# How massive does a main sequence star need to be to go type 1 supernova?

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We know the mass a white dwarf needs to be. That's well defined by the Chandrasekhar limit, but before a main sequence star turns into a white dwarf it tends to lose a fair bit of its matter in a stellar nebula.

According to this site, the white dwarf that remains is about half the mass of the main sequence star, with larger stars losing a bit more.

So, the question: Is it correct to say that a star with a mass of about three solar masses will eventually go supernova, similar to a type 1 supernova, even when it's not part of a binary system? Has that kind of supernova ever been observed?

Or does something else happen like in the final stages of that star? Does it keeps going though collapse and expand cycles, losing enough mass that when it finally becomes a white dwarf it's below the Chandrasekhar limit in mass?

Mostly, what I've read on supernovae says that type 1 supernovae happen when a white dwarf accretes extra matter and reaches the limit and type 2 supernovae are much larger and require about 8-11 solar masses to generate the iron core which triggers the supernova. What happens with the death of the star between three solar masses and eight solar masses?

This is ground that is probably duplicated in a variety of questions here and on Physics SE, so I'll keep it brief. You have also mixed in several different questions.

The Chandrasekhar mass has very little to do with determining what initial mass of object will end up as what particular type of stellar remnant (or black hole).

Whether a star will end up exploding as a supernova depends primarily on its initial mass, but also whether it has a binary companions. There are (basically) two routes to supernovahood.

1. If the star is more massive than about $8M_{odot}$ it will progress through several nuclear burning stages. The core of the star does not become degenerate and continues to get more dense and hot through each burning stage. It ends up as iron. Once the core mass of iron exceeds about $1.2M_{odot}$ (which is the Chandrasekhar mass for an iron composition), then it collapses and we get a type II (core-collapse) supernova.

In this route a $3 M_{odot}$ star gets nowhere near being able to go supernova. It will burn hydrogen and helium, produce a degenerate core of carbon and oxygen. This degenerate core can cool whilst maintaining the same pressure. The outer layers are shed through thermal pulsations and a dense stellar wind in the asymptotic giant branch phase, leaving behind a white dwarf. The relationship between the initial mass of the progenitor and the final mass of the white dwarf is not a straightforward fraction. It probably is about 50% for a star like the Sun, but the fraction is more like 15% for a $7M_{odot}$ initial mass. The maximum mass of a white dwarf formed in this way is probably about $1.1-1.2M_{odot}$ and some way below the Chandrasekhar limit for a C/O white dwarf ($simeq 1.39M_{odot}$).

The preceding paragraph is more-or-less what should happen for all stars between about $0.6 M_{odot}$ (except they haven't had time to do so yet) and $8M_{odot}$, except that there is a small "grey area" at the upper mass end ($7-9M_{odot}$) where you might produce slightly more massive O/Ne white dwarfs.

1. Once a white dwarf has formed and if it is in a binary system, then the white dwarf could merge or accrete more mass. At some point close to the Chandrasekhar limit, it ignites. This causes a type Ia (detonation or deflagration) supernova explosion (or at least this is the leading model for how this works). This is really the only route whereby a star with initial mass $<8M_{odot}$ could end up going supernova.

## Contents

In the early part of the 20th century, information about the types and distances of stars became more readily available. The spectra of stars were shown to have distinctive features, which allowed them to be categorized. Annie Jump Cannon and Edward C. Pickering at Harvard College Observatory developed a method of categorization that became known as the Harvard Classification Scheme, published in the Harvard Annals in 1901. [2]

In Potsdam in 1906, the Danish astronomer Ejnar Hertzsprung noticed that the reddest stars—classified as K and M in the Harvard scheme—could be divided into two distinct groups. These stars are either much brighter than the Sun, or much fainter. To distinguish these groups, he called them "giant" and "dwarf" stars. The following year he began studying star clusters large groupings of stars that are co-located at approximately the same distance. He published the first plots of color versus luminosity for these stars. These plots showed a prominent and continuous sequence of stars, which he named the Main Sequence. [3]

