Helioseismological sound-speed profiles severely constrain possible deviations from standard solar models , allowing us to derive new limits on anomalous solar energy losses by the Primakoff emission of axions . For an axion-photon coupling g _ { a \gamma } \lesssim 5 \times 10 ^ { -10 } ~ { } { GeV } ^ { -1 } the solar model is almost indistinguishable from the standard case , while g _ { a \gamma } \gtrsim 10 \times 10 ^ { -10 } ~ { } { GeV } ^ { -1 } is probably excluded , corresponding to an axion luminosity of about 0.20 L _ { \odot } . This constraint on g _ { a \gamma } is much weaker than the well-known globular-cluster limit , but about a factor of 3 more restrictive than previous solar limits . Our result is primarily of interest to the large number of current or proposed search experiments for solar axions because our limit defines the maximum g _ { a \gamma } for which it is self-consistent to use a standard solar model to calculate the axion luminosity .