DIRBE Minus 2MASS: Confirming the CIRB in 40 New Regions
at 2.2 and 3.5 Microns
L.R. Levenson & E.L. Wright
Department of Physics and Astronomy, University of California, Los Angeles, CA
90095-1562
levenson@physics.ucla.edu
B.D. Johnson
Dept. of Astronomy, Columbia University, 550 W. 120th St., New York, NY 10027
ABSTRACT
With the release of the 2MASS All-Sky Point Source Catalog, stellar fluxes
from 2MASS are used to remove the contribution due to Galactic stars from the
intensity measured by DIRBE in 40 new regions in the North and South Galactic
polar caps. After subtracting the interplanetary and Galactic foregrounds, a
consistent residual intensity of 14.69 ± 4.49 kJy sr−1 at 2.2 µm is found. Allowing
for a constant calibration factor between the DIRBE 3.5 µm and the 2MASS 2.2
µm fluxes, a similar analysis leaves a residual intensity of 15.62 ± 3.34 kJy sr−1
at 3.5 µm. The intercepts of the DIRBE minus 2MASS correlation at 1.25 µm
show more scatter and are a smaller fraction of the foreground, leading to a still
weak limit on the CIRB of 8.88 ± 6.26 kJy sr−1 (1 σ).
Subject headings: cosmology: observations — diffuse radiation —infrared: gen-
1. Introduction
The Cosmic InfraRed Background (CIRB) is the aggregate of the short wavelength
radiation from the era of structure formation following the decoupling of matter and radiation
in the early universe, redshifted to near infrared wavelengths by cosmological redshifting and
far infrared wavelengths by dust-reprocessing, i.e. absorption and re-emission of starlight
by intervening dust. Particle decay models also allow for a contribution to the CIRB from
photons produced in the decay of weakly interacting massive particles such as big bang
http://arxiv.org/abs/0704.1498v3
– 2 –
relic neutrinos (Bond et al. 1986). The Diffuse InfraRed Background Experiment (DIRBE)
on the COsmic Background Explorer (COBE, see Boggess et al. (1992)), which observed
the entire sky in 10 infrared wavelengths from 1.25 to 240 µm, was primarily intended to
measure the CIRB. A determination of the CIRB turned out to be exceedingly difficult due to
bright foreground contamination including Galactic starlight and the strong thermal emission
and reflection of sunlight by dust in the solar neighborhood in many of the DIRBE bands,
especially in the near infrared (NIR). The DIRBE team estimated this zodiacal contribution
by fitting a computed brightness, based on a physical model of the InterPlanetary Dust
(IPD) cloud, to the weekly variations in the DIRBE brightness due to COBE’s changing
position in the solar system as the Earth orbited the Sun (Kelsall et al. 1998). The modeled
brightness was computed by integrating a source function, multiplied by a three dimensional
density distribution function, along the line of sight. Using this model for zodiacal light
subtraction, the DIRBE team succeeded in measuring an isotropic CIRB of 25 ± 7 nW m−2
sr−1 (1170 ± 328 kJy sr−1) and 14 ± 3 nW m−2 sr−1 (1123 ± 241 kJy sr−1) at 140 and 240
µm respectively (Hauser et al. 1998). In the NIR bands, they reported only upper limits on
the CIRB.
Using the “very strong no-zodi principle” of Wright (1997), another model of the zodiacal
light was determined and is described in Wright (1998) and Gorjian et al. (2000). After
creating DIRBE all sky maps with this new model subtracted, the problem of subtracting
Galactic starlight in the NIR was addressed by Gorjian et al. (2000) at 2.2 and 3.5 µm by
directly observing Galactic stars in a 2◦ × 2◦ region of the sky, smoothing the observed
intensities to the DIRBE pixel size and subtracting the resulting intensities from DIRBE
maps with the Wright (1998) zodiacal light model subtracted. Wright (2001) used this same
procedure of subtracting Galactic starlight from the DIRBE maps using stellar fluxes from
the 2MASS 2nd incremental release Point Source Catalog (PSC) in four regions in the North
and South Galactic poles. Dwek & Arendt (1998) showed that the DIRBE 3.5 µm intensity
was strongly correlated with the DIRBE 2.2 µm intensity at high Galactic latitudes and used
this correlation to convert a lower limit on the 2.2 µm CIRB, based on galaxy counts, into
a lower limit on the 3.5 µm CIRB. Wright & Johnson (2001) extended the Wright (2001)
analysis to 13 regions at 2.2 µm and combined the Wright (2001) and Dwek & Arendt (1998)
techniques to obtain estimates of the CIRB for those 13 regions at 3.5 µm. In this work
we extend the Wright & Johnson (2001) analysis to 40 new regions to further constrain the
CIRB at 1.25, 2.2 and 3.5 µm.
– 3 –
2. Data Sets
The two main datasets in this paper are the zodi-subtacted DIRBE maps and the
2MASS All-Sky Point Source Catalog (PSC).
DIRBE has a large 0.7◦ × 0.7◦ square beam with a diagonal of 1◦. Pixel intensities in
the DIRBE maps are averages of all observations made while the beam was centered in a
given pixel in the COBE Quadrilateralized Spherical Cube (CSC) projection. Due to the
large beam size, bright stars outside of a particular pixel will, depending on the exact center
position and position angle of the beam, occasionally affect the observed brightness in that
pixel. Thus a thick buffer ring is needed around any studied field to keep bright stars out-
side the field from influencing the measured DIRBE intensity. The resulting inefficiency was
minimized by using the darkest possible 2◦ circular regions which have the largest possible
area:perimeter ratio. A list of dark spots was created by smoothing the 3.5 µm DIRBE Zo-
diacal Subtracted Mission Average (ZSMA) map to 1/64th it’s original resolution, reducing
the 393,216 0.32◦ × 0.32◦ pixels to 6144 pixels approximately 2.5◦ × 2.5◦ using a straight
average of nearest neighbor pixels and sorting the resulting low resolution map. The 40
darkest regions not used in previous analyses were used.
However, the DIRBE ZSMA project data set only uses a fraction of the DIRBE data
since extreme solar elongations were dropped. Therefore, a set of mission averaged zodiacal
subtracted DIRBE maps were created by Wright (2001) using the zodiacal light model of
Wright (1998). The physical model is similar to the Kelsall et al. (1998) model, with an
added constraint. The “very strong no-zodi principle,” described in Wright (1997) and
Gorjian et al. (2000), requires that at high Galactic latitudes, at 25 µm, the background
emission should be isotropic and adds a single pseudo-observation of zero emission to the
nearly 105 observations used to fit the time variation in the weekly maps to the model
brightness. At 1.25 and 2.2 µm, no correction for interstellar dust emission is needed, while
at 3.5 µm, there is a very small correction (Arendt et al. 1998). The ith pixel in these maps
provides the DIRBE data DZi.
Using the NASA/IPAC InfraRed Science Archive (IRSA), fluxes from all stars in each
of the 40 regions brighter than K = 14 in the all-sky release of the 2MASS PSC were
obtained. Again due to the large beam size and effectively random distribution of the
beam center and position angle, these fluxes were converted into intensities by smearing
with a 0.7◦ × 0.7◦ square beam with a center uniformly distributed in the DIRBE pixel and
orientation uniformly distributed in position angle, to obtain the cataloged star contribution,
Bi, to the DIRBE intensity. This smearing process is described fully in Section 3. For the
J-band contribution, only stars with J and K less than 14 were used. This dual wavelength
magnitude selection is essentially equivalent to a simple J < 14 selection (Wright 2001).
– 4 –
3. Analysis
The zodi-subtracted DIRBE intensity in the ith pixel, DZi, should be the sum of the
cataloged stars, Bi; the faint stars, Fq, assumed constant for all pixels in the q
th region; and
the CIRB, C ,which is isotropic, i.e.
DZi = Bi + Fq + C . (1)
The cataloged star contribution was computed using the “smearing” described in Gorjian et al.
(2000) and Wright (2001),
pijSj , (2)
where Ωb is the solid angle of the DIRBE beam, Sj is the flux of the j
th star and pij is the
probability of the jth star affecting the ith pixel under the assumptions that over the many
observations in which the DIRBE beam was centered in the ith pixel, the beam center was
uniformly distributed within the pixel and the beam orientation is uniformly distributed in
position angle. Due to the random distribution of the orientation of the square 0.7◦ × 0.7◦
beam, the probablility as a function of the angular distance, r[(α, δ), (α⋆, δ⋆)], between the
beam center (α, δ) and a particular star at (α⋆, δ⋆) is
P (r) =
0, for r > l√
arccos l
, for l
≤ r ≤ l√
1, for r < l
where l is the width of the beam (0.7 deg) and,
r = arccos[cos(α− α⋆) cos(δ) cos(δ⋆) + sin(δ) sin(δ⋆)] . (4)
Then, to account for the random position of the beam center within the pixel, this probability
must be averaged over the area of the pixel by integrating P(r) over the solid angle of the
pixel and dividing by the pixel solid angle, Ωi, so that
pij =
P (r)dΩi
. (5)
Uncertainties in Bi were calculated as in Wright (2001):
σ2(Bi) =
[pij(1− pij) + pij
2(0.001 + (0.4 ln 10)2σ2(mj))]Sj
2 . (6)
The first term is noise due to stars near the edge of the DIRBE beam which will“flicker” in
and out of the beam when observed with various centers and position angles. The second
– 5 –
term is the flux error with an added allowance for variation in the fluxes between the DIRBE
and 2MASS observations as in Wright (2001), with the modification that the allowance for
variable stars was reduced from 0.1 to 0.001, reducing this allowance from σ = 0.34 to σ =
0.03 magnitudes. Statistically, the σ’s computed with the Wright (2001) value of 0.1 were
too large to be justifiable. Upon dividing the residuals from the linear fit to the DIRBE vs.
