This document summarizes recent research on how the sizes and densities of galaxies have changed over time. Studies have found that galaxies at high redshift had smaller sizes than present-day galaxies of the same mass, often by a factor of 2-3 within 1 kpc and over 100 times within the effective radius. Various mechanisms are discussed for how galaxies could have grown, including minor mergers which could increase size more than mass over time. The document also examines constraints on the amount of growth massive galaxies could have experienced through mergers between redshifts of 0.8 to 0.1 based on the luminosity and stellar mass functions remaining largely unchanged over this period.

1. Decomposing Profiles of SDSS
Galaxies: Systematics in the
local L-R relation
and Luminosity function
M. Bernardi, A. Meert, et al.

2. SDSS
z~0.1
Cimatti et al. 2008
Z ~ 1.8
5 kpc @ z~0 → 0.9 kpc @ z~2
van Dokkum et al. 2008
Z ~ 2.3
Recent work in sizes …..
At fixed stellar mass, high-z sizes are smaller by (1+z)-1
or more (e.g. Trujillo et al. 2007; Cimatti et al. 2008; van Dokkum et al.
2008; Saglia et al. 2011; Bruce et al. 2012; Fan et al. 2013)

3. Different ways …..
Major merger Minor merger Disk instability
Duc et al. 2011
Major mergers (mass
roughly equal) increase
size and mass
proportionally
Minor mergers tend to
increase size more then
mass and decrease
velocity dispersion
Minor mergers is the
preferred scenario, but
problems still exist
Some growth scenarios ….

4. The densities < 1kpc
are higher by a factor
of 2–3!
The densities < Re are
higher by a factor >
100!
Bezanson et al. 2009
Inside-out growth scenario (minor mergers) is
plausible, in which the compact high z galaxies make up
the centers of normal nearby Es.
More on mergers …..

5. Impact of Major Dry Mergers at M* > 2 x 1011
Bernardi et al. 2011b
Evidence of
Major dry mergers
Wet mergers
Two scales:
3x1010 and
2x1011 MSun

6. Less curvature with
+

7. van der Wel et al. 2011
65%±15% of the population of massive, quiescent z ~ 2 galaxies are disk-dominated
“The much-discussed ultra-dense high-redshift galaxies should generally be thought of
as disk-like stellar systems with the majority of stars formed from gas that had time to
settle into a disk”

8. Red Fraction or Early-type Fraction?
Bernardi et al. 2010

9. Bernardi et al. 2010
E
Red g–r
Red g–r
E
~ 30-40% disk
contamination

10. Model where a galaxy has doubled its luminosity
through 1:1 mergers between z ~ 0.8 and z ~ 0.1
Using 1:1 mergers
Merger rates > 25% are ruled out
with 50% confidence
Using 1:3 mergers
Merger rates up to 40% are
allowed at 50% confidence
The total stellar mass in massive red
galaxies from z~0.9 must not have
grown by more than 50%
(Brown et al. 2007 -> 80%
of M* in 4L* galaxies
was already in place at z~0.7
Wake et al. 2006 -> 50% of M* in LRGs
already assembled by z~0.6)
In contrast L* galaxies have increased their
stellar mass by a factor of ~2
Little evolution in the Luminosity Function
(e.g. Wake et al. 2006; Brown et al. 2007; Cool et al. 2008)
Z ~ 0.8
Cool et al. 2008
Z~0.8

11. Bernardi et al. 2010
Uncertainties in the local M*F

12. Dependence on how L is computed
Bernardi et al. 2013b

13. Luminosity Function
Bernardi et al. 2013b

14. M* Function
Bernardi et al. 2013b

16. Dependence on Morphology

17. Some conclusions ….
• higher stellar mass density at z ~ 0 resolves the
tension with respect to the total mass density
inferred from the integrated SFR
• allows for a higher incidence of major (in addition
to minor) mergers in driving the M* growth of
the most massive central galaxies at late times
• Constraints on halo models
• Limits effects due to AGN feedback
• Constraints on IMF