Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://star.arm.ac.uk/~ambn/323jgd.ps Äàòà èçìåíåíèÿ: Tue Oct 26 12:13:15 1999 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 21:07:39 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: ñïðàéòû

A&A manuscript no.
(will be inserted by hand later)
Your thesaurus codes are:
02.13.2; 02.12.3; 06.01.2; 06.03.2; 06.20.1; 06.21.1
ASTRONOMY
AND
ASTROPHYSICS
October 25, 1999
Letter to the Editor
New insight into transition region dynamics via SUMER
observations and numerical modelling
L. Teriaca 1 , J.G. Doyle 1 , R. Erd'elyi 2 , and L.M. Sarro 3
1 Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland
Email:lte@star.arm.ac.uk, jgd@star.arm.ac.uk
2 Space & Atmosphere Research Center, Department of Applied Mathematics, University of Sheffield, England
Email: Robertus@sheffield.ac.uk
3 Laboratorio de Astrofisica Espacial y Fisica Fundamental (LAEFF) INTA, 28080 Madrid, Spain
Received date, accepted date
Abstract. We explore the idea that the occurrence of
nano­flares in a magnetic loop around the O vi forma­
tion temperature could explain the observed red­shift of
mid­low transition region lines as well as the blue­shift
observed in low coronal lines (T ? 6 10 5 K). Observa­
tions are compared to numerical simulations of the re­
sponse of the solar atmosphere to an energy perturbation
of 4 10 24 ergs representing an energy release during mag­
netic reconnection in a 1­D semi­circular flux tube. The
temporal evolution of the thermodynamic state of the loop
is converted into C iv 1548, O vi 1032 and Ne viii 770
line profiles in non­equilibrium ionization. Performing an
integration over the entire period of simulations, a red­
shift of ¸ 6 km s \Gamma1 is found in C iv, while a blue­shift
of ¸ 2 km s \Gamma1 and ¸ 10 km s \Gamma1 were derived for O vi
and Ne viii, respectively, in reasonable agreement with
observations.
Key words: Transition region --- line shifts --- numerical
simulations
1. Introduction
During the last two decades, observations of red­shifted
emission lines formed at transition region (TR) temper­
atures were obtained by many authors using several UV
instruments with different spatial resolution (see Brekke
et al. 1997 and references therein). Brekke et al. (1997)
and Chae et al. (1998a) have shown that for the `quiet'
Sun the red­shift is peaked around 1:5 10 5 K with a value
of 11 km s \Gamma1 . Their data suggested it to be also present
at higher temperatures with a value of around 5 km s \Gamma1
for Ne viii 770 š A in the `quiet' Sun. On­the­other­hand,
Peter & Judge (1999) found blue­shifts at disk center for
three coronal lines (i.e., Ne viii at 770 š A and 780 š A and
Send offprint requests to: L. Teriaca
Fig. 1. SUMER measurement of radial velocities in active re­
gion NOAA 7946 (top panel) and in the `quiet' Sun (lower
panel). The solid line represent a polynomial fit (Teriaca et al.
1999).
Mg x at 625 š A). This difference in the value of Doppler
shift for Ne viii 770 is due to the assumption of a new rest
wavelength of 770.428 š A, confirmed by Dammasch et al.
(1999). Recently, Teriaca et al. (1999) found evidence for

2 Teriaca et al.: Solar Transition Region Dynamics
blue­shift in both the `quiet' Sun and in an active region
at upper TR and coronal temperatures.
In this Letter we investigate the consequences of these
observational results via a comparison with numerical
studies. The simulations were carried out representing a
reconnection­type of physical process with the calculations
being converted into UV line profiles in non­equilibrium
ionization (see Erd'elyi et al. 1998, 1999, Sarro et al. 1999
for earlier work in relation to the modelling of UV explo­
sive events).
