their data indicate a deviation from a purely Planckian

spectrum on the Wein side of the blackbody spectrum, corresponding to an energy excess

amounting to about 10% of that in the CMBR. The deviation is clearly visible in Figure

2. We caution that because of the low flux on the \Vein side of the spectrum there is

always the possibility that the effect could be instrumental; another rocket flew the same

instrument this past September and the data should soon be analyzed. In addition, Cosmic

Background Explorer (COBE) is scheduled to fly this November. We also mention that

a similar deviation has been seen by Gush, 1° although his experiment had instrumental

problems for which he had to correct. A number of theoretical models have been proposed

to explain the submillimeter excess including neutrino decays, other relic particle decays,

dust emission, and decay of vacuum energy. 11,14 None of the models yet discussed seems

completely plausible or compelling. If the distortion is real, the enormous energy budget

strongly suggests that the explanation involves fundamental physics--e.g., the decay of

some relic species. W'e should know soon!

In closing, we mention that study of the CMBR is a most active and important area

of ongoing cosmological research. Additional measurements of the Rayleigh-Jeans region

are being carried out by Levin, et al. 12 and De Amici, et al.;13 these measurements are

important because they provide the opportunity to accurately determine the temperature

of the CMBR over two decades in wavelength, and in so doing serve to severely constrain

any model of spectral distortion. The COBE satellite will provide high accuracy measurements over a large region of the spectrum. We currently have a good view of the night sky

at microwave wavelengths, and it should only continue to improve.

INFRARED (1 #m - 100 pro)

The infrared (IR) region of the DEBRA is one of great cosmological interest; however,

it is one of the most difficult regions to study owing to the enormous opacity of the

Earth's atmosphere and ubiquitous dust. Many interesting and important cosmological

and astrophysical events taking place between red shift z ,.- few to 1000 should contribute

to the background of diffuse IR radiation. These sources include pop III stars, galaxy

formation, dust-filled galaxies, decaying relic particles, etc. (see e.g. Bond, Carr, and

Hogan; 14 McDowell; 15 Rowan-Robinson and Carr; 16 Carr, 17 and references therein). One

5
might expect it to be a simple matter to compare the predictions to the observations, and

thereby test the multitude of cosmological scenarios. However, this is not the case because

of the difficulty in interpreting the observations. This difficulty is summed up in a single

word, "dust." Technology has advanced to the point where instrumental contamination can

be accurately corrected for; however, every observation is contaminated by interplanetary

(zodiacal) and interstellar dust emission. Thus, every measurement of the extragalactic

component depends upon modeling these contributions and then subtracting them from

the total flux to obtain the residual DEBRA flux.

We will take the IR portion of the spectrum to include the wavelengths from 10-2cm

(100/_m) to 10-4cm (1 #m). For the majority of the data we present the extragalactic

component has been obtained by removing estimates of dust emission. Therefore, the

reported fluxes are dependent upon the models for dust emission that the investigators use;

one may wish to refer to the original papers to see what procedures were used to obtain

the results quoted here. In some cases no attempt was made to extract the extragalactic

contribution to the flux, and we have used the measurement itself as an upper limit to the

diffuse flux.

In the region near 100 #m there are two data sets to consider. 7,1s,]9 The first is that

from the rocket flight of Matsumoto, et al. v On the same rocket flight that revealed the

deviation from a Planck spectrum in the submillimeter portion of the CMBR, Matsumoto,

et al.v also obtained measurements in three narrow IR bands centered at wavelengths of

262 pm, 137 pro, and 102 pm. They find that their data are well fit by interstellar dust at

a temperature TIS D "J 20 K. They are presently attempting to extract the extragalactic

: component from these data, and resultS Should be forthcoming. 2° For the moment, their

data should be taken to be an upper limit to any diffuse background. The second data set is

from IRAS observations, ls'19 At 100 pm Boulanger and Perault 19 have corrected the IRAS

data using a particular dust emission model to derive a value for the residual DEBRA. They

detail their procedure, and are careful to state that the inherent uncertainties associated

with their model are as large as the residual flux itself. Their derived extragalactic flux at

100 pm ties substantially below the 102 pm measurement of Matusmoto, et al. 7 At 60 pm

Rowan-Robinson and Carr 16 have used another subtraction scheme to obtain the value of

IE that we have used here. Once again we caution that the theoretical uncertainties are

at least as large as the deduced DEBRA. Finally, in the region from 50 pm to 10 #m the

only measurements that exist are for the total IR flux, and no attempt has been made to

extract the diffuse component. To set our upper limits we have used the measurements

of Hauser, et al. Is at the galactic poles and earlier measurements of Soifer, Houck, and

Harwitt. 21

From 1 pm - 10 _tm, commonly referred to as the "near IR," it is possible to attempt

absolute measurements of the DEBRA, although dust emission is still a problem. Observations of the DEBRA are quite inte:resting in this region as it is possible that such

radiation includes a component from the red shifted light associated with the initial epoch

of galaxy, formation. The majority of the data we have shown in the near IR is from the

