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Magnetic reconnection in solar coronal loops
Adv.SpclccRes.Vol. 19,No. 12,pp. 1875-1878.1997 0 1997 COSPARPublishedby ElsevierScience Ltd.All rightsn~erved Printedin GreatBritain 0273-l177/97$17.00+ 0.00
PII:s02734177@7)ooo914
MAGNETIC RECONNECTION IN SOLAR CORONAL LOOPS G. Einaudi*, R. Lionello** and M. Velli** *Dipartimento di Fisica, Universitb di Piss, 56100 Piss Italy
** Dipartimento di Astronomiae Scienzedell0 Spazio, Universitddi Firenze, 50125 Firenze, Italy
ABSTRACT Simulations of the evolution of kink modes in line-tied coronal loops are presented which demonstrate the occurrence of magnetic reconnection in the non-linear stage of the instability. In loops which do not carry a net axial current (and are confined by a potential purely axial field) the reconnection is limited
to the initial current-carrying
channel and no overall loss of confinement
loops which carry a net current on the other hand, reconnection
progressively
is observed.
In
involves field lines at
greater and greater distances from the axis and even regions where the field was initially potential, 0 1997 COSPAR. Published by Elsevier Science Ltd. leading to a total disruption of the magnetic field topology.
WFRODUCTION High-resolution
observations
of the solar corona clearly show that the main building block of coronal
structure is the magnetised coronal loop. Such loops are often twisted and can store magnetic energy in a stable manner for very long times before undergoing periods of violent activity. The stability of current-carrying coronal loops has been shown to arise both from the effects of inertial line-tying in the dense photosphere
(Raadu
presence of ambient potential (Einaudi
1972, Hood & Priest 1979, Einaudi & Van Hoven 1981) and the
magnetic fields, though the latter have a much less important
& Van Hoven 1983) The Fourier analysis technique
developed
efl%ct
by Einaudi & Van Hoven
(1981) to compute the stability threshold for line-tied coronal loops was extended by Velli et al. (1990) to obtain the growth-rates of ideal and resistive instabilities and describe the linear properties of ideal kinks. One of the main questions that remained to be addressed concerned the subsequent non-linear evolution
of these modes and in particular whether or not magnetic
reconnection
could arise as a
consequence of the evolution of the ideal instability. Simulations of ideal modes in the nonlinear regime by Baty & Heyvaerts (1996) h ave shown that current concentrations on scales approaching the resolution seem to occur at finite times, indicating that simulations including resistivity are necessary to understand the later stages of evolution. SIMULATIONS Here we follow the complete history of the kink instability for two different field models (hereafter a and b): in model (a) the field has a finite current flowing in the cent,ral region of the loop (model (a) in Velb et al. 1990), while in the oth;cr (Lionello et al. 1996a) upflowing and downflowing currents
1876
Figure : 1: Field instan .ts (linear
G. Einaudi er ai.
line plots
for model
phase, early resistive
(a)
(left
column)
phase, saturation).
and model
(b)
(right
column)
at dif& xwnt
Rsconmction in Coronal Loops
fall
yield a null total current in the loop. In both cases the currents are confined within the same radius (T = 5). The linear stability properties of the two models are different, as discussed in Velli et al. 1996: in particular the critical length for stability is bigger for model (b); what is important here is that the length of the loop is chosen so that the loop is kink unstable and we therefore take the length of model (b) to be twice that of model (a). W e use a three-dimensional MI-ID code, which is an updated version of the program used in M&it et al. 1990 (LionelIo et al., 199613). The system evolution proceeds in the framework of ideal MHD until current sheets at the resolution scale are formed, after which resistivity is turned on and the subsequent reconnection of field lines is examined. The way in which reconnection proceeds strongly depends on the net axial current flowing in the central region of the loop.