At Princeton University, Henry Norris Russell was following a similar course of research. He was studying the relationship between the spectral classification of stars and their actual brightness as corrected for distance—their absolute magnitude. For this purpose he used a set of stars that had reliable parallaxes and many of which had been categorized at Harvard. When he plotted the spectral types of these stars against their absolute magnitude, he found that dwarf stars followed a distinct relationship. This allowed the real brightness of a dwarf star to be predicted with reasonable accuracy. [4]

Of the red stars observed by Hertzsprung, the dwarf stars also followed the spectra-luminosity relationship discovered by Russell. However, the giant stars are much brighter than dwarfs and so do not follow the same relationship. Russell proposed that the "giant stars must have low density or great surface-brightness, and the reverse is true of dwarf stars". The same curve also showed that there were very few faint white stars. [4]

In 1933, Bengt Strömgren introduced the term Hertzsprung–Russell diagram to denote a luminosity-spectral class diagram. [5] This name reflected the parallel development of this technique by both Hertzsprung and Russell earlier in the century. [3]

As evolutionary models of stars were developed during the 1930s, it was shown that, for stars of a uniform chemical composition, a relationship exists between a star's mass and its luminosity and radius. That is, for a given mass and composition, there is a unique solution for determining the star's radius and luminosity. This became known as the Vogt–Russell theorem named after Heinrich Vogt and Henry Norris Russell. By this theorem, when a star's chemical composition and its position on the main sequence is known, so too is the star's mass and radius. (However, it was subsequently discovered that the theorem breaks down somewhat for stars of non-uniform composition.) [6]

A refined scheme for stellar classification was published in 1943 by William Wilson Morgan and Philip Childs Keenan. [7] The MK classification assigned each star a spectral type—based on the Harvard classification—and a luminosity class. The Harvard classification had been developed by assigning a different letter to each star based on the strength of the hydrogen spectral line, before the relationship between spectra and temperature was known. When ordered by temperature and when duplicate classes were removed, the spectral types of stars followed, in order of decreasing temperature with colors ranging from blue to red, the sequence O, B, A, F, G, K and M. (A popular mnemonic for memorizing this sequence of stellar classes is "Oh Be A Fine Girl/Guy, Kiss Me".) The luminosity class ranged from I to V, in order of decreasing luminosity. Stars of luminosity class V belonged to the main sequence. [8]

In April 2018, astronomers reported the detection of the most distant "ordinary" (i.e., main sequence) star, named Icarus (formally, MACS J1149 Lensed Star 1), at 9 billion light-years away from Earth. [9] [10]

When a protostar is formed from the collapse of a giant molecular cloud of gas and dust in the local interstellar medium, the initial composition is homogeneous throughout, consisting of about 70% hydrogen, 28% helium and trace amounts of other elements, by mass. [11] The initial mass of the star depends on the local conditions within the cloud. (The mass distribution of newly formed stars is described empirically by the initial mass function.) [12] During the initial collapse, this pre-main-sequence star generates energy through gravitational contraction. Once sufficiently dense, stars begin converting hydrogen into helium and giving off energy through an exothermic nuclear fusion process. [8]

## Main Sequence

Main sequence stars fuse hydrogen into helium. Stars live the majority (about 90%) of their lives in this stage of their evolution. Our Sun is thought to be about 5 billion years into its 10 billion year main-sequence lifetime.

In a main sequence star, the inward gravitational force (due to the mass of the star) is balanced by the outward gas pressure (due to nuclear fusion reactions in the core). This balance is called hydrostatic equilibrium.

Figure 1: Hydrostatic equilibrium.
Credit: Brian Woodahl (http://woodahl.physics.iupui.edu/Astro105/)

If the star starts to release less energy from the core the forces are no longer balanced. The gravitational force will cause the star to begin to contract. This contraction increases the temperature and pressure deep within the star. These conditions allow the core to release more energy which increases the outward gas pressure. The star returns to equilibrium, though may have a slightly different radius.

