Large Scale Structure

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Large Scale Structure in the Two Micron All Sky
Survey
Ariyeh Maller Daniel McIntosh Neal Katz Martin
Weinberg
UMASS
2mass at Umass at http//www.astro.umass.edu/ari/
2mass.html
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Outline

• The Two Micron All Sky Survey (2MASS)
• The Cosmological Dipole
• The Angular Correlation Function
• The Three Dimensional Power Spectrum

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2MASS

• First all Sky Survey in near-infrared bands
• J (1.25 mm), H (1.65 mm) and Ks (2.17 mm) bands
• 500,000,000 point sources
• 1,600,000 extended sources
• 98 reliable (b gt 20) (Jarett et al. 2000)
• 90 complete (b gt 20)(Jarett et al. 2000)
• 97.5 of galaxies in the SDSS early data release
  (Bell et al 2003)

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Two Detected Telescopes
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A Galaxy Catalog

• Nstar lt 104 stars /deg2
• Dust correct using Schlegel et al 1998 maps
• Ks lt 13.57
• 0.8 lt J-K lt 1.4 for Ks lt 12
• Leaves 775,562 galaxies

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The Clustering Dipole

• Gravity and Flux fall off as r-2
• In linear theory velocity is proportional to g
• The Local Group velocity can be measured as a
  dipole against the CMB
• Which means we can solve for a combination of ?m
  , ?K and b.

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Fill the masked region either by cloning regions
above and below or using random galaxies
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The clustering dipole quickly converges as a
function of apparent magnitude The magnitude of
the dipole is 11.9 the flux from the sun.
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The dipole is with in 11 degrees of the
CMB However it is 19 degrees from the dipole
measured using Pscz
Taking ?m0.27 then ?K71 Msun/Lsun
and therefore the velocity of the Local Group in
linear theory is 815 km/s compared to the CMB
dipole of 622 km/s which implies the linear
bias b 1.2 /- 0.2 in the Ks band.
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The Angular Correlation Function

• The probability of finding objects in both d?1
  and d?2 compared to random.
• We use the estimator (Landy and Szalay 1993)
• where DD, DR and RR are the number of data-data,
  data-random and random-random pairs at angular
  seperations ?.

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Cross correlations with possible contaminants
We check that the cross correlation with possible
contaminants is less then the auto
correlation This requires cuts on the data of
b gt 20 and dust extinction less than 0.05 mags.
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The angular clustering in 2MASS is
considerably stronger than in SDSS or the APM
survey. The best fit power law gives an
amplitude at 1 degree of 0.11 with a power
law index of -0.76. Based on the different
redshift distribution we would expect 2MASS to
have an amplitude 5 times that of SDSS, but it
is 8.5 times as strongly clustered.
A
However 2MASS galaxies are 2 magnitudes more
luminous than SDSS galaxies which increases
their clustering strength.
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Limber Scaling
The amplitude of w(?) scales with apparent
magnitude as expected from Limber's equation,
suggesting that we are truly measuring
clustering.
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The deviation from power law is significant,
because the errors are correlated. A power law
fit is rejected with ?2/d.o.f. 3.9.
Such oscillations are expected in halo
occupation descriptions of galaxy formation
Berlind and Weinberg 2002
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Northern and Southern Hemispheres
Dividing the sample into the northern and
southern hemispheres gives identical angular
correlation functions at small scales and
slightly stronger clustering in the northern
galactic sky at large angles. This is not
surprising as this stronger clustering in the
north can be seen in the galaxy map.
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Dividing by Surface Brightness
We divide the sample by surface brightness
which is related to galaxy morphology. High
surface brightness galaxies are more clustered
than low surface brightness galaxies
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The 3D Power Spectrum

• The 3D Power Spectrum, P(k) can be inferred
  form the angular correlation function with
  knowledge of the redshift distribution of the
  galaxies.

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Singular Value Decomposition

• In practice we descritize the integrals
• w is a N? vector and P is a Nk vector
• then w GP where G is a N? x Nk matrix
• P G-1 w
• SVD tells us that G can be expressed as
• G U W Vt
• where W is a diagonalized matrix of eigenvalues
• G-1 V W-1 Ut

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Stability of the Solution
SVD also allows one to check the dependence on
small eigenvalue modes. We see including all 18
eigenvalues leads to wild oscillations in the
solution. We use 16 eigenvalues which gives ?2
4.1 for 9 degrees of freedom.
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The best fit Power Spectrum
Shown is the power spectrum inverted from 2MASS,
APM and SDSS. One sees they are all in fairly
good agreement. The best fit CDM type power
spectrum is also plotted. The CDM model is a good
fit with ?2/d.o.f.1.5 for k lt 0.2. Thus the
apparent drop off in power at small k is not
statistically significant.
2MASS
APM
SDSS
CDM
(Allgood et al 2001) (Gaztanaga and Baugh 1998)
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Best fit CDM models
zero baryon CDM power spectrum can be
parameterized by ?8 and ?eff. We fit this
type of power spectra resulting in the
constraints shown in the figure. In comparison
2dfGRS find ?eff 0.16 /- 0.04 (Percival et al.
2002) and WMAP find ?eff0.15 /- 0.01.
(Spergel et al. 2003)
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Conclusions

• The 2MASS clustering dipole is within 11 degrees
  of the CMB dipole.
• The implied K-band linear bias is 1.2 /- 0.2.
• The 2MASS angular correlation function shows
  oscillations from a power law.
• The inverted power spectrum is well fit by CDM
  type models
• ?80.96 /- 0.15 and ?eff 0.116 /- 0.009 for
  2MASS galaxies at z0.074