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We investigate the scalar mode quadrupole radiation of gravitational waves in$F(R)$ modified gravity. In $F(R)$ gravity a massive scalar mode appears in thegravitational waves.  We find explicit expressions for the quadrupole radiation and the energycurrent of the scalar mode in general $F(R)$ gravity models.  We consider a binary star and a bouncing star as astronomical sources of thegravitational waves and calculate the quadrupole radiation of the scalar andtensor modes.  The scalar mode radiates under spherically symmetric conditions, but thetensor modes do not.  The scalar mode mass is estimated for some typical energy scales. We show apossibility to detect the scalar mode in the future gravitational wavesobservation.

Scalar Mode Quadrupole Radiation from Astronomical Sources in $F(R)$ Modified Gravity