Name of number after solar flare class?

[Drax Spacex]

What do you call the number to the right of a solar flare class?

For example, M7.8, the class is M, but what is 7.8 called?

There doesn't seem to be a consensus.

Candidates after some web searching include:
scale, finer scale, subdivision, numeric suffix, relative strength within class, factor, multiplier

Ultimately, both the class and the number after the class represent factors, which when multiplied together provide the solar flare's Peak Flux in Watts/m^2

Also, in:
https://www.spaceweatherlive.com/en/help/what-are-solar-flares.html
"Each X-ray class category is divided into a logarithmic scale from 1 to 9. For example: B1 to B9, C1 to C9, etc."
I don't think it is accurate to use the term "logarithmic scale" for this number as it actually a linear relationship in terms of flux value (even though it is plotted on a logarithmic graph).  I suggest using just "scale" here to avoid confusion.
 

[Newbie]

1 hour ago, Drax Spacex said:

What do you call the number to the right of a solar flare class?

For example, M7.8, the class is M, but what is 7.8 called?

There doesn't seem to be a consensus.

Candidates after some web searching include:
scale, finer scale, subdivision, numeric suffix, relative strength within class, factor, multiplier

Ultimately, both the class and the number after the class represent factors, which when multiplied together provide the solar flare's Peak Flux in Watts/m^2

Also, in:
https://www.spaceweatherlive.com/en/help/what-are-solar-flares.html
"Each X-ray class category is divided into a logarithmic scale from 1 to 9. For example: B1 to B9, C1 to C9, etc."
I don't think it is accurate to use the term "logarithmic scale" for this number as it actually a linear relationship in terms of flux value (even though it is plotted on a logarithmic graph).  I suggest using just "scale" here to avoid confusion.
 

I always considered the number after the flare classification to indicate the strength or intensity of the flare within that specific class..

The number is a measure of the flare's peak X-ray flux in the 1 to 8 angstrom energy range, measured in watts per square meter (W/m²) as you mention.

For example, an M8.0 solar flare is stronger than an M7.0 flare but weaker than an M9.0 flare within the M-class category. The scale is logarithmic, meaning each increase by one represents a tenfold increase in intensity. Therefore, an M8.0 flare is ten times more intense than an M7.0 flare and so on. 

Although the scale is often represented on a logarithmic graph, the relationship between the numbers is linear in terms of flux value as you say. Using the term "scale" without specifying it as logarithmic or linear conveys the information and helps avoid potential confusion.

N.

Edited February 16 by Newbie
Funny I didn’t see what topic you posted it in

[Drax Spacex]

On 2/16/2024 at 4:52 PM, Newbie said:

I always considered the number after the flare classification to indicate the strength or intensity of the flare within that specific class..

The number is a measure of the flare's peak X-ray flux in the 1 to 8 angstrom energy range, measured in watts per square meter (W/m²) as you mention.

For example, an M8.0 solar flare is stronger than an M7.0 flare but weaker than an M9.0 flare within the M-class category. The scale is logarithmic, meaning each increase by one represents a tenfold increase in intensity. Therefore, an M8.0 flare is ten times more intense than an M7.0 flare and so on. 

Although the scale is often represented on a logarithmic graph, the relationship between the numbers is linear in terms of flux value as you say. Using the term "scale" without specifying it as logarithmic or linear conveys the information and helps avoid potential confusion.

N.

This is a good example of the confusion that arises.  M8.0 is 8/7ths of the flux of a M7.0 flare.  X8.0 is ten times higher in flux than a M8.0 flare.  There's conflicting source information out there.  I've noticed that AI, using these sources, gets confused and gives different answers in different drafts when asked for example, "What is the X-ray flux value in Watts/m^2 of a M7.8 solar flare?"  The answer should be 7.8x(10^-5).

I placed this topic here so that the admins might review the descriptions for solar flare class and maybe elaborate on the calculation of X-ray flux of solar flares - so that spaceweatherlive is a definitively correct and complete source for such information.