2MASS intensities (described below) by the computed σ’s, we noticed that the residual/σ
at all pixels was less than one. The new value of 0.001 gives a statistically more reasonable
distribution of residual/σ values which is described at the end of this Section. The error
estimates for all stars brighter than K = 5.5 or J = 6.5 were set to ± 1 mag to effectively
remove pixels affected by confusion due to saturation from the final analysis. Stars with
reported null uncertainties were assigned an uncertainty of ± 0.5 mag. Since the error in the
DIRBE data is negligible (Hauser et al. 1998), all of the error comes from the calculation of
Bi and is ascribed to DZi for the fits. Figures 1, 2 and 3 show plots of DZi vs. Bi for all
pixels in each of the 40 regions in K, J, and L respectively where the point sizes are inversely
proportional to the above σ’s.
The fits in K, J and L have slopes of κK = 0.88, κJ = 0.97 and κL = 0.43 respectively
with 40 independent intercepts in each band, derived using a weighted median procedure,
i.e. finding the values of κ and DZ(0) that minimize the sum:
|(DZi − κBi −DZ(0))/σi| . (7)
Derived intercepts for each field are given in Tables 1, 2 and 3 for K, J, and L respectively.
The contributions from stars fainter than the 14th magnitude were evaluated statistically
by fitting a power series of the form nq(m) = n◦,q10
αm to counts of 2MASS stars in each
of the 40 regions, binned into 3 one-magnitude bins centered on m= 11.5, 12.5 and 13.5.
The fits resulted in 40 individual n◦,q and αK = 0.288 and αJ = 0.276 where any α < 0.4
results in a converging flux contribution. The intensity contribution from faint stars in the
qth region with solid angle Ωq is then
F◦(λ)n◦,q
m=14.5
10(α−0.4)m (8)
or, in the limit of infinitely fine bins,
F◦(λ)n◦,q
10(α−0.4)mdm , (9)
which was computed analytically. At L, the faint source contribution in each region is the
2.2 µm value multiplied by the calibration ratio of 0.491. These Fq are listed in Tables 1,
– 6 –
2 and 3 for K, J and L. An uncertainty of 20% of the total prediction is assigned to this
correction, and is listed in Table 5 under “Faint Source.”
The CIRB in each region is then the derived intercept, DZ(0), minus the faint star
contribution Fq, C = DZ(0) - F. These values are also listed in Tables 1, 2 and 3. The mean
of these CIRB estimates are 14.59 ± 0.14, 8.83 ± 0.51 and 15.57 ± 0.20 kJy sr−1 for K, J
and L. These standard deviations of the means are listed in Table 5 as “Scatter.”
2MASS magnitudes at K and J were converted into fluxes using F◦(K) = 614 Jy and
F◦(J) = 1512 Jy which were derived by Wright (2001) and Gorjian et al. (2000). However,
the derived slopes at K and J indicate DIRBE fluxes for a zero magnitude 2MASS star
of 540 and 1467 Jy respectively. The ratio of the calibration factors at 3.5 and 2.2 µm is
0.491, consistent with those found by Dwek & Arendt (1998), Wright & Reese (2000) and
Wright & Johnson (2001). Uncertainties in the CIRB due to calibration error were estimated
using the change in the median DZ(0) when the slopes, κ, were forced to change by ±5%
at J and L, or ±10% at K due to the large difference (Wright & Johnson 2001) between the
fitted value of 0.88 and the expected value of 1. The change in the medians are ∓ 2.24, 1.77,
and 0.60 kJy sr−1 at K, J and L respectively and are listed in Table 5 under “Calibration.”
There is a small correction for faint galaxies that appear in the 2MASS PSC. These
have been subtracted along with the Galactic stars, but should be included in the CIRB.
Wright (2001) estimates this correction is 0.1 and 0.05 kJy sr−1 at 2.2 and 1.25 µm. The
0.1 kJy sr−1 correction at 2.2 µm implies a 0.05 kJy sr−1 correction at 3.5 µm due to the
relative calibration factor of 0.491. These corrections have been added back after taking the
mean of C = DZ(0) - F in the 40 regions. Thus, the final reported values of the CIRB are
the mean of the values C in Tables 1, 2 and 3 plus this correction. An uncertainty of 100%
of this correction is included in Table 5 under “Galaxies.”
Gorjian et al. (2000) adopt an uncertainty of 5% of the zodiacal intensity at the ecliptic
poles. These uncertainties are listed in Table 5 under “Zodiacal.”
After adding errors in quadrature, we obtain a CIRB of 14.69 ± 4.49 kJy sr−1 at 2.2
µm, a weak limit of 8.88 ± 6.26 kJy sr−1 at 1.25 µm and a CIRB of 15.62 ± 3.34 kJy sr−1
at 3.5 µm.
Figures 4, 5, and 6 show histograms of the residuals DZi − κBi − DZ(0) for all 2971
pixels in K, J and L with interquartile ranges of 2.85, 3.57 and 2.11 respectively. Dividing
these residuals by σ(Bi) at each pixel gives a non-Gaussian distribution which is tightly
packed near zero with a few pixels extending out to large values. The number of pixels with
|(DZi − κBi − DZ(0))/σ(Bi)| less than {0.5, 1.0, 2.0, 3.0} at K, J and L are {2424, 2832,
2930, 2951}, {2588, 2873, 2955, 2955} and {2590, 2867, 2947, 2955}. For comparison, with
– 7 –
a Gaussian distribution, one would expect these numbers to be, {1138, 2028, 2835, 2963};
more spread out in the center, with fewer pixels in the extended tail. We have used a robust,
least sum of absolute values fitting method, which, by it’s nature, is insensitive to the few
pixels with large residual/σ. Thus the fit for the slopes, κ, and intercepts, DZ(0), is to the
pixels in the narrow core, and the outliers have little effect on their derived values and the
final CIRB values.
Figures 7, 8, and 9 show the derived intercepts, DZ(0), vs. ecliptic latitude in the
three bands. We see here the same trends with ecliptic latitude as were apparent in
Wright & Johnson (2001). While the K-band intercepts appear reasonably independent of
ecliptic latitude, there is a strong trend in J and a slight negative trend in the L-band. The
zodiacal light is fainter at 3.5 µm than at 2.2 µm, and so the stronger dependence on β
at L than at K may seem surprising. However, at 3.5 µm, we begin to see thermal emis-
sion from the interplanetary dust, in addition to the scattered sunlight. From a modeling
standpoint, this gives another free parameter which should provide a better fit, but from
a physical standpoint, we are likely seeing a more complicated emission/scattering pattern
on the sky which is more difficult to model correctly. There is an overall scaling factor at
each wavelength in the zodiacal light model, but the parameters that determine the physical
shape of the dust cloud were fit simultaneously to observations at 8 DIRBE bands. The
trend with ecliptic latitude at both J and L indicates a problem with the modeled shape of
the cloud. The better fit to the scattered sunlight at K could be a coincidence, rather than
better modeling in that band. This remaining solar system dependence in two of the three
analyzed bands is evidence of a problem with the zodiacal light model that still prevents us
from claiming a detection at 1.25 µm. The model may be improved by requiring that these
DIRBE minus 2MASS intercepts be ecliptic independent simultaneously in all three bands.
Improvements to the zodiacal light model will be addressed in future work.
4. Discussion
The results of this DIRBE minus 2MASS subtraction in these 40 regions of the sky
give a statistically significant isotropic background of 14.69 ± 4.49 kJy sr−1 at 2.2 µm and
15.62 ± 3.34 kJy sr−1 at 3.5 µm where the uncertainty has not been significantly reduced
since the dominant sources of error are systematic. These results are consistent with earlier
results, summarized in Table 4 , including Gorjian et al. (2000), Wright & Reese (2000),
Wright (2001) and with the 13 similarly analyzed regions from Wright & Johnson (2001) all
of which used the same zodiacal light model considered here (Wright 1998).
In the J-band, we have weak limit on the 1.25 µm CIRB of 8.88 ± 6.26 kJy sr−1. This
– 8 –
is also consistent with the 1.25 µm values in Table 4, which were reported in Wright (2001)
and Wright & Johnson (2001), also using the same zodiacal light model used here. The
Kelsall et al. (1998) zodiacal light model gives a zodiacal intensity at the ecliptic pole 3.9,
9.2 and 4.0 kJy sr−1 lower at K, J and L. Allowing for this difference in the models, these
results are also consistent with those reported in Cambresy et al. (2001) and Matsumoto
(2000) at 1.25 and 2.2 µm and Matsumoto et al. (2005) at 2.2 and 3.5 µm, also shown in
Table 4.
