Oil agent for carbon-fiber-precursor acrylic fiber, oil agent composition for carbon-fiber-precursor acrylic fiber, oil-treatment-liquid for carbon-fiber-precursor acrylic fiber, and carbon-fiber-precursor acrylic fiber bundle

A carbon-fiber-precursor acrylic fiber bundle, comprising:

• carbon fiber precursor acrylic fibers, wherein an oil agent is applied thereon, and
• the oil agent comprises
• a hydroxybenzoate (A) of formula (1a);
• an amino-modified silicone (H) of formula (3e) below;
• and
• an organic compound (X), which has affinity with the hydroxybenzoate (A), and a residual mass rate (R1) of 70 to 100 mass % at 300° C. measured by thermogravimetry in air, and which is liquid at 100° C.
• wherein in formula (1a), R1a is a C8 to C20 hydrocarbon group;
• wherein in formula (3e), “qe” and “re” are respectively any number of 1 or greater, “se” is any number of 1 to 5, and the dimethylsiloxane units and methylaminoalkyl-siloxane units are in a random sequence.