Edited February 19 by Drax Spacex
scientific notation

[Newbie]

39 minutes ago, Drax Spacex said:

This is a good example of the confusion that arises.  M8.0 is 8/7ths of the flux of a M7.0 flare.  X8.0 is ten times higher in flux than a M8.0 flare.  There's conflicting source information out there.  I've noticed that AI, using these sources, gets confused and gives different answers in different drafts when asked for example, "What is the X-ray flux value in Watts/m^2 of a M7.8 solar flare?"  The answer should be (10e-5)*7.8.

@Drax Spacex You do highlight well the difference in the relative increase in flux between Solar Flare classes and also the conflicting information that may arise from various sources.

I believe that giving the empirical answer to the strength of a solar flare ie the mathematical calculation may challenge understanding in some instances although it would have its place within the scientific community.

I also believe all grasp the fact that an M8.0 is stronger than an M7.9 and if anyone wants to delve deeper then do the math. 
Sorry I didn’t see your edited message. I agree with your sentiments….and I didn’t realise you put it in the admins topic. Nonetheless an interesting discussion thanks. 😊

N.

Edited February 16 by Newbie
Should be able to figure out!

[Sapphire828]

I've never seen the value called a "magnitude", but it makes sense to me.

M7.8

Class: M, Magnitude: 7.8

[hamateur 1953]

I

16 minutes ago, Sapphire828 said:

I've never seen the value called a "magnitude", but it makes sense to me.

M7.8

Class: M, Magnitude: 7.8

Sounds more like a sunquake, doesn’t it?  Haha  @Sapphire828

[Philalethes]

2 hours ago, Drax Spacex said:

What do you call the number to the right of a solar flare class?

For example, M7.8, the class is M, but what is 7.8 called?

There doesn't seem to be a consensus.

Candidates after some web searching include:
scale, finer scale, subdivision, numeric suffix, relative strength within class, factor, multiplier

Ultimately, both the class and the number after the class represent factors, which when multiplied together provide the solar flare's Peak Flux in Watts/m^2

Also, in:
https://www.spaceweatherlive.com/en/help/what-are-solar-flares.html
"Each X-ray class category is divided into a logarithmic scale from 1 to 9. For example: B1 to B9, C1 to C9, etc."
I don't think it is accurate to use the term "logarithmic scale" for this number as it actually a linear relationship in terms of flux value (even though it is plotted on a logarithmic graph).  I suggest using just "scale" here to avoid confusion.
 

1 hour ago, Drax Spacex said:

This is a good example of the confusion that arises.  M8.0 is 8/7ths of the flux of a M7.0 flare.  X8.0 is ten times higher in flux than a M8.0 flare.  There's conflicting source information out there.  I've noticed that AI, using these sources, gets confused and gives different answers in different drafts when asked for example, "What is the X-ray flux value in Watts/m^2 of a M7.8 solar flare?"  The answer should be (10e-5)*7.8.

I placed this topic here so that the admins might review the descriptions for solar flare class and maybe elaborate on the calculation of X-ray flux of solar flares - so that spaceweatherlive is a definitively correct and complete source for such information.

I doubt there's any precedent for naming the numeric part of those terms specifically. Based on your suggestions I would suggest "relative magnitude" (as a shorter form of "relative strength within each class", which would be the same), which in this context would be the total magnitude divided by the relative factor that depends on the flare class, i.e. for M-class flares you'd divide by 10^(-5) (which I believe would be notated 1e-5 rather than 10e-5), and so on.

As for the scale in this particular context, I agree that it doesn't sound quite appropriate to say that each class is divided into a logarithmic scale, since the scale is indeed linear within each class; a logarithmic scale within each class would imply that e.g. a C2 would be ten times (or whatever other base of logarithm) as strong as a C1, and so on. And since specifying that it's a linear scale might confuse people due to the logarithmic scale of the classes themselves and how they're drawn, I agree that simply writing "scale" might be the best option to avoid confusion.