The cumulative light from galaxies is a strict lower limit on the CIRB. A determination
of the total contribution of resolved galaxies to the CIRB was determined via galaxy number
counts by Fazio et al. (2004). Using the InfraRed Array Camera (IRAC) on the Spitzer Space
Telescope (Eisenhardt et al. 2004), surveys were done of the Boötes region, the Extended
Groth Strip and a deep image surrounding the QSO HS 1700+6416. After integrating the
light from galaxies from the 10th to the 21st magnitudes, a total integrated intensity of
5.4 nW m−2 sr−1 (6.5 kJy sr−1) at 3.6 µm is reported, which is less than half of the CIRB
determined at that wavelength by this and other similar studies. This 3.6 µm value is the final
entry in Table 4. This discrepancy may be partially resolved by improving the photometry
of these and other Spitzer surveys. But, the dominant source of error in these DIRBE minus
2MASS measurements comes from the estimation of the zodiacal light, and based on the
strong ecliptic dependence of our J-band results, it will likely take an improvement of the
zodiacal light models to make significant progress in determining whether we can resolve this
discrepancy with improvements in data analysis, or if we truly require some exotic diffuse
source as suggested by Cambresy et al. (2001).
It is also interesting to note another indirect constraint on the CIRB from the attenua-
tion of TeV γ-rays by e+e− pair production through collisions with CIRB photons. A recent
attempt by Mapelli et al. (2004) to fit the TeV spectrum of the blazar H1426+428 found
that the spectrum can not be fit using only the integrated light from galaxies. Their best
fit uses the Wright (2001) determination of the CIRB favoring the higher values determined
from direct observations of the total sky brightness. However, H.E.S.S. observations of the
blazars H2356-309 and 1ES 1101-232 by Aharonian et al. (2006) suggest that the CIRB can
not be much higher than the lower limits from galaxy counts. The Wright (2001) 1.25 and
2.2 µm values and the Dwek & Arendt (1998) 3.5 µm value were used by Aharonian et al.
(2006) in fitting a model of the Extragalactic Background Light (EBL) needed for estimating
γ-ray attenuation, resulting in their P1.0 EBL model which is the top curve in Figure 10.
This model gives (11,18,16) kJy sr−1 at 1.25, 2.2 and 3.5 µm and assuming a power law
blazar spectrum (dN/dE [photons cm−2 s−1 TeV−1] ∝ E−Γ) results in a power law index for
the spectrum of the blazar 1ES 1101-232 of Γ = -0.1. The model must be scaled down by a
factor of 0.45 to the P0.45 model (lower curve in Figure 10) to give a power law index of at
– 9 –
least 1.5, which is considered by Aharonian et al. (2006) to be the lowest acceptable value.
Mapelli et al. (2006) show however that an EBL model, also based on the Wright (2001)
values at 1.25 and 2.2 µm, but with a steeper decline from 4 to 10 µm results in a power
law index of Γ = +0.5. They consider Γ = 0.6 to be the lowest acceptable index based on
physical considerations and suggest then that while the DIRBE minus 2MASS CIRB values
at 1.25 and 2.2 µm from Wright (2001) do require a hard spectrum, and the lower limits
from galaxy counts are favored, they, and the slightly lower values reported here ((9,15,16)
kJy sr−1), can not be ruled out based on the current H.E.S.S. data. While the implications
of γ-ray attenuation for CIRB measurement are still limited by the small number of observed
sources, this independent limit on the CIRB will only improve as more blazars are observed
by H.E.S.S. and eventually, VERITAS.
There is still a substantial difference between the Fazio et al. (2004) lower limits from
galaxy counts and the intensities determined here. Progress can be made in resolving this
discrepancy with improvements in the photometry of survey data from Spitzer, as well as
improvements in the zodiacal light models and further data on gamma-ray attenuation.
However, the dominant source of error in directly measuring the CIRB, the model based
subtraction of the zodiacal light, will not be significantly reduced with currently available
data. A directly measured map of the zodiacal light, which would have to be observed from
outside the bulk of the IPD cloud, beyond about 3AU, would allow accurate removal of
the zodiacal light from the DIRBE maps and thus an accurate, direct measurement of the
Cosmic Infrared Background. We have shown here that the subtraction of catalogued stars
from low resolution maps works well, thus an instrument with a field of view of a few square
degrees and a resolution of a few arcminutes would suffice. The main requirements would be
sensitivity to extremely low surface brightnesses, down to less than 1 nW m−2 sr−1 for good
signal to noise, and an accurate, absolute flux calibration. Such an instrument could be a
camera on a probe to one of the outer planets. It would also be useful to have observations
from different positions with respect to the IPD cloud. This could be accomplished either
by observing the same fields at widely different solar elongations during a long lived mission
as the craft orbits the sun, or by observing during the cruise from 1 to 3 AU as the dust
density decreases. While we will continue to improve our understanding of the CIRB in the
mean time, a space mission of this type will ultimately be required.
The COBE datasets were developed by the NASA Goddard Space Flight Center under
the direction of the COBE Science Working Group and were provided by the NSSDC. This
publication makes use of the data product from the Two Micron All Sky Survey, which is
a joint project of the University of Massachusetts and the Infrared Processing and Analysis
Center, funded by the National Aeronautics and Space Administration and the National
– 10 –
Science Foundation. This research has also made use of the NASA/ IPAC Infrared Sci-
ence Archive, which is operated by the Jet Propulsion Laboratory, California Institute of
Technology, under contract with the National Aeronautics and Space Administration
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– 12 –
Table 1. K-band Results
l b β Npix DZ(0) [kJy sr
−1] F [kJy sr−1] C [kJy sr−1]
204.4 67.8 20.9 79 18.83 4.11 14.72
293.9 -72.5 -46.2 74 19.71 4.55 15.16
191.5 72.1 26.6 75 19.43 3.83 15.60
227.8 75.1 19.6 75 19.37 3.70 15.67
150.5 67.6 41.0 73 19.11 3.86 15.25
193.5 76.9 27.5 75 18.23 3.68 14.55
208.7 78.3 24.7 77 20.89 3.72 17.17
146.7 69.3 41.6 75 19.09 3.88 15.21
150.6 72.6 38.9 72 19.18 3.90 15.28
164.0 79.0 33.2 77 17.72 3.73 13.99
158.3 81.1 38.2 74 20.53 3.77 16.76
127.6 53.8 57.0 76 19.03 4.93 14.10
143.2 79.4 36.5 73 18.41 3.62 14.79
166.0 86.3 31.2 71 16.98 3.67 13.31
133.5 80.8 36.7 73 18.00 3.63 14.37
317.5 76.8 19.7 74 18.24 3.96 14.28
115.4 65.7 52.4 74 19.40 4.18 15.22
355.1 81.7 27.7 75 18.29 4.07 14.22
43.5 82.9 34.1 73 18.05 3.88 14.17
115.8 56.4 60.2 76 18.99 4.74 14.25
72.2 81.9 36.9 73 18.55 3.89 14.66
15.3 81.9 30.9 77 18.15 3.85 14.30
79.3 79.1 40.4 72 17.78 3.90 13.88
347.9 76.1 24.5 74 18.85 4.10 14.75
49.7 79.4 36.5 74 18.32 4.67 13.65
111.6 57.0 60.6 75 18.97 4.61 14.36
93.3 70.0 49.5 72 16.84 4.02 12.82
103.0 57.8 61.5 73 19.89 4.80 15.09
42.2 72.6 39.0 72 18.98 4.23 14.75
56.4 68.5 44.7 75 18.28 4.25 14.03
83.8 63.3 55.3 73 18.65 4.44 14.21
109.1 46.2 70.8 73 19.66 5.75 13.91
84.7 60.4 58.2 75 18.48 4.73 13.75
74.3 62.1 54.5 76 18.76 4.52 14.24
44.6 64.0 43.2 76 19.31 4.61 14.70
69.8 61.2 53.8 76 17.79 4.82 12.97
45.1 59.8 44.4 71 20.29 5.07 15.22
252.6 -71.8 -45.9 74 18.93 4.42 14.51
255.8 -59.2 -57.6 77 20.02 5.13 14.89
254.1 -53.0 -61.4 74 20.27 5.60 14.67
Note. — Mean of the CIRB over all 40 regions (2971 pixels) at 2.2 microns is 14.59
± 0.14 kJy sr−1 . This uncertainty is listed in Table 5 under “Scatter.”
aIntercepts derived using a weighted median procedure resulting in a global slope of
0.88 and 40 separate intercepts, DZ(0).
– 13 –
Table 2. J-band Results
l b β Npix DZ(0)
b [kJy sr−1] F [kJy sr−1] C [kJy sr−1]
204.4 67.8 20.9 79 8.77 5.60 3.17
293.9 -72.5 -46.2 74 16.21 6.20 10.01
191.5 72.1 26.6 75 12.35 5.38 6.97
227.8 75.1 19.6 75 7.94 5.12 2.82
150.5 67.6 41.0 73 15.55 5.32 10.23
193.5 76.9 27.5 75 10.14 4.92 5.22
208.7 78.3 24.7 77 11.95 5.11 6.84
146.7 69.3 41.6 75 15.50 5.40 10.10
150.6 72.6 38.9 72 14.26 5.29 8.97
164.0 79.0 33.2 77 11.65 5.14 6.51
158.3 81.1 38.2 74 16.27 5.17 11.10
127.6 53.8 57.0 76 18.06 6.74 11.32
143.2 79.4 36.5 73 12.90 4.95 7.95
166.0 86.3 31.2 71 10.38 5.01 5.37
133.5 80.8 36.7 73 11.44 4.89 6.55
317.5 76.8 19.7 74 7.20 5.45 1.75
115.4 65.7 52.4 74 18.38 5.81 12.57
355.1 81.7 27.7 75 10.38 5.51 4.87
43.5 82.9 34.1 73 12.10 5.41 6.69
115.8 56.4 60.2 76 18.19 6.44 11.75
72.2 81.9 36.9 73 12.22 5.30 6.92
15.3 81.9 30.9 77 11.05 5.14 5.91
79.3 79.1 40.4 72 13.80 5.11 8.69
347.9 76.1 24.5 74 8.69 5.54 3.15
49.7 79.4 36.5 74 12.37 6.50 5.87
111.6 57.0 60.6 75 18.00 6.23 11.77
93.3 70.0 49.5 72 15.01 5.56 9.45
103.0 57.8 61.5 73 18.95 6.57 12.38
42.2 72.6 39.0 72 14.35 5.97 8.38
56.4 68.5 44.7 75 16.42 5.82 10.60
83.8 63.3 55.3 73 18.89 5.98 12.91
109.1 46.2 70.8 73 20.99 8.11 12.88
84.7 60.4 58.2 75 19.38 6.43 12.95
74.3 62.1 54.5 76 17.71 6.28 11.43
44.6 64.0 43.2 76 17.78 6.42 11.36
69.8 61.2 53.8 76 17.37 6.64 10.73
45.1 59.8 44.4 71 18.61 6.91 11.70
252.6 -71.8 -45.9 74 16.19 6.12 10.07
255.8 -59.2 -57.6 77 19.50 7.05 12.45
254.1 -53.0 -61.4 74 20.69 7.76 12.93
Note. — Mean of the CIRB over all 40 regions (2971 pixels) at 1.25 microns is 8.83
± 0.51 kJy sr−1 . This uncertainty is listed in Table 5 under “Scatter.”
