Parker Footpoint Predictions - Meaning and Terminology

Sam Badman�

samuel.badman@cfa.harvard.edu

​

With thanks to Lindsay Glesener, Cindy Cattell, Reed Masek, Tamar Ervin, Robert Allen and the CfA SWEAP group for the discussions leading to these slides, and to Pete Riley and the Parker footpoint prediction team.

View these slides

Goal

• Disambiguate “instantaneous magnetic connection” and “source position on the Sun”
• What do we mean when we quote a source position as (time, lat, lon)?�
• Specify the source position most relevant to different types of disturbances/connections

Context

• Ahead of each Parker perihelion, we gather footpoint predictions (time*, carrington lon, carrington lat) from multiple models with multiple boundary conditions.�
• We form ensembles of footpoints within discrete time windows, fit a distribution, and define its centroid as our “consensus footpoint location”�
• We then package these consensus locations up into CSV files containing solar-disk source locations for the use of remote observers to make coordinated observations.

* What we mean by time is the subject of these slides.

Disk-referenced

Heliographic

For more details on the modeling of the connectivity and the consensus methodology see: Badman,Riley,Jones+2023 (JGR Space Physics - Accepted) Arxiv: 2303.04852

What we predict:

Ω_S △t

“Carrington coordinates of source whose plasma reaches Parker at time t”

“Helioprojective coordinates of that source on the solar disk at time t”

“Helioprojective coordinates of that source at time t-△t where △t is an estimate of the plasma parcel travel time”

Illustrative Movie :

Parker E10 in inertial coordinates

Black Arrow: Stream source to keep track of�

Multicolored blobs : Plasma parcels being emitted and traveling radially from the black arrow-marked source. The magnetic field connected back to the black arrow is frozen into these blobs, forming the Parker spiral.

​

Blue line : Parker’s trajectory�

Black square : Parker’s instantaneous position�

Black dashed curve : What I call “instantaneous magnetic field connection at time t_psp”�

Red circle : The magnetic footpoint of the instantaneous connection. I contend this is also the source of the plasma reaching Parker at time t_psp. It left the Sun from that source at time t_psp - r_psp*v_sw

​

Green Arrow : The direction of Earth / longitude of disk center.

Key moment 1 : Plasma Parcel from stream of interest reaches Parker

Parker receives a plasma parcel which originated at the black arrow (reddish blob)

​

At this moment, the “predicted footpoint” is the black arrow

​

This is the location of the source at the time the plasma parcel reaches Parker, t_psp = 2021/11/21 0800

​

It is not the location of the source at the time that that plasma parcel was released except if expressed in Carrington coordinates

Key moment 2 : Plasma Parcel from stream of interest released at 1 Rs

That same plasma parcel was released at 1Rs at t_release = t_psp - (r_psp/vsw). R_psp was ~13Rs and Vsw (for the visualization) was set to 200km/s, giving t_release ~ t_psp - 12hr = 2021/11/20 20:00

​

At this time, a line following the source longitude radially outwards intersects PSP’s orbit at the location where the measurement will take place in 12 hours.

​

This longitude is still the same Carrington longitude (e.g. it could be the same coronal hole rotating with the Sun), however it is at a different location in inertial space, and a different location on the solar disk relative to earth (green arrow points along the earth-sun line)

How we present this information in the predictions :

Solar disk-referenced coordinates at t_emit: Where on the disk is the source (i.e. coronal hole) at time it emits plasma that will later arrive at Parker. �

Most relevant for trying to observe disturbances which advect with the solar wind that will correspond to Parker in situ data later at t_psp

t_psp

Carrington Coordinates :

True at both t_psp and t_emit

t_emit

Solar disk-referenced coordinates at t_psp. Where on the disk is the source (i.e. coronal hole) at time its plasma arrives at Parker and therefore at the time Parker is instantaneously magnetically connected to it.

​

Most relevant if you expect your emission at a given source to travel much faster than the solar wind.

What about intermediate cases?

• So far, we have produced two source predictions 1) Assuming a disturbance propagates at Vsw, and 2) Assuming a disturbance propagates near-instantaneously. (For our purposes, t_transit << delta t (prediction) = 1 hour)�
• However what if the disturbance is between these limits?�
• For any relevance to the model, we need to at least restrict attention to disturbances which are guided along field lines, e.g. type III electron beams. In this case, the motion of the disturbance in the inertial frame is the sum of the ejections radial velocity, and the angular velocity of the field line it is on.�
• Its trajectory is still fixed in the Carrington reference frame, meaning the Carrington coordinates of PSP at t_psp are always associated with the Carrington coordinates of its instantaneous photospheric connection (within the assumption of a time-static model), no matter what time the disturbance is emitted from that source.�
• However, in order to produce a set of predictions of on-disk coordinates relevant for a given disturbance, we need to know the disturbance propagation speed. This parameter tells us the actual trajectory of that disturbance in inertial space, which is intermediate between the limits of a radial trajectory at Vsw (plasma parcels) and a pure-parker spiral trajectory for near instantaneous propagations guided down the field line.

Schematic of all three cases

• In all three cases, (1) the disturbance intersects Parker at t_psp, (2) the disturbance is emitted from the same physical source in Carrington coordinates�
• However, the disturbances leave the source at different times, and due to solar rotation, the source location is at a different location on the disk relative to where it is when the disturbance is received.�
• The disk location and emission time is a function of the source propagation speed. -> For the purpose of publishing predictions, I’m not sure how to account for this. Really, you’d want the prediction lookup table to take v_disturbance as a parameter and recompute.�
• The instantaneous connection to the source only occurs at t_psp. Earlier in time (red+orange squares), Parker is not in general intersecting the field lines from the source.

Parker@t_psp,r_psp

Source@ t_psp

Source@ t_int

Source@ t_emit

Parker@t_int

Parker@t_emit

Modeling Limitations

• Time independence
• Solar wind acceleration - ballistic approximation as a lower bound on transit time.
• No field line random walking / turbulent effects (propagation time & possible footpoint location effects)

Extra : Estimating Speed at Parker from 1AU

• For our predictions, to produce an estimate of the emission time and on-disk source location at emission time, we need to choose a solar wind speed.

​

• Prior to Parker encounters we don’t have the data to do this directly.

​

• Instead, we use the previous carrington rotation of Vsw measurements made at L1 (e.g. by ACE and Wind), ballistically map those measurements down to where they intersect Parker’s upcoming orbit, and use the mapped associated orbital positions as our first guess of Vsw to predict emission times.�
• Next step : Use numerical Parker solar wind solution to integrate V(r) and get a more realistic transit time estimate. E.g. Koukras+2022