2. Observational Results
Teriaca et al. (1999) have shown that the temperature
variations of the Doppler shifts and non­thermal veloci­
ties in the `quiet' Sun and active region have important
implications for the validity of the physical models for the
red­shift (or down­flow) problem. In Fig. 1 we show the
behaviour of the Doppler shift versus temperature of for­
mation both for a `quiet' Sun and an active region as re­
ported by Teriaca et al. (1999). From their measurements
it is possible to infer that the Doppler shift reversal from
red­shift to blue­shift takes place around Log T = 5:7 K
(5 10 5 K) in the active region while in the `quiet' Sun a
value between Log T = 5:7 and Log T = 5:75 (5:0 10 5 ­
5:6 10 5 K) can be estimated.
3. Modelling
There are a few different models in the literature which at­
tempt to explain the down­flow problem, e.g., the return of
spicular material, siphon flows through loops, nano­flares
and explosive events (see Brekke et al. 1997; Peter & Judge
1999, Sarro et al. 1999 and reference therein). Out of all
these we found the most relevant and consistent with our
observations is the one by Hansteen (1993). He consid­
ers nano­flares occurring at the top of coronal loops, gen­
erating MHD waves that propagate downward along the
magnetic fields towards and through the transition region.
This model was extended by Hansteen et al. (1996)
including the reflection that the chromosphere exerts on
the downward travelling waves. Also this model predicts
red­shifts in the `quiet' Sun of ¸ 15 km s \Gamma1 at the
C iii formation temperature (8 10 4 K) and blue­shifts of
¸ \Gamma15 km s \Gamma1 at the Mg ix formation temperature (10 6
K). These are large with respect to the `quiet' Sun results
(see Fig. 1). However, it is able (as also pointed out by
Peter & Judge 1999) to explain the presence of blue­shift
together with red­shift within one model.
Following the suggestion of Peter & Judge (1999) we
support the idea of the prevalent occurrence of mag­
netic reconnection around the O vi formation temperature
(3 10 5 K) as a source for the red­shift observed in the low
and middle transition region and for the blue­shift seen in
the upper transition region and coronal lines. This can also
explain the peak of the non­thermal velocity versus tem­
perature curves at the O vi formation temperature (see
Chae et al. 1998b; Teriaca et al. 1999). From this point
of view the larger range of values detected for the active
region could be explained in terms of a higher frequency
of occurrence and/or energy of nano­flares events in the
active region with respect to the `quiet' Sun.
4. Hydrodynamical Simulations
The Doppler shifts are interpreted as the response of the
solar atmosphere to a sudden release of energy (e.g., recon­
nection). However, the ultimate origin of the input energy
that drives these flows of material has not yet been estab­
lished (e.g., we do not exclude an explanation based on
wave theory especially nonlinear MHD waves).
In the present work the small­scale energy depositions
are simulated in a one­dimensional semi­circular rigid
magnetic flux tube (see, e.g., Sterling et al. 1991,1993,
Mariska 1992, Sarro et al. 1999). The distance along the
loop is s, with s = 0 fixed at the left boundary of the tube.
The length of the loop is taken to be 13,000 km, with a
chromosphere 1,500 km thick at both ends of the loop.
Gravity forces, g(s) = g 0 cos ff, are taken into account,
where g 0 = g j s=0 = 2:7 10 2 m s \Gamma2 and ff denotes the
angle between the component of gravity along the loop at
point s, and the gravity vector downwards. The governing
equations of physical processes in the loop can be written
in the form:
@ae
@t
+ @(aev)
@s
= 0; (1)
@(aev)
@t
+ @(aev 2 )
@s
= \Gammaaeg(s) \Gamma
@p
@s
; (2)
@E
@t
+ @
@s
Ÿ
(E + p)v \Gamma Ÿ
@T
@s
–
= \Gammaaevg(s) \Gamma L + S; (3)
where
E = 1
2 \Delta aev 2 + p
fl \Gamma 1 : (4)
Here L denotes the radiative loss function and S de­
notes the volume heating rate. For the radiative loss func­
tion we use the analytical expression given by Sterling
et al. (1991), while for the input heating rate we take a
constant value per unit volume of 3:6 10 \Gamma4 ergs cm \Gamma3 s \Gamma1 .
