The Borg & Solar Flares

[l33telboi]

A long time ago i heard an argument that said that Borg are weak because their ships can't even fend off Solar Flares that have been calced at 1MT. This supposedly happened in "Descent Part 2". But this was some time ago already and back then i had neither seen the relevant episode nor did i know that stellar phenomenon that has anything to do with the sun is highly improbable to involve such measly figures as 1MT.

So, does anyone know anything about said calc? Or do you have any imput on the matter yourselves? I'm asking because i've seen the screencaps on trekcore and i'm currently in the process of getting the relevant episode. And there have been a lot of calcs involving solar activity on SB.com as of late. It would be relatively easy to plug the numbers into the formula to see what the end result is. And i highly doubt the figure will be anything near 1MT.

And yes, i do now realize that the ship involved wasn't even Borg. But in any case, this would be a great way to establish a minimum of damage the Enterprises shields can repell.

[Mike DiCenso]

A few things that might be needed here:

The episode does not state what altitude the rogue Borg ship is holding at. The characters state that they only need to get into the star's corona to escape the Borg ship, but the visual FX clearly shows that both the E-D was well as the Borg ship well inside it. In fact, the Borg ship is close enough to the star's surface for it to appear nearly flat, perhaps very near the photosphere and chromosphere of the star. The E-D definately appears to enter below the photosphere.

If a fixed altitude could be worked out, a velocity for the material being expelled by the star can be worked out more accurately.
-Mike

[l33telboi]

Merely having the ED flying around inside the Corona would most likely give us numbers in the single digit megaton per second range. As for the solar flare, i suppose one could use a standard solar flare as a gauge, Wikipedia gives the number of something close to 1 000 000 km/h for speed, the amount of material in that flare is an unkown though. But if we at least had some indication of how much material there is in the standard flare, it would be realtively easy to figure out the Kinetic Impact on the vessel.

In any case, i just wanted to hear if anything like this had already been done. It would be kinda pointless to calc this if someone had already done it.

[Mr. Oragahn]

Wouldn't 1 MT/s be a bit too high for a decent distance from the core, within the corona, but more accurate for a distance near the photosphere.
I'm assuming a star similar to our sun in the main sequence. I haven't seen any pic.

[l33telboi]

Wouldn't 1 MT/s be a bit too high for a decent distance from the core, within the corona, but more accurate for a distance near the photosphere.
I'm assuming a star similar to our sun in the main sequence. I haven't seen any pic.

Well, that was merely a guess on my part. I haven't even seen the episode yet, just a couple of screenshots on trekcore. But MT/sec doesn't seem to high, considering a similar calc involving a blue giant gave results of about double digit MT/sec. A great portion will of course be dependant on how large the ship in question is.

But the screencaps i've seen are a bit odd though. The corona is described as a layer of plasma extremely thin. But in the pics it seems quite thick. I wonder if it really is the corona we're seing or if it's rather the chromosphere.

[Jedi Master Spock]

There exists no reliable calculation of the artificial solar "burst" used to attack the Borg ship in that episode... although the E-D clearly absorbed more than a megaton of energy itself. The calculation has been made incorrectly before, and it basically comes from what you would look up on Wikipedia with a few mistakes thrown in.

The erroneous 1 megaton figure originates with a SDN article:

;The largest solar prominences are known as "coronal mass ejections", or CME's, and in such a prominence, the mass and velocity of ejecta are typically around 1E12 kg and 400 km/s. Anomalously large CME's have involved masses and speeds of as much as 1E13 kg and 2000 km/s in the past. However, the prominence in "Descent Part 2" was nowhere near this size- it was barely wide enough to engulf the Borg vessel which was, in turn, no wider than 5km. However, a large CME is more than 250,000km wide. If we assume that the Borg cube was hit with a large CME in spite of the 40 billion to 1 size discrepancy, then we can use the ~1E25 joule energy content of the largest observed solar CME's to estimate that roughly 1 forty billionth of such a vast CME would actually strike the Borg ship. In other words, the Borg ship was hit with a burst of energy equal to, at most, 4000 TJ.

Basically speaking, this comes from trying to scale down a meteorological phenomenon the size of Jupiter down to the size of a Borg cube - and failing.