6
rocket flight of Matsumoto, Akiba, and Murakami 22 (also see Matsumoto2a). Here too,

one must correct for dust emission to obtain a residual isotropic component that may

be extragalactic in origin. This experiment had some difficulty with contamination from

rocket exhaust; nonetheless, the authors feel confident that the signal detected at 2.2 pm is

real. However, the other detections are not as firm. For comparison, we have included two

other measurements. The first by Boughn and Kuhn 24 is an upper limit to the DEBRA

at 2.2 pro. The second is a measurement at 2.4 #m by Hofmann and Lemke. 25 With this

measurement, we have used the _otal measured flux as the upper limit for the error bar

in order to give the reader an idea of the amount of dust emission that must be removed

from the data (typically a factor of ,-_ 10 higher than the diffuse flux that is derived).

In conclusion, in the IR our knowledge of the diffuse extragalactic spectrum is rapidly

improving; however, one must still treat the results with care as they are very dependent

upon the dust emission models that are used to extract the extragalactic component.

OPTICAL AND ULTRAVIOLET (10/_ - 104/_)

Observers still detect more photons in the optical than in any other part of the spectrum; however, due to the relatively narrow bandwidth of the optical, AA/)_ _ 1, we will

consider it together with the more extensive ultraviolet (UV) band. In keeping with our

rather rough definitions of spectral regions we will take the optical/UV to extend from

about 10-4cm (10,000/_) to about 10-7cm (10/_). In the usual astronomical parlance this

includes the optical, UV, far UV, extreme UV, and a portion of the soft x-ray band.

There have been a variety of searches for the optical component of the DEBRA. As

yet, no detection has been claimed, and so we present only upper limits. In comparing the

data one must deal with the $10 unit, which is defined differently by different authors. (For

reference Lang _6 defines the $10 unit as one 10th magnitude star per square degree, while

Toller 2_ defines it as 1 S10(V)G2IV ---- 1.2 × 10-9ergcm-2s-1/_-lsr-1 at 4400_.) For the

sake of the reader's (as well as our own) sanity we have converted to our cgs flux units. We

have included 4 upper limits to the DEBRA in the optical in Figure 4. They are: Boughn

and Kuhn 24 at 6500._; Dube, Wickes, and Wilkinson 2s at 5115/_; 'roller 2_ at 4400/_; and

Spinrad and Stone 29 at 4000/_. The different authors have chosen to deal with background

subtraction with different methods, and we refer the reader to the cited articles for details

regarding this point.

From the end of the optical (near 3000A) to the Lyman limit (912/_) there are a

number of claimed detections of the DEBRA. Observations at these wavelengths are especially interesting because neutrinos with cosmologically interesting masses could decay and

produce a diffuse background, z° Unfortunately the observations are not of the sensitivity

required to reach the intensity levels predicted by the simplest models, where neutrino

decay proceeds through the usual weak interactions. (In more exotic models with horizontal or family symmetries, it may be possible that neutrinos or other particles have

sufficiently short lifetimes to be of interest; see below.) Due to the opacity of the atmosphere at these wavelengths, observations must be made with satellite-borne instruments.
This also largely circumvents the problem of airglow. Unfortunately, there are a number

of other possible "contaminants" that must be carefully removed from the data before a

true estimate of the DEBRA can be made. These contaminants are discussed in detail

by Paxesce and Jakobson, 31 and they include: zodiacal light, backscatter of radiation off

interstellar gas, and hot stars in the field of view. Many observers now feel that they have

these problems under control, and that they can make reliable measurements of the UV

background radiation. That is not to say that this point is without controversy; see e.g.

Martin and Bowyer. 32 (This paper also reports several measurements in this region of the

spectrum and provides a good discussion of the effect of galactic evolution upon the UV

component of DEBRA.) In any case, the reader should be aware that the reported DEBRA

measurements are a only small fraction of the total signal detected.

To summarize the data we have shown; we have used the data from the review of

Paresce and Jakobson 31 at 3300/_ and 2980/_.. The data at 2200/_ and 1690/_ are from

observations made by Joubert, et al. 33 using the D2B Aura satellite. The points at 1440._

and 1715._ are from a rocket flight by Anderson, et al. 34 as revised by Feldman, Brune,

and Henry. 3_ (This data is also presented in Henry. 36) Observations at 1360_ were carried out by \Veller, 37 using an instrument on the Solrad 11 satellite. We also include a

measurement that provides an upper limit in the region from 1200,_ to 500._. Using the

UV spectrometer aboard the Voyager 2 _,.pacecraft Holberg found no residual signal after

removing the interplanetary lines. 3s Finally, we include data for two regions that have

been surveyed spectroscopically. First, i:a the region 1200._, < A < 1700._, Murthy, et

al. 39 carried out a survey with 17._ resolution using a shuttle-borne spectrometer (this

group also has data extendingup to 3100,_. but it is not yet published). (Hurwitz, Martin,

and Bowyer 4° flew a similar instrument on the same shuttle flight and are said to have

found similar flux levels.) In the region 1700/_ < A < 2850._ we have included the 50/_

resolution data of Tennyson, et al.41 In both cases we have displayed the data with a box

that indicates the uncertalnitles. For more details, the reader should consult the original

papers.