bIntercepts derived using a weighted median procedure resulting in a global slope of
0.97 and 40 separate intercepts, DZ(0).
– 14 –
Table 3. L-band Results
l b β Npix DZ(0)
c [kJy sr−1] F [kJy sr−1] C [kJy sr−1]
204.4 67.8 20.9 79 19.54 2.00 17.54
293.9 -72.5 -46.2 74 18.35 2.21 16.14
191.5 72.1 26.6 75 19.50 1.86 17.64
227.8 75.1 19.6 75 20.18 1.80 18.38
150.5 67.6 41.0 73 18.07 1.88 16.19
193.5 76.9 27.5 75 18.78 1.79 16.99
208.7 78.3 24.7 77 20.18 1.81 18.37
146.7 69.3 41.6 75 17.44 1.89 15.55
150.6 72.6 38.9 72 17.77 1.90 15.87
164.0 79.0 33.2 77 18.02 1.81 16.21
158.3 81.1 38.2 74 18.37 1.84 16.53
127.6 53.8 57.0 76 16.46 2.40 14.06
143.2 79.4 36.5 73 17.70 1.76 15.94
166.0 86.3 31.2 71 17.17 1.79 15.38
133.5 80.8 36.7 73 17.60 1.77 15.83
317.5 76.8 19.7 74 18.76 1.93 16.83
115.4 65.7 52.4 74 17.30 2.03 15.27
355.1 81.7 27.7 75 19.11 1.98 17.13
43.5 82.9 34.1 73 17.74 1.89 15.85
115.8 56.4 60.2 76 16.68 2.31 14.37
72.2 81.9 36.9 73 17.46 1.90 15.56
15.3 81.9 30.9 77 17.65 1.87 15.78
79.3 79.1 40.4 72 16.60 1.90 14.70
347.9 76.1 24.5 74 18.71 1.99 16.72
49.7 79.4 36.5 74 16.85 2.27 14.58
111.6 57.0 60.6 75 16.02 2.24 13.78
93.3 70.0 49.5 72 15.86 1.96 13.90
103.0 57.8 61.5 73 16.52 2.34 14.18
42.2 72.6 39.0 72 17.72 2.06 15.66
56.4 68.5 44.7 75 16.26 2.07 14.19
83.8 63.3 55.3 73 16.54 2.16 14.38
109.1 46.2 70.8 73 16.30 2.80 13.50
84.7 60.4 58.2 75 17.07 2.30 14.77
74.3 62.1 54.5 76 16.22 2.20 14.02
44.6 64.0 43.2 76 17.36 2.24 15.12
69.8 61.2 53.8 76 16.09 2.34 13.75
45.1 59.8 44.4 71 17.57 2.47 15.10
252.6 -71.8 -45.9 74 18.90 2.15 16.75
255.8 -59.2 -57.6 77 17.91 2.50 15.41
254.1 -53.0 -61.4 74 17.76 2.73 15.03
Note. — Mean of the CIRB over all 40 regions (2971 pixels) at 3.5 microns is 15.57 ±
0.20 kJy sr−1 . This standard deviation of the mean is listed in Table 5 under “Scatter.”
cIntercepts derived using a weighted median procedure resulting in a global slope of
0.43 and 40 separate intercepts, DZ(0).
– 15 –
Table 4. Previous determinations of the CIRB [kJy sr−1]
Authors 1.25 µm 2.2 µm 3.5 µm Model
Gorjian et al. (2000) · · · 16.4 ± 4.4 12.8 ± 3.8 Wright (1998)
Wright & Reese (2000) · · · 16.9 ±4.4 14.4 ±3.7 Wright (1998)
Wright (2001) 12 ±7 14.8 ± 4.6 · · · Wright (1998)
Wright & Johnson (2001) 10.1 ± 7.4 17.6 ± 4.4 16.1 ± 4 Wright (1998)
This Work 8.9 ±6.3 14.7 ± 4.5 15.6 ± 3.3 Wright (1998)
Matsumoto (2000) 25 ± 6.3 20.5 ± 3.7 · · · Kelsall et al. (1998)
Cambresy et al. (2001) 22.9 ± 7.0 20.4 ± 4.9 · · · Kelsall et al. (1998)
Matsumoto et al. (2005) · · · 22.3 ± 4 16.9 ± 3.5 Kelsall et al. (1998)
Fazio et al. (2004) · · · · · · > 6.5 N.A. (galaxy counts)
Note. — The Kelsall et al. (1998) model gives a CIRB 9.2, 3.9 & 4.0 kJy sr−1 higher at
1.25, 2.2 and 3.5 µm.
– 16 –
Table 5. Error Budget for the CIRB
Component 1.25 µm 2.2 µm 3.5 µm
Scatter 0.51 0.14 0.20
Faint Source 1.17 0.85 0.42
Galaxies 0.05 0.10 0.05
Calibration 1.77 2.24 0.60
Zodiacal 5.87 3.79 3.25
Quadrature Sum 6.26 4.49 3.34
– 17 –
0 50 0 50 0 50 0 50 0 50 0 50 0 50 0 50
Intensity at K from 2MASS stars [kJy/sr]
Fig. 1.— K-band: DIRBE 2.2 µm intensities vs. 2MASS 2.2 µm stellar intensities for the
forty new regions. Fitted lines show a weighted median fit, resulting in a common slope of
0.88 and 40 different intercepts, to the data points. Intercepts along with region l,b and β
are listed in Table 1. Reading left to right and top to bottom, the panels are in the same
order as Table 1. Point sizes are inversely proportional to σi.
– 18 –
0 50 0 50 0 50 0 50 0 50 0 50 0 50 0 50
Intensity at J from 2MASS stars [kJy/sr]
Fig. 2.— J-band: DIRBE 1.25 µm Intensities vs. 2MASS 1.25 µm stellar intensities for the
forty new regions. Fitted lines show a weighted median fit, resulting in a common slope of
0.97 and 40 different intercepts, to the data points. Intercepts along with region l,b and β
are listed in Table 2. Reading left to right and top to bottom, the panels are in the same
order as Table 2. Point sizes are inversely proportional to σi.
– 19 –
0 50 0 50 0 50 0 50 0 50 0 50 0 50 0 50
Intensity at K from 2MASS stars [kJy/sr]
Fig. 3.— DIRBE L vs. 2MASS K: DIRBE 3.5 µm Intensities vs. 2MASS 2.2 µm stellar
intensities for the forty new regions. Fitted lines show a weighted median fit, resulting in a
common slope of 0.43 and 40 different intercepts, to the data points. Intercepts along with
region l,b and β are listed in Table 3. Reading left to right and top to bottom, the panels
are in the same order as Table 3. Point sizes are inversely proportional to σi.
– 20 –
Fig. 4.— Histogram of DZi − κBi −DZ(0) at 2.2 µm for all regions combined where κ =
0.88.
– 21 –
Fig. 5.— Histogram of DZi − κBi −DZ(0) at 1.25 µm for all regions combined where κ =
0.97.
– 22 –
Fig. 6.— Histogram of DZi − κBi −DZ(0) at 3.5 µm for all regions combined where κ =
0.43.
– 23 –
Fig. 7.— Derived intercepts, DZ(0), versus Ecliptic Latitude at 2.2 µm.
– 24 –
Fig. 8.— Derived intercepts, DZ(0), versus Ecliptic Latitude at 1.25 µm.
– 25 –
Fig. 9.— Derived intercepts, DZ(0), versus Ecliptic Latitude at 3.5 µm.
– 26 –
Fig. 10.— Filled black squares are the CIRB values reported here. Gray stars are
Matsumoto et al. (2005) values from IRTS observations. The open gray triangle is the
Fazio et al. (2004) lower limit at 3.6µm. For comparison, the upper and lower black curves
are the P1.0 and P0.45 models used by Aharonian et al. (2006) to estimate the attenuation of
TeV γ-rays by the CIRB. P1.0 was normalized by Aharonian et al. (2006) to fit the 1.25-3.5
µm values from Dwek & Arendt (1998) and Wright (2001). P0.45 is the P1.0 scaled down
by a factor of 0.45, which was required, using this shape for the CIRB, to give blazar spectra
with power law spectral indices of at least 1.5.
