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Chapter 18: Problem 18

In what ways is the internal structure of a \(1-\mathrm{M}_{\odot}\) mainsequence star different from that of a \(5-\mathrm{M}_{\odot}\) main- sequence star? From that of a \(0.5-\mathrm{M}_{\odot}\) main-sequence star? What features are common to all these stars?

Short Answer

Expert verified
The internal structure of main-sequence stars varies with their mass. A \(5-\mathrm{M}_{\odot}\) star has a hotter core which triggers the CNO cycle, a radiative zone, and a convective envelope. A \(1-\mathrm{M}_{\odot}\) star has energy transport mainly through radiation in the inner part and convection in the outer part while the \(0.5-\mathrm{M}_{\odot}\) star transports energy solely through convection. However, all these stars are in their main sequence phase, burning hydrogen in their cores in hydrostatic equilibrium, balancing the forces of pressure and gravity.

Step by step solution

01

Understand the differences

The internal structure of a main-sequence star significantly depends on its mass. Larger stars have much hotter cores than smaller ones. In a \(5-\mathrm{M}_{\odot}\) star, the core temperature is high enough to trigger the CNO cycle. Additionally, such stars have a radiative zone and a convective envelope. However, in a \(1-\mathrm{M}_{\odot}\) star like the sun, energy transport is mainly through radiation in the inner part and convection in the outer part. For a \(0.5-\mathrm{M}_{\odot}\) star, there is no radiative zone, and they transport energy solely through convection.
02

Identify common features

Despite the structural differences, there are some common features among these stars. All these stars are in their main sequence phase, meaning they are in the stable period of their life where they burn hydrogen in their core. All main-sequence stars, including the ones specified, are in hydrostatic equilibrium - the inward force of gravity is balanced by the outward pressure.
03

Review the concepts

Both the differences and similarities in these main-sequence stars come from their basic properties and the physical laws governing their behavior. The differences arise due to the unique conditions like mass, temperature, and pressure present in each star, while the similarities exist due to the universal application of laws of physics and stellar dynamics.

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