4
., .,: u _,,, _,
,?ny..... \” ,,GY’_,” -.~,.;+$~ ‘&J.Y,.,?::.., _ . _.__._;-:‘.’ c,., .*>’ .,__._... ..‘.‘_ .’ ----..Q-K ....._..,,, ..,,_,,_,,
__~,
2
0 -y)
-20
,yic.. I:\\
-10
:
10
20
Jo
Figure 2: Radial distance of field lines for model (a) (top panels) and model (b) (bottom panels) as a function of the axial coordinate T = T(Z) in the early resistive phase (left), and at saturation (right). In field configuration (a) the ideal instability creates an extended global kink mode which involves field lines at all distances from the loop axis. The kink grows in amplitude and the shape of the currents involved is typical of an m=l structure which wraps around the loop in a helicoidal fashion. As the amplitude grows, peaks in the current form where the kink folds on itself, i.e. not at the centre of the loop but about midway from the line-tied ends to loop centre. This is due to the linetying effect in the non-linear regime, which contrasts the linear stabilising effect: a kinked current which would otherwise distribute itself along the loop is here forced to collapse where the geometry permits it, leading to reconnection of magnetic field lines in these areas. This is illustrated in Figure 1, where we have drawn the magnetic lines originating at different radii at three different times (left panel). The top image refers to the end of the linear kink phase, the middle right after resistivity has
1878
G. Einadi ef al.
been turned on, and the lower image is at saturation, harmonics stop growing.
i.e. when the subsequent
(m > 1) azimuthal
The non-linear evolution of field configuration (b) on the other hand is dominated by a second stronger current sheet which develops in the loop apex at the interface between the current-carrying channel and the potential
outer axial magnetic
field.
outer lines across this sheet leeds to an unwrapping
stages of evolution
in the right-hand
(i.e. ideal phase, onset of
saturation).
A better visualisation function
between inner field lines and
of the loop as demonstrated
panel of Figure 1. The images refer to corresponding reconnection,
Reconnection.
of reconnection
of the axial coordinate
the run, corresponding
T = r(r).
is given by plots of the radial distance of field lines as a These are shown in Figure 2 at two merent
instants of
to the early stage of the resistive phase, and when the instability
Top panels refer to model (a) and bottom
saturates.
panels to model (b).
Note that field lines whose ends are rooted at the same radius may or may not reconnect,
depend-
ing on their angular position, i.e., depending on whether their trajectory brings them in the vicinity of the current sheet. Reconnection starts at different radii and at different heights for the two models because the dominant current sheets are located in different positions and the subsequent evolution is completely dominated by reconnection itself. In fact, the linear ideal mode gives a good indication of these differences ( Velli et al. 1996). CONCLUSIONS Magnetic reconnection in line-tied coronal loops occurs during the non-linear evolution of a kink instability as a result of the creation of intense current sheets. The change of magnetic field topology makes the non-potential part of magnetic energy stored in the equilibrium configuration available on what appear to be ideal timescales (our simulations are performed using moderate resolution (64x32~64)). T~I‘s d e p en d s on the delicate point of whether current sheets really form on the ideal timescale since the subsequent dynamics is dominated by such sheets. Interestingly enough, in loops which do not carry a net axial current the field tends to become a purely axial potential field and the loop maintains its large-scale shape during the release of magnetic energy. In this phase we observe a ten-fold increase in temperature,
and even greater around current sheets, as will be shown in detail
elsewhere. This result may have important
applications
in explaining
compact
loop flares.
REFERENCES Baty H., Heyvaerts J.: 1996, Astron. Astrophys., Einaudi G., Van Hoven G.: 1981, Phys. Fluids, Einaudi G., Van Hoven G.: 1983, Solar Phys.,
308,
935
24, 1092 88, 163
Hood A.W., Priest E.R.: 1979, Solar Phys., 04, 303 Lionello R., Velli M., Einaudi G., M&it 2.: 1996a, Non linear MHD evolution
of line-tied coronal
loops, in preparation Lionello R., Mikic Z., Schnack D.D.:
1996b, Magnetohydrodynamics
of solar coronal plasmas in
cylindrical geometry, in preparation Mikit Z., Schnack D.D., Van Hoven G.: 1990, Astrophys. J., 361,690 Raadu M.A.: 1972, Solar Phys., 22, 425 Velli M., Einaudi G., Hood A.W.: 1990, Astrophys. J., 350, 419 Velli M., Einaudi G., Hood A.W.: 1990, Astrophys. J., 350, 428 Velli M., Lionello R., Einaudi Phys., submitted
G.:
1996, Kink modes and current sheets in coronal loops,
Solar
PII:s02734177@7)ooo914
MAGNETIC RECONNECTION IN SOLAR CORONAL LOOPS G. Einaudi*, R. Lionello** and M. Velli** *Dipartimento di Fisica, Universitb di Piss, 56100 Piss Italy
** Dipartimento di Astronomiae Scienzedell0 Spazio, Universitddi Firenze, 50125 Firenze, Italy
ABSTRACT Simulations of the evolution of kink modes in line-tied coronal loops are presented which demonstrate the occurrence of magnetic reconnection in the non-linear stage of the instability. In loops which do not carry a net axial current (and are confined by a potential purely axial field) the reconnection is limited
to the initial current-carrying
channel and no overall loss of confinement
loops which carry a net current on the other hand, reconnection
progressively
is observed.
