Because of strong and spatially highly variable interstellar extinction and extreme source crowding , the faint ( K \geq 15 ) stellar population in the Milky Way ’ s nuclear cluster is still poorly studied .
RR Lyrae stars provide us with a tool to estimate the mass of the oldest , relative dim stellar population .
Recently , we analyzed HST /WFC3/IR observations of the central 2.3′ \times 2.3′ of the Milky Way and found 21 variable stars with periods between 0.2 and 1d .
Here , we present a further comprehensive analysis of these stars .
The period-luminosity relationship of RR Lyrae is used to derive their extinctions and distances .
Using multiple approaches , we classify our sample as four RRc , four RRab and three candidates , ten binaries .
Especially , the four RRabs show sawtooth light curves and fall exactly onto the Oosterhoff I division in the Bailey diagram .
Compared to the RRabs reported by Minniti et al , 2016 , our new RRabs have higher extinction ( A _ { K } > 1.8 ) and should be closer to the Galactic Centre .
The extinction and distance of one RRab match those for the nuclear star cluster given in previous works .
We perform simulations and find that after correcting for incompleteness , there could be no more than 40 RRabs within the nuclear star cluster and in our field-of-view .
Through comparing with the known globular clusters of the Milky Way , we estimate that if there exists an old , metal-poor ( -1.5 < [ Fe/H ] < -1 ) stellar population in the Milky Way nuclear star cluster on a scale of 5 \times 5pc , then it contributes at most 4.7 \times 10 ^ { 5 } ~ { } M _ { \odot } , i.e. , \sim 18 % of the stellar mass .