	Introduction
	Data Sets
	Analysis
	Discussion

  With the release of the 2MASS All-Sky Point Source Catalog, stellar fluxes
from 2MASS are used to remove the contribution due to Galactic stars from the
intensity measured by DIRBE in 40 new regions in the North and South Galactic
polar caps. After subtracting the interplanetary and Galactic foregrounds, a
consistent residual intensity of 14.69 +/- 4.49 kJy/sr at 2.2 microns is found.
Allowing for a constant calibration factor between the DIRBE 3.5 microns and
the 2MASS 2.2 microns fluxes, a similar analysis leaves a residual intensity of
15.62 +/- 3.34 kJy/sr at 3.5 microns. The intercepts of the DIRBE minus 2MASS
correlation at 1.25 microns show more scatter and are a smaller fraction of the
foreground, leading to a still weak limit on the CIRB of 8.88 +/- 6.26 kJy/sr
(1 sigma).

Introduction
The Cosmic InfraRed Background (CIRB) is the aggregate of the short wavelength
radiation from the era of structure formation following the decoupling of matter and radiation
in the early universe, redshifted to near infrared wavelengths by cosmological redshifting and
far infrared wavelengths by dust-reprocessing, i.e. absorption and re-emission of starlight
by intervening dust. Particle decay models also allow for a contribution to the CIRB from
photons produced in the decay of weakly interacting massive particles such as big bang
http://arxiv.org/abs/0704.1498v3
– 2 –
relic neutrinos (Bond et al. 1986). The Diffuse InfraRed Background Experiment (DIRBE)
on the COsmic Background Explorer (COBE, see Boggess et al. (1992)), which observed
the entire sky in 10 infrared wavelengths from 1.25 to 240 µm, was primarily intended to
measure the CIRB. A determination of the CIRB turned out to be exceedingly difficult due to
bright foreground contamination including Galactic starlight and the strong thermal emission
and reflection of sunlight by dust in the solar neighborhood in many of the DIRBE bands,
especially in the near infrared (NIR). The DIRBE team estimated this zodiacal contribution
by fitting a computed brightness, based on a physical model of the InterPlanetary Dust
(IPD) cloud, to the weekly variations in the DIRBE brightness due to COBE’s changing
position in the solar system as the Earth orbited the Sun (Kelsall et al. 1998). The modeled
brightness was computed by integrating a source function, multiplied by a three dimensional
density distribution function, along the line of sight. Using this model for zodiacal light
subtraction, the DIRBE team succeeded in measuring an isotropic CIRB of 25 ± 7 nW m−2
sr−1 (1170 ± 328 kJy sr−1) and 14 ± 3 nW m−2 sr−1 (1123 ± 241 kJy sr−1) at 140 and 240
µm respectively (Hauser et al. 1998). In the NIR bands, they reported only upper limits on
the CIRB.
Using the “very strong no-zodi principle” of Wright (1997), another model of the zodiacal
light was determined and is described in Wright (1998) and Gorjian et al. (2000). After
creating DIRBE all sky maps with this new model subtracted, the problem of subtracting
Galactic starlight in the NIR was addressed by Gorjian et al. (2000) at 2.2 and 3.5 µm by
directly observing Galactic stars in a 2◦ × 2◦ region of the sky, smoothing the observed
intensities to the DIRBE pixel size and subtracting the resulting intensities from DIRBE
maps with the Wright (1998) zodiacal light model subtracted. Wright (2001) used this same
procedure of subtracting Galactic starlight from the DIRBE maps using stellar fluxes from
the 2MASS 2nd incremental release Point Source Catalog (PSC) in four regions in the North
and South Galactic poles. Dwek & Arendt (1998) showed that the DIRBE 3.5 µm intensity
was strongly correlated with the DIRBE 2.2 µm intensity at high Galactic latitudes and used
this correlation to convert a lower limit on the 2.2 µm CIRB, based on galaxy counts, into
a lower limit on the 3.5 µm CIRB. Wright & Johnson (2001) extended the Wright (2001)
analysis to 13 regions at 2.2 µm and combined the Wright (2001) and Dwek & Arendt (1998)
techniques to obtain estimates of the CIRB for those 13 regions at 3.5 µm. In this work
we extend the Wright & Johnson (2001) analysis to 40 new regions to further constrain the
CIRB at 1.25, 2.2 and 3.5 µm.
– 3 –
2. Data Sets
The two main datasets in this paper are the zodi-subtacted DIRBE maps and the
2MASS All-Sky Point Source Catalog (PSC).
DIRBE has a large 0.7◦ × 0.7◦ square beam with a diagonal of 1◦. Pixel intensities in
the DIRBE maps are averages of all observations made while the beam was centered in a
given pixel in the COBE Quadrilateralized Spherical Cube (CSC) projection. Due to the
large beam size, bright stars outside of a particular pixel will, depending on the exact center
position and position angle of the beam, occasionally affect the observed brightness in that
pixel. Thus a thick buffer ring is needed around any studied field to keep bright stars out-
side the field from influencing the measured DIRBE intensity. The resulting inefficiency was
minimized by using the darkest possible 2◦ circular regions which have the largest possible
area:perimeter ratio. A list of dark spots was created by smoothing the 3.5 µm DIRBE Zo-
diacal Subtracted Mission Average (ZSMA) map to 1/64th it’s original resolution, reducing
the 393,216 0.32◦ × 0.32◦ pixels to 6144 pixels approximately 2.5◦ × 2.5◦ using a straight
average of nearest neighbor pixels and sorting the resulting low resolution map. The 40
darkest regions not used in previous analyses were used.
However, the DIRBE ZSMA project data set only uses a fraction of the DIRBE data
since extreme solar elongations were dropped. Therefore, a set of mission averaged zodiacal
subtracted DIRBE maps were created by Wright (2001) using the zodiacal light model of
Wright (1998). The physical model is similar to the Kelsall et al. (1998) model, with an
added constraint. The “very strong no-zodi principle,” described in Wright (1997) and
Gorjian et al. (2000), requires that at high Galactic latitudes, at 25 µm, the background
emission should be isotropic and adds a single pseudo-observation of zero emission to the
nearly 105 observations used to fit the time variation in the weekly maps to the model
brightness. At 1.25 and 2.2 µm, no correction for interstellar dust emission is needed, while
at 3.5 µm, there is a very small correction (Arendt et al. 1998). The ith pixel in these maps
provides the DIRBE data DZi.
Using the NASA/IPAC InfraRed Science Archive (IRSA), fluxes from all stars in each
of the 40 regions brighter than K = 14 in the all-sky release of the 2MASS PSC were
obtained. Again due to the large beam size and effectively random distribution of the
beam center and position angle, these fluxes were converted into intensities by smearing
with a 0.7◦ × 0.7◦ square beam with a center uniformly distributed in the DIRBE pixel and
orientation uniformly distributed in position angle, to obtain the cataloged star contribution,
Bi, to the DIRBE intensity. This smearing process is described fully in Section 3. For the
J-band contribution, only stars with J and K less than 14 were used. This dual wavelength
magnitude selection is essentially equivalent to a simple J < 14 selection (Wright 2001).
– 4 –
3. Analysis
The zodi-subtracted DIRBE intensity in the ith pixel, DZi, should be the sum of the
cataloged stars, Bi; the faint stars, Fq, assumed constant for all pixels in the q
th region; and
the CIRB, C ,which is isotropic, i.e.
DZi = Bi + Fq + C . (1)
The cataloged star contribution was computed using the “smearing” described in Gorjian et al.
(2000) and Wright (2001),
pijSj , (2)
where Ωb is the solid angle of the DIRBE beam, Sj is the flux of the j
th star and pij is the
probability of the jth star affecting the ith pixel under the assumptions that over the many
observations in which the DIRBE beam was centered in the ith pixel, the beam center was
uniformly distributed within the pixel and the beam orientation is uniformly distributed in
position angle. Due to the random distribution of the orientation of the square 0.7◦ × 0.7◦
beam, the probablility as a function of the angular distance, r[(α, δ), (α⋆, δ⋆)], between the
beam center (α, δ) and a particular star at (α⋆, δ⋆) is
P (r) =
0, for r > l√
arccos l
, for l
≤ r ≤ l√
1, for r < l
where l is the width of the beam (0.7 deg) and,
r = arccos[cos(α− α⋆) cos(δ) cos(δ⋆) + sin(δ) sin(δ⋆)] . (4)
Then, to account for the random position of the beam center within the pixel, this probability
must be averaged over the area of the pixel by integrating P(r) over the solid angle of the
pixel and dividing by the pixel solid angle, Ωi, so that
pij =
P (r)dΩi
. (5)
Uncertainties in Bi were calculated as in Wright (2001):
σ2(Bi) =
[pij(1− pij) + pij
2(0.001 + (0.4 ln 10)2σ2(mj))]Sj
2 . (6)
The first term is noise due to stars near the edge of the DIRBE beam which will“flicker” in
and out of the beam when observed with various centers and position angles. The second
– 5 –
term is the flux error with an added allowance for variation in the fluxes between the DIRBE
and 2MASS observations as in Wright (2001), with the modification that the allowance for
variable stars was reduced from 0.1 to 0.001, reducing this allowance from σ = 0.34 to σ =
0.03 magnitudes. Statistically, the σ’s computed with the Wright (2001) value of 0.1 were
too large to be justifiable. Upon dividing the residuals from the linear fit to the DIRBE vs.