Shortward of 912._ is known as the extreme UV (EUV). Because of the large cross

section for absorption by interstellar HI (neutral hydrogen) there is little chance of ever

acquiring a spectrum of the DEBRA. (The ISM is known to be patchy, and it is possible

that one could probe the DEBRA in the EUV by looking through a "hole" .) The absorption

cross section decreases as E -3, a(E) _ 6 x 10-23(E/keV) -3 cm 2, and so the interstellar

medium becomes transparent again at wavelengths of order 100/_. Measurements between

912/_. and 100/_. can be used to learn a great deal about the gas content of our own galaxy.

The upper limit of Holberg 38 extends from 1200]k down to 500/_. The other points we show

are from Stern and Bowyer 42 and Paresce and Stern, 43 and they extend from about 700_

down to about 20/_ (E _ 18 eV to 0.62 keV). The shortest wavelength measurements are

actually in the soft x-ray band. The data shortward of 912._ are reliable, but because of

strong absorption by the local ISM, they must be considered as a local flux. At the highest

energies (A _< 100_), the data should provide a reliable upper limit to the DEBRA. The
measurementsof the optical and UV are displayedin Figure 4.

X RAY and 7 RAY (1 keV - 100 MeV)

The diffuse extragalactic x-ray and 7-ray backgroundsare very well measuredin the

energy range of 1 keV to 100 MeV (X __10-7cm to A __10-1_cm). Sincethese backgrounds are similar in nature we have displayedthem together in Figure 5. Following the

conventional nomenclature, we will refer to keV photons as x rays and MeV (and above)

photons as ?_rays. The x-ray background has been reviewedextensively; see,e.g., the

excellentreviews by Boldt.44As he discusses,discrete sourcessuchasquasarsand Seyfert

galaxies contribute a substantial fraction of the cosmic x- and "),-ray backgrounds. It is

also believed by many, based upon the shape of the x-ray spectrum, that another substantial part may be due to a hot (T ,,_ 109 K) diffuse plasma. There is no consensus as

to the relative proportions of the two contributions---or if there is another significant, yet

unidentified, component.

The x-ray spectrum from 1 keV to 3 keV is fit by a simple power law 45

IE = 7.7 lke\' E )-o.4 ergcm-2s-lerg-lsr-l" (5)

From 3 keV to 50 keV Marshall, et al. 46 have found their data to be well fit by an opticallythin, thermal bremsstrahlung model with temperature kT = 40 4- 5keV. Gruber, et al. 47

confirm this form of the spectrum in the energy interval from 15 keV to 100 keV, except

they derive /,'T = 43 + 1 keV. In Figure 5 we have displayed the representation used by

Boldt ,44

( .E )°exp(-E/kT) (6) IE = A 3 keV

where A = 5.6 ergcm-2s-lerg-lsr -1, kT = 40 keV, and _ = 0.29. To give an impression

of the size of the measurement uncertainties we have also shown the data of Gruber, et

al. 47 (without error bars since they are quite small) in this range. From 100 keV to 1 MeV

we have shown the data of Gruber, et al.47 (with error bars).

In the 3,-ray portion of the spectrum from 0.3 MeV to 10 MeV we have used the

data of Trombka, et al. 48 The central line shown is the data, and the upper and lower

lines represent the l_r error limits. We call the reader's attention to the relatively good

agreement between this data set and that of Gruber et al.47 where they overlap. There

are no definite detections between 10 MeV and 35 MeV; however, we have included 2

upper limits, which indicate that there are no big surprises (see Trombka et al.48). Finally,

we display the SAS II data of Fichtel, Simpson, and Thompson 49 which extends from 35

MeV to 100 MeV. For a discussion of this portion of the spectrum we refer the reader to

Fichtel 5° and the earlier review of Silk. 51 We have displayed the data of Fichtel, et al.49 as

a parallelogram that specifies the la allowed region in the IE-E plane (also see Rothschild

et al.52). Finally, there is also one measurement from the COS-B satellite at 70 MeV, but

we defer comment upon this until the next section.

9
HE, VHE, UHE, and UHE "_ RAYS and COSMIC RAYS (E > 100 MeV)

The region of the spectrum from 100 MeV to the very highest energies observed,

about 102°eV, is a very interesting one. Unfortunately, a diffuse flux is extremely difficult

to measure. In fact, at these energies there are no claimed measurements of a diffuse

extragalactic--as opposed to a galm=tic--component. There are a number of detections of

a diffuse component that can be used as upper limits to any extragalactic component. Even

so, there are large parts of the electromagnetic spectrum that have never been surveyed

in any manner whatsoever. For example, DogieI, et al. sa point out that there has never

been an experiment to search for cosmic "y rays in the energy range 4--400 GeV, despite

the fact that this region is a potentially interesting one (e.g., dark-matter decays and

annihilations in the haloSaa). (The EGRET instrument on the Gamma Ray Observatory

(GRO) will explore the region of 20 MeV to 30 GeV when GRO is launched next year.