When it comes to AI, the language models that are currently often considered such are notorious for being terrible at mathematics and physics due to not actually performing anything analogous to actual reasoning from first principles, they are pretty much all just extremely good at imitating the language structures they've integrated into their models. This has especially been criticized when it comes to their imitations of scientific papers, which can often look extremely convincing at a glance due to being coherently structured linguistically, but with the results being complete fabrications that have no basis in any real scientific investigations at all. I've tried asking a few such models some basic questions about mathematics and physics myself, and they really tend to struggle unless you hold their hand and lead them to the right answer; at least that's my experience. That being said there are definitely developments in approaches that implement reasoning (like this), when mature I bet such models would much more readily be able to discern and explain how the flare classifications in question work, but I guess we'll see when we get there. In any case I'll leave comments about AI at that so as to not sidetrack the thread if it should continue in that direction.

[auclectic]

I have been wondering the algorithm for the flares we see on limbs. Where the measurement is based on partial X-ray brightness, because the rest is obscured. The flare is measured by that specifically but I've also seen estimates on where it would land if it were earth facing/classified-- is this based on the area of the sunspot that's now obscured assuming it didn't change in shape or complexity? 

[Philalethes]

5 hours ago, auclectic said:

I have been wondering the algorithm for the flares we see on limbs. Where the measurement is based on partial X-ray brightness, because the rest is obscured. The flare is measured by that specifically but I've also seen estimates on where it would land if it were earth facing/classified-- is this based on the area of the sunspot that's now obscured assuming it didn't change in shape or complexity? 

As far as I'm aware those estimates are either based on educated guesswork if we don't have any satellite coverage there, or on such coverage (like from SolO or STEREO-A if they're in the right position). For example there seemed to be little agreement about the recent explosive X3.3 flare from 3575 as it had just turned past the limb, with some claiming it could have been as strong as X10, while others claimed that it was probably not much stronger than what was observed. The reason you can't really use the area in that way is that the source of the flaring often is above the surface (photosphere), especially for the strongest flares; in the case of the aforementioned flare I believe it happened when no parts of the AR itself were still visible at all (I didn't check though, maybe I'm not remembering correctly).

I suppose that's really not got anything to do with the topic of this thread though, but hopefully that helps.

[Vancanneyt Sander]

Yeah it could be rephrased 👍🏻
While I'm at it, we will also update the flare strength of the mentioned X28 to remove the correction factor and remove a reference to GOES-15 which isn't in use anymore.
Won't be visible for a while as the translations need to be updated as well and the volunteers who do this will need time as well.

[Drax Spacex]

FWIW, the NOAA PRF August 2012 (no copyright or other restrictions) provides a good history and description of the letter classifications of solar flares:

https://www.swpc.noaa.gov/sites/default/files/images/u2/Usr_guide.pdf

excerpt: "The letter designates the order of magnitude of the peak value and the number following the letter is the multiplicative factor. A C3.2 event for example, indicates an x-ray burst with 3.2x10-6Wm-2 peak flux."

[Vancanneyt Sander]

33 minuten geleden, Drax Spacex zei:

FWIW, the NOAA PRF August 2012 (no copyright or other restrictions) provides a good history and description of the letter classifications of solar flares:

https://www.swpc.noaa.gov/sites/default/files/images/u2/Usr_guide.pdf

excerpt: "The letter designates the order of magnitude of the peak value and the number following the letter is the multiplicative factor. A C3.2 event for example, indicates an x-ray burst with 3.2x10-6Wm-2 peak flux."

We won’t change it again, for the sake of our translators not to redo it again. Changes will be uploaded once most translations are in.

[Philalethes]

2 hours ago, Drax Spacex said:

FWIW, the NOAA PRF August 2012 (no copyright or other restrictions) provides a good history and description of the letter classifications of solar flares:

https://www.swpc.noaa.gov/sites/default/files/images/u2/Usr_guide.pdf

excerpt: "The letter designates the order of magnitude of the peak value and the number following the letter is the multiplicative factor. A C3.2 event for example, indicates an x-ray burst with 3.2x10-6Wm-2 peak flux."

