Why are red dwarf stars cooler than the Sun?

[hyunxu]

'Hotter' means more energetic photons are being emitted.
Usually this is a simple consequence of how massive the star is.
However other factors such as the composition of the star's elements play a part in stars luminosity profile.

So Does hotter star mean a massive star?

More hotter the star , more massive it is?
Or

More massive the star, more hotter it is?

 

[rootone]

In general yes, more massive stars emit much more energetic EM radiation (= hotter).
One consequence of this is that more massive stars have short lives compared to smaller ones.

 

[hyunxu]

One consequence of this is that more massive stars have short lives compared to smaller ones.

Yes. That's right. By the equation e= mc^2 , every second , the Sun slims down by 5 million tonnes. This may sound like a huge amount , but during the life of the Sun it only amounts to 0.01% of its mass. So Is Sun's mass average?

(As hotness depends on mass)

 

[snorkack]

So Is Sun's mass average?

Average over what?

Of the 50 brightest stars, 14 are dwarfs. All of them are more massive than Sun, save Sun itself.
Of the remaining 36 subgiants, giants, bright giants and supergiants, 12 are G or cooler. The rest are F or hotter.

All the dwarfs brighter than Sun are also more massive. And hotter. On main sequence, it is fairly consistent tat a more massive star has bigger total luminosity, higher temperature as well as larger area.
About the giants: as stars exhaust part of their fuel (protium in centre first), they tend to fuse the remaining fuel at increasing rate. At equal mass, an older star is brighter.
The temperature varies widely. Many old stars cool down - they become bright, but acquire a large area and low temperature. Yet most giants are still hotter than Sun.
Most of the giants that are bright in sky are still more massive than Sun. Not all. Some, notably Arcturus, are suspected of being only as massive as Sun, but older, brighter, bigger and cooler.

 

[hyunxu]

Some, notably Arcturus, are suspected of being only as massive as Sun, but older, brighter, bigger and cooler.

Here mass is same , but why does the area varies?

 

[snorkack]

Here mass is same , but why does the area varies?

Because the luminosity varies.

 

[hyunxu]

Because the luminosity varies.

High luminosity or low luminosity ?
How surface area depends on the luminosity?

 

[snorkack]

High luminosity or low luminosity ?
How surface area depends on the luminosity?

As the core of the star produces increasing amounts of heat, the surface layers of the star must emit the light somehow.
They might emit it by remaining the same size and getting hotter. But gases expand on heating, so surface area necessarily increases at least somewhat.
For red giants, the expansion is actually so large that the star finally comes to equilibrium where its surface area has increased even more than luminosity and the surface temperature has therefore fallen.

 

[stefan r]

Here mass is same , but why does the area varies?View attachment 227071

The core of Arcturus is not the same as the core of the sun. When astronomers say "temperature of a star" they mean the observable surface of the star. The Sun's corona is much hotter(5 million°K) than the Sun's photosphere(5772°K). The Sun's core is closer to 16 million°K. The hydrogen at the core in Arcturus burned up. Hydrogen fusion occurs in a shell around a much smaller core made of mostly helium. The core in red giant branch stars is less than around 100 to 200 million °K. When the temperature gets higher the helium will fuse and Arcturus will move to the next stage.

Because Arcturus has a hotter core the fusion rate in the shell is higher than the fusion rate in the Sun's core. The surfaces of both stars are held up by radiation pressure. Increased reaction rates inflate the star and makes the surface puff outward. If you take any gas and compress it you change the temperature. Gas law. Arcturus has around 25 times the Sun's radius so around 16,000 times the volume. If you created a sample of Arcturus gas in a laboratory and then you compacted it to the density of the Sun's gas you would expect the temperature/pressure to rise by a factor of 16,000 if it was an "ideal gas". The internal structure is different and the gases are not ideal but the general idea applies. Air conditioners and refrigerators work using temperature change in a gas that expands and compresses. If you took a sample of solar gas at 5772°K in a laboratory container and expanded to 16,000 times the volume the temperature will be much lower than Arcturus (4286°K).

 

[Ken G]

Because Arcturus has a hotter core the fusion rate in the shell is higher than the fusion rate in the Sun's core. The surfaces of both stars are held up by radiation pressure. Increased reaction rates inflate the star and makes the surface puff outward.

You're right that there is a high shell fusion rate in Arcturus, but neither the Sun nor Arcturus experiences any significant radiation pressure anywhere in the star. It's well over 99% gas pressure.

 

[davenn]

The Sun's corona is much hotter(5 million°K) than the Sun's photosphere(5772°K).

ohhh and by the way, just for your physics learning ...
It isn't deg Kelvin, it is just plain Kelvin ... 5 million K ... 5772 K etc

Dave

 

[hyunxu]

Still we say that radiation from Sun is dangerous. But what about the radiation from the star which is hotter than Sun? Is there any relationship between hotness and radiation?

(Still it's about hotness of the sun)

 

[glappkaeft]

It depends on which radiation you are talking about. Electromagnetic or particle? If EM what frequency are you discussing.? If particle, which particle? Are you concerned about average levels or peaks associated with things like solar flares?

 

[Drakkith]

Still we say that radiation from Sun is dangerous. But what about the radiation from the star which is hotter than Sun? Is there any relationship between hotness and radiation?

(Still it's about hotness of the sun)

The hotter the star, the more UV radiation is emitted. For example, at 5,000 K the Sun emits about 3.8 W/sr/m² at a wavelength of 100 nm, while a star at 20,000 K would emit almost 9x10⁹W/sr/m² at the same wavelength. That's about a 3-billion-fold increase. It's even 1,000 times more than the Sun emits at 500 nm, which is approximately green light. Basically, if you go outside at noon on a sunny day and feel the heat from the Sun, a star at a temperature of 20,000 K would put out more than 1,000 times that much energy just in the UV portion of the spectrum.

 

[rootone]

what about the radiation from the star which is hotter than Sun?

Sun bathing somewhere near a blue giant isn't anything to worry about really.
All of your water molecules would be disassociated in less than a microsecond.