More ambitious experiments that probe the region of 1 GeV to 1 TeV have been proposed

for the Freedom Space Station.) Because of the paucity of data, we have turned to cosmic

ray (CR) measurements to provide absolute upper limits. (Except for the muon content

and shower shape, at these energies there is verb' little difference between photon- and

hadron-induced showers. For reference, where both 0' and CR data are available, the ")-ray

flux is at least 3 to 4 orders of magnitude smaller.) We have scrounged for any 7-ray

data available, and the reader should be forewarned that much of the data is open to

interpretation. Let us discuss the data that we have chosen to display in Figure 6.

The "_-ray data in the range from 70 MeV to 3.3 GeV are .verb, reliable. We have

used the COS-B data for the galactic anti-center region (Sachet and Sch5nfelder; 54 also

see Mayer-Hasse!wander, et al. 55). This data is Confined to a wedge -4- 30 degrees from the

galactic plane that is far removed from the galactic center. It should be relatively free of

"galactic contamination," and at the lea,;t provide a reasonably good upper limit to any

extragalactic flux. (For reference, the ratio of the flux in the direction of the galactic center

to that in the direction of the galactic anti-center is about 5).

From 3 GeV to 1 TeV there is very little data available. Moreover, we were unable to

locate any suitable data for energies of 3 to 30 GeV. From 30 GeV to 1 TeV we mention

the measurements of Nishimura, et al. 56 The group flew a balloon-borne instrument at an

atmospheric depth of about 4 gcm -2 for the purpose of measuring the CR electron flux.

In so doing they detected a flux of atmospheric 0' rays with spectrum given by

Q

" -- erg cm-2s- 1erg- 1sr -1 . (7)

They were able to attribute the entire fll:ux to secondary 3' rays from r ° decays. The _r°'s

are produced by the interactions of primary hadronic CR's in the atmosphere. At the very

least, this data provides an absolute upper limit to any diffuse flux of "I, rays because of

the shallow atmospheric depth of the experiment. (The interaction length for -y rays in the

atmosphere is about 47 g cm-2, 57'5s much. less than the 4 gcm -2 depth of the instrument.)

10
Since cosmic 7 rays of energies greater than 100 GeV behave much like hadronic CR's

in their interactions with matter, they should have been detected in any experiment that

measures the total CR flux. Thus, we have used the total CR flux above 100 GeV (from

Linsley 59 and Hillas 6°) as a very firm upper limit to the "_-ray flux above 100 GeV. Moreover, since the CR spectrum is of interest in its own right we have presented this data in

a rather complete manner. We have relied upon the summary given by Hillas. 6° (Other

extensive reviews exist; see e.g., Watson 61 and Linsley. 59) The Hillas compilation includes

data from the Proton 4 satellite and the Tien Shan, Akeno, Haverah Park, and Yakutsk

extensive air shower arrays. The reader is referred to his review for a more complete

bibliography.

The very highest energy cosmic ray data, 1017 eV _< E < 1020 eV, comes from the Fly's

Eye array 6e as well as the Haverah Park and Yakutsk arrays mentioned above. There is

some evidence in the Fly's Eye data for the so-called Griesen cut off at an energy of about

7 x 1019eV; the cut off arises as this is the threshold energy for r meson production off

CMBR photons, p + 73I< _ P + 7r. The other feature in the CR data is the "knee" at an

energy of about 1015eV, which (probably) traces to the large gyro radius for cosmic rays

above this energy which allows them to more easily escape magnetic confinement within

the Galaxy.

It is the very tough job of the "),-ray astronomer to separate out the small residual

flux of primary "t rays from the large "background" of hadronic cosmic rays. This is

difficult to do for two reasons. First, the _t-ray flux expected is only 10 -3 to 10 -4 of the

CR flux, which is itself falling rapidly with energy. 63'64'_s Second, in order to do so one

must differentiate between "7- and hadron-induced showers, and the differences are subtle---

shower development and shape, and muon content. Photon-induced showers are expected

to be narrower and muon-poor. Moreover, because photons maintain their directionality

(whereas charged CR's are strongly influenced by the galactic magnetic field), much of the

")'-ray astronomy effort is devoted to searching for point sources. The "telescope," whether

an atmospheric Cerenkov mirror or a particle detector array, is pointed toward the source

for a time and then taken "off source" for an equal time, and the two measurements are

subtracted to obtain the source signal. (See Weekes 66 for a lucid and in depth description

of the experimental techniques.) While this technique is useful for eliminating background,

it also eliminates the DEBRA component. There are, however, several measurements of a

diffuse component associated with the galactic disk and in some directions on the sky that

we will present.

