if a white dwarf can exist only if its mass is less than 1.4 times the sun's mass, how can a star having 5 times the sun's mass end as a white dwarf?

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what can astronomers learn about a star from its spectral lines?

To understand how a star with a mass five times that of the Sun can end up as a white dwarf, we need to look at the process of stellar evolution.

Stars typically follow a life cycle, starting as protostars, then becoming main sequence stars, and eventually evolving into different types of stellar remnants. The fate of a star depends on its initial mass.

In the case of a star with a mass less than about 8 times that of the Sun, it will eventually end up as a white dwarf. White dwarfs are the remnants of low- to medium-mass stars that have exhausted their nuclear fuel. When a star runs out of fuel, it enters a phase called the red giant phase, during which it expands and sheds its outer layers. The core of the star, composed mostly of carbon and oxygen, contracts under its own gravity to form a white dwarf.

However, the detailed process by which a white dwarf forms depends on the mass of the star. For stars with a mass less than 1.4 times that of the Sun (known as the Chandrasekhar limit), the electron degeneracy pressure is sufficient to support the star against its own gravity. Such stars become white dwarfs.

In the case of a star with a mass five times that of the Sun, it will evolve differently. This mass is more than the Chandrasekhar limit, and electron degeneracy pressure alone cannot support the star against its own gravity. Instead, more massive stars undergo a supernova explosion at the end of their lives. During a supernova, the outer layers of the star are expelled into space, leaving behind a dense core known as a neutron star or, if the explosion is more energetic, a black hole.

In summary, stars with a mass five times that of the Sun will not end up as white dwarfs. Their fate is to either become neutron stars or, in some cases, black holes.

Regarding the second question, astronomers can learn a wealth of information about a star from its spectral lines. When light from a star passes through a spectrograph, it produces a spectrum consisting of dark lines, known as absorption lines, at specific wavelengths. These lines correspond to specific elements or molecules in the star's atmosphere. Here are a few examples of what astronomers can determine from spectral lines:

1. Chemical Composition: The presence and strength of specific absorption lines reveal the elements present in the star. By identifying these lines, astronomers can determine the chemical composition of the star.

2. Temperature: The width and shape of the absorption lines provide information about the star's temperature. Higher temperatures result in broader, more blurred lines, while lower temperatures produce narrower, sharper lines.

3. Stellar Motion: The Doppler shift of the spectral lines can indicate whether the star is moving away from or toward Earth. This information helps determine the star's radial velocity and motion in space.

4. Stellar Age and Activity: Certain spectral features, such as emission lines or peculiar line shapes, can indicate stellar activity, such as flares, pulsations, or magnetic fields. These features help determine the star's age and level of activity.

Overall, spectroscopy, specifically the analysis of spectral lines, plays a crucial role in determining the physical properties of stars and understanding their behavior.