Planetary Nebulea - thoughts following Alan's Lecture

[John Murrell]

In last weeks lecture Alan said the temperature of White Dwarfs range from around 200k Kelvin to 10k Kelvin. When I thought about it this was rather odd – the White Dwarf is essentially the core of the star compressed so it heats up more. The Sun’s core burning Hydrogen is at around 15 million Kelvin. This rises to around 100 million Kelvin when the Helium burns into Carbon and the outer layers are blown off into the planetary nebula. When the helium burning stops the core collapses and gets even hotter due to gravitational energy.

 

So the question is why is the temperature of the white dwarf only a few times 10^4 Kelvin rather than over 100 million K ?

 

The result from looking at various books quite surprised me. The core of the white dwarf is still at over 100 m Kelvin but the outer ( rather thin) atmosphere is such a good insulator that the outside ( observable ) surface is much cooler. As a result of this the core only cools at about 6 Kelvin per year. Thus takes a long time to cool compared to the life of the planetary nebula.

 

Regards

 

John Murrell

Astronomer Without Portfolio

Website www.JohnMurrell.org.uk

 

 

[Roy Easto]

Much like the Earth see attached,

Roy

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[John Murrell]

Hello Roy,

 

The difference is the Earth is still generating heat through radioactive decay – the white dwarf core is all at the same temperature (Isothermal) due to the de-generate state of the core. As a result the temperatute falls from .c. 100 M K at the base of the (thin) atmosphere to a few time 10^4 K at the top. Sounds like good stuff to insulate your house with ! Also it absorbs all the X-Rays from the core ( assuming degenerate matter at 100M K generates X-Rays)

 

Does anyone know what the Earth’s surface temperature would be from core heating only ? I seem to recall the power loss is around a couple of watts per square meter on average ?

[Roy Easto]

I was thinking more about the insulating effect of the crust being so relatively thin with high temperatures on one side and black space on the other. And I liked the picture.

There was an article recently about mass loss/gain from the Earth. The Earth generates 24TW in energy through radioactive decay. If the Earth has an area of 4 * pi * (6000000)^2 = 4521 trillion square meters then we would have around 5mW per square meter? The mass loss for the whole Earth (converted into energy) would be 24*10^12 / (3*10^8)^2 = 0.2 grams per second. Compared to the Sun's 4 million tons per second although it does have a mass 330000 times larger than the Earth.

So 4000000/330000/0.0002 = 60000 which is the ratio of heat generated by 1 kg of the Sun compared to 1kg of the Earth (unless I've made a simple mistake(s) somewhere.

Roy

[John Murrell]

Hi everyone,

 

There is a page on Wikipedia about the Earths thermal loss at http://en.wikipedia.org/wiki/Geothermal_gradient  that quotes 44.2 TW as the power of which 30TW is from radioactive decay .

 

People generate far more heat per kg than either the Earth or the Sun about 100 – 120 W thus around 1 to 2 Watts per Kg.

 

Therefore if you built the Sun out of people ( ignoring the need for Oxygen & food plus disposal of waste & CO2)  it would be much hotter !