Weekes 66 has reviewed much of the data we present at energies above 1 TeV; we will

only mention the measurements that are pertinent to the diffuse background. First, a few

general points. All of the data are presented as integral fluxes, i.e., IE(> E). All the

data from extensive air shower (EAS) arrays are selected based upon being muon-poor

showers. Monte Carlo calculations indicate that EAS's initiated by primary "), rays should

be deficient in muons by a factor of about 30 as compared to hadron-initiated showers.

(Whether or not "/-induced showers are truly muon poor is presently a matter of debate.

11
In the past few years,a number of point-source detections havebeenmade67'6swhere the

showeris apparently not muon-poor. Since the sources involved, Cyg X-3 and Her X-l,

are at distances of many kpc's it is certain that the primary particle must be neutral--to

maintain its directionality--and long lived suggesting that it is indeed a photon. If the

observations are correct, either the primary particle is not a photon, or photon-induced

showers at energies greater than about 1 TeV are not really muon poor.)

Next, the mean-free path for primary "7's with energies of 1014 to 1015 eV is very

short, A,_Ip ,_ 10_sofkpcs, because this energy is the threshold for e+e - pair production

off CMBR photons (7 + 73I< _ e + + e-). For higher-energy photons the mean-free

path grows slowly but does not really reach cosmological distances even at energies of

102°eV. Thus, there is little hope of measuring a truly eztragaIactic background at these

energies. (For a discussion of this issue see Protheroe, 69 and Zdziarski and Svensson. 7°)

Finally, because fluxes and event rates m:e small, the statistical significance of any of the

measurements discussed is far from being secure_but the data we mention here are the

best presently available.

Now the individual observations of the diffuse 7-ray background. For energies greater

than 0.5 TeV and 1.8 TeV we have shown two differential measurements (on minus off)

in the galactic plane made by Fazio, et al. _u For energies above 30 TeV we use the all-sky

flux of p-poor showers recorded at the C.haca!taya EAS array in the 1960's as an upper

limit to any diffuse 7-ray flux. 72 For energies above 100 TeV we also show the diffuse

flux of muon- and hadron-poor showers found over a large region of the sky by Suga, et

al. 7_ in a re-analysis of the Chacaltaya data. Gawin, et al. TM determined an upper limit

to the photon flux at energies above 800 TeV from the p-poor EAS data available at the

time. Weekes 66 argues that the most reliable data comes from the Tien Shah EAS which

is for energies of 1 PeV (1015eV) and above, v5 The Tien Shan array has excellent particle

discrimination and they ha_,,e selected only those shower events with very few muons and

hadrons to derive an all-sky diffuse 7-ray :flux. Their flux corresponds to 5 7 rays in 12,900

hours of observation. At energies above 2 x 101*eV Dzikowski, et al. 76 have measured

a diffuse flux in the galactic plane, and we use their measurement as an upper limit to

the diffuse extragalactic 7-ray flux. The highest energy point, E > 101VeV, is from the

Yakutsk EAS array and is based upon one p-poor shower, v7 All of the claimed detections

of a diffuse "r-ray flux correspond to about 0.1% of the CR flux--in agreement with the

theoretical expectations mentioned above. Not only are there no definitive measurements

of the diffuse 7-ray flux at energies abow_ 10 GeV, but also the very interesting question

of whether -y-induced showers are muon poor has yet to be answered.

For purposes of comparison we have included rough representations of the CR electron

(plus positron) flUX, the atmospheric-muon flux, and the atmospheric-neutrino flux in

Figure 6. The electrons (and positrons) are generally believed to be cosmic ray primaries,

while the muons and neutrinos are produced by the interaction of hadronic CR primaries

in the Earth's atmosphere (through r, K, etc. meson decays). The spectrum of electrons

and positrons extends from I MeV to 2 TeV and is a compilation of data taken by Meyer, v8

12
Golden, et al., 79 Tang, s° and Nishimura, et al.56 The spectrum is dominated by electrons

but positrons do a contribute at the 10% level; see e.g., M/iller and Tang. sl (Most of the

positron flux is believed to arise from the decays of mesons that are produced by CR

interactions with the ISM; more exotic sources have also been suggested: e.g., dark matter

annihilations in the halo.) We present the sea level atmospheric muon data from Allkofer s2

in the energy region from 0.2 GeV to 105 GeV. It consists of the differential measurements

from 0.2 GeV to 1 TeV of Allkofer, et al.s3 and an integral spectrum converted to a

differential spectrum (using a spectral index of n = 3.57) from 1 TeV to 100 TeV.

Finally, the atmospheric-neutrino spectrum includes v,, P,, vu, and P u neutrinos and is

the theoretical spectrum based upon known nuclear and particle physics and the measured

flux of muons at sea level. From 10 MeV to 10 GeV we have used the calculations of Gaisser

and Stanev, s4 and from 10 GeV to 107 GeV those of Volkova. s_ The two calculations are

in reasonable agreement in their region of overlap, but note the slight jump in IE. The

atmospheric-neutrino flux is an important background for large underground detectors

such as IMB, Kamiokande, Soudan, Frejus, NUSEX, and KGF. Moreover, the flux of

atmospheric neutrinos has been measured in several of these experiments; see Svoboda, et

al., s7 Krishnaswamy, et al.,ss and Reines, et al.s9 Finally, Krauss, et al. s6 have calculated

the background of antineutrinos expected from radioactive decays within the Earth and

various astrophysical sources (Sun, supernovae, etc.).