In
involves field lines at
greater and greater distances from the axis and even regions where the field was initially potential, 0 1997 COSPAR. Published by Elsevier Science Ltd. leading to a total disruption of the magnetic field topology.
WFRODUCTION High-resolution
observations
of the solar corona clearly show that the main building block of coronal
structure is the magnetised coronal loop. Such loops are often twisted and can store magnetic energy in a stable manner for very long times before undergoing periods of violent activity. The stability of current-carrying coronal loops has been shown to arise both from the effects of inertial line-tying in the dense photosphere
(Raadu
presence of ambient potential (Einaudi
1972, Hood & Priest 1979, Einaudi & Van Hoven 1981) and the
magnetic fields, though the latter have a much less important
& Van Hoven 1983) The Fourier analysis technique
developed
efl%ct
by Einaudi & Van Hoven
(1981) to compute the stability threshold for line-tied coronal loops was extended by Velli et al. (1990) to obtain the growth-rates of ideal and resistive instabilities and describe the linear properties of ideal kinks. One of the main questions that remained to be addressed concerned the subsequent non-linear evolution
of these modes and in particular whether or not magnetic
reconnection
could arise as a
consequence of the evolution of the ideal instability. Simulations of ideal modes in the nonlinear regime by Baty & Heyvaerts (1996) h ave shown that current concentrations on scales approaching the resolution seem to occur at finite times, indicating that simulations including resistivity are necessary to understand the later stages of evolution. SIMULATIONS Here we follow the complete history of the kink instability for two different field models (hereafter a and b): in model (a) the field has a finite current flowing in the cent,ral region of the loop (model (a) in Velb et al. 1990), while in the oth;cr (Lionello et al. 1996a) upflowing and downflowing currents
1876
Figure : 1: Field instan .ts (linear
G. Einaudi er ai.
line plots
for model
phase, early resistive
(a)
(left
column)
phase, saturation).
and model
(b)
(right
column)
at dif& xwnt
Rsconmction in Coronal Loops
fall
yield a null total current in the loop. In both cases the currents are confined within the same radius (T = 5). The linear stability properties of the two models are different, as discussed in Velli et al. 1996: in particular the critical length for stability is bigger for model (b); what is important here is that the length of the loop is chosen so that the loop is kink unstable and we therefore take the length of model (b) to be twice that of model (a). W e use a three-dimensional MI-ID code, which is an updated version of the program used in M&it et al. 1990 (LionelIo et al., 199613). The system evolution proceeds in the framework of ideal MHD until current sheets at the resolution scale are formed, after which resistivity is turned on and the subsequent reconnection of field lines is examined. The way in which reconnection proceeds strongly depends on the net axial current flowing in the central region of the loop.
