observational properties of z~6 galaxies rychard j. bouwens ucsc special thanks to roderik overzier,...
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Observational Properties of z~6 Galaxies
Rychard J. BouwensUCSC
Special thanks to Roderik Overzier, Mauro Giavalisco, Haojing Yan for helping me prepare this talk
The End of the Dark Ages / STScI / March 14, 2005
Collaborators:
Garth Illingworth, Ivo Labbe, Marijn Franx, Roderik Overzier, John Blakeslee, Dan Magee
z~6 -- An Exciting Epoch!
Mass of ~L* galaxiesSpringel et al. (2005)
Rapid Buildup of L* galaxies
z~6 represents a key transition
point of change between z~10
and z~3
High Redshift Frontier
1990: z = 3.80 Radio Galaxy (Chambers et al.)1997: z = 4.92 Lensed Dropout around CL1358+62 (Franx et al.)1998: z = 5.34 Lyman-alpha emitting Object (Dey et al.) 1998: z = 5.60 LBG in HDF North (Weymann et al.)1999: z = 5.74 Lyman-alpha emitter (Hu et al.)2001: z = 6.28 SDSS quasar (Fan et al.)2002: z = 6.56 Lyman-alpha emitter (Hu et al.)2003: z = 6.58 Lyman-alpha emitter (Kodaira et al.)2004: z ~ 6.6 Lensed Dropout (Kneib et al.) 2005: z = 6.7 Malhotra et al.
2
Highest Redshift Spectroscopically Confirmed Object / Some Mileposts
Wasn’t until the 2000s that we crossed the z~6 barrier…
Interesting how so many different techniques have been useful in finding the highest redshift objects: * Lyman-alpha emitters, QSOs, Lyman Break Galaxies * gravitational lensing, wide-area surveys, deep HST surveys
Finding Sources at z~6
z~6 Sloan QSOs
z = 6.56 Ly emitter (Hu et al. 2002)
(leverages i+z band imaging over very large area)
Ly
(leverages narrowband preselection + gravitational lensing)
9120 N R
HST WFPC2
Space has big advantages in searching for high-z objects due to much lower background.
However, until 2002, WFPC2 was the only camera in space to use for exploring the z>5 universe.
U B V I
HST Advanced Camera for Surveys
Redder, more efficient filters for exploring z > 5.5 universe
U B V i z
i
HST ACS
U B V I
HST WFPC2
Can select dropouts in much redder filter
with ACS!
Redder, more efficient filters for exploring z > 5.5 universe
U B V i z
i
HST ACS
U B V I
HST WFPC2
Can select dropouts in much redder filter
with ACS!
From Stanway et al. (2003) z~6 galaxy cuts off at the boundary
beween the i and z filters
Ideally we would do the z~6 i-dropout selection using the familiar two color diagram, i.e.,
Lyman Break Color
Strong Break
No Break
Continuum ColorBlue Red
z~6 objects
U B V i z
Ideally we would do the z~6 i-dropout selection using the familiar two color diagram, i.e.,
Lyman Break Color
Strong Break
No Break
Continuum ColorBlue Red
Unfortunately, you get the continuum
color you need deep infrared
imaging which is very expensive
z~6 objects
U B V i z IR
Single color i-dropout selection
Lyman Break Color
Strong Break i - z > 1.3
selection
No Break
RedshiftBunker et al. (2004)
Initial Round of Papers on i-dropouts
Stanway et al. (2003)
Yan et al. (2003) Bouwens et al. (2003)
Dickinson et al. (2004)~ 6 candidates
~ 30 candidates ~ 23 candidates
~ 251 candidates
Finding Real z~6 Galaxies Amongst Possible Contaminants
Evolved z~2-3 Sources did not appear to be an important concern
Bouwens et al. (2003)
Lyman Break Color
Strong Break
No Break
Continuum Color
Blue Red
All resolved sources here Stellar Locus
Size
z850 bandmag
Stanway et al. (2003)
i-dropouts are sufficiently resolved to exclude stellar contaminants
Stars
Galaxies
Surface Brightness Selection Biases(Incompleteness)
U-dropout from HDF-N artificially redshifted to z~6.0
Cosmic Surface Brightness Dimming Substantial
Factor of 10 from z~3
to z~6
Did surface brightness selection effects represent an important bias for the SFH?
