Using plasma dynamics to determine the strength of a promin - PowerPoint Presentation

Slide1

Using plasma dynamics to determine the strength of a prominence's magnetic fieldsGCOE Symposium 2013 @ Kyoto UniversityAndrew HillierSlide2

What is a Quiescent Prominence?

~10 Mm

Image: Quiescent prominence observed on 2007/10/03 01:56 UT in the Ca II H line (3968.5 Å)

Temperature:

6000K~10,000K

(Tandberg-

Hanssen

1995)

Number Density:

10

10

~10

11

cm

-3

(

eg

Labrosse

2010 &

Hirayama 1986)

Magnetic field strength:

3~30 G

(Leroy 1989)

Ionisation

fraction:

~0.2 at centre

(

Gunar

et al 2008)Slide3

Prominences and Space WeatherProminence eruption on August 31, 2012 observed by the Solar Dynamics Observatory satellite (courtesy of NASA)Slide4

How Well Do We Understand Quiescent Prominences?

~10 Mm

Image: Quiescent prominence observed on 2007/10/03 01:56 UT in the Ca II H line (3968.5 Å)

Magnetic field strength:

3~30 G (Leroy 1989)

But only ~15 prominences have had their magnetic field measured (to my knowledge)

But we need to know the field strength to be able to model prominences, discuss there dynamics etcSlide5

The Plumes in Prominences

Fig: Prominence observed in Hα on 8

th Aug 2007 using Hinode SOTCourtesy of T. Berger

First observed by

Stellmacher

&

Wiehr

1973

Rediscovered by Berger et al 2008 & De

Toma

et al 2008Slide6

The Plumes Created by the Magnetic Rayleigh-Taylor Instability The plumes (fingers of low density material rising through the dense prominence material) were hypothesized to be created by the Rayleigh-Taylor instability by Berger et al 2008 & 2010

Key Point 1:

plumes have an elliptical headKey Point 2: Constant rise velocity (10 – 30 km/s)

Image: Quiescent prominence observed on 2007/10/03 03:30 UT in the Ca II H line (3968.5 Å)Slide7

The Plumes Created by the Magnetic Rayleigh-Taylor Instability Simulations by Hillier et al (2012) investigated the 3D mode of the magnetic Rayleigh-Taylor instability in a prominence model

Key Point 3:

Creates filamentary structure aligned with Magnetic fieldSlide8

Using The Key Points to Make a ModelKey Point 1: plumes have an elliptical head (change coordinates to make a circle)

Key Point 2: Constant rise velocity (10 – 30 km/s) (Change reference frame)

Key Point 3: Creates filamentary structure aligned with Magnetic field (Makes it like a tube

)Slide9

Flow around a circular cylinderThis has now reduced to a classic fluid dynamics problemUsing the assumptions of invisicid

, irrotational and incompressible it is possible to calculate the potential flow around a circular cylinder

Potential HD flow around a circular cylinder – Source WikipediaSlide10

Compression at Top of PlumesFor some plumes we see a thick, bright hat. As the emission of prominences is mainly scattering, this is showing

higher density regions

Image: Left - Quiescent prominence observed on 2007/10/03 02:56 UT in the Ca II H line (3968.5 Å). Right – Zoomed image of plume

Plume rises

Material is compressed

High total pressure drives material out the waySlide11

Mathematical model for the CompressionImage: Compressible MHD flow round a circular cylinder. Magnetic field into screen

We can use a classic solution of

flow around a circular cylinder

+ MHD (Horizontal field only)

+Compressibility correction

to get the density distribution (van Dyke 1975).Slide12

How can this be used?By modelling the intensity in terms of density, the compression at the top of the plume can be calculated.This will allow for the plasma beta

to be solved for.Slide13

Estimate of Prominence Plasma Beta – Calculating Plume Size and Velocity

The dimension of the plume head (needed for normalisation) are a~900km and b~1700km

The rise velocity is Slide14

Estimate of Prominence Plasma Beta – Fitting Intensity to calculate β

Assuming that the emission is only proportional to the density we can fit to solve for M

*, giving an estimate of the plasma beta of

for Slide15

ConclusionsWe now have a new way to estimate the plasma beta of quiescent prominences using the Rayleigh-Taylor plumesApplication to one prominence gives the plasma β as β

=0.47 – 1.13 for γ=1.4 – 1.7.There are many

potential improvements that can be made, that will improve the accuracy AND the

amount of information

we can extract from the prominence

For greater detail, please see:

Hillier, Hillier &

Tripathi

(2012) ApJ

, 761,

106Slide16
Slide17

Setting for SimulationsKippenhahn-Schlűter prominence model (Priest

1982)Buoyant tube put in centre of prominence to make it unstable and a velocity perturbation in the y direction to excite interchange of magnetic field

Ideal MHD used (grid 90*150*400)Length normalised to pressure scale height

Fig: Mass density (

colour

) and field lines (contour) of prominence model. A is x-z cut and B is y-z

cut (y boundary is symmetric)Slide18

Movie: Temporal evolution of instability in x=0 plane. Colour shows density, arrows show velocity

2D Density Slice of simulation

Swirling, vortex like structures formed once instability is initiated

Reach height of approx 6Mm

Upflows

: ~ 6 km/s (approximately constant)

Width of

upflows

inversely cascades from ~100 km to ~1Mm

Makes threads in the prominence materialSlide19

Evolution shown in 3DRise of cavity

releases the magnetic tension, flattening the field lines. Instability starts on small scaleMultiple plumes formed, plume magnetic field begins to move through the prominence

Magnetic field lines glide passed each other in an interchange process

Fig: Temporal evolution of instability in 3D, lines represent magnetic field with density

isosurfaceSlide20

Application to Simulation Results

To check the data, first we revise the axis to give a circular head. Note there is

no density increase at the top of the plumeSlide21

Application to Simulation Results – Velocity Around Plume HeadVelocities along curve shown in previous slide (both simulated – solid, and predicted -dashed)Slide22

Application to Simulation Results – Matching Density Distribution

Integrating the density along the x-axis shows the increase in column density at the head of the plume

The above figure shows the simulated density along the slit and predicted densitySlide23

Application to Simulation Results – Calculating χ2

By calculating the χ

2 for fits to the density profile for different values of plasma β, we can show that the smallest χ

2

corresponds to the simulation plasma

β

of ~0.55Slide24

Can we model the Bright Emission?For some plumes we see a thick, bright hat. As the emission of prominences is mainly scattering, this is showing higher density regions

Image: Left - Quiescent prominence observed on 2007/10/03 02:56 UT in the Ca II H line (3968.5 Å).

Right – Zoomed movie of plumeSlide25

What if the Magnetic Field is VerticalIf the field is vertical, then the compression doesn’t occur at the head of the plumeRarefaction occurs insteadIt is hard to understand the observations of the plume if the prominence field is vertical

Courtesy of Roger Scott, Montana State UniversitySlide26

Estimate of Prominence Plasma Beta – β as a Function of γSlide27

Necessary improvements for the ModelDeal with projection effects and magnetic field that is not along the line of sight (use velocity equations combined with observed Doppler shifts)Include

shear between the plume magnetic field and the prominence magnetic field to give direction of the magnetic field (use most unstable mode of magnetic Rayleigh-Taylor instability under shear and the with the observed plume width)

Improved model for emission (there must be a way to improve my simple model for the emission – Suggestions Please!)