2MASS intensities (described below) by the computed σ’s, we noticed that the residual/σ
at all pixels was less than one. The new value of 0.001 gives a statistically more reasonable
distribution of residual/σ values which is described at the end of this Section. The error
estimates for all stars brighter than K = 5.5 or J = 6.5 were set to ± 1 mag to effectively
remove pixels affected by confusion due to saturation from the final analysis. Stars with
reported null uncertainties were assigned an uncertainty of ± 0.5 mag. Since the error in the
DIRBE data is negligible (Hauser et al. 1998), all of the error comes from the calculation of
Bi and is ascribed to DZi for the fits. Figures 1, 2 and 3 show plots of DZi vs. Bi for all
pixels in each of the 40 regions in K, J, and L respectively where the point sizes are inversely
proportional to the above σ’s.
The fits in K, J and L have slopes of κK = 0.88, κJ = 0.97 and κL = 0.43 respectively
with 40 independent intercepts in each band, derived using a weighted median procedure,
i.e. finding the values of κ and DZ(0) that minimize the sum:
|(DZi − κBi −DZ(0))/σi| . (7)
Derived intercepts for each field are given in Tables 1, 2 and 3 for K, J, and L respectively.
The contributions from stars fainter than the 14th magnitude were evaluated statistically
by fitting a power series of the form nq(m) = n◦,q10
αm to counts of 2MASS stars in each
of the 40 regions, binned into 3 one-magnitude bins centered on m= 11.5, 12.5 and 13.5.
The fits resulted in 40 individual n◦,q and αK = 0.288 and αJ = 0.276 where any α < 0.4
results in a converging flux contribution. The intensity contribution from faint stars in the
qth region with solid angle Ωq is then
F◦(λ)n◦,q
m=14.5
10(α−0.4)m (8)
or, in the limit of infinitely fine bins,
F◦(λ)n◦,q
10(α−0.4)mdm , (9)
which was computed analytically. At L, the faint source contribution in each region is the
2.2 µm value multiplied by the calibration ratio of 0.491. These Fq are listed in Tables 1,
– 6 –
2 and 3 for K, J and L. An uncertainty of 20% of the total prediction is assigned to this
correction, and is listed in Table 5 under “Faint Source.”
The CIRB in each region is then the derived intercept, DZ(0), minus the faint star
contribution Fq, C = DZ(0) - F. These values are also listed in Tables 1, 2 and 3. The mean
of these CIRB estimates are 14.59 ± 0.14, 8.83 ± 0.51 and 15.57 ± 0.20 kJy sr−1 for K, J
and L. These standard deviations of the means are listed in Table 5 as “Scatter.”
2MASS magnitudes at K and J were converted into fluxes using F◦(K) = 614 Jy and
F◦(J) = 1512 Jy which were derived by Wright (2001) and Gorjian et al. (2000). However,
the derived slopes at K and J indicate DIRBE fluxes for a zero magnitude 2MASS star
of 540 and 1467 Jy respectively. The ratio of the calibration factors at 3.5 and 2.2 µm is
0.491, consistent with those found by Dwek & Arendt (1998), Wright & Reese (2000) and
Wright & Johnson (2001). Uncertainties in the CIRB due to calibration error were estimated
using the change in the median DZ(0) when the slopes, κ, were forced to change by ±5%
at J and L, or ±10% at K due to the large difference (Wright & Johnson 2001) between the
fitted value of 0.88 and the expected value of 1. The change in the medians are ∓ 2.24, 1.77,
and 0.60 kJy sr−1 at K, J and L respectively and are listed in Table 5 under “Calibration.”
There is a small correction for faint galaxies that appear in the 2MASS PSC. These
have been subtracted along with the Galactic stars, but should be included in the CIRB.
Wright (2001) estimates this correction is 0.1 and 0.05 kJy sr−1 at 2.2 and 1.25 µm. The
0.1 kJy sr−1 correction at 2.2 µm implies a 0.05 kJy sr−1 correction at 3.5 µm due to the
relative calibration factor of 0.491. These corrections have been added back after taking the
mean of C = DZ(0) - F in the 40 regions. Thus, the final reported values of the CIRB are
the mean of the values C in Tables 1, 2 and 3 plus this correction. An uncertainty of 100%
of this correction is included in Table 5 under “Galaxies.”
Gorjian et al. (2000) adopt an uncertainty of 5% of the zodiacal intensity at the ecliptic
poles. These uncertainties are listed in Table 5 under “Zodiacal.”
After adding errors in quadrature, we obtain a CIRB of 14.69 ± 4.49 kJy sr−1 at 2.2
µm, a weak limit of 8.88 ± 6.26 kJy sr−1 at 1.25 µm and a CIRB of 15.62 ± 3.34 kJy sr−1
at 3.5 µm.
Figures 4, 5, and 6 show histograms of the residuals DZi − κBi − DZ(0) for all 2971
pixels in K, J and L with interquartile ranges of 2.85, 3.57 and 2.11 respectively. Dividing
these residuals by σ(Bi) at each pixel gives a non-Gaussian distribution which is tightly
packed near zero with a few pixels extending out to large values. The number of pixels with
|(DZi − κBi − DZ(0))/σ(Bi)| less than {0.5, 1.0, 2.0, 3.0} at K, J and L are {2424, 2832,
2930, 2951}, {2588, 2873, 2955, 2955} and {2590, 2867, 2947, 2955}. For comparison, with
– 7 –
a Gaussian distribution, one would expect these numbers to be, {1138, 2028, 2835, 2963};
more spread out in the center, with fewer pixels in the extended tail. We have used a robust,
least sum of absolute values fitting method, which, by it’s nature, is insensitive to the few
pixels with large residual/σ. Thus the fit for the slopes, κ, and intercepts, DZ(0), is to the
pixels in the narrow core, and the outliers have little effect on their derived values and the
final CIRB values.
Figures 7, 8, and 9 show the derived intercepts, DZ(0), vs. ecliptic latitude in the
three bands. We see here the same trends with ecliptic latitude as were apparent in
Wright & Johnson (2001). While the K-band intercepts appear reasonably independent of
ecliptic latitude, there is a strong trend in J and a slight negative trend in the L-band. The
zodiacal light is fainter at 3.5 µm than at 2.2 µm, and so the stronger dependence on β
at L than at K may seem surprising. However, at 3.5 µm, we begin to see thermal emis-
sion from the interplanetary dust, in addition to the scattered sunlight. From a modeling
standpoint, this gives another free parameter which should provide a better fit, but from
a physical standpoint, we are likely seeing a more complicated emission/scattering pattern
on the sky which is more difficult to model correctly. There is an overall scaling factor at
each wavelength in the zodiacal light model, but the parameters that determine the physical
shape of the dust cloud were fit simultaneously to observations at 8 DIRBE bands. The
trend with ecliptic latitude at both J and L indicates a problem with the modeled shape of
the cloud. The better fit to the scattered sunlight at K could be a coincidence, rather than
better modeling in that band. This remaining solar system dependence in two of the three
analyzed bands is evidence of a problem with the zodiacal light model that still prevents us
from claiming a detection at 1.25 µm. The model may be improved by requiring that these
DIRBE minus 2MASS intercepts be ecliptic independent simultaneously in all three bands.
Improvements to the zodiacal light model will be addressed in future work.
4. Discussion
The results of this DIRBE minus 2MASS subtraction in these 40 regions of the sky
give a statistically significant isotropic background of 14.69 ± 4.49 kJy sr−1 at 2.2 µm and
15.62 ± 3.34 kJy sr−1 at 3.5 µm where the uncertainty has not been significantly reduced
since the dominant sources of error are systematic. These results are consistent with earlier
results, summarized in Table 4 , including Gorjian et al. (2000), Wright & Reese (2000),
Wright (2001) and with the 13 similarly analyzed regions from Wright & Johnson (2001) all
of which used the same zodiacal light model considered here (Wright 1998).
In the J-band, we have weak limit on the 1.25 µm CIRB of 8.88 ± 6.26 kJy sr−1. This
– 8 –
is also consistent with the 1.25 µm values in Table 4, which were reported in Wright (2001)
and Wright & Johnson (2001), also using the same zodiacal light model used here. The
Kelsall et al. (1998) zodiacal light model gives a zodiacal intensity at the ecliptic pole 3.9,
9.2 and 4.0 kJy sr−1 lower at K, J and L. Allowing for this difference in the models, these
results are also consistent with those reported in Cambresy et al. (2001) and Matsumoto
(2000) at 1.25 and 2.2 µm and Matsumoto et al. (2005) at 2.2 and 3.5 µm, also shown in
Table 4.
The cumulative light from galaxies is a strict lower limit on the CIRB. A determination
of the total contribution of resolved galaxies to the CIRB was determined via galaxy number
counts by Fazio et al. (2004). Using the InfraRed Array Camera (IRAC) on the Spitzer Space
Telescope (Eisenhardt et al. 2004), surveys were done of the Boötes region, the Extended
Groth Strip and a deep image surrounding the QSO HS 1700+6416. After integrating the
light from galaxies from the 10th to the 21st magnitudes, a total integrated intensity of
5.4 nW m−2 sr−1 (6.5 kJy sr−1) at 3.6 µm is reported, which is less than half of the CIRB
determined at that wavelength by this and other similar studies. This 3.6 µm value is the final
entry in Table 4. This discrepancy may be partially resolved by improving the photometry
of these and other Spitzer surveys. But, the dominant source of error in these DIRBE minus
2MASS measurements comes from the estimation of the zodiacal light, and based on the
strong ecliptic dependence of our J-band results, it will likely take an improvement of the
zodiacal light models to make significant progress in determining whether we can resolve this
discrepancy with improvements in data analysis, or if we truly require some exotic diffuse
source as suggested by Cambresy et al. (2001).