SFRdensity
Redshift
Lanzetta et al. (2002)
After correction for SB selection effects?
Or selection effects not so significant?
High Redshift Size Evolution
Sizes
Redshift
Ferguson et al. (2004) did not plot a point at z~6 since surface brightness selection biases were still very important in the data used to construct this plot.
Ferguson et al. (2004)
Standard ruler
H(z)-1 ~ (1+z)-1.5
H(z)-2/3 ~ (1+z)-1
Data appear to be in good agreement with the scalings expected from this simple theory
High redshift galaxies are expected to be smaller because their halos collapse earlier and therefore more concentrated
Extending Size Measurements to z~6
Size vs. redshift
The sizes of i-dropouts are in good agreement with size-redshift trends found in Ferguson et al. (2004)
Sizes
Bouwens et al. (2004)
This suggests z>7 galaxies are likely to have half-light radii of ~0.1”
Size vs. magnitude
Sizes
~0.14”-0.15”
UDF
i-dropouts are small (~0.15”)
Bouwens et al. (2006); see also Bunker et al. (2004)
z~6 observations versus z~3
Volume Density
Rest-frame UV Continuum Luminosity Function
z~3 (Steidel et al. 1999)
Rest frame UV 1350 Å
z~6 observations versus z~3
Volume Density
Rest-frame UV Continuum Luminosity Function
z~3 (Steidel et al. 1999)
Yan (2003)
Rest frame UV 1350 Å
z~6 observations versus z~3
Volume Density
Rest-frame UV Continuum Luminosity Function
z~3 (Steidel et al. 1999)
Yan (2003)
Stanway (2003)
6x
Rest frame UV 1350 Å
z~6 observations versus z~3
Volume Density
Rest-frame UV Continuum Luminosity Function
z~3 (Steidel et al. 1999)
Yan (2003)
Stanway (2003)
Bouwens (2003)
6x
Rest frame UV 1350 Å
z~6 observations versus z~3
Volume Density
Rest-frame UV Continuum Luminosity Function
z~3 (Steidel et al. 1999)
Yan (2003)
Stanway (2003)
Bouwens (2003)
6x
Dickinson (2004)
Rest frame UV 1350 Å
z~6 observations versus z~3
Volume Density
Rest-frame UV Continuum Luminosity Function
z~3 (Steidel et al. 1999)
Yan (2003)
Stanway (2003)
Bouwens (2003)
6x
Dickinson (2004)
Rest frame UV 1350 Å
z~6 observations versus z~3
Volume Density
Rest-frame UV Continuum Luminosity Function
z~3 (Steidel et al. 1999)
Stanway (2003)
Bouwens (2003)
6x
Dickinson (2004)
Rest frame UV 1350 Å
z~6 observations versus z~3
Volume Density
Rest-frame UV Continuum Luminosity Function
z~3 (Steidel et al. 1999)
Stanway (2003)
Bouwens (2003)
6x
Dickinson (2004)
Disagree?
Rest frame UV 1350 Å
The two GOODS fields (~150 arcmin2 each) were key search areas in the earlier work.
Overall approach:
UDF UDF-IR
Hubble Ultra-Deep Field
UDF UDF-IR
ACS and NICMOS
5 limit: in UDF is ~30-31AB mag in BViz; in UDF-IR ~27.5AB mag in JH
Images of z~6 Galaxies
>100 i-dropouts in the UDF
Credit: Image by Zolt Levay
Yan & Windhorst (2005); Bouwens et al. (2006) see also Bunker et al. (2004)
(vs. much smaller numbers in the other fields)
Message from HUDF was that there are many faint galaxies
Surface Density of i-dropouts
z-band magnitude
No-evolution (NE) predictions from z~3
At bright mags: z~6 observations are much
lower than NE z~3 predictions
At faint mags:z~6 observations nearly equal to
NE z~3 predictions
Bouwens et al. (2006)
Bright Faint
Observedsurface density of z~6 galaxies
(uses UDF + shallower datasets)
Early work by Dickinson et al. (2004) before HUDF suggested there were more
faint galaxies than bright ones.
