Lopsided spiral galaxies and a limit on the galaxy accretion rate

We present a measurement of lopsidedness for the stellar disks of 60 field spiral galaxies in terms of the azimuthal m = 1 Fourier amplitude, A₁, of the stellar light. We confirm the previous result (Rix & Zaritsky) that ∼30% of field spiral galaxies in a magnitude-limited sample exhibit significant lopsidedness (〈A₁/A₀〉 ≥ 0.2) at large radii (R > 1.5 disk scalelengths). 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) 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 population models (Bruzual & Chariot) to estimate the time since that interaction. Second, we use the N-body simulation of an infalling satellite by Walker, Mihos, & Hernquist 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 ~10% parent galaxy mass) that lies in the range 0.07-0.25 Gyr^-1. The principal uncertainty in this limit arises from ambiguities in the interpretation of the correlation between lopsidedness and M_B.