How Long Can Tiny H i Clouds Survive?

We estimate the evaporation timescale for spherical HI clouds consisting ofthe cold neutral medium surrounded by the warm neutral medium. We focus onclouds smaller than 1pc, which corresponds to tiny HI clouds recentlydiscovered by Braun & Kanekar and Stanimirovi{\'c} & Heiles. By performingone-dimensional spherically symmetric numerical simulations of the two-phaseinterstellar medium (ISM), we derive the timescales as a function of the cloudsize and of pressure of the ambient warm medium. We find that the evaporationtimescale of the clouds of 0.01 pc is about 1Myr with standard ISM pressure,$p/k_{B}\sim 10^{3.5}$ K cm$^{-3}$, and for clouds larger than about 0.1 pc itdepends strongly on the pressure. In high pressure cases, there exists acritical radius for clouds growing as a function of pressure, but the minimumcritical size is $\sim$ 0.03 pc for a standard environment. If tiny HI cloudsexist ubiquitously, our analysis suggests two implications: tiny HI clouds areformed continuously with the timescale of 1Myr, or the ambient pressure aroundthe clouds is much higher than the standard ISM pressure. We also find that theresults agree well with those obtained by assuming quasi-steady stateevolution. The cloud-size dependence of the timescale is well explained by ananalytic approximate formula derived by Nagashima, Koyama & Inutsuka. We alsocompare it with the evaporation rate given by McKee & Cowie.Comment: 4 pages, 3 figure