Identify and describe the primary distinguishing features of the birds shown in the image, using LaTeX for any mathematical expressions.

• Toucan: Large, brightly colored beak, up to one-third of body length.
• Arctic Tern: Migrates annually from the North Pole to the South Pole and back.
• Barn Owl: Nocturnal, heart-shaped face, silent flight.
• Blue Jay: Blue, black, and white plumage, prominent blue crest.
• Emu: Second largest living bird, two eyelids.
• Penguin: Southern hemisphere, swims with flippers.
• Sarus Crane: World's tallest flying bird.

a) Toucan: This bird has a distinctive, large, and brightly colored beak, which can measure up to $\frac{1}{3}$ of its body length.

b) Arctic Tern: It is known for its annual migration, flying from the North Pole to the South Pole and back every year.

c) Barn Owl: A nocturnal bird, it has a distinctive heart-shaped face, pale feathers, and is known for its silent flight.

d) Blue Jay: This medium-sized songbird features striking blue, black, and white plumage and a prominent blue crest.

e) Emu: As the second largest living bird, it has two eyelids: one for blinking and the other for preventing dust from entering its eyes.

f) Penguin: Found mostly in the southern hemisphere, it can swim in water using its wing-type flippers.

g) Sarus Crane: This is the world's tallest flying bird, found in India, Southeast Asia, and Australia.