Equations (1) -- (3) are solved using the Fortran 90
code EMMA D (De Sterck et al. 1998) based on high
resolution shock capturing schemes and an approximate
Riemann solver. We use a fixed grid spacing correspond­
ing to 13 km per grid cell. The code is implemented with
solid wall boundary conditions. At both foot­points, the
temperature and the pressure are fixed at 10,000 K and
2.1 dyn cm \Gamma2 , respectively. After the hydrodynamics vari­
ables are computed, we calculate the ion populations for
three different ions, and finally a line synthesis program
gives UV line profiles suitable for comparison with obser­
vations (see x5).

Teriaca et al. : Solar Transition Region Dynamics 3
Fig. 2. Response to an energy perturbation representing the en­
ergy release during a nano­flare, in a 1­D semi­circular mag­
netic loop. The temporal evolution of the thermodynamic state
of the loop is converted into C iv 1548 š A (top panel), O vi
1032 š A (mid panel) and Ne viii 770 š A (bottom panel) line pro­
files (integrated over 9 consecutive seconds) in non­equilibrium
ionization.
5. Observational Consequences
In order to calculate the ion populations along the loop for
a given time we have to integrate the ionization equations,
i.e.,
@N i
@t
+ @(N i \Delta v)
@s
= N e (N i+1 ff i+1 +N i\Gamma1 S i\Gamma1 \GammaN i (ff i +S i ))(5)
where ff i and S i are the recombination and ionization co­
efficients of ionization stage i and N i is the volume number
density of ion i. From the observed Doppler shifts in Fig. 1
we have selected the resonance line of C iv at 1548 š A, O vi
1032 š A, and Ne viii 770 š A whose ion populations is go­
ing to be determined. This offers an easy comparison of
Doppler shift observations and numerical predictions of
the time evolution of observational signatures. Analyses
also show that it is evident that strong deviations from
the equilibrium values of the ion populations occur. We
do not represent here a careful study of this deviation. We
refer the detailed analysis of the evolution of the fractional
ion populations with respect to the equilibrium values to
a recent PhD thesis (Sarro 1998) devoted to the study of
the evolution of the ionization state of several species in a
loop subject to these kinds of energy perturbations.
Once the ion populations are computed, the emissivity
of a given emission line per unit interval of wavelength in
an optically thin, collisionally excited resonance line can
be obtained by using the standard equation
E– /
hc
–\Omega !
N 1
N ion
N ion
N elem
N elem
NH
NHN e
exp \GammaW
KbT
p
T
OE(–) (6)
Given a distribution of emissivities along the loop, the
total intensity can be calculated as
I – =
se
Z
0
E–ds (7)
where s e is the total length of the loop.
6. Numerical Results
We compare our observations with the response to an en­
ergy deposition representing nano­flaring due to reconnec­
tion in the high part of a 1­D semi­circular magnetic flux
tube (Erd'elyi et al. 1998,1999, Sarro et al. 1999). After the
hydrodynamical simulations, the calculations are turned
into UV line profiles applying the non­equilibrium ion­
ization condition in order to make a direct comparison
with observable quantities. Note, the condition of non­
equilibrium ionization has a major effect on the line for­
mation as was discussed by Sarro et al. (1999).
In the results shown in Figs. 2 & 3, an energy input
of 4 10 24 ergs was released at an height of 5400 km (cor­
responding to log T = 5:7) in a 1­D magnetic loop. The
temporal evolution of the thermodynamic state of the loop

4 Teriaca et al.: Solar Transition Region Dynamics
Fig. 3. Time evolution of the total intensity (upper panel) and
of the central position (lower panel) for the three modelled lines.
is converted into C iv 1548 š A, O vi 1032 š A and Ne viii
770 š A line profiles (see Fig. 2).