The mass of a star controls how much time a star spends in the main sequence stage. More massive stars use up their fuel more rapidly than less massive ones. When stars run out of fuel, they cannot keep the gravitational and gas pressure forces in balance. This results in a star expanding and evolving to become either a red giant or a supergiant star.

## The Main Sequence

This phase is the longest in the life cycle of a massive star, often continuing for millions to billions of years. At this stage, the inward gravitational pull of the mass of the star is balanced by the outward push of the fusion core. The balance between the inward and outward force keeps the star stable and shining for eons.

The star now is called the Main Sequence star and it stably gives light and heat. All the hydrogen is fused together and helium is produced. The sun has a main sequence span of nearly 10 billion years! But massive stars have less period, some even a few million years.

## The main sequence

Besides the small red stars, the medium white stars and the big blue stars, there are of course all the in-between stars, and some strange ones that are both large and red. A hundred years ago, when astronomers were first cataloging stars, this was absolutely a confusing mess, with apparently no rhyme or reason between a star's color and its brightness and size.

The solution came with what we now call the Hertzsprung-Russell diagram, which is the backbone of understanding how stars live even today. The Hertzsprung-Russell Russell diagram is a plot of the temperature of a star (which we can get from its color) and its brightness.

If you take a whole bunch of stars and plot their temperature and their brightness, with one point for each star on the diagram, you find something surprising. It turns out that stars don't have all sorts of color and brightness combinations. Instead there is a stripe running diagonally that the vast majority of stars live on. This stripe runs from the dim, red end to the bright, blue end.

This stripe is known as the main sequence, and stars that burn hydrogen in their cores (the primary fuel source for the vast majority of a star's life) will live somewhere on this stripe. As stars age, they slowly and gently move up the track along the main sequence, becoming steadily brighter and bluer as the eons go by.

How long they live on that track, burning hydrogen in their cores, depends on how massive they are. A low-mass red dwarf can spend trillions of years on the main sequence, while a giant star bigger than our sun may only last a few million years at best.

Once hydrogen fusion ends inside of the core of a star, it moves off the main sequence and evolves in different directions. Large stars become red giants, which occupy their own positions on the Hertzsprung-Russell diagram. Other stars might zigzag back and forth, alternating between blueness and redness as heavy elements attempt to fuse deep in their hearts.

## From protostar to main sequence:

--- after initial collapse, protostar is likely still to be surrounded by remnant of the cloud from which it formed (need to observe at long wavelengths to see through the dust)

• -- protostars are frequently observed to have circumstellar disks (are these where planets form?) and 'jets' or outflows from their poles

• -- eventually the star completes its collapse and begins to burn H, blows away surrounding material and it is then observed as a normal main sequence star

What happens if the collapsing cloud is too large?

If the mass of the cloud exceeds about 100 M, it will collapse and heat up very quickly. Nuclear reactions occur so rapidly that the star becomes very luminous and blows itself apart -- either catastrophically or more gently by blowing off only the outer layers.

## Contents

The revised Yerkes Atlas system (Johnson & Morgan 1953) [4] listed a dense grid of F-type dwarf spectral standard stars however, not all of these have survived to this day as standards. The anchor points of the MK spectral classification system among the F-type main-sequence dwarf stars, i.e. those standard stars that have remained unchanged over years and can be used to define the system, are considered to be 78 Ursae Majoris (F2 V) and pi3 Orionis (F6 V). [5] In addition to those two standards, Morgan & Keenan (1973) [6] considered the following stars to be dagger standards: HR 1279 (F3 V), HD 27524 (F5 V), HD 27808 (F8 V), HD 27383 (F9 V), and Beta Virginis (F9 V). Other primary MK standard stars include HD 23585 (F0 V), HD 26015 (F3 V), and HD 27534 (F5 V). [7] Note that two Hyades members with almost identical HD names (HD 27524 and HD 27534) are both considered strong F5 V standard stars, and indeed they share nearly identical colors and magnitudes. Gray & Garrison (1989) [8] provide a modern table of dwarf standards for the hotter F-type stars. F1 and F7 dwarf standards stars are rarely listed, but have changed slightly over the years among expert classifiers. Often-used standard stars include 37 Ursae Majoris (F1 V) and Iota Piscium (F7 V). No F4 V standard stars have been published. Unfortunately F9 V defines the boundary between the hot stars classified by Morgan, and the cooler stars classified by Keenan, and there are discrepancies in the literature on which stars define the F/G dwarf boundary. Morgan & Keenan (1973) [6] listed Beta Virginis and HD 27383 as F9 V standards, but Keenan & McNeil (1989) [9] listed HD 10647 as their F9 V standard. Eta Cassiopeiae A should probably be avoided as a standard star because it was often considered F9 V in Keenan's publications, [9] but G0 V in Morgan's publications. [7]

