Evaluating K bands for Nancy Grace Roman Space Telescope Rest-Frame NIR
  SN Ia Distances
  Recently, the Nancy Grace Roman Space Telescope (Roman) Project raised the
possibility of adding another filter to Roman. Based on the Filter Working
Group's recommendations, this filter may be a K-band filter, extending
significantly redder than the current-reddest F184. Among other scientific
possibilities, this K filter raises the possibility of measuring SNe Ia in the
rest-frame NIR out to higher redshifts than is possible with the current filter
complement. I perform a simple survey optimization for NIR SN Ia distances with
Roman, simultaneously optimizing both filter cutoffs and survey strategy. I
find that the roughly optimal K band extends from 19,000A--23,000A (giving
exposure times roughly half that of a 20,000A--23,000A Ks filter). Moving the K
much redder than this range dramatically increases the thermal background,
while moving the K band much bluer limits the redshift reach. Thus I find any
large modification reduces or eliminates the gain over the current F184. I
consider both rest-frame Y band and rest-frame J band surveys. Although the
proposed K band is too expensive for a large rest-frame Y band survey, it
increases the rest-frame J Figure of Merit by 59%.