Message from HUDF was that there are many faint galaxies
No-evolution (NE) Predictions From z~3
Corrected i-dropoutcounts
Surface Density
z-band magnitude
BrightFaint
Many fewer bright z~6 objects found predicted from
z~3 assuming NE
Message from HUDF was that there are many faint galaxies
Yan & Windhorst (2004):Used UDF to argue faint-end slope of z~6 LF was very steep, = 1.8
z~6 LF
Faint-end slope at z~6
Bright Faint
Malhotra et al. (2005):
Best fit to z~6 galaxies (HUDF) had a fainter characteristic luminosity than at z~3
(compare to = -1.6 at z=3)
Bright Faint
Galaxies at z~6 (i-dropouts):
Bouwens et al 2006
Wide Deep
z850,AB~ 27.1 (10) (vers: 1.0)
UDF-Parallels UDF
z850,AB~ 28.4 (10)z850,AB~ 29.2 (10)
506 z~6 i-dropouts!
17 arcmin2
11 arcmin2
316 arcmin2
GOODS
CDF-SHDF-N
1.927.5 Since original GOODS program, a significant amount of SNe search data has been taken
over the GOODS fields.
z~6 UV Luminosity Function
Applied a well-tested i-z > 1.3 criterion to select i-dropouts in all fields.
Used detailed degradation experiments on our deeper fields to perform completeness and flux corrections.
Carefully matched up surface densities of all fields to remove field-to-field variations (35% effect)
Accounted for blending with foreground objects (5-10% effect)
Determined contamination level (5-10% effect): Intrinsically-red objects Photometric scatter Stars Spurious sources
Selection function determined by using best estimates of UV colors and sizes of z~6 objects.
Rigorous i-dropout luminosity function determination
z~6 UV Luminosity Function
Bouwens et al 2006
Rest frame UV 1350 Å
Log # mag-1 Mpc-3
z~6
Bright Faint
z~6 UV Luminosity Function
Bouwens et al 2006
Rest frame UV 1350 Å
Log # mag-1 Mpc-3
z~6
z~3LF at z~6: goes ~3 mag below L*
Bright Faint
z~6 UV Luminosity Function
Bouwens et al 2006
Rest frame UV 1350 Å
Luminosity evolutionprovides the best fit - not density evolution
Log # mag-1 Mpc-3
z~6
z~3
Luminosity Evolution Provides a good fit
Bright Faint
z~6 UV Luminosity Function
Bouwens et al 2006 Rest frame UV 1350 Å
z~6Faint-endSlope
The characteristic luminosity at z~6
(L*UV,z~6) is ~50% of (L*UV,z~3) at z~3.Faint Bright
z~6 UV Luminosity Function
Bouwens et al 2006 Rest frame UV 1350 Å
z~6Faint-endSlope
The characteristic luminosity at z~6
(L*UV,z~6) is ~50% of (L*UV,z~3) at z~3.Faint Bright
Weak constraints on faint-end slope
Star Formation History
Luminosity Density (Star Formation Rate
Density - no extinction)
Log10
M yr-1Mpc-3
Star Formation History -- z ~ 0 - 6
z~6 result
z~6 result
Brighter FluxLimit
Fainter FluxLimit
Evolution in SFR density is much more
dramatic to brighter flux limits
Bouwens et al. 2006
Star Formation History
Luminosity Density (Star Formation Rate
Density - no extinction)
Star Formation History -- z ~ 0 - 6
Shimasaku et al. 2005
Bright (zR<25.4) wide-area i-dropout search with Subaru
Fainter i-dropout search (Bouwens et al. 2004)
SFR density to bright limit
SFR density to fainter limit
Evolution of the UV LF
Hierarchical Buildup
AGN Feedback?Gas Exhaustion?
Transition between Hot/Cold Cooling
Flows?
Bright
Faint
z~6 observations versus z~3
Volume Density
Rest-frame UV Continuum Luminosity Function
z~3 (Steidel et al. 1999)
Stanway (2003)
Bouwens (2003)
6x
Dickinson (2004)
Disagree?
Rest frame UV 1350 Å
z~6 observations versus z~3
Volume Density
Rest-frame UV Continuum Luminosity Function
Rest frame UV 1350 Å
z~3 (Steidel et al. 1999)Dickinson (2004)
Bouwens (2003)
Stanway (2003)
6x
?
z~6 observations versus z~3
Volume Density
Rest-frame UV Continuum Luminosity Function
z~3 (Steidel et al. 1999)
Stanway (2003)
Bouwens (2003)
6x
Dickinson (2004)
Evolution Factor is Luminosity Dependent
Don’t Disagree!
