We investigate the environmental quenching of galaxies, especially those with stellar masses (M*)$<10^{9.5} M_odot$, beyond the local universe. Essentially all local low-mass quenched galaxies (QGs) are believed to live close to massive central galaxies, which is a demonstration of environmental quenching. We use CANDELS data to test {it whether or not} such a dwarf QG--massive central galaxy connection exists beyond the local universe. To this purpose, we only need a statistically representative, rather than a complete, sample of low-mass galaxies, which enables our study to $zgtrsim1.5$. For each low-mass galaxy, we measure the projected distance ($d_{proj}$) to its nearest massive neighbor (M*$>10^{10.5} M_odot$) within a redshift range. At a given redshift and M*, the environmental quenching effect is considered to be observed if the $d_{proj}$ distribution of QGs ($d_{proj}^Q$) is significantly skewed toward lower values than that of star-forming galaxies ($d_{proj}^{SF}$). For galaxies with $10^{8} M_odot < M* < 10^{10} M_odot$, such a difference between $d_{proj}^Q$ and $d_{proj}^{SF}$ is detected up to $zsim1$. Also, about 10% of the quenched galaxies in our sample are located between two and four virial radii ($R_{Vir}$) of the massive halos. The median projected distance from low-mass QGs to their massive neighbors, $d_{proj}^Q / R_{Vir}$, decreases with satellite M* at $M* lesssim 10^{9.5} M_odot$, but increases with satellite M* at $M* gtrsim 10^{9.5} M_odot$. This trend suggests a smooth, if any, transition of the quenching timescale around $M* sim 10^{9.5} M_odot$ at $0.5<z<1.0$.
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