That certainly also sounds like a very reasonable term for it; it also makes the connection to scientific notation even more clear, which means one could also use terms directly associated with that:

Quote

In scientific notation, nonzero numbers are written in the form

m * 10^n

or m times ten raised to the power of n, where n is an integer, and the coefficient m is a nonzero real number (usually between 1 and 10 in absolute value, and nearly always written as a terminating decimal). The integer n is called the exponent and the real number m is called the significand or mantissa.

The article on significand, which seems to be the most unambiguous term for that part of scientific notation, also provides more terms that are used for it:

Quote

The significand (also coefficient, sometimes also argument, or more ambiguously mantissa, fraction, or characteristic) refers to the first (left) part of a number in scientific notation or related concepts in floating-point representation, consisting of its significant digits.

[Drax Spacex]

You're right.  Scientific notation would be most appropriate.  I was scrambling engineering notation, scientific notation, and FORTRAN!

[Philalethes]

2 minutes ago, Drax Spacex said:

You're right.  Scientific notation would be most appropriate.  I was scrambling engineering notation, scientific notation, and FORTRAN!

I was about to add this to the above post, but I might as well reply here instead:

After having thought about it a bit I think the best term for the number of all the above would be "coefficient", as it's both precise based on its mathematical meaning and in more widespread use than the others, e.g. "flare coefficient" would be very descriptive; alternatives like "flare multiplier" or "flare factor" would also work just fine, but personally I'd go with coefficient.

And for clarity I don't think any of that needs to be mentioned to the article here on SWL, at least the only thing I would have clarified there would have been that previously mentioned part about subdivisions not being logarithmic, but I'm sure a good way to formulate it will be found anyway.

A separate point I realized when reading about why the term "mantissa" is more ambiguous due to its different use in logarithms is also that the subdivisions wouldn't quite work like what I described above if they were logarithmic; in that case each step n would rather indicate a multiplication of 10^(0.1n), so that e.g. a C1 would mean a strength equal to a flare coefficient of 10^(0.1) = ~1.26 (i.e. what we'd currently call a C1.26), and a C2 would have a coefficient of 10^(0.2) = ~1.58 (C1.58 in our scale), and curiously but entirely coincidentally, a C3 would mean a coefficient of 10^0.3 = ~2, so funnily enough a C3 in that scale would be what we'd call a C2, at least with rounding to two decimal points like in the other cases.

It would also mean that a C10 wouldn't be equivalent to an M1 anymore, and you'd have to introduce a 0 to the scale to make it work, due to how C10 would have a coefficient of 10^1 = 10, which would thus be equivalent to an M0 with coefficient 10^0 = 1 (with the exactly single order of magnitude having been moved from the coefficient to the exponent as denoted by the class).

This difference can of course be seen on the GOES X-ray flux graph in how the different levels are plotted logarithmically, the same way logarithmic scales in general are plotted. Given how a logarithmic C3 corresponds to what we call ~C2, we see that C2 is plotted roughly where the 0.3 mark of the class would be if divided evenly into 10, which in more exact terms is exactly at log_10(2) = ~0.301; likewise we can easily calculate exactly where the other marks are drawn by simply taking log_10(c) where c is the flare coefficient, e.g. log_10(6) = ~0.778 to see where in the C-class a C6 would be drawn in, which we can see is correct. This also makes it obvious why there's no 0 on that scale and why e.g. C10 = M1, since taking any logarithm of 0 is undefined (no base can ever be raised to any number to yield 0), and that what we call C1 would correspond to C0 logarithmically, since taking any logarithm of 1 is 0.

Not that this is any amazing discovery, it's of course what is being used to draw the marks in the first place, but it certainly helps to conceptualize how it works, and maybe someone else might find it interesting to think about.

As a concluding remark, maybe we'd actually be better off using the logarithmic subdivisions for how we designate flares (e.g. a C2 would correspond to a flare strength of 1.58 * 10^(-6) instead); that way you'd get equally spaced ticks of geometrically increasing (with a factor of 10^(0.1) = ~1.259 each step) flare strengths even within each class. In terms of what we actually are interested in I think this could be superior in some ways, since we'd no longer see the big curves right as the flux gets into a new class that might make e.g. M1- and M2-flares look overly impressive. It would be like how we arrange frequencies on a keyboard with equal temperament, equally spaced with a geometrically increasing frequency for each semitone, although with a factor of 2^(1/12) rather than 10^(1/10) as in this case. Just a thought, since the actual flux value itself isn't that interesting in this context, and since it'd be easy to convert between the two anyway.