The actual numbers seen in that quote are incorrectly computed besides - it is highly inappropriate to round 2e25 down to "~1e25," or neglect thermal energy, or ignore the fact that smaller solar flares have a higher energy density. The only possible reason for picking the largest possible prominence is in order to use the small energy density therein. If you wanted to try to use this methodology (scaling down natural prominences) most appropriately, you'd start with the high-intensity bursts.

Solar flares - marginally nearer in scale to the event seen in "Descent" - have much higher intensities than the gross scale CMEs...

We should also mention that the thermal form of kinetic energy is more important here in the tens of millions of kelvin and 0.1c range. A 1 kilogram mass at 2 km/s (~0.007c) has a kinetic energy of 2 megajoules.

The energy of 1 kilogram of hydrogen/helium plasma at 10 million kelvin? I know of a couple different ways to calculate it... it's much larger though. I'll give a you guys several hints to play with:

• Avagadro's number gives you particles per mol.
• Thermal energy, per particle, per degree of freedom, is generalized as 1/2 kT, where k is Boltzmann's constant.
• A monoatomic particle has three axes it can move along.
• If you're having trouble crunching numbers, helium gas has a specific heat capacity of 5.2 joules per kelvin per gram, and helium's mass as an atom is 4u.
• At one point in its development, a nuclear weapon's blast consists of a relatively small fireball with temperatures of the order of millions of kelvins.

Now, granted, after you work through that physics, you'll find "Descent" does still give one of the lower durabilities for a Borg vessel, but a megaton is absolutely ludicrous.

[l33telboi]

Well, that was a wee bit complicated for a simple-minded grunt like me. Figuring out the Kinetic Energy is easy enough, but how do you apply the Thermal Energy to that?

[Jedi Master Spock]

The quick and easy way is the chemist's route.

A beginning chemistry student should say "Hey! This is - or acts like - an ideal gas!" by treating each H proton as individual atom and guessing that in the hot plasma, the hydrogen is completely atomized.

Monoatomic gases - i.e., gases that act like ideal gases - all have a specific heat capacity of ~20.8 joules per mol per kelvin. 1 mol of hydrogen atoms, or H-/H+ ions, would be one gram. 1 kilogram would be 20.8 kilojoules per kelvin; for a ten megakelvin temperature, typical of solar flares, that's 208 gigajoules of energy.

Go ahead and check that figure. 208 gigajoules.

Now... I must admit that in a hydrogen plasma, we actually have a messy mix of particles running around (H-,H+,H2+,H3+ ions, H atoms, and H2 molecules), some of which have additional vibrational modes, and helium does make up a significant portion of the mass involved (~25% in our own Sun, giving us a variety of particles of mass 4u), so that's actually a bit high (call it about a third too high, exactly how much depends on the composition of the Sun in "Descent" as well as the actual temperature and density of the plasma). For a pure helium plasma, it'd be a quarter of what I told you in the first paragraph, for example, although helium is unlikely to make up too much more than 25% of the star.

Realistically, we're looking at the general order of hundred-gigajoule-per-kilogram energy densities for flare-temperature plasma.

For those of you who slipped up in the prefixes between "mega" and "giga," that's roughly five orders of magnitude more. Granted, the rest of the analysis in the article I quoted is also off in a variety of interesting ways. The flares in question last for hours, usually (for example) and have higher flux densities than the CMEs... etc. If you really care about it, you can refine the estimate further (and yes, I can too) to answer the question of exactly how many gigatons of particle energy the Borg ate under the flare model. The short of it, though, is that it really matters how hot the plasma is, more than how fast the plasma burst itself is moving through the corona.

The flare model is a bit questionable, IMO. We're dealing with something that's really not on the scale, in size or behavior, of the flares we study. This is small, this is short, and we're not really sure on what its intensity or temperature really is.

[Mr. Oragahn]

Wouldn't 1 MT/s be a bit too high for a decent distance from the core, within the corona, but more accurate for a distance near the photosphere.
I'm assuming a star similar to our sun in the main sequence. I haven't seen any pic.

Well, that was merely a guess on my part. I haven't even seen the episode yet, just a couple of screenshots on trekcore. But MT/sec doesn't seem to high, considering a similar calc involving a blue giant gave results of about double digit MT/sec. A great portion will of course be dependant on how large the ship in question is.

But a blue giant's power surpasses an average G star's by much more than the difference in sizes.
So it quickly becomes less impressive when you "only" deal with stars such as our sun, at similar distances, like somewhere in the corona.