To summarize our review of the DEBRA, we present in Figure 7 "the grand unified

photon spectrum" (or GUPS). From the GUPS one can clearly see that most of the diffuse photons in the Universe reside in the CMBR. In terms of the energy content of the

diffuse background it is a close--and still undecided--contest between the CMBR and the

submillimeter/IR region of the spectrum. While the photon flux at energies above 1 eV

is falling rapidly, this part of the spectrum may contain important information and clues

concerning interesting cosmological as well as contemporary astrophysical events.

A WORKED EXAMPLE: CONSTRAINTS TO UNSTABLE NEUTRINOS

To illustrate one of the uses of the GUPS we will consider the wide variety of constraints

to the mass and lifetime of an unstable neutrino species that derive from it. If neutrinos

are massive, then the different flavor eigenstates (e,/1, and v) can--and indeed are likely

to--mix, and transitions between different neutrino types are possible. Thus, a massive

neutrino is expected to be unstable. Within the context of the standard electroweak

interactions, a massive neutrino can decay, UH _ UL + 7, with a lifetime

7-,, ... 1027 sin-2(20)(m,,c2/eV )-%ec (s)

(/-/H = "heavier" neutrino, V L ---- "lighter" neutrino); neutrinos heavier than 1 MeV can

decay, UH _ /-_L + C t" -I- ¢-, with a lifetime

r,, -._ 102` sin-2(20)(m,,c2/eV )-Ssec. (0)

13
Further, if there exist new flavor changing (or horizontal) interactions characterized by an

energy scale, F, a heavy neutrino can decay VH ----* VL "4-X (where X is some unspecified

scalar particle, e.g., majoron, familon, etc.), with a lifetime

~ F m; -3 10 (F/10 CeV) (r c2/eV )-3see. (10)

In most models with horizontal (or family) interactions, the energy scale F must be greater

than about 109 GeV to be consistent with the absence of various flavor-changing neutral

current processes.

So we see that massive neutrinos are very likely to be unstable---and with long lifetimes.

Thus their decays are probably beyond the "reach" of terrestrial laboratories. Because a

long-lived neutrino with mass in the 30 eV range is cosmologically interesting many groups

have searched for neutrino-decay produced photons in the UV portion of the spectrum;

see e.g., De Rtljula and Glashow, 3° Ho!berg and Barber, 9° and Henry. 37 (For reference,

f_,_ = rn,/91h 2 eV where _ is the fraction of critical density contributed by relic neutrinos and here h is the Hubble constant in units of 100 km sec -1 Mpc -I.) There has yet

to be any convincing evidence for relic neutrino decay, and so the present data serve to

provide upper limits to the lifetime, r_, of the neutrino. Since the anticipated lifetimes are

long and usually inaccessible in the laboratory, astrophysics and cosmology can provide

unique information as to the possibility of neutrino decay--even if neutrino masses are not

cosmologically interesting. In this section we will consider an unstable neutrino species

of mass rl_, and lifetime r, that has a branching ratio, B_, to a radiative decay mode.

The "source of the neutrinos" for our cosmological laboratory is the big bang, and we will

assume the "standard" relic abundance for a neutrino species (see below). In addition we

shall assume that these relic neutrinos are uniformly distrlbuted--if they should be clustered with galaxies or galaxy clusters the.' constraints that follow are even more stringent.

We will use the GUPS to exclude regions of the mass-lifetime plane (which depend upon

The limits that we obtain depend upon the epoch during which the neutrinos decay. To

simplify the analysis, we consider four qualitatively different lifetime regimes: 1) lifetimes

longer than the age of the universe, tu; 2) lifetimes shorter than tu but longer than the age

of the Universe at matter-radiation decoupling (red shift z "-" 1100); 3) lifetimes between

the time of matter-radiation decoupling emd the time at which double-Compton scattering

(-y + e- --_ e- + 3' + 3") becomes effective at thermalizing the decay photons (z __ 10v); 4)

lifetimes such that the neutrino species is relativistic at decay.

For an unstable neutrino species that has a lifetime longer than tu "-' 4 x 1017see relic

neutrinos are still decaying today and produce an intensity

IE - 4_T_Ho nvc(E-t) rnY/2 3/2 B_, (11)

where we have assumed a flat Universe aJ_d a two-body decay so that each decay-produced

photon has an energy E- r = rn,c2/2. (The decay photons are mono-energetic when produced; however, because they decay over a range of red shifts, there is a spectrum of

14
photons at the present epoch.) The present neutrino number density, nv, depends upon

whether the neutrinos were relativistic or non-relativistic at the time when they decoupled. A light neutrino species (rn, << 1 MeV) decouples at. a temperature of a few MeV,

when it is still relativistic, and such a species today is about as abundant as photons:

n_ = ll5cm -a. A heavy neutrino species (rn_, >> 1 MeV) decouples when it is nonrelativistic (kTd _- rn_c2/20), and its present relic abundance is approximately

