【Appear】 , 【loom】 and 【emerge】 all mean to come out into view. In use, however, they are only rarely interchangeable.

【Appear】 is weakest in its implication of a definite physical background or a source; consequently it sometimes means merely to become visible or to become apparent (see EVIDENT).

• one by one the stars appeared in the sky
• nothing appears in the testimony to cause doubt of the defendant′s guilt

Sometimes it means to present oneself in public in a particular capacity or to be presented or given out to the public.

• Clarence Darrow appeared as counsel for the defendant
• Booth appeared nightly as Hamlet for the last two weeks of his run
• the new biography of Lincoln will 【appear】 next month
• weeklies usually 【appear】 on Thursday or Friday

【Loom】 means appearing as through a mist or haze.

• a smear o f . . . lead-colored paint had been laid on to obliterate Henchard′s name, though its letters dimly loomed through like ships in a fog
  —Hardy
• between the bed and the ottoman . . . the cot loomed in the shadows
  —Bennett

Because things seen in a fog are often magnified by their indistinct outlines, 【loom】 , especially when followed in figurative use by large or great or when followed by up, suggests apparent and sometimes appalling magnitude.

• some mornings it [a mesa] would 【loom】 up above the dark river like a blazing volcanic mountain
  —Cather
• that which loomed immense to fancy low before my reason lies
  —Browning

【Emerge】 definitely implies a coming out into the open from something that envelops: the word therefore presupposes a period or condition of concealment, obscurity, gestation, or insignificance

• the sun emerged from the clouds
• after a long hunt for him, we saw him emerging from the crowd
• that part of northern Ohio where the Bentley farms lay had begun to 【emerge】 from pioneer life
  —Anderson
• Lord Sligo emerges from this account as an able and conscientious administrator
  —Times Lit. Sup.