Rest frame UV 1350 Å
Implications for Reionization
Using the standard Madau description, we find that the number of I-dropouts at z~6 appears to be approximately consistent with the numbers necessary to reionize the universe,assuming an escape fraction of 0.5 and clumping factor of 30.
6x
Dickinson (2004)
Rest frame UV 1350 Å
Field-to-field variations can be significant
# of i-dropouts / field at same depth
UDF
First ACS parallel to UDF NICMOS field
Second ACS parallel to UDF NICMOS field
18
50
44
~35% RMS variations for single ACS fields (Bouwens et al. 2006; see also
Bunker et al. 2004)
Large Scale Structure significantly limits our
ability to determine M*,
Surface Density of i-dropouts from GOODS + UDF-Ps + UDF
Significant Poisson Noise
UDF +UDF-Ps
GOODS
Relative normalization of bright + faint probes uncertain due to large-
scale structure
~ L*z=6
Unfortunately, L* is just at the edge of what can be probed with
the wide-area GOODS fields
Including LSS uncertainties
Ignoring LSS uncertainties
Large Scale Structure significantly limits our
ability to determine M*,
Surface Density of i-dropouts from GOODS + UDF-Ps + UDF
Significant Poisson Noise
UDF +UDF-Ps
GOODS
Relative normalization of bright + faint probes uncertain due to large-
scale structure
~ L*z=6
Unfortunately, L* is just at the edge of what can be probed with
the wide-area GOODS fields
Including LSS uncertainties
Ignoring LSS uncertainties
==> Need more deep fields
Deep i-dropout Search Fields
ACS Parallels to the UDF NICMOS data
UDF
CDF South
Deep i-dropout Search Fields
ACS Parallels to the UDF NICMOS data
UDF
UDF05 (PI: Stiavelli)
CDF South
Key New Data
Ground Based Spectroscopy
Keck
GeminiVLT Subaru
z~6 spectroscopic samples
Malhotra et al. 2005
GRAPES
23 objects
Dow-Hygelund et al. 2006
8 objects
UCSC/Keck
GOODS Team
GLARE/Exeter~20 objects
+ 80(?) more from the PEARS program
=> ~100 z~6 objects spectroscopically confirmed!
47 objects
Vanzella et al. 2005, 2006; Stern et al., in prep; Dawson et al. 2002
(also includes a few redshifts from GRAPES here)
Spectroscopy on z~6 galaxies
Bunker et al. 2003
z=5.78
Vanzella et al. 2006, in prep
z=5.52
Dow-Hygelund et al. 2005
Some noteworthy examples of z~6 spectra
Stack of 25 emission line galaxies
Composition of z~6 spectroscopic samples
~30% of i-dropouts show Ly emission (EW: >20 A)vs. 25% of U-dropouts at z~3 (Dow-Hygelund et al. 2006)
Contamination rates for current I-dropout selections appears to very low.
Red
UV continuum slope
Blue
Dust Properties(important for calculating unobscured star formation rate)
()
UV
UV
Low Dust
extinction High Dust
extinction
Red
UV continuum slope
Blue
Most LightAbsorbed By
Dust First
Infrared Light
UV Light
Most LightEscapesWithout
Absorption
Dust Properties(important for calculating unobscured star formation rate)
Correction Factor (Meurer et al. 1999)
()
UV
UV
Low Dust
extinction High Dust
extinction
Evolution in UV Continuum Slope
UV continuum slope vs. z
Bouwens et al. 2004, 2006b,c; See also Stanway et al. 2005; Lehnert et al. 2003; Yan et al. 2005
Red
UV continuum slope
Blue
Dusty
Dust Free
Galaxies appear to become less dusty at high redshift
Significant Dust at z~6.5?
Chary et al. (2005)
HCM6AAbell 370Hu et al. (2002)
z = 6.56
Anomalous jump in the flux density at ~6000 A rest-
frame
Is this due to Hemission?
If so, suggestssignificant dust
extinction ?