[Drax Spacex]

Drifting a bit here, should admins want to splice or relocate this topic

Significand would be a good answer in a numeric representation specification, but may be a bit esoteric.  Coefficient works too but has varied definitions in different contexts (coefficient of static friction, the number before a variable).  I still veer towards some more generic term like scale, factor, multiplier, etc.  The number is unitless if we presume the W/m^2 is attached to the class letter.

A, B, C, M, and X are powers of 10 and are amenable to reduction / compaction by applying the logarithm (base 10) function.  The class letter effectively refers to constants in a look-up or hash table which is the lowest flux for a given class (flux units W/m^2):  A=10^-8, B=10^-7, C=10^-6, M=10^-5, X=10^-4

For a hypothetical completely logarithmic formula for solar flare magnitude as a function of flux, you could do something like this:

flare_magnitude = max(0.0, log(flux)+9)

where flux=flux_from_class_lookup[$letter]  * flare_coefficient_or_scale_in_class

This formula would result in these value ranges of flare_magnitude for each flare class:
A=0.0-1.999
B=2.0-2.999
C=3.0-3.999
M=4.0-4.999
X=5.0-inf

This may indeed be the formula (or similar) used when calculating the pixel Y position on a digital logarithmic Y-axis graph.

But as you discussed, you lose the simplicity of relative scale within an single class.  e.g. we know a C4 is four times as strong as a C1.  Using the flare_magnitude formula above, C4=3.602, and C1=3.0.  The relative strength is not as clear.

And this may be in part why the x-ray solar flare classification was designed as it was - to readily discern relative flare strength both across classes (factors of 10) and within the same class (simple linear ratios) and makes sense when comparing flare values (C1 vs C4, M2 vs X2).

I agree the way these are graphed, however, doesn't readily convey this relationship - because of convention, and also because there's only so much space on a page or screen to depict a full scale.  But within the same space, the subdivisions within each class could be changed to linear-spaced instead of logarithmic.  That would convey well the relative flare strength within a class.  Ah, convention!

[Philalethes]

1 hour ago, Drax Spacex said:

Drifting a bit here, should admins want to splice or relocate this topic

Significand would be a good answer in a numeric representation specification, but may be a bit esoteric.  Coefficient works too but has varied definitions in different contexts (coefficient of static friction, the number before a variable).  I still veer towards some more generic term like scale, factor, multiplier, etc.  The number is unitless if we presume the W/m^2 is attached to the class letter.

A, B, C, M, and X are powers of 10 and are amenable to reduction / compaction by applying the logarithm (base 10) function.  The class letter effectively refers to constants in a look-up or hash table which is the lowest flux for a given class (flux units W/m^2):  A=10^-8, B=10^-7, C=10^-6, M=10^-5, X=10^-4

For a hypothetical completely logarithmic formula for solar flare magnitude as a function of flux, you could do something like this:

flare_magnitude = max(0.0, log(flux)+9)

where flux=flux_from_class_lookup[$letter]  * flare_coefficient_or_scale_in_class

This formula would result in these value ranges of flare_magnitude for each flare class:
A=0.0-1.999
B=2.0-2.999
C=3.0-3.999
M=4.0-4.999
X=5.0-inf

This may indeed be the formula (or similar) used when calculating the pixel Y position on a digital logarithmic Y-axis graph.

But as you discussed, you lose the simplicity of relative scale within an single class.  e.g. we know a C4 is four times as strong as a C1.  Using the flare_magnitude formula above, C4=3.602, and C1=3.0.  The relative strength is not as clear.

And this may be in part why the x-ray solar flare classification was designed as it was - to readily discern relative flare strength both across classes (factors of 10) and within the same class (simple linear ratios) and makes sense when comparing flare values (C1 vs C4, M2 vs X2).

