The characteristic size of early-type galaxies ( ETGs ) of given stellar mass is observed to increase significantly with cosmic time , from redshift { { { { z { \mathrel { \mathchoice { \lower 2.9 pt \vbox { \halign { \cr } $ \displaystyle \hfil > $% \cr$ \displaystyle \hfil \sim$ } } } { \lower 2.9 pt \vbox { \halign { \cr } $ \textstyle \hfil > % $ \cr$ \textstyle \hfil \sim$ } } } { \lower 2.9 pt \vbox { \halign { \cr } $ \scriptstyle \hfil > % $ \cr$ \scriptstyle \hfil \sim$ } } } { \lower 2.9 pt \vbox { \halign { \cr } $% \scriptscriptstyle \hfil > $ \cr$ \scriptscriptstyle \hfil \sim$ } } } } } 2 to the present .
A popular explanation for this size evolution is that ETGs grow through dissipationless ( “ dry ” ) mergers , thus becoming less compact .
Combining N-body simulations with up-to-date scaling relations of local ETGs , we show that such an explanation is problematic , because dry mergers do not decrease the galaxy stellar-mass surface-density enough to explain the observed size evolution , and also introduce substantial scatter in the scaling relations .
Based on our set of simulations , we estimate that major and minor dry mergers increase half-light radius and projected velocity dispersion with stellar mass as R _ { e } \propto M _ { * } ^ { 1.09 \pm 0.29 } and \sigma _ { e 2 } \propto M _ { * } ^ { 0.07 \pm 0.11 } , respectively .
This implies that : 1 ) if the high- z ETGs are indeed as dense as estimated , they can not evolve into present-day ETGs via dry mergers ; 2 ) present-day ETGs can not have assembled more than \sim 45 \% of their stellar mass via dry mergers .
Alternatively , dry mergers could be reconciled with the observations if there was extreme fine tuning between merger history and galaxy properties , at variance with our assumptions .
Full cosmological simulations will be needed to evaluate whether this fine-tuned solution is acceptable .