The Evolution of the SFR density
Bouwens et al. 2006
SFRdensity
TrueSFR density
SFR density (not counting
for dust)
Correcting for dust extinction accentuates the size of SFR density
peak at z~1-3
X-ray Properties
Chandra
Independent Method:SFR density from X-ray emission
Lehnert et al 2005A Recent stack of a larger ~400 object i-dropout sample from GOODS is undetected in x-ray
Lehnert et al 2006, private communication
- There is a known incidence of high mass x-ray binaries in SF regions
- X-ray light is much less affected by dust than UV light
Spitzer Space Telescope
(Measuring Stellar Masses)
UV Optical Rest-frame
Size of break tells us how
many old stars there
are
Age
Age
Age
Age
NIR Observed IRAC
Rest-optical & -IR at z~6
Kneib et al. (2004) lensed object at z~6.6
J
Hz~6.6 source
3.6 4.5
Stellar Mass = ~109 Msol
Best Fit (e-decay) = 100 Myr
z~6.6 source
IRAC Imaging
Egami et al. (2005)
Stellar Masses in select GOODS/UDF i-dropouts
ch2, 4.5mrest=6600A
Yan et al. (2005); see also Eyles et al. (2005)
Major results:• Very massive galaxies (M>1010 Msun)
existed at z ~ 6• A few hundred million years old (must
form well before z ~ 6)• Modest reddening (best-fits all have zero
reddening)
IRAC 3.6J110z850
z850
(zoomed)
SED fitting using Bruzual & Charlot SED fitting using Bruzual & Charlot (2003) models with exponentially decay (2003) models with exponentially decay star formation historiesstar formation histories
Significantly Larger z~6 Samples
Yan et al. 2006 (to be submitted)12’
12’
53 i-dropouts from GOODS with firm IRAC detections 79 i-dropouts are invisible
in their individual IRAC exposures
Move to complete samples of i-dropouts over the GOODS fields (~200 objects)
To make statistically significant statements:
z850 - IRAC 3.6 colors for ~170 i-dropouts
Yan et al. 2006 (to be submitted)
Balmer Break
z850-band magnitude
i-dropouts detected in 3.6 IRAC imaging
i-dropouts undetected in 3.6 IRAC imaging
Old
Young
Bright FaintControl
Stack of I-dropouts which are undetected individually
Implications
Yan et al. 2006 (to be submitted)
<z850 - 3.6>AB = 1.33
Detected with IRAC (~40% of the sample)
Individually undetected with IRAC (~60% of the sample)
<z850 - 3.6>AB = 0.4
Constant SFR
Simple Stellar Population
>100 Myr old=> 1 Gyr of constant SF is not enough
Stellar mass density lower limits based on full-epoch GOODS results
Yan et al. 2006 (to be submitted)
Stellar Mass Density
Integral ofSFR History
Diagram
1 + Redshift
New Point
None, or at least very few, of these objects appear to have solar masses as large as the
Mobasher et al. (2005) JD2 object or the Wiklind et al. (2006) objects.
Clustering of i-dropouts
181 i-dropouts
CDF South GOODS
Overzier et al. (2006)
HDF North GOODS
151 i-dropouts
Bouwens et al. (2006) sample of i-dropoutsBased upon original GOODS v1.0 data + SNe search data
(twice as deep)
Useful for learning about the halo masses
Clustering of i-dropouts
Clusteringw()
Angular Separation (“)
Clustering significant at 99.9% confidence
Overzier et al. (2006)It is true that better statistics would be ideal, but larger
samples are unlikely to be available soon
Invert using Limber’s Equation
Overzier et al. (2006)
Redshift Distribution
€
w(θ) = Awθ−β
Angular Correlation Function
Limber’s Equation
€
Aw =C0γ
F(z)Dθ1−γ (z)N(z)2g(z)dz
0
∞
∫N(z)2dz
0
∞
∫
€
γ= +1
Real Space Correlation Function
€
ξ(r) = (r /r0)−γ
Results in Real Space
Overzier et al. (2006)
Correlation LengthsMore luminous i-dropouts appear to be more clustered than the faint ones.