Some of the nearest F-type stars known to have planets include Upsilon Andromedae, Tau Boötis, HD 10647, HD 33564, HD 142, HD 60532, and KOI-3010.

Some studies show that there is a possibility that life could also develop on planets that orbit an F-type star. [10] It is estimated that the habitable zone of a relatively hot F0 star would extend from about 2.0 AU to 3.7 AU and between 1.1 and 2.2 AU for a relatively cool F8 star. [10] However, relative to a G-type star the main problems for a hypothetical lifeform in this particular scenario would be the more intense light and the shorter stellar lifespan of the home star. [10]

F-type stars are known to emit much higher energy forms of light, such as UV radiation, which in the long term can have a profoundly negative effect on DNA molecules. [10] Studies have shown that, for a hypothetical planet positioned at an equivalent habitable distance from an F-type star as the Earth is from the Sun (this is further away from the F-type star, inside the habitable zone), and with a similar atmosphere, life on its surface would receive about 2.5 to 7.1 times more damage from UV light compared to that on Earth. [11] Thus, for its native lifeforms to survive, the hypothetical planet would need to have sufficient atmospheric shielding, such as an ozone layer in the upper atmosphere. [10] Without a robust ozone layer, life could theoretically develop on the planet's surface, but it would most likely be confined to underwater or underground regions. [10]

## What is the difference between a type I and type II supernovas?

A type I supernova is caused by a white dwarf and a type II supernova is caused by a massive star.

#### Explanation:

Both types of supernova are caused by a star's core collapsing under gravity. When this happens temperatures and pressures increase until the point where new fusion reactions start. These fusion reactions can consume huge amounts of material in a short time which causes the star to explode violently.

A type I supernova occurs in closed binary systems where two average stars orbit around each other quite closely. When one of the stars exhausts its hydrogen it will enter the red giant stage and then collapse into a white dwarf.

When the second star becomes a red giant, if the stars are close together the white dwarf will accrete (=capture) material from the red giant increasing its mass. When the mass of the white dwarf gets to the Chandrasekhar limit of 1.44 solar masses its core will collapse. The collapse raises the temperature and pressure to the point where carbon fusion starts. A large amount ofd the white dwarf's material fuses in a short period of time the star explodes.

A type II supernova occurs in larger stars of around 10 solar masses. After it leaves the main sequence it starts fusing increasingly heavy elements in shells around the core. At some point the energy produced by the fusion process in the core isn't sufficient to overcome gravity and the core collapses. If the star still has an outer envelope of hydrogen, the core collapse will ignite a fusion process in the hydrogen layer which will trigger the supernova explosion.

## Pulsars

Astronomers suspect that all neutron stars rotate and do so quite rapidly. As a result, some observations of neutron stars yield a "pulsed" emission signature. So neutron stars are often referred to as PULSating stARS (or PULSARS), but differ from other stars that have variable emission. The pulsation from neutron stars is due to their rotation, where as other stars that pulsate (such as cephid stars) pulsate as the star expands and contracts.

Neutron stars, pulsars, and black holes are some of the most exotic stellar objects in the universe. Understanding them is only part of learning about the physics of giant stars and how they are born, live, and die.