Hypothetical "8-Minute Warning" From The Sun Question

[McKeown]

I am aware of past dustups over the assertion of an "absolute now." I have no desire to venture there. My question is much smaller in ambition.

 

Let's stipulate a margin of error for our measurements which allows the discussion to remain on the level of the non-specialist of higher mathematics. For duration measurements, let stipulate a few seconds either way may be ignored, for distance, several kilometers may be ignored.

 

Imagine a human observer on Earth, as we know it on Sunday, 9/2/2012. At a given time stamp, let's call it minute Zero, the first signal of a coronal mass ejection is observed from our Sun at a fixed point on Earth. I believe that most experts would agree that from the observer's point of reference, the CME actually began to erupt eight of her minutes ago.

 

Based on her initial measurements, she predicts (w/r/t her frame of reference), that the size and velocity of the CME indicate an impact of subluminal-velocity energetic protons with some highly sensitive satellite at a range of her minutes whose bounds are her timestamp minute 1500 at the earliest to her timestamp 1650 at the latest.

 

Each passing minute, her measurements continue to track the CME. By some arbitrary minute, let's say minute 48, her measurements indicate a revised impact time range at the satellite of minute 1400 - 1480.

 

As the CME wave of energetic particles continues to evolve, her measurements continue to produce a narrowing range of predictive impact times. Eventually, the impact will occur and the validity of the predictive history can be evaluated.

 

Let's say her predictive envelope of impact times successfully narrowed down to the actual impact time within some final range of error, say 20 minutes.

 

Here is the rhetorically iffy part that risks making me sound like the ignorant noob which I most likely am:

 

Would the observer be well- or ill-served, in terms of forecast accuracy, if she had subtracted some subluminal factor of 8 minutes from her initial forecast impact time range, the factor based on the observed initial velocity of the wave front of the protons in question? This is not an "absolute now" question. It is a "my now" question. For an event of this local duration and distance scale, whose only concern is to protect the satellite while preserving maximum in-service time, is it not reasonable to "assume" that the initially observed particles have, in fact, been traveling for some less-than 8 minutes number of minutes "already" when the first measurement was taken at minute Zero?

 

Many thanks for any thoughts, and many more for any less-than-greek-letter technical advice on considering the problem.

[Buffy]

Would the observer be well- or ill-served, in terms of forecast accuracy, if she had subtracted some subluminal factor of 8 minutes from her initial forecast impact time range, the factor based on the observed initial velocity of the wave front of the protons in question?

 

In theory, CME's propagation wave's acceleration should drop to zero very quickly after the ejection occurs since all of the force is imparted at that initial ejection and space provides little in the way of opportunities for deceleration. Since speed is linear, no matter where you sample the speed to get an ETA, you're going to get the same answer, and not subtracting the 8 minutes merely means your ETA will be off by 8 minutes....

 

I have noticed that the people who are late are often so much jollier than the people who have to wait for them, :phones:

Buffy

[CraigD]

Welcom to hypography, McKeown! :) Good, interesting first post. :thumbs_up

 

I am aware of past dustups over the assertion of an "absolute now." I have no desire to venture there. My question is much smaller in ambition.

 

Let's stipulate a margin of error for our measurements which allows the discussion to remain on the level of the non-specialist of higher mathematics. For duration measurements, let stipulate a few seconds either way may be ignored, for distance, several kilometers may be ignored.

Agreed.

 

I think you’re referring to the lack of absolute time and simultaneity implied by special relativity.

 

In the context of the subject of predicting the transit time of coronal mass ejections from the Sun to the Earth (astrophysicists usually refer to CMEs as Interplanetary, ie: ICMEs), because the relative velocities of the various observers involved, on Earth and various spacecraft, have magnitudes that are a small fraction of the speed of light, relativistic effects would change calculations by less than seconds, so can be ignored – not because they’re esoteric of “philosophical”, but because they’re insignificant.