Further, Fig. 3 shows the time evolution of the total
intensity (upper panel) and the central wavelength posi­
tion (lower panel) for the three modelled UV lines. An
analysis of Fig. 3 shows that indeed purely red­shift is
produced in C iv while blue­shift is produced during the
second part of the simulation in O vi and in Ne viii. Due
to the much higher intensity of the latter two lines dur­
ing the blue­shift part, this results in a predominance of
blue­shift in Ne viii and to a lesser extent in O vi, which
is in agreement with observations. Performing an integra­
tion over the entire period of simulations (55 seconds), a
redshift of ¸ 6 km s \Gamma1 is found in C iv, while a blue­shift
of ¸ \Gamma2 km s \Gamma1 and ¸ \Gamma10 km s \Gamma1 were derived for O vi
and Ne viii, respectively. This is in reasonable agreement
with recent observations.
We trust our results shed further light into the physics
and modelling of the complexity of the solar (and stellar)
transition region. Furthermore our observations provide
clues for the possible role of nano­flare events in the tran­
sition region as a suitable source for the observed Doppler
shift. We plan to develop the modelling of the nano­flare
mechanism exploring in detail the parameter space, cal­
culating the response of the model to different amount of
deposited energy at different temperatures. Furthermore,
we plan to perform full 2­D MHD simulations, including
2D non­equilibrium ionization in order to determine the
role of the magnetic field.
Acknowledgements. Research at Armagh Observatory is grant­
aided by the Dept. of Education for N. Ireland while partial
support for software and hardware is provided by the STAR­
LINK Project which is funded by the UK PPARC. This work
was partly supported by PPARC grant GR/K43315 and a
grant from the British Council ­ Acciones Integradas (Spain)
ref. no. 1814. SUMER is part of SOHO, the Solar and He­
liospheric Observatory of ESA and NASA. We would like to
thank the referee Nils Brynildsen for his comments. R. Erd'elyi
thanks M. K'eray for patient encouragement.
References
Brekke P., Hassler D.M. & Wilhelm K., 1997, Sol Phys 175,
349
Chae J., Yun H.S. & Poland A.I., 1998a, ApJ S 114, 151
Chae J. Sch¨uhle U. & Lemaire F., 1998b, ApJ 505, 975
Dammasch I.E., Wilhelm K., Curdt W. & Hassler D.M., 1999,
A&A 364, 285
De Sterck H., Poedts S. & Goedbloed J.P., 1998, J. of Plasma
Phys. 59, 277
Erd'elyi R., Sarro L.M. & Doyle J.G., 1998, `Explosive Events
Modelled in the View of SOHO Observations', ESA SP,
421, 207
Erd'elyi R., Sarro L.M. & Doyle J.G., 1999, `Observations and
Modelling of Small­Scale Energetic Transients in the Solar
Atmosphere', ESA SP, 446, in press
Hansteen V.H., 1993, ApJ 402, 741
Hansteen V.H., Maltby P., Malagoli A., 1996, in R. D. Bentley,
J. T. Mariska (eds.), Magnetic Reconnection in the Solar
Atmosphere, ASP Conference Series 111, 116
Mariska J.T., 1992, The Solar Transition Region, Cambridge
University Press, Cambridge
Peter H. & Judge P.G., 1999, ApJ 522, 1148
Sarro, L.M., 1998, PhD Thesis
Sarro L.M., Erd'elyi R., Doyle J.G. & P'erez M.E., 1999, A&A
(in press)
Sterling A.C., Mariska J.T., Shibata K. & Suematu Y., 1991,
ApJ 381, 313
Sterling A.C., Shibata K. & Mariska J.T., 1993, ApJ 407, 778
Teriaca L., Banerjee D. & Doyle J.G., 1999, A&A 349, 636