Patat et al. recently inferred the existence of circumstellar material around a normal Type Ia supernova (SN) for the first time, finding time-variable Na I D absorption lines in the spectrum of SN 2006X. We present high-resolution spectroscopy of the bright SN Ia 2007af at three epochs and search for variability in any of the Na D absorption components. Over the time range from 4 days before to 24 days after maximum light, we find that the host-galaxy Na D lines appear to be of interstellar rather than circumstellar origin and do not vary down to the level of 18 mA (column density of 2 x 10^11 cm^-2). We limit any circumstellar absorption lines to be weaker than ~10 mA (6 x 10^10 cm^-2). For the case of material distributed in spherically symmetric shells of radius ~10^16 cm surrounding the progenitor system, we place an upper limit on the shell mass of ~(3 x 10^-8)/X Msun, where X is the Na ionization fraction. We also show that SN 2007af is a photometrically and spectroscopically normal SN Ia. Assuming that the variable Na D lines in SN 2006X came from circumstellar matter, we therefore conclude that either there is a preferred geometry for the detection of variable absorption components in Type Ia supernovae, or SN 2007af and SN 2006X had different types of progenitor systems.
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