# 23.1 The death of low-mass stars

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## Learning objectives

By the end of this section, you will be able to:

• Describe the physical characteristics of degenerate matter and explain how the mass and radius of degenerate stars are related
• Plot the future evolution of a white dwarf and show how its observable features will change over time
• Distinguish which stars will become white dwarfs

Let’s begin with those stars whose final mass just before death is less than about 1.4 times the mass of the Sun ( M Sun ). (We will explain why this mass is the crucial dividing line in a moment.) Note that most stars in the universe fall into this category. The number of stars decreases as mass increases; really massive stars are rare (see The Stars: A Celestial Census ). This is similar to the music business where only a few musicians ever become superstars. Furthermore, many stars with an initial mass much greater than 1.4 M Sun will be reduced to that level by the time they die. For example, we now know that stars that start out with masses of at least 8.0 M Sun (and possibly as much as 10 M Sun ) manage to lose enough mass during their lives to fit into this category (an accomplishment anyone who has ever attempted to lose weight would surely envy).

## A star in crisis

In the last chapter, we left the life story of a star with a mass like the Sun’s just after it had climbed up to the red-giant region of the H–R diagram for a second time and had shed some of its outer layers to form a planetary nebula. Recall that during this time, the core of the star was undergoing an “energy crisis.” Earlier in its life, during a brief stable period, helium in the core had gotten hot enough to fuse into carbon (and oxygen). But after this helium was exhausted, the star’s core had once more found itself without a source of pressure to balance gravity and so had begun to contract.

This collapse is the final event in the life of the core. Because the star’s mass is relatively low, it cannot push its core temperature high enough to begin another round of fusion (in the same way larger-mass stars can). The core continues to shrink until it reaches a density equal to nearly a million times the density of water! That is 200,000 times greater than the average density of Earth. At this extreme density, a new and different way for matter to behave kicks in and helps the star achieve a final state of equilibrium. In the process, what remains of the star becomes one of the strange white dwarfs that we met in The Stars: A Celestial Census .

## Degenerate stars

Because white dwarfs are far denser than any substance on Earth, the matter inside them behaves in a very unusual way—unlike anything we know from everyday experience. At this high density, gravity is incredibly strong and tries to shrink the star still further, but all the electrons resist being pushed closer together and set up a powerful pressure inside the core. This pressure is the result of the fundamental rules that govern the behavior of electrons (the quantum physics you were introduced to in The Sun: A Nuclear Powerhouse ). According to these rules (known to physicists as the Pauli exclusion principle ), which have been verified in studies of atoms in the laboratory, no two electrons can be in the same place at the same time doing the same thing. We specify the place of an electron by its position in space, and we specify what it is doing by its motion and the way it is spinning.

