We study a sample of approximately 16 , 500 galaxies with I _ { ACS,AB } \leq 22.5 in the central 38 % of the COSMOS field ( ( 41 ) , this volume ) , which are extracted from a catalog constructed from the Cycle 12 ACS F814W COSMOS data set .
Structural information on the galaxies is derived by fitting single Sérsic ( ( 42 ) ) models to their two-dimensional surface brightness distributions . In this paper we focus on the disk galaxy population ( as classified by the Zurich Estimator of Structural Types , ZEST ; ( 35 ) , this volume ) , and investigate the evolution of the number density of disk galaxies larger than approximately 5 kpc between redshift z \sim 1 and the present epoch .
Specifically , we use the measurements of the half-light radii derived from the Sérsic fits to construct , as a function of redshift , the size function \Phi ( r _ { 1 / 2 } ,z ) of both the total disk galaxy population and of disk galaxies split in four bins of bulge-to-disk ratio .
In each redshift bin , the size function specifies the number of galaxies per unit comoving volume and per unit half-light radius r _ { 1 / 2 } .
Furthermore , we use a selected sample of roughly 1800 SDSS galaxies to calibrate our results with respect to the local universe .
We find that : ( i ) The number density of disk galaxies with intermediate sizes ( r _ { 1 / 2 } \sim 5-7 kpc ) remains nearly constant from z \sim 1 to today .
Unless the growth and destruction of such systems exactly balanced in the last eight billion years , they must have neither grown nor been destroyed over this period . ( ii ) The number density of the largest disks ( r _ { 1 / 2 } > 7 kpc ) decreases by a factor of about two out to z \sim 1 . ( iii ) There is a constancy - or even slight increase - in the number density of large bulgeless disks out to z \sim 1 ; the deficit of large disks at early epochs seems to arise from a smaller number of bulged disks . Our results indicate that the bulk of the large disk galaxy population has completed its growth by z \sim 1 , and support that secular evolution processes produce – or at least add stellar mass to – the bulge components of disk galaxies .