[l33telboi]

But a blue giant's power surpasses an average G star's by much more than the difference in sizes.
So it quickly becomes less impressive when you "only" deal with stars such as our sun, at similar distances, like somewhere in the corona.

Indeed, but like i said, it was merely a guess. But we can plug in some numbers to get a closer look at what the difference is.

Blue giant:

Lsun: (3.827x10^26) * 20,000 = 7.654x10^30W
Radius: (6.96x10^8) * 7 = 4.827 x 10^9m
Surface Area: 4*pi*r^2 = 2.928 x 10^20 m^2
Luminosity/Area: 2.614 x 10^10 W/m^2

Our sun:

Lsun: 3.827x10^26W
Radius 6.96x10^8m
SA: 4*pi*r^2 = 6.09e18 m^2
L/A: 62840722.5W/m^2

BG: 2.614 x 10^10 W/m^2
OS: 6.28 x 10^7 W/m^2

Our sun has three orders of magnitude lower energy per square meter when compared to a blue giant apparently. So my guess was off almost by two orders of a magnitude. Given that what i just did is right, which i'm in no way guaranteeing.

[Mr. Oragahn]

Yep. That's pretty much it. Somehow, I think I've seen similar calcs somewhere, but I can't remember where though.

[l33telboi]

Yep. That's pretty much it. Somehow, I think I've seen similar calcs somewhere, but I can't remember where though.

Like i said, there's been alot of calcs involving solar activity on SB.com, most likely you've seen them there. The calc for the Blue Giant was used to see how much the Ha'Tak could withstand in SG-1 "Enemies". This was the same formula, without factoring in the dimensions of the craft of course.

[Mike DiCenso]

Jedi Master Spock wrote:
The flare model is a bit questionable, IMO. We're dealing with something that's really not on the scale, in size or behavior, of the flares we study. This is small, this is short, and we're not really sure on what its intensity or temperature really is.

This is all very true. Not only is it possible the intensity and temperature is higher for this flare, as compared to a natural one, but the velocity of the material being ejected from the star is much higher as well. A natural CME is on the order of 277 km a second, while the "Decent" flare is at least an order of magnitude faster based on the time it takes for it to reach the Borg vessel from the surface of the star.

Of note: a similar thing occurs with the G-type star in "Relics" [TNG6], the first visuals of the flare eruptions as seen on the E-D viewscreens shows the material reaching 150,000 km in just under 3 seconds!
-Mike

[l33telboi]

Two questions now that i've seen the episodes in full:

1. Is this the same Borg vessel Data described as a Recon/Scout vessel in "I, Borg", or is it some form of completly alien vessel that was later assimilated and appropriated by the renegade Borg?

2. Was the Enterprise in the Corona or in the Chromosphere? Dialogue says they'll be entering the corona, but by that point, according to visuals, they've been inside the corona for a while already. Also, the Borg ship is quite clearly inside the corona, yet it was stated to be holding position on the outside. I've also seen that in another episode the Enterprise has been able to sit in the corona for quite some time. Is it all plausible that they were indeed sitting in the chromosphere while the Borg were in the Corona?

[Mike DiCenso]

l33telboi wrote:

Two questions now that i've seen the episodes in full:

1. Is this the same Borg vessel Data described as a Recon/Scout vessel in "I, Borg", or is it some form of completly alien vessel that was later assimilated and appropriated by the renegade Borg?

No. The scout cube is clearly smaller in dimensions, as well as had only 5 drones on board. The Decent ship is a big unknown. We next see it in VOY's "Scorpion, Part II" on a readout display, and Seven of Nine describes it as a "multi-kinetic neutronic mine". Go figure.

l33telboi wrote:
2. Was the Enterprise in the Corona or in the Chromosphere? Dialogue says they'll be entering the corona, but by that point, according to visuals, they've been inside the corona for a while already. Also, the Borg ship is quite clearly inside the corona, yet it was stated to be holding position on the outside. I've also seen that in another episode the Enterprise has been able to sit in the corona for quite some time. Is it all plausible that they were indeed sitting in the chromosphere while the Borg were in the Corona?

I made this point earlier in the thread. The visuals clearly in and in all ways contradict the character dialog. So take it as you will. If you take the character dialog over the visuals, then the star's flare stayed in an extremely concentrated form for up to a million km from the star's surface, and travelled at nearly the speed of c!
-Mike