this question is for atheists what created humans , how did they evolve
not entirely sure what this question has to do with Atheism but, firstly, there is no "who", life evolved in multiple paths, humans are simply one of those paths. The process of how life evolves is a very complicated but very well researched field of biology, so it would be worth doing research...
ben
...into that field, evolution isnt disputed. However, the direct path from the common ancestor (that we share with chimps) has not yet been completed. But know for sure that humans didn't just magically appear one day, it was over millions of years of evolution
ben
(I must ask though, what has this got to do with Atheism?)
ben
idk i thought believers will say god created us
ilyes
there are many types of believers one say that god created consciousness, one say we just magically appeared out of nowhere, and one say universe was created by God(all based on people I have met so far)
Tanmay
yes why not you don't need to ask anyone for permission
Tanmay
-Why there are moons in every planet but there's note in mercure ?
Well with mercury Venus also does not have moon.The reason that Mercury is not having moons is since it is too close to sun and thus if it would have any moon orbiting it ,then the moon will eventually attracted by sun due to it's high gravitational force whereas mercury has the lowest gravity
Anjali
The gravitational force of mercury is lowest in solar system and it won't be able to hold a moon in it's orbit
Anjali
Nice explanation
Asim
Thank you brother
Anjali
Did general theory of relativity leads us to singularity?
Asim
yes the general theory of relativity leads us to singularity
Anjali
But Einstein was not a believer of big bang. And singularity lead us to big bang?
Asim
yes Einstein was really astonished by his mathmatical answers that came fron his equations (this is what almost every one says)
Tanmay
and there are many theories stating how our universe came in which one is big bang
Tanmay
Einstein was against the fact that anything can come from nothing that our big bang says and he also thought that singularity (infinite mass in zero volume) can not be real(also what most people say)
Tanmay
also what most people say means that there is no evidence that he was against all these things
Tanmay
Okay
Asim
Tanmay
Asim
anything else
Tanmay
Do you believe that grand unified theory can be complete in future?
Asim
Do you believe that grand unified theory will be complete in future?
Asim
yes I do believe in it as I also believe big bang
Tanmay
Well i don't believe in big bang like Einstein didn't.
Asim
do you believe in wormholes are real?
Amit
@Asim then what do you think our universe came from or how it started
Tanmay
Well it's a myth.
Asim
@Amit I believe wormholes are real
Tanmay
It came from nothing Tanmay.
Asim
Even I believe in wormholes
Anjali
So Tanmay you must believe in baby universes.?
Asim
I believe that they are many things we can't explain or give prove but they are theories,imaginations and they are the basics for new discoveries
Anjali
So ,it is useless to argue over them
Anjali
But we should try to find new possibilities if we don't believe in old ones
Anjali
you are right @anjali
Amit
what is dark matter?
Amit
can a star turn into planet?
Amit
I have doubt on how Stephen hawking posses ideas of black hole by himself?
why do people believe in God and how are humans made
ilyes
No amit star can't turn into planet.
Asim
you are wrong asim
Amit
also Asim, please tell me why you think the big bang is a myth?
ben
@Asim what do you mean by it came from nothing what came from nothing
Tanmay
@Asik I don't know what baby universe is if you mean early universe then the question doesn't make sense
Tanmay
@Amit starts can become cold enough for us to live at high altitude but their surface will still be made of plasma
Tanmay
@Amit dark matter is a type of substance that doesn't interact with normal matter and also gives galaxies enough mass to hold its stars rather than to fly out by its rotation
Tanmay
Sorry Asim for wrong spelling of your name
Tanmay
Amit
@Tanmay but a star can turn into a planet, but this transformation only happens for a very particular type of star known as a brown dwarf.
Amit
ben
I will check and then I will tell you if it's true or not thanks for the question
Tanmay
I will check as it is really wierd but thanks for your question
Tanmay
(oh no I was joking hahaha, Amit just took the definition that you see first on google and pasted)
ben
Tanmay baby universes is when something fell in black hole it's went into another universe called baby universe according to Stephen hawking. Well i don't know weather to believe it or not.
Asim
Amit brown dwarf are not planet or stars they have their own classification these are basically failed star, not massive enough to power hydrogen fission reaction.
Asim
ahh, didn't he use that to explain where "information" goes? because recently a paper was published stating that information may actually be re-emitted by the black hole as 'encoded' hawking radiation
ben
(so it may not be going to another universe, but instead coming back into our own)
ben
Hawking radiation are basically the the radiation emitted by black hole boundaries called event horizon.
Asim
Amit
So re-emitting doesn't make scene.
Asim
every black hole contains a singularity?
Amit
Yep absolutely.
Asim
ohhh, no worries dude, and yeah hawking radiation is a consequence of both quantum mechanics and relativity, really cool. And look it up Asim, it's a really interesting read
ben
but a singularity is a point in space where there is a mass with a infinte density. the problem is that infinities never exist in real world.
Amit
Ben it's really difficult to relate quantum mechanics to relativity.
Asim
Dude if you have done nobel price is waiting for you. (haha)
Asim
consequence of both quantum mechanics and relativity.!!!
Amit
Amit read theory of relativity and black hole singularities in Google. Everything will be cleared.
Asim
🤣🤣🤣
Amit
Amit
hahahahaha, yeah that's true I'm being lazy as hell there haha, I mean more it's something relates the big and small (it's cool to see quantum phenomena having a direct effect on something predicted by relativity)
ben
(if a GUT is found I genuinely doubt I'd be able to comprehend the maths hahaha, maybe a long a way down the road but not yet)
ben
ben you are nominated for nobel as well as oscar for your thoughts..(hahaha)
Amit
what's you thinks about gravitational waves gentlemen?
Amit
hahahaha, and I love what I know so far but honestly dude, I've learnt essentially nothing about gravitational waves at university yet, I'm hoping that's going to be next year
ben
I would love to ask someone what the effects of constructive ans destructive interference of gravitational waves would be. Would total destructive interference lead to black holes?