It is also interesting to note another indirect constraint on the CIRB from the attenua-
tion of TeV γ-rays by e+e− pair production through collisions with CIRB photons. A recent
attempt by Mapelli et al. (2004) to fit the TeV spectrum of the blazar H1426+428 found
that the spectrum can not be fit using only the integrated light from galaxies. Their best
fit uses the Wright (2001) determination of the CIRB favoring the higher values determined
from direct observations of the total sky brightness. However, H.E.S.S. observations of the
blazars H2356-309 and 1ES 1101-232 by Aharonian et al. (2006) suggest that the CIRB can
not be much higher than the lower limits from galaxy counts. The Wright (2001) 1.25 and
2.2 µm values and the Dwek & Arendt (1998) 3.5 µm value were used by Aharonian et al.
(2006) in fitting a model of the Extragalactic Background Light (EBL) needed for estimating
γ-ray attenuation, resulting in their P1.0 EBL model which is the top curve in Figure 10.
This model gives (11,18,16) kJy sr−1 at 1.25, 2.2 and 3.5 µm and assuming a power law
blazar spectrum (dN/dE [photons cm−2 s−1 TeV−1] ∝ E−Γ) results in a power law index for
the spectrum of the blazar 1ES 1101-232 of Γ = -0.1. The model must be scaled down by a
factor of 0.45 to the P0.45 model (lower curve in Figure 10) to give a power law index of at
– 9 –
least 1.5, which is considered by Aharonian et al. (2006) to be the lowest acceptable value.
Mapelli et al. (2006) show however that an EBL model, also based on the Wright (2001)
values at 1.25 and 2.2 µm, but with a steeper decline from 4 to 10 µm results in a power
law index of Γ = +0.5. They consider Γ = 0.6 to be the lowest acceptable index based on
physical considerations and suggest then that while the DIRBE minus 2MASS CIRB values
at 1.25 and 2.2 µm from Wright (2001) do require a hard spectrum, and the lower limits
from galaxy counts are favored, they, and the slightly lower values reported here ((9,15,16)
kJy sr−1), can not be ruled out based on the current H.E.S.S. data. While the implications
of γ-ray attenuation for CIRB measurement are still limited by the small number of observed
sources, this independent limit on the CIRB will only improve as more blazars are observed
by H.E.S.S. and eventually, VERITAS.
There is still a substantial difference between the Fazio et al. (2004) lower limits from
galaxy counts and the intensities determined here. Progress can be made in resolving this
discrepancy with improvements in the photometry of survey data from Spitzer, as well as
improvements in the zodiacal light models and further data on gamma-ray attenuation.
However, the dominant source of error in directly measuring the CIRB, the model based
subtraction of the zodiacal light, will not be significantly reduced with currently available
data. A directly measured map of the zodiacal light, which would have to be observed from
outside the bulk of the IPD cloud, beyond about 3AU, would allow accurate removal of
the zodiacal light from the DIRBE maps and thus an accurate, direct measurement of the
Cosmic Infrared Background. We have shown here that the subtraction of catalogued stars
from low resolution maps works well, thus an instrument with a field of view of a few square
degrees and a resolution of a few arcminutes would suffice. The main requirements would be
sensitivity to extremely low surface brightnesses, down to less than 1 nW m−2 sr−1 for good
signal to noise, and an accurate, absolute flux calibration. Such an instrument could be a
camera on a probe to one of the outer planets. It would also be useful to have observations
from different positions with respect to the IPD cloud. This could be accomplished either
by observing the same fields at widely different solar elongations during a long lived mission
as the craft orbits the sun, or by observing during the cruise from 1 to 3 AU as the dust
density decreases. While we will continue to improve our understanding of the CIRB in the
mean time, a space mission of this type will ultimately be required.
The COBE datasets were developed by the NASA Goddard Space Flight Center under
the direction of the COBE Science Working Group and were provided by the NSSDC. This
publication makes use of the data product from the Two Micron All Sky Survey, which is
a joint project of the University of Massachusetts and the Infrared Processing and Analysis
Center, funded by the National Aeronautics and Space Administration and the National
– 10 –
Science Foundation. This research has also made use of the NASA/ IPAC Infrared Sci-
ence Archive, which is operated by the Jet Propulsion Laboratory, California Institute of
Technology, under contract with the National Aeronautics and Space Administration
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Wright, E. & Johnson, B. 2001, astro-ph/0107205 v2
This preprint was prepared with the AAS LATEX macros v5.2.
http://arxiv.org/abs/astro-ph/0107205
– 12 –
Table 1. K-band Results
l b β Npix DZ(0) [kJy sr
−1] F [kJy sr−1] C [kJy sr−1]
204.4 67.8 20.9 79 18.83 4.11 14.72
293.9 -72.5 -46.2 74 19.71 4.55 15.16
191.5 72.1 26.6 75 19.43 3.83 15.60
227.8 75.1 19.6 75 19.37 3.70 15.67
150.5 67.6 41.0 73 19.11 3.86 15.25
193.5 76.9 27.5 75 18.23 3.68 14.55
208.7 78.3 24.7 77 20.89 3.72 17.17
146.7 69.3 41.6 75 19.09 3.88 15.21
150.6 72.6 38.9 72 19.18 3.90 15.28
164.0 79.0 33.2 77 17.72 3.73 13.99
158.3 81.1 38.2 74 20.53 3.77 16.76
127.6 53.8 57.0 76 19.03 4.93 14.10
143.2 79.4 36.5 73 18.41 3.62 14.79
166.0 86.3 31.2 71 16.98 3.67 13.31
133.5 80.8 36.7 73 18.00 3.63 14.37
317.5 76.8 19.7 74 18.24 3.96 14.28
115.4 65.7 52.4 74 19.40 4.18 15.22
355.1 81.7 27.7 75 18.29 4.07 14.22
43.5 82.9 34.1 73 18.05 3.88 14.17
115.8 56.4 60.2 76 18.99 4.74 14.25
72.2 81.9 36.9 73 18.55 3.89 14.66
15.3 81.9 30.9 77 18.15 3.85 14.30
79.3 79.1 40.4 72 17.78 3.90 13.88
347.9 76.1 24.5 74 18.85 4.10 14.75
49.7 79.4 36.5 74 18.32 4.67 13.65
111.6 57.0 60.6 75 18.97 4.61 14.36
93.3 70.0 49.5 72 16.84 4.02 12.82
103.0 57.8 61.5 73 19.89 4.80 15.09
42.2 72.6 39.0 72 18.98 4.23 14.75
56.4 68.5 44.7 75 18.28 4.25 14.03
83.8 63.3 55.3 73 18.65 4.44 14.21
109.1 46.2 70.8 73 19.66 5.75 13.91
84.7 60.4 58.2 75 18.48 4.73 13.75
74.3 62.1 54.5 76 18.76 4.52 14.24
44.6 64.0 43.2 76 19.31 4.61 14.70
69.8 61.2 53.8 76 17.79 4.82 12.97
45.1 59.8 44.4 71 20.29 5.07 15.22
252.6 -71.8 -45.9 74 18.93 4.42 14.51
255.8 -59.2 -57.6 77 20.02 5.13 14.89
254.1 -53.0 -61.4 74 20.27 5.60 14.67
Note. — Mean of the CIRB over all 40 regions (2971 pixels) at 2.2 microns is 14.59
± 0.14 kJy sr−1 . This uncertainty is listed in Table 5 under “Scatter.”
aIntercepts derived using a weighted median procedure resulting in a global slope of
0.88 and 40 separate intercepts, DZ(0).
– 13 –
Table 2. J-band Results
l b β Npix DZ(0)
b [kJy sr−1] F [kJy sr−1] C [kJy sr−1]
204.4 67.8 20.9 79 8.77 5.60 3.17
293.9 -72.5 -46.2 74 16.21 6.20 10.01
191.5 72.1 26.6 75 12.35 5.38 6.97
227.8 75.1 19.6 75 7.94 5.12 2.82
150.5 67.6 41.0 73 15.55 5.32 10.23
193.5 76.9 27.5 75 10.14 4.92 5.22
208.7 78.3 24.7 77 11.95 5.11 6.84
146.7 69.3 41.6 75 15.50 5.40 10.10
150.6 72.6 38.9 72 14.26 5.29 8.97
164.0 79.0 33.2 77 11.65 5.14 6.51
158.3 81.1 38.2 74 16.27 5.17 11.10
127.6 53.8 57.0 76 18.06 6.74 11.32
143.2 79.4 36.5 73 12.90 4.95 7.95
166.0 86.3 31.2 71 10.38 5.01 5.37
133.5 80.8 36.7 73 11.44 4.89 6.55
317.5 76.8 19.7 74 7.20 5.45 1.75
115.4 65.7 52.4 74 18.38 5.81 12.57
355.1 81.7 27.7 75 10.38 5.51 4.87
43.5 82.9 34.1 73 12.10 5.41 6.69
115.8 56.4 60.2 76 18.19 6.44 11.75
72.2 81.9 36.9 73 12.22 5.30 6.92
15.3 81.9 30.9 77 11.05 5.14 5.91
79.3 79.1 40.4 72 13.80 5.11 8.69
347.9 76.1 24.5 74 8.69 5.54 3.15
49.7 79.4 36.5 74 12.37 6.50 5.87
111.6 57.0 60.6 75 18.00 6.23 11.77
93.3 70.0 49.5 72 15.01 5.56 9.45
103.0 57.8 61.5 73 18.95 6.57 12.38
42.2 72.6 39.0 72 14.35 5.97 8.38
56.4 68.5 44.7 75 16.42 5.82 10.60
83.8 63.3 55.3 73 18.89 5.98 12.91
109.1 46.2 70.8 73 20.99 8.11 12.88
84.7 60.4 58.2 75 19.38 6.43 12.95
74.3 62.1 54.5 76 17.71 6.28 11.43
44.6 64.0 43.2 76 17.78 6.42 11.36
69.8 61.2 53.8 76 17.37 6.64 10.73
45.1 59.8 44.4 71 18.61 6.91 11.70
252.6 -71.8 -45.9 74 16.19 6.12 10.07
255.8 -59.2 -57.6 77 19.50 7.05 12.45
254.1 -53.0 -61.4 74 20.69 7.76 12.93
Note. — Mean of the CIRB over all 40 regions (2971 pixels) at 1.25 microns is 8.83
± 0.51 kJy sr−1 . This uncertainty is listed in Table 5 under “Scatter.”
bIntercepts derived using a weighted median procedure resulting in a global slope of
0.97 and 40 separate intercepts, DZ(0).
