A Question Concerning Solar Flares

[|Glitch|]

According to both NOAA and Wikipedia, an X1 Class solar flare produces 0.0001 watts of energy per square meter, or greater. Therefore, an X45 solar flare would produce 0.0045 watts of energy per square meter. However, that cannot be correct. That is too absurdly small.

http://www.spaceweatherlive.com/en/help/the-classification-of-solar-flares [/URL]
[URL='http://en.wikipedia.org/wiki/Solar_flare#Classification']Solar flare - Wikipedia, the free encyclopedia[/url]

If a logarithmic scale is used, where:

X1 = 0.0001 watts/m^2;
X2 = 0.0002 watts/m^2;
X3 = 0.0004 watts/m^2;
X4 = 0.0008 watts/m^2;
...
X42 = 219,902,325.5552 watts/m^2;
X43 = 439,804,651.1104 watts/m^2;
X44 = 879,609,302.2208 watts/m^2;
X45 = 1,759,218,604.4416 watts/m^2.
​

That does not appear to be correct either. That is too absurdly large.

Outside of Earth's atmosphere the sun normally produces ~1,300 watts of energy per square meter. However, the atmosphere of the planet absorbs some of this energy and by the time the sunlight reaches the surface of the planet it produces ~1,000 watts of energy per square meter.

I cannot figure out this solar flare classification scheme. In order to cause an aurora, much less having the ionized particles reach he surface of the planet, there must be considerably more energy than 1,300 watts per square meter hitting the planet.

The article below is what got me thinking about the amount of power involved in solar flares:

NASA's Swift Mission Observes Mega Flares from a Mini Star

On April 23, NASA's Swift satellite detected the strongest, hottest, and longest-lasting sequence of stellar flares ever seen from a nearby red dwarf star. The initial blast from this record-setting series of explosions was as much as 10,000 times more powerful than the largest solar flare ever recorded.

"We used to think major flaring episodes from red dwarfs lasted no more than a day, but Swift detected at least seven powerful eruptions over a period of about two weeks," said Stephen Drake, an astrophysicist at NASA's Goddard Space Flight Center in Greenbelt, Maryland, who gave a presentation on the "superflare" at the August meeting of the American Astronomical Society’s High Energy Astrophysics Division. "This was a very complex event."



Source: NASA's Swift Mission Observes Mega Flares from a Mini Star

If the solar flare classification scheme uses a logarithmic scale, then a solar flare that is 10,000 times more powerful that an X45 solar flare would be producing 17.6 trillion watts of energy per square meter (the equivalent of 17.6 trillion Joules per second). Is that even possible, or am I way out in left field?

Hopefully, someone can clear up my obvious confusion.

 

[Simon Bridge]

The figures are not total energy from the flare but the energy from x-rays with wavelengths between 1 and 8 angstroms.
Comparing figures you can see that only a very small percentage of the total energy is released in that range.
http://hesperia.gsfc.nasa.gov/hessi/flares.htm

 

[mfb]

Why do you think linear and powers of two are the only options?
The linked page suggests a power of 10 every 10 steps and linear scales in between, so X45 is 50000 times as intense as X1.

The power reaching us from solar flares is tiny compared to the regular sunlight, otherwise they would completely burn the surface. Auroras are also extremely weak compared to bright sunshine - that's why you typically do not see them in daylight.

In addition, you have to distinguish between "power per solar surface area" and "power per Earth surface area". The first one is always larger by a factor of ~50,000 (given by the ratio AU^2/(radius of sun)^2)

 

[|Glitch|]

The figures are not total energy from the flare but the energy from x-rays with wavelengths between 1 and 8 angstroms.
Comparing figures you can see that only a very small percentage of the total energy is released in that range.
http://hesperia.gsfc.nasa.gov/hessi/flares.htm

Thanks, that makes it a bit clearer. I was under the impression that they measured the energy from the solar flare across the full spectrum. I did not realize that they were only measuring the x-ray and gamma-ray emissions.

 

[|Glitch|]

Why do you think linear and powers of two are the only options?

Because solar flare types A through M are linear. Each type goes from 1 to 9 before becoming the next type. Type X solar flares, apparently, are the exception.

The linked page suggests a power of 10 every 10 steps and linear scales in between, so X45 is 50000 times as intense as X1.

Actually, both linked pages show a linear progression, until you get to the type X solar flares. Wikipedia even provides an example:

"Within a class there is a linear scale from 1 to 9.n (apart from X), so an X2 flare is twice as powerful as an X1 flare, and is four times more powerful than an M5 flare."​

Which would make an X2 flare equal to 0.0002 watts/m^2, and an X45 flare equal to 0.0045 watts/m^2.

In the YouTube video at 1:40 she says this solar flare from the red dwarf, DG CVn, was equivalent to an X100,000. Which would be 10 watts/m^2 using the linear scale.

The power reaching us from solar flares is tiny compared to the regular sunlight, otherwise they would completely burn the surface. Auroras are also extremely weak compared to bright sunshine - that's why you typically do not see them in daylight.

In addition, you have to distinguish between "power per solar surface area" and "power per Earth surface area". The first one is always larger by a factor of ~50,000 (given by the ratio AU^2/(radius of sun)^2)

Thanks, I did not realize that they were only measuring wavelengths between 1 and 8 angstroms. That is a very narrow band, and certainly does not reflect the full power of the flare. Just the power of the flare in those specific wavelengths.

It also makes perfect sense that it would have to be much less powerful than regular sunlight, otherwise as you say, they would be visible during the day.

 

[|Glitch|]

It was also pointed out to me that when you take the wattage per square meter and apply that to half of the surface area of the Earth, it does indeed become a large number. A X1 flare would be hitting the planet with 9,845 Joules per second with x-ray and gamma radiation. An X45 flare would hit Earth with 443,025 Joules per second with x-ray and gamma radiation everywhere across half the planet.

So I am beginning to see why that would be a problem. oo)

 

[mfb]

They are just linear within the classes - or groups of 10 in case of the X designations. This is ciearly described in the Wikipedia page.

As relative values (relative to C1), you get this:
C1 -> 1
C2 -> 2
C3 -> 3
... linear up to
C9 -> 9
M1 -> 10
M2 -> 20 (note the changed step size)
M3 -> 30
...
M9 -> 90
X1 -> 100
X2 -> 200 (again, changed step size)
...
X9 -> 900
X11 -> 1000
X12 -> 2000 (changed step size)
...

You can read X28 as (X2)8 where X2 is the class that corresponds to 10000, so X28 corresponds to 80000.

It was also pointed out to me that when you take the wattage per square meter and apply that to half of the surface area of the Earth

That would require the full flare emission to hit Earth - a highly unrealistic scenario.
J/s is not an intensity, do you mean J/(s m^2)?

 

[D H]

That's just wrong, mfb. There is no change of step size within the X-class flares. The X17 flare on October 28, 2003 had a peak flux of 17*10^-4 W/m². The multiplier is 17, not 70. Similarly, an X45 flare (the Carrington event) does not have 50,000 times the flux of an X1 flare. It's just a factor of 45. A flare with 50,000 times the X-ray flux of an X1 flare would wipe out life on the side of the Earth facing the Sun.

 

[mfb]

Oh sorry, I misread numbers in the linked page. Fine, linear X scale.