# A Rundown on White Dwarves When a star very similar to our sun dies, it turns into a white dwarf. By this point if you're even >[!Warning]- More on Quantum Physics - A Snippet >heisenberg uncertainty principle (we cannot predict with 100% certainty where a quantum particle is) >pauli exclusion principle (no two fermions (spin1/2, like electrons) can be occupying the same space) # A White Dwarf's Internals At some point, gravity cannot push electrons down further thanks to the pauli exclusion principle. This means that the higher the mass you're trying to add, the higher the energy. When a degenerate gas gets heavier, it actually gets smaller --> this means that the gas gets more and more and more compressed, meaning that electrons have to fill all of the energy levels. at some point, helium can fuse, with a helium-fusing core surrounded by a hydrogen-burning shell. ## The Chandrasekhar Limit Understanding the internals of a white dwarf is key to unlocking its deepest, darkest secrets. Now that we've gotten its internal mechanisms done and dusted with, it's time to give a value for the maximum %%chandrasekhar limit pls when available%% This gives us a maximum value for the white dwarf as around 1.4 solar masses. Once the white dwarf passes this limit there will be consequences... ## White Dwarf Evolutionary Stages The evolution of a white dwarf is typically interpreted as almost static in school textbooks. At least, that's what I think - I'm not here to reiterate from a school textbook, after all! In fact, the evolution of a white dwarf follows a linear yet convoluted path to get to the "degenerate cooling" stage that we're all familiar with it. Below are the series of stages that a white dwarf is required to move down in order to reach it's end state - a **Black Dwarf**. %%add diagrams for each - explain each photo please%% #### Stage 1: The Red Giant moves into the Post-AGB branch At this stage, the Red Giant completes the AGB Branch - the shell of helium and hydrogen is now so close to the centre that one more thermal pulse will lead to very fast mass loss. By this point, the radius of the white dwarf is around an Earth mass and the star slowly loses mass in the form of its outer layers, creating a **planetary nebula**. This stage ends when the star reaches a temperature of 30,000 Kelvins, ionising the gas around it. ![[Pasted image 20230717184934.png]] #### Stage 2: The Hot Core of the Star is revealed By this stage, enough of the diffuse outer layers have been shed off that the hot inner core (which can reach surface temperatures of upwards of 100,000 Kelvins) is revealed, allowing for the white dwarf to glow initially blue. The gravitational force and temperatures combined allow a white dwarf to rip apart heavier nuclei at its surface, creating an atmosphere (pseudo-corona?) of hydrogen and helium. ![[Pasted image 20230717185441.png]] #### Stage 3: Degenerate Cooling By this point the white dwarf does not have any internal mechanism allowing it to generate energy. Instead, it is propped up by the **electron degeneracy pressure** mentioned previously, which leads it to slowly cool as it radiates energy in the form of light. Eventually, the white dwarf will reach a constant temperature value, the same as the Universe. This turns it into a **black dwarf.** >[!Example]- Case Study - Sirius A and B >white dwarves shine brighter in X-rays! Below are diagrams in visible and X-Rays respectively. white dwarves shine in X-Rays as they are very, very hot when young, emitting high-energy wavelengths. Sirius A is cooler than Sirius B, emitting mostly in UV, hence the colour difference. The first image is of the Sirius system in visible light (where the small dot is Sirius B) and the second image is of the Sirius system in > >![[Pasted image 20230711103832.png]] >![[Pasted image 20230711103839.png]] > > > >[!Question]- What's the upper limit mass which can still become a WD? Equivalently: how much mass is it possible for a star to shed? >Studies of young clusters tell us that the limit is 8 solar masses. Stars can sometimes shed their outer layers at 6.6 solar masses. Past this, carbon can typically fuse, creating opaque outer layers (and if the star is massive enough, even create **Wolf-Rayet Stars**!) We can find the amount of mass shed by a star by subtracting the mass of the white dwarf with the mass of the original main sequence star. As word equations are bad and stupid, here it is in LaTeX form: $M_{ej} = M_{MS} - M_{WD}$ ## Inferring the Mass of a Main Sequence Star from its White Dwarf >[!Danger]- Gravitational Acceleration on a White Dwarf's Surface (CASE STUDY PROMPT) >Now it's time for my favourite part - rigorous, somewhat mundane physics! It is our goal to now find the gravitational acceleration on a white dwarf's surface - and to draw our conclusions about some of the phenomena going on on a white dwarf by comparing it to Earth's gravity. > >It's given that the average mass of a white dwarf is $2.8 \times 10^{30}\ kg$, and the density of a white dwarf is $1 \times 10^9$. How can we find the gravitational attraction given this? >[!Abstract]- Gravitational Acceleration Case Study Solution >A white dwarf can be generalised into a uniform sphere with radius $r$. Given that the formula for the volume of a sphere is $\frac{4}{3}\pi r^3$ where $r$ is the radius of the sphere, we can create an expression for the density $\rho$ of the white dwarf, letting $M$ be its mass: >$\rho = \frac{M}{\frac{4}{3}\pi r^3}$ >Remember the formula for gravitational acceleration $a$ shown as follows: >$a = \frac{GM}{r^2}$ >Since we're given the values for density and mass we can rearrange the density equation above to isolate and obtain $r$: >$r = ^3\sqrt{\frac{M}{\frac{4}{3}\pi\rho}}$ >This gives us a value for $r$ as: >$r = ^3\\sqrt{ \frac{2.8 \times 10^{30}}{\frac{4}{3}\pi 1 \times 10^9} } = 8.74 \times 10^6 metres $ >Substitute this value of $r$ into the gravitational acceleration formula to yield our final value for $a$: >$a = \frac{6.67\times10^{-11}\times2.8\times10^{30}}{874000^2}$ >$a = 2.44 × 10^6 m/s$ # What's Next? For the next instalment in the AstroVault, go here to learn all about planetary nebulae: [[Nebulae (Astro)]] To learn about the consequences if a white dwarf ever exceeds the Chandrasekhar limit, go here: [[Other Supernovae (Astro)]] For a more in-depth look into Newton's Law of Gravitation, here: [[Newton's Law of Gravitation - The Intro]]