4
., .,: u _,,, _,
,?ny..... \” ,,GY’_,” -.~,.;+$~ ‘&J.Y,.,?::.., _ . _.__._;-:‘.’ c,., .*>’ .,__._... ..‘.‘_ .’ ----..Q-K ....._..,,, ..,,_,,_,,
__~,
2
0 -y)
-20
,yic.. I:\\
-10
:
10
20
Jo
Figure 2: Radial distance of field lines for model (a) (top panels) and model (b) (bottom panels) as a function of the axial coordinate T = T(Z) in the early resistive phase (left), and at saturation (right). In field configuration (a) the ideal instability creates an extended global kink mode which involves field lines at all distances from the loop axis. The kink grows in amplitude and the shape of the currents involved is typical of an m=l structure which wraps around the loop in a helicoidal fashion. As the amplitude grows, peaks in the current form where the kink folds on itself, i.e. not at the centre of the loop but about midway from the line-tied ends to loop centre. This is due to the linetying effect in the non-linear regime, which contrasts the linear stabilising effect: a kinked current which would otherwise distribute itself along the loop is here forced to collapse where the geometry permits it, leading to reconnection of magnetic field lines in these areas. This is illustrated in Figure 1, where we have drawn the magnetic lines originating at different radii at three different times (left panel). The top image refers to the end of the linear kink phase, the middle right after resistivity has
1878
G. Einadi ef al.
been turned on, and the lower image is at saturation, harmonics stop growing.
i.e. when the subsequent
(m > 1) azimuthal
The non-linear evolution of field configuration (b) on the other hand is dominated by a second stronger current sheet which develops in the loop apex at the interface between the current-carrying channel and the potential
outer axial magnetic
field.
outer lines across this sheet leeds to an unwrapping
stages of evolution
in the right-hand
(i.e. ideal phase, onset of
saturation).
A better visualisation function
between inner field lines and
of the loop as demonstrated
panel of Figure 1. The images refer to corresponding reconnection,
Reconnection.
of reconnection
of the axial coordinate
the run, corresponding
T = r(r).
is given by plots of the radial distance of field lines as a These are shown in Figure 2 at two merent
instants of
to the early stage of the resistive phase, and when the instability
Top panels refer to model (a) and bottom
saturates.
panels to model (b).
Note that field lines whose ends are rooted at the same radius may or may not reconnect,
depend-
ing on their angular position, i.e., depending on whether their trajectory brings them in the vicinity of the current sheet. Reconnection starts at different radii and at different heights for the two models because the dominant current sheets are located in different positions and the subsequent evolution is completely dominated by reconnection itself. In fact, the linear ideal mode gives a good indication of these differences ( Velli et al. 1996). CONCLUSIONS Magnetic reconnection in line-tied coronal loops occurs during the non-linear evolution of a kink instability as a result of the creation of intense current sheets. The change of magnetic field topology makes the non-potential part of magnetic energy stored in the equilibrium configuration available on what appear to be ideal timescales (our simulations are performed using moderate resolution (64x32~64)). T~I‘s d e p en d s on the delicate point of whether current sheets really form on the ideal timescale since the subsequent dynamics is dominated by such sheets. Interestingly enough, in loops which do not carry a net axial current the field tends to become a purely axial potential field and the loop maintains its large-scale shape during the release of magnetic energy. In this phase we observe a ten-fold increase in temperature,
and even greater around current sheets, as will be shown in detail
elsewhere. This result may have important
applications
in explaining
compact
loop flares.
REFERENCES Baty H., Heyvaerts J.: 1996, Astron. Astrophys., Einaudi G., Van Hoven G.: 1981, Phys. Fluids, Einaudi G., Van Hoven G.: 1983, Solar Phys.,
308,
935
24, 1092 88, 163
Hood A.W., Priest E.R.: 1979, Solar Phys., 04, 303 Lionello R., Velli M., Einaudi G., M&it 2.: 1996a, Non linear MHD evolution
of line-tied coronal
loops, in preparation Lionello R., Mikic Z., Schnack D.D.:
1996b, Magnetohydrodynamics
of solar coronal plasmas in
cylindrical geometry, in preparation Mikit Z., Schnack D.D., Van Hoven G.: 1990, Astrophys. J., 361,690 Raadu M.A.: 1972, Solar Phys., 22, 425 Velli M., Einaudi G., Hood A.W.: 1990, Astrophys. J., 350, 419 Velli M., Einaudi G., Hood A.W.: 1990, Astrophys. J., 350, 428 Velli M., Lionello R., Einaudi Phys., submitted
G.:
1996, Kink modes and current sheets in coronal loops,
Solar