Modeling Nitrogen Fractionation in the Protoplanetary Disk around TW
  Hya: Model Constraints on Grain Population and Carbon-to-Oxygen Elemental
  Abundance Ratio
  Observations conducted using the Atacama Large Millimeter/submillimeter Array
on the protoplanetary disk around TW Hya show the nitrogen fractionation of HCN
molecules in HC$^{14}$N/HC$^{15}$N $\sim$120 at a radius of $\sim$20 AU. In
this study, we investigated the physical and chemical conditions that control
this nitrogen fractionation process. To this end, a new disk model was
developed, in which the isotope-selective photodissociation of N$_2$ and
isotope-exchange chemical reactions have been incorporated. Our model can
successfully reproduce the observed HCN column density when the elemental
abundances of the gas-phase carbon and oxygen are depleted by two orders of
magnitude relative to those in the interstellar medium and carbon is more
abundant than oxygen ([C/O]$_{\rm elem}>$ 1). The isotope-selective
photodissociation of N$_2$ is the dominant nitrogen fractionation process in
our models. The observed HC$^{14}$N/HC$^{15}$N ratio, which increases outwards,
can also be reproduced by the model by assuming that the small dust grains in
the atmosphere of the outer disk are depleted more than those in the inner
disk. This is consistent with grain evolution models, according to which small
dust grains are continuously replenished in the inner disk due to fragmentation
of the large dust grains that radially drift from the outer disk.