ben
good luck for your next year... ben
Amit
if such things happen that's gonna be amazing.....
Amit
eyy thank you dude, likewise man, wish you all the best for your endeavours
ben
eyy cheers dude, likewise for you man, wishing all the best for you
ben
thanks buddy..
Amit
💝❤
Amit
Gravitational Waves could help us travel faster in the space, if we are to set on an adventure like the one in The Interstellar, lol. Just saying
Awesh
what do u think created the universe
ilyes
m curious
ilyes
I believe in the theory where it states that our universe came from death of another universe and after our universe's death another universe will come from it
Tanmay
@Amit if that's what baby universe is then
Tanmay
my current understanding of universe and black holes, I would have to disbelief it
Tanmay
@Asim @Amit there is a feild in physics where we study about the physics of those objects who have intermediate size and follow some rules of quantum physics and relativity
Tanmay
@Ben what is full form of GUT?
Tanmay
@Ben I have never seen anyone spotting interference with gravitational waves but most of the people think that it will just be like interference in waves like light or sound. Do that means it's amplitude will change and will not create and black holes or stuff
Tanmay
@Awesh yes many people in youtube(some have good degrees and are astrophysicist) say that warping space is possible using gravitational waves
Tanmay
Do you all believe in multiverse
Anjali
I believe in multiverse
Tanmay
what is the model about the earth being the center of the universe called?
geocentric model
SCIENCE
SCIENCE
heliocentric universe
Jason
you are wrong Jason skerbinc
SCIENCE
in heliocentric model sun is at the center of the universe
Tanmay
what is black hole and stellar black hole
does Millikan consider electron axial spin in his discovery of electrons mass using q/m ratio ? If No how it is possible that he found rest mass of electron (9×10^31 Kg) ?
how did light from up
Before there stars , there was matter and radiation . Before there were neutral atoms ,there was an ionized plasma ,and when that plasma froms neutral atoms , those allow the Universe to deliver the earliest light we see today .......
Apsara
how to know the distance of a star
What is time
Sourav
Technical Infinite Measurement of Evolution
Doc
not by the book but the simplicity of word play ....
Doc
to calculate the distance of a star we use parallax method (as far as my school has taught me).
Tanmay
in this method we see the star from one point and then after traveling some distance perpendicular to the distance of star we see it again. With this we can make a triangle and then it's median will give our distance
Tanmay
And time is just a way of defining when an event happened
Tanmay
oh and we will know the distance of all the 3 sides of triangle formed above if we multiply the time taken by light with speed of light and the third side will be known to us as it is dependent on our will
Tanmay
what are wormholes?
Neil
What is the difference between black hole and white hole ?
Apsara
black hole is the place where the massive body makes a large disturbance in space time fabric causing large gravity even light can't escape from it and all the bodies enter into on reaching a specific distance.
SCIENCE
A white hole is a hypothetical region of spacetime and singularity which cannot be entered from the outside, although energy-matter and light can escape from it. In this sense, it is the reverse of a black hole, which can be entered only from the outside and from which energy-matter and light can
SCIENCE
White holes appear in the theory of eternal black holes
SCIENCE
worm holes join 2 distant region of spacetime through which you can travel, covering large distance in short time
Tanmay
for example if you need to travel from A to B on a plane of paper then you can travel in a straight line joining those points but a worm hole will join those points using 3rd dimention which will make you travel that distance in short time
Tanmay
Hi,Do you known Kyaw Nyein Chan Hein!
No
Astrophysicist
Hello : I'm Kyaw Nyein Chan
zin
Hi I'm Kyaw Nyein Chan
Hello : good moring, I'm Kyaw Nyein Chan
hello good morning
Astrophysicist
good morning bro
Tanmay
how do you do?
Astrophysicist
I am fine what about you?
Tanmay
same as you
Astrophysicist
cool
Tanmay
How the Big Bang is made .
Kyaw Nyein Chan
zin
What is heliocentric
helio is from the greek god helios or ilios and means sun. Centric is from central. So heliocentric means with the sun in the middle
Robin
Usually in the context of astronomy its about the moment the world goes from the idea of 'earth in the middle of the solar system' to the idea that the sun is in the center of the solar system
Robin
so from a geocentric (geo meaning earth) to a heliocentric idea
Robin
yes correct this theory states that sun is in the middle of the solar system rather than earth
Tanmay
oh you have already said this
Tanmay
Hello: good afternoon
zin
hello
Tanmay
Thankyou to all to solve my doubt . I don't know more about the solar system beacause i am a small little girl my old is 9 and i love science but i am trying to learn more about science .
Apsara
that's great you should definitely check science in a nutshell YouTube channel it will provide you with good information
Tanmay
that's great you should definitely check science in a nutshell YouTube channel it will provide you with good information
Tanmay
that's great you should definitely check science in a nutshell YouTube channel it will provide you with good information
Tanmay
Tanmay
You not alone Apsara I'm 14 but know little about the universe
Swazi
what is solar system
Himanshi
what do you mean by astronomy
Himanshi
astronomy is a study of planetary science.
Astronomy is a branch of Physics that deals with the study of celestial bodies.
Satyam
An astronomy is a scientist in the field of astronomy who focuses their studies on a specific questions or field outside the scope of Earth 🌍🌎🌏 . They observe astronomical objects such as star's , planets , moon , comets and galaxies - in either observational (by analyzing the data)
Apsara
what is the difference between astronomy and cosmology
Astrophysicist
The collection of eight planets and their moon's in orbit around the Sun , together with smaller bodies in the form of asteroids , meteoroids and comets . The planet of the solar system are ( in order of distance from the sun ) Mercury , Venues , Earth ,Mass , Jupiter , Sartune ,Uranus , Neptune .
Apsara
In Astronomy, we study about celestial objects but in cosmology we study the origin and the formation of universe.
Satyam
how much temperature were can find on neptune
the temperature is between -200 to -218 degree Celsius
Tanmay