I agree the way these are graphed, however, doesn't readily convey this relationship - because of convention, and also because there's only so much space on a page or screen to depict a full scale.  But within the same space, the subdivisions within each class could be changed to linear-spaced instead of logarithmic.  That would convey well the relative flare strength within a class.  Ah, convention!

I'd say we're still on-topic for the most part, shouldn't be a problem in my view at least.

As for "coefficient" as a term, it's true that it serves a slightly different role in the context of friction, but even then it's still a factor/multiplier between the two values in question. The terms "factor" and "multiplier" are of course also essentially synonyms to it in either context, and would work just fine too. The term "scale" would be more of a separate category in my view, since it would apply to a way of ordering these numbers. In any case you are of course entitled to your own opinion, but personally I'd still definitely stick with coefficient after having given it some thought, since it's exactly the type of multiplicative term that's being used in many similar contexts. If I were to argue against it it would be on the grounds that it might also sound a bit too esoteric (let alone the downright arcane term "significand"), and that terms like "factor" and "multiplier" are even simpler, so I could definitely see why you'd want to use that in less technical contexts.

But yep, the purely logarithmic way of doing it that you just described is indeed what I was talking about above, where you could simply use the fractional part of the logarithm (the mantissa) directly too, you can even simply do log_10(flux) and use the integer part (the "characteristic", another reason why that was listed as ambiguous for the other term) for the class directly by translating from -6 to C and so on (or add 9 like you suggest for an easier overview) and use the mantissa for the subdivisions instead of a coefficient/factor/multiplier as you would with a linear subdivision, again doing some simple conversion for classes that would be above X. And yeah, that's exactly how the positions of the y-values are graphed indeed.

I also certainly agree you would no longer have that simple relationship where C4 is exactly four times stronger than a C1 if you were to do it purely logarithmically, which would be the downside. My primary argument against that would be that measuring the relative strengths that way might not actually be as informative as it seems at first sight, since when classifying such phenomena you typically want each class and subclass to represent a category of its own. Maybe it's not so clear what I mean by that, but it's essentially something along the lines of how the increase from a C1 to a C2 is very large in relative terms, a doubling, whereas the increase from a C6 to a C7 is much smaller; this actually works in the opposite way of how the classes themselves are arranged (since they are logarithmic), and also how other classification hierarchies in space weather works (e.g. how the difference between a G4 and a G5 is significantly larger than the difference between a G3 and a G4). You can naturally argue that this is perfectly fine for flares, and that the division into classes is more than sufficient for this purpose anyway, which is perfectly reasonable, and indeed probably why it's being done that way now, as you say.

It also leads to something else I was hinting at above, namely how the difference between a C9 and an M1 is very small in relative terms, but then immediately switches to the huge increase between M1 and M2, which is reflected in how the logarithmic ticks on the plot get closer together near the top of each class, and then suddenly become spaced very widely apart. There is of course nothing inherently wrong with that, and it's very common to represent linear relationships within logarithmic plots like that, but I was just adding that thought as a concluding remark as a suggestion that there could perhaps be something to be said for it. If one were in fact to do such a logarithmic scale all the way down to within each class, then you'd get an equal scaling factor between every single step, i.e. a C9 would be exactly as many times larger as a C8 that a C10/M0 would be larger than a C9, and that an M1 would be larger than an M0, and so on.

I'm of course not suggesting that we or SWL or any other site should start to use something like that instead, just mentioning it as a possibility that could have something going for it.

As for the suggestion in your last paragraph, that could certainly also have been a possibility; the only issue I see with that is that it might be confusing to have a graph that's a hybrid of logarithmic and linear in that way, it might throw off some intuitions about how the scaling works at least. The way it's plotted now actually represents the purely logarithmic scaling we've talked about, just with the subdivisions skewed accordingly, and an increase of a specific height along any part of the y-axis would correspond to the exact same factor as an increase of the same height anywhere else on the axis, which I personally think is a good thing.

 

Edited February 19 by Philalethes
small addition