--3

nj,= 1.78x 10 .5 1GeV 1+ 15 "

(For the derivation and discussion of these results see Kolb and Turner. 91)

For simplicity we will assume that the dividing line between a "heavy" and a "light"

neutrino species is m,,c 2 = 1 Me\'. It is now straightforward to constrain the quantity

r,,/Br by comparing the predicted flux with that observed and requiring that the predicted flux of decay photons not exceed the observed flux. (Note, except for a narrow

wavelength interval around the Lyman limit, the Universe is transparent to the decayproduced photons.) We display the results of this exercise in Figure 8 for neutrino masses

in the range 10 -a eV < m,c 2 < 100 GeV. The upper mass limit is determined by the fact

that n, as a function of m, must change form for neutrinos more massive than the Z °

boson; moreover, it is not obvious that a neutrino more massive than a few hundred GeV

can be self-consistently incorporated into the electroweak theory. The lower limit follows

from the fact that these neutrinos are relativistic today and must be treated separately,

which we shall do shortly. Finally, we mention that long-lived neutrinos of mass between

91h 2 eV and 2 GeV are forbidden by another very familiar cosmological argument; namely

the fact that their present mass density would be excessive.

For a neutrino species that has a lifetime shorter than tu but longer than the age of

the Universe at matter-radiation decoupling, tDEC _' 5.6 x 1012(_oh2)-1/2 see, a slightly

different analysis must be performed. The main differences are: (i) because all the relic

neutrinos have decayed by the present, only Br and rn, are relevant; (ii) the expression

for IE is simpler because each relic neutrino produces one photon, from which it follows

that

G = f sEXdE - n_c -4-7 

Here n_ is the number density that the neutrinos would have today had they not decayed

and 9v._ is the number flux of relic photons ( cm-2sr-1 sec -1 ). Again, assuming a two-body

decay, the decay-produced photons are mono-energetic, with energy E.y _- rn,,c2/(1 + za),

where the red shift at the epoch of decay is

(1 + zd) "- 4.8 x 109(r_,/sec )-1/2 (ta _ tee2) (14a)

(1 + ze) = 3.8 x lO"(r./sec)-213(aoh2)-_la (re > tEq) (14b)

where tee2 is the age of the Universe at the epoch of matter-radiation equality: tEq = 4.4 x

10_°(120h2) -_ see. Since the decays occur over a red shift interval Az/z ,., O(1), AE._/E._ ,,,

15
O(1), and IE _-- .T_ = Brn,c/47r. Using this approximation we can obtain a limit to Br

for neutrino masses in the range 10 -3 eV < m,c 2 < 100 GeV by comparing the predicted

flux to the GUPS (as we did before). Our constraint is shown in Figure 9.

For an unstable neutrino species that decays when it relativistic, a slightly different

chain of reasoning applies. Such a neutrino species will have maintained the thermal

equilibrium distribution it had when it decoupled, but with a red shifted temperature:

T,(t) = TdRd/R(t). Thus it will have an energy density given by

p,. = aT: = _ aT_ __ 0.23aT¢, (15)

where the factor of 7/8 comes from Fermi-Dirac statistics and the factor of (4/11) 4/3 arises

because the photon temperature increases relative to the neutrino temperature at the epoch

of e+e - annihilation, which occurs after neutrinos decouple from the plasma. Since the

energy density in the CMBR is ate, it follows that the energy density in neutrino-decay

produced photons amounts to 0.11Br times that in the CMBR (assuming that on average

each decay-produced photon carries away half the energy of its parent neutrino). These

neutrino-decay-produced photons have typical energies that are comparable to, but less

than that of, a typical CMBR photon, and the total energy content of the decay-produced

photons is about 0.1!B_. Unless they can be thermalized, or unless B,- _ 0.1, unacceptable

distortions of the CMBR will result. The decay-produced-photons can be thermalized--as

opposed to scattered--only if the decays occur early enough so that the double-Compton

process is effective (t < tPC "" 106 sec ). Thus we can conclude that an unstable neutrino

species with Br > 0.1 that decays after t =- tDC "" 106 sec and before the pffesent epoch is

forbidden on cosmological grounds; the excluded region of the mass-lifetime plane is given

by

0_00see/e\.' <v_/mvc 2 <4× !02°(Q0h2)l/3sec/eV, (16)

subject to the condition that the neutrino species be relativistic when it decays, which

corresponds to

rove _ < 3.5 × lOS(_oh2) -'/_ ( _'_ )-2/3 eV (_-_ > tEQ), (17)

x seE ]

7-v _-1/2 mS < 4.6 x 10 , s- c eV < tEQ). (lS)

In Figure 10 we show this constraint (for F_oh 2 = 1/4).

