We present a measurement of lopsidedness for the stellar disks of 60 field spiral galaxies in terms of the azimuthal m=1 Fourier amplitude, A_1, of the stellar light. We conjecture that this lopsidedness is caused by tidal interactions and calculate an UPPER limit on the accretion rate of small galaxies. We exploit the correlation between lopsidedness and photometric measures of recent star formation (Zaritsky 1995) to obtain two independent estimates of the lifetime of these m=1 distortions. First, we show that lopsided galaxies have an excess of blue luminosity relative to that of symmetric galaxies with the same H I linewidth, which we attribute to a recent star formation episode that was triggered by an interaction between the galaxy and a companion. We use stellar populations models (Bruzual and Charlot 1993) to estimate the time since that interaction. Second, we use the N-body simulation of an infalling satellite by Walker, Mihos, and Hernquist (1996) to estimate how fast tidally induced m=1 distortions are erased through phase mixing. Both approaches indicate that the observations are consistent with a hypothesized tidal interaction that occurred about 1 Gyr ago for galaxies that are lopsided at the 20% level. By combining this lifetime estimate for lopsidedness, the observed frequency of such distortions, and a correction to the survey volume that depends on the increase in luminosity during an interaction, we derive an upper limit on the current companion accretion rate of field spiral galaxies (for companion masses of about 10% parent galaxy mass) that lies in the range 0.07 - 0.25 per Gyr. The principal uncertainty in this limit arises from ambiguities in the interpretation of the correlation between lopsidedness and M_B.

uuencoded, compressed text only. Full preprint with Figures will be emailed on request. To appear in the Astrophysical Journal