 Solution

The differing maps follow from radiative transfer and from the different source functions of the bands. Low-frequency radio synchrotron emission passes through dust and follows cosmic-ray electrons and magnetic fields over a thick halo. Infrared emission follows dust mixed with dense gas and reprocessed starlight, whereas optical light follows unobscured stars and is strongly reshaped by extinction. The same matter distribution can therefore appear smooth at radio wavelengths, thin and clumpy in the infrared, and broken by dark dust lanes in the optical.

The Galactic scale height of a material tracer is set by vertical gravity balanced by its random, thermal, turbulent, magnetic, or cosmic-ray support. It also depends on source lifetime and transport. Cold molecular gas and dust have small velocity dispersions and settle into a thin layer. Relativistic electrons diffuse or advect far from their sources and radiate in a vertically extended magnetic field, so Galactic synchrotron emission is broad. Cosmic rays similarly fill a halo, and inverse-Compton gamma rays can be produced wherever they meet an extended radiation field; gamma-ray absorption within the Galaxy is also weak. Molecular and infrared emission remain concentrated around the thin cold-gas and young-star disk.

The spatial correlation between infrared and CO emission follows because molecular clouds contain dust and are the sites of massive-star formation. Young stars heat nearby dust, while CO maps their molecular fuel. Converting integrated CO intensity to ${\mathrm{H}}_2$ column density gives a molecular-gas surface-density profile; converting extinction-corrected infrared luminosity to a star formation rate gives the corresponding star-formation profile. Kinematic distances from velocity-resolved CO, with care near the Galactic center and for the near--far distance ambiguity, then estimate the radial relation between gas and star formation.

The three-dimensional Galactic bar is reconstructed by combining complementary distance and velocity information. Extinction-corrected near-infrared star counts reveal its projected stellar density, and standard-candle populations such as red-clump stars show that its near end is brighter and closer than its far end. CO and H I longitude--velocity diagrams trace noncircular gas streams and shocks in a barred potential. Maser parallaxes, proper motions, radial velocities, and dynamical forward models then constrain the bar angle, length, pattern speed, and vertical box or peanut shape.

Solved by gpt-5.6-sol high.