Now consider a neutrino species that decays when it is non-relativistic and has a

lifetime in the range tDe < rv < tDE C. Neutrinos that decay during this epoch will

deposit energy into the CMBR that can be scattered but cannot be thermalized because of

the ineffectiveness of the double-Compton process. This will result in a CMBR spectrum

that is characterized by a Bose-Einstein distribution with non-zero chemical potential.

Because the CMBR spectrum is that of a black body to high precision, we can set limits

16
to combinations of r_, rn_, and B_. If we crudely characterize the allowed distortion by

requiring that the ratio of energy density in the decay-produced photons to that in the

CMBR be less than 0.1, we arrive at the following limits for rn,c 2 < 1 MeV and m_c 2 >

1 MeV respectively:

mvc 2 < 2 × 10 ° (,'_B_) -'n eV , (19)

rn_,cl E 8x 106 [1 + 31n(mvc21GeV)]5 '1_ eV. (20)

The logarithm term in the second expression arises from the formula for the relic

abundances of a heavy neutrino species. (We have assumed that the Universe is radiation

dominated during the decay epoch; if not previously discussed constraints apply.) This

constraint is shown in Figure 10.

The electromagnetic energy released by an unstable neutrino species that decays at a

time earlier than about 106 see should become well thermalized so that it will not distort

the CMBR. (It will of course increase the entropy of the Universe, however the limit that

follows is not particularly severe; see Ref. 91.) For further discussion of the constraints

that apply to an unstable neutrino species and a complete list of references, see Ref. 91.

CONCLUDING REMARKS

The diffuse spectrum of electromagnetic radiation extends from 105 cm to 10 -24 cm,

some 29 orders of magnitude. It is dominated by the CMBR. With the exception of a

small portion of the UV, it provides a unique and very large window on the Universe

out to cosmological distances, allowing one to study physical processes as diverse as star

formation and relic-particle decays. Two regions of the extragalactic background remain

almost unexplored: the IR and that above energies of a few GeV, and both are of great

cosmological interest.

In closing, we should mention the earlier reviews of the diffuse background that exist;

: hey include those of Longair, 92 Lequeux, 9a and Sharer. 94 We also caution the reader that

our synthesis of the diffuse background data and review of the literature has by no means

been exhaustive. Our bibliography, while extensive, is not complete, and we have in most

cases deferred to review articles for more complete surveys of the literature.

Acknowledgments

We wish to thank Bill Collins, Rocky Kolb, and Brian Yanny for their valuable assistance. This work was supported in part by the DoE (at Chicago and Fermilab), by NASA

(at Fermilab), and by MTR's NASA GSRP fellowship at Chicago.

17
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21
FIGURE CAPTIONS

Figure 1 -- The radio region of the spectrum. Note the long wavelength tail of the CMBR

in the lower right corner.

Figure 2 -- The microwave/submillimeter region of the spectrum which is dominated by

the CMBR. The energy flux from a black body with a temperature 2.74 K is shown for

comparison; note the submillimeter excess found by Matsumoto, et al.T

Figure 3 -- The infrared region of the spectrum. The majority of the measurements have

been corrected for galactic dust emission; see text for details.

Figure 4 -- The optical and ultraviolet region of the spectrum. Here too the majority of

the measurements have had various contaminants removed by modelling.

Figure 5 -- The x-ray and "/-ray region of the spectrum (up to an energy of 100 MeV).

The curve at upper right is the fit of Boldt 44 joined to the power law fit of Schwartz 45.

The three lines in the center represent the measurements Trombka, et al. 48 with 1 a error

bars. The parallelogram in the lower right hand corner indicates the data of Fichtel, et

al. 49 (with 1 a error flags).

Figure 6 -- The ")l-ray region of the spectrum (E :> 100 MeV) and the cosmic ray spectrum

above 100 GeV. Circles denote the all-particle CR spectrum as summarized by Hillas6°;

triangles the all-particle CR spectrum from the Fly's Eye62; and squares the claimed "r-ray

fluxes and upper limits using air Cerenko_" and muon-poor air shower techniques (see text

for details). The solid line is the upper limit to the photon flux from Nishimura, et al. 56

For reference we show the CR e_- flux, the atmospheric-muon flux, and the atmospheric

neutrino flux.

Figure 7 -- The grand unified photon spectrum, or GUPS. This figure is a synthesis of

Figures 1-6.

Figure 8 -- Lifetime/branching ratio constraints for an unstable neutrino species whose

lifetime is longer than the age of the Universe. The boundary of the "excluded" region and

"a/lowed" regions is defined by the locus of points (and line segments) that are shown.

Figure 9 -- Branching ratio constraint for an unstable neutrino species with lifetime

tDEC < ru < tu. The boundary of the "excluded" region and "allowed" regions is defined

by the locus of points (and line segments) that are shown.

Figure 10 -- The constraints that apply to an unstable neutrino species that decays

while it is relativistic (dashed line) and one that decays while it is non-relativistic and

between decoup]Jng and the epoch that the double-Compton process became ineffective

(solid lines). Note, for the former limit the branching ratio Br must be _> 0.1, otherwise

there is no constraint.

22
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