Final answer:
Arcturus, with a surface temperature of 4560 K and a luminosity of 170, is classified as a red giant due to its high luminosity and relatively lower temperature compared to other star types like white dwarfs, main sequence stars, and neutron stars.
Step-by-step explanation:
Based on the characteristics given for the star Arcturus — a surface temperature of 4560 K and a luminosity of 170 — it can be classified as a red giant. This classification is supported by comparing it to other known red giants, which are characterized by high luminosity and relatively low surface temperatures, similar to Arcturus. Such stars are enormous in size and can be many times the diameter of the Sun. Red giants represent a later stage of stellar evolution where the star has exhausted the hydrogen in its core and expanded as a result of the fusion of heavier elements occurring in shells around the core.
In contrast, while white dwarfs are also stars with high luminosity, they must have high surface temperatures to be so luminescent because they are very small in size with low total surface area. Meanwhile, main sequence stars have a luminosity and temperature that place them along the main sequence of the Hertzsprung-Russell diagram, and neutron stars are the remnants of supernovae with incredibly high densities and typically neither high luminosity nor low temperatures characteristic of red giants.