Bright
Correlation Length
Strongly clustered
Weakly clustered
FaintSimilar to findings at z~3-5 (Giavalisco & Dickinson 2001; Ouchi et al. 2004;
Lee et al. 2006) Suggests that the most luminous starbursts live in the most massive halos.
i-dropoutsz~6
z~4
z~5
Bias / Halo Mass
Lee et al. (2006); Overzier et al. (2006)
Galaxies at z~3-4 live
in ~1012 Msol halos
z~6
z~4
z~5
Bias
However, galaxies at z~5-6 appear to live in ~1011 Msol halos
This suggests star formation is much more efficient at z>5 than it is at z~3-4 in producing UV photons
May be partially due to an evolution in dust content:
i.e., more dust at z~3-4=> less UV photons escaping
M1700 < -20.0
Bias / Halo Mass
Lee et al. (2006); Overzier et al. (2006)
Galaxies at z~3-4 live
in ~1012 Msol halos
z~6
z~4
z~5
Bias
However, galaxies at z~5-6 appear to live in ~1011 Msol halos
This suggests star formation is much more efficient at z>5 than it is at z~3-4 in producing UV photons
May be partially due to an evolution in dust content:
i.e., more dust at z~3-4=> less UV photons escaping
M1700 < -20.0
Change in Efficiency can Explain Slow Evolution in LF from z~6 to z~3
Mass of ~L* galaxies
Springel et al. (2005)
Evolution of Mass Function
~10x increase in number
of 1012 Msol halos from z~6 to z~3
z=6
z=3
Change in Efficiency can Explain Slow Evolution in LF from z~6 to z~3
Mass of ~L* galaxies
Springel et al. (2005)
Evolution of Mass Function
But the efficiency of star formation
changes from z~6 to z~3
Compare 1011 Msol halos at
z~6
z=6
z=3 with1012 Msol halos at
z~3
Change in Efficiency can Explain Slow Evolution in LF from z~6 to z~3
Springel et al. (2005)
Evolution of Mass Function
Compare 1011 Msol halos at
z~6
z=6
z=3 with1012 Msol halos at
z~3
Now measure increase differently
Change between z~6 and z~3 much less
Star Formation History
Luminosity Density (Star Formation Rate
Density - no extinction)
2006 End of Dark Ages 03/14/06 RJB
Log10
M yr-1Mpc-3
z~6 result
Star Formation History -- z > 6
Star Formation History
Luminosity Density (Star Formation Rate
Density - no extinction)
Log10
M yr-1Mpc-3
UDF z~7-8 sample
z~6 result
Star Formation History -- Previous Results
2006 End of Dark Ages 03/14/06 RJB
Star Formation History
Previous J-dropout search
Luminosity Density (Star Formation Rate
Density - no extinction)
Log10
M yr-1Mpc-3
UDF z~7-8 sample
z~6 result
Star Formation History -- Previous Results
2006 End of Dark Ages 03/14/06 RJB
Luminosity Density (Star Formation Rate
Density - no extinction)
Log10
M yr-1Mpc-3
z~6 result
Star Formation History
2006 End of Dark Ages 03/14/06 RJB
Samples of >500 galaxies are now available at z~6 from HST data.
z~6 UV LF rigorously determined to ~3 magnitudes below L*.
Substantial evolution occurs at the bright end of the UV LF from z~6 to z~3. The characteristic luminosity at z~6 (L*UV) is 2 smaller than what it is at z~3.
z~6 galaxies appear to be less dusty on average than galaxies at lower redshift. This accentuates the rise in SFR density from z~6 to z~3.
~80-100 z~6 objects have now been spectroscopically confirmed.
Observational Properties of z~6 Galaxies
Conclusions
Observational Properties of z~6 Galaxies
Conclusions A small fraction z~6 objects has solar masses in excess of 1010 Msolar.
40% appear to be at least 100 Myr old.
L* objects at z~6 appear to predominantly live in 1011 solar mass halos. This is smaller than at z~3, suggesting there is an increase in the SF efficiency from z~6 to z~3.
Our improved knowledge of the z~6 universe puts us in an ideal
position to interpret the z>6 universe.
Determining the z~6 UV LF
But, to determine the LF, we need to divide the numbers
by the volume, i.e.,
Surface Density of i-dropouts with magnitude z850,AB
€
ϕ (m) =Number(m)
Volume (m)GOODS
UDF-Ps
UDF
After many corrections
Estimating the Selection Volume
Probability of Selecting a galaxy with magnitude z850
and redshift z as an i-dropout
Too faint to be
detected
How to calculate?
1. Create artificial galaxies
2. Add these galaxies to real images
3. Reapply Selection Procedure
z~6 UV Luminosity Function
Bouwens et al 2006
Rest frame UV 1350 Å
Log # mag-1 Mpc-3
z~6
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