 

Imagine a human observer on Earth, as we know it on Sunday, 9/2/2012. At a given time stamp, let's call it minute Zero, the first signal of a coronal mass ejection is observed from our Sun at a fixed point on Earth. I believe that most experts would agree that from the observer's point of reference, the CME actually began to erupt eight of her minutes ago.

Give the accuracy of ICME transit time estimates (more on that below), 8 minutes (480 s) is a reasonable figure to use for Sun-Earth light travel time, though the actual figure is between 488 and 507 s, depending of the point of origin of the feature on the Sun, and the Earth’s current distance from the Sun.

 

Based on her initial measurements, she predicts (w/r/t her frame of reference), that the size and velocity of the CME indicate an impact of subluminal-velocity energetic protons with some highly sensitive satellite ...

Before answering this question, I think we need to explore and understand some basics of CME observation and Sun-Earth (AKA “1 AU”) transit time ([imath]\tau[/imath]) estimation.

 

All the [imath]\tau[/imath] estimates I know of are made via a two-step process:

• Measuring the speed of the CME’s various regions, most commonly its “hot bright edge” from a series of timestamped coronograph images from instruments such SOHO’s LASCO. LASCO can image CMEs up to a distance of 32 solar radii (about 7 x 10⁸ m, or 75 light-seconds) from the Sun
  
• Apply calculations to account for the “drag” deceleration of the ICME as it travels the remaining distance (about 85%) to the Earth, at about 1 UA.
  

The first step of this process is pretty precise. Trouble comes from 2 main sources:

• A near-Earth coronagraph image (SOHO is at the Earth-Sun L1 point, about 0.99 AU, so is near-Earth) from a single observation point appear as on a plane perpendicular to a line from the Earth to the Sun, but the actual ICME edge is an expanding irregular spherical structure. What would be ideal is something like SOHO keeping station directly above a pole of the Sun, or several in a polar Solar orbit (Like Ulysses, but closer and more circular) but no such spacecraft exists at present.
  
• The detailed dynamics of the drag deceleration of the ICME is not well understood. Present best models are simplified and empirical.
  

 

Here’re my sources: Predictions of the arrival time of Coronal Mass Ejections at 1AU: an analysis of the causes of errors (2004) M. Owens and P. Cargill; An Analytical Model to Predict the Arrival Time of Interplanetary CMEs (2010) W.B. Song

 

Given all this, systematic error in 1 AU [imath]\tau[/imath] estimates are, according to Owens and Cargill’s 2004 paper, around 15%. The shortest [imath]\tau[/imath] is around 24 hours, so this error is on the order of 3 hours.

 

Would the observer be well- or ill-served, in terms of forecast accuracy, if she had subtracted some subluminal factor of 8 minutes from her initial forecast impact time range, the factor based on the observed initial velocity of the wave front of the protons in question?

Because, as a rule, any valid added factor improves the accuracy of an estimate, accounting for the roughly 8 light travel time can’t but improve a 1 AU [imath]\tau[/imath] estimate, but given a systematic error on the order of 200 minutes, the improvement isn’t be dramatic. Though I’ve not read details of a 1 AU[imath]\tau[/imath] calculation, I assume that, the folk that make them being pretty smart folk, they include such a correction.

[McKeown]

Thank you CraigD and Buffy.

 

I see from the first cite that within the three equations examined, the most likely input for a correction for the "already traveled distance" could be thought of either as the Heliocentric estimated altitude from the solar point of origin at the time of the first observation, or as the Terra-centric distance from a given impact point.

 

So, for a simplified example, if the initial observation were of a velocity of 1000km/s at an altitude of 0.20 solar radii, the initial estimate of position would be (approximately) 480 seconds Xs 1000km, or 480,000km closer (or "higher") than the observation, before correcting for aerodynamic acc/deceleration, sheath depth, magnetic field strength, etc.

 

I see the forecasting models are quite a bit noisier than I thought, and that there are bigger occlusions in the understanding of the dynamics than the light transit delay.

 

Thanks again for the thinking. I'll need to absorb all this for a while.