– 14 –
Table 3. L-band Results
l b β Npix DZ(0)
c [kJy sr−1] F [kJy sr−1] C [kJy sr−1]
204.4 67.8 20.9 79 19.54 2.00 17.54
293.9 -72.5 -46.2 74 18.35 2.21 16.14
191.5 72.1 26.6 75 19.50 1.86 17.64
227.8 75.1 19.6 75 20.18 1.80 18.38
150.5 67.6 41.0 73 18.07 1.88 16.19
193.5 76.9 27.5 75 18.78 1.79 16.99
208.7 78.3 24.7 77 20.18 1.81 18.37
146.7 69.3 41.6 75 17.44 1.89 15.55
150.6 72.6 38.9 72 17.77 1.90 15.87
164.0 79.0 33.2 77 18.02 1.81 16.21
158.3 81.1 38.2 74 18.37 1.84 16.53
127.6 53.8 57.0 76 16.46 2.40 14.06
143.2 79.4 36.5 73 17.70 1.76 15.94
166.0 86.3 31.2 71 17.17 1.79 15.38
133.5 80.8 36.7 73 17.60 1.77 15.83
317.5 76.8 19.7 74 18.76 1.93 16.83
115.4 65.7 52.4 74 17.30 2.03 15.27
355.1 81.7 27.7 75 19.11 1.98 17.13
43.5 82.9 34.1 73 17.74 1.89 15.85
115.8 56.4 60.2 76 16.68 2.31 14.37
72.2 81.9 36.9 73 17.46 1.90 15.56
15.3 81.9 30.9 77 17.65 1.87 15.78
79.3 79.1 40.4 72 16.60 1.90 14.70
347.9 76.1 24.5 74 18.71 1.99 16.72
49.7 79.4 36.5 74 16.85 2.27 14.58
111.6 57.0 60.6 75 16.02 2.24 13.78
93.3 70.0 49.5 72 15.86 1.96 13.90
103.0 57.8 61.5 73 16.52 2.34 14.18
42.2 72.6 39.0 72 17.72 2.06 15.66
56.4 68.5 44.7 75 16.26 2.07 14.19
83.8 63.3 55.3 73 16.54 2.16 14.38
109.1 46.2 70.8 73 16.30 2.80 13.50
84.7 60.4 58.2 75 17.07 2.30 14.77
74.3 62.1 54.5 76 16.22 2.20 14.02
44.6 64.0 43.2 76 17.36 2.24 15.12
69.8 61.2 53.8 76 16.09 2.34 13.75
45.1 59.8 44.4 71 17.57 2.47 15.10
252.6 -71.8 -45.9 74 18.90 2.15 16.75
255.8 -59.2 -57.6 77 17.91 2.50 15.41
254.1 -53.0 -61.4 74 17.76 2.73 15.03
Note. — Mean of the CIRB over all 40 regions (2971 pixels) at 3.5 microns is 15.57 ±
0.20 kJy sr−1 . This standard deviation of the mean is listed in Table 5 under “Scatter.”
cIntercepts derived using a weighted median procedure resulting in a global slope of
0.43 and 40 separate intercepts, DZ(0).
– 15 –
Table 4. Previous determinations of the CIRB [kJy sr−1]
Authors 1.25 µm 2.2 µm 3.5 µm Model
Gorjian et al. (2000) · · · 16.4 ± 4.4 12.8 ± 3.8 Wright (1998)
Wright & Reese (2000) · · · 16.9 ±4.4 14.4 ±3.7 Wright (1998)
Wright (2001) 12 ±7 14.8 ± 4.6 · · · Wright (1998)
Wright & Johnson (2001) 10.1 ± 7.4 17.6 ± 4.4 16.1 ± 4 Wright (1998)
This Work 8.9 ±6.3 14.7 ± 4.5 15.6 ± 3.3 Wright (1998)
Matsumoto (2000) 25 ± 6.3 20.5 ± 3.7 · · · Kelsall et al. (1998)
Cambresy et al. (2001) 22.9 ± 7.0 20.4 ± 4.9 · · · Kelsall et al. (1998)
Matsumoto et al. (2005) · · · 22.3 ± 4 16.9 ± 3.5 Kelsall et al. (1998)
Fazio et al. (2004) · · · · · · > 6.5 N.A. (galaxy counts)
Note. — The Kelsall et al. (1998) model gives a CIRB 9.2, 3.9 & 4.0 kJy sr−1 higher at
1.25, 2.2 and 3.5 µm.
– 16 –
Table 5. Error Budget for the CIRB
Component 1.25 µm 2.2 µm 3.5 µm
Scatter 0.51 0.14 0.20
Faint Source 1.17 0.85 0.42
Galaxies 0.05 0.10 0.05
Calibration 1.77 2.24 0.60
Zodiacal 5.87 3.79 3.25
Quadrature Sum 6.26 4.49 3.34
– 17 –
0 50 0 50 0 50 0 50 0 50 0 50 0 50 0 50
Intensity at K from 2MASS stars [kJy/sr]
Fig. 1.— K-band: DIRBE 2.2 µm intensities vs. 2MASS 2.2 µm stellar intensities for the
forty new regions. Fitted lines show a weighted median fit, resulting in a common slope of
0.88 and 40 different intercepts, to the data points. Intercepts along with region l,b and β
are listed in Table 1. Reading left to right and top to bottom, the panels are in the same
order as Table 1. Point sizes are inversely proportional to σi.
– 18 –
0 50 0 50 0 50 0 50 0 50 0 50 0 50 0 50
Intensity at J from 2MASS stars [kJy/sr]
Fig. 2.— J-band: DIRBE 1.25 µm Intensities vs. 2MASS 1.25 µm stellar intensities for the
forty new regions. Fitted lines show a weighted median fit, resulting in a common slope of
0.97 and 40 different intercepts, to the data points. Intercepts along with region l,b and β
are listed in Table 2. Reading left to right and top to bottom, the panels are in the same
order as Table 2. Point sizes are inversely proportional to σi.
– 19 –
0 50 0 50 0 50 0 50 0 50 0 50 0 50 0 50
Intensity at K from 2MASS stars [kJy/sr]
Fig. 3.— DIRBE L vs. 2MASS K: DIRBE 3.5 µm Intensities vs. 2MASS 2.2 µm stellar
intensities for the forty new regions. Fitted lines show a weighted median fit, resulting in a
common slope of 0.43 and 40 different intercepts, to the data points. Intercepts along with
region l,b and β are listed in Table 3. Reading left to right and top to bottom, the panels
are in the same order as Table 3. Point sizes are inversely proportional to σi.
– 20 –
Fig. 4.— Histogram of DZi − κBi −DZ(0) at 2.2 µm for all regions combined where κ =
0.88.
– 21 –
Fig. 5.— Histogram of DZi − κBi −DZ(0) at 1.25 µm for all regions combined where κ =
0.97.
– 22 –
Fig. 6.— Histogram of DZi − κBi −DZ(0) at 3.5 µm for all regions combined where κ =
0.43.
– 23 –
Fig. 7.— Derived intercepts, DZ(0), versus Ecliptic Latitude at 2.2 µm.
– 24 –
Fig. 8.— Derived intercepts, DZ(0), versus Ecliptic Latitude at 1.25 µm.
– 25 –
Fig. 9.— Derived intercepts, DZ(0), versus Ecliptic Latitude at 3.5 µm.
– 26 –
Fig. 10.— Filled black squares are the CIRB values reported here. Gray stars are
Matsumoto et al. (2005) values from IRTS observations. The open gray triangle is the
Fazio et al. (2004) lower limit at 3.6µm. For comparison, the upper and lower black curves
are the P1.0 and P0.45 models used by Aharonian et al. (2006) to estimate the attenuation of
TeV γ-rays by the CIRB. P1.0 was normalized by Aharonian et al. (2006) to fit the 1.25-3.5
µm values from Dwek & Arendt (1998) and Wright (2001). P0.45 is the P1.0 scaled down
by a factor of 0.45, which was required, using this shape for the CIRB, to give blazar spectra
with power law spectral indices of at least 1.5.
	Introduction
	Data Sets
	Analysis
	Discussion
