The flux distribution of network and intranetwork magnetic
        elements on the Quiet Sun

Aad van Ballegooijen & Robert Noyes

Abstract:

   We propose to analyze existing MDI magnetograph data to determine
the flux distribution of magnetic network and intranetwork elements
on the Quiet Sun. Various regions will be studied: predominantly unipolar
regions with different values of the net flux density, as well as mixed
polarity regions and regions near polarity inversion lines.
The observed distributions will be compared with results from model
calculations which include the effects of emergence, cancellation,
merging and break-up of magnetic elements.

Description of Proposed Research:

   Wang et al. (1995) show that intranetwork fields play an important role
is the magnetic flux balance of the Quiet Sun: about 10^23 Mx emerges and
disappears on the Sun each day. This is one tenth of the total flux present
at the time of cycle maximum. The intranetwork field is convected to the
supergranule cell boundaries where it interacts with the magnetic network:
like-polarity elements merge while opposite polarity elements cancel.
Large network elements may also break up as a result of gradients in the
supergranular flow. These processes act to produce a certain flux
distribution of magnetic elements (i.e., histogram of the number of elements
as function of their magnetic flux, per unit area of the solar surface).
The distribution will depend on the level of the net flux density, and will
reflect the balance between competing processes of flux emergence,
cancellation, merging and break-up. Near polarity inversion lines the
flux distribution may be further affected by intermixing of opposite
polarities.

  We propose to use MDI magnetograms obtained in low- and high-resolution
modes to derive observational constraints on the flux distribution of
magnetic elements on the Quiet Sun. We will develop methods for identifying
individual magnetic features and apply these methods to different data sets.
We will measure the size and magnetic flux of magnetic elements in
different subregions within the magnetograms: predominantly unipolar
regions with different levels of net flux, mixed polarity regions,
and regions near polarity inversion lines. Histograms of element size
and flux will be produced. We hope to study how the flux distribution
of elements depends on the level of the net flux density. In order to
detect weak intranetwork fields it may be necessary to combine magnetograms
taken over periods of several minutes to tens of minutes.

  Network elements are known to consist of flux tubes which have
strong, radially oriented magnetic fields. Intranetwork fields may have
intrinsically weaker fields, and the field may be more inclined relative
to the vertical. The visibility of features in line-of-sight magnetograms
is likely to be affected by the strength and orientation of the magnetic
field. To determine how the visibility is affected, we propose to study
the center-to-limb variation of the flux distribution in a large unipolar
region (using low-resolution data). We will follow a low-latitude region
for several days as it rotates across the solar disk. Although individual
magnetic elements cannot be traced for such long periods, the flux
distribution should be more or less constant over such periods and
any variations can probably be attributed to visibility effects.

  In the initial phase of the project we would use existing MDI data to
explore its potential for observing intranetwork fields and to develop
analysis techniques. In a later phase we may request dedicated observations
aimed at obtaining the highest magnetic sensitivity. The duration of such
observation should be several tens of hours, and would also provide valuable
information on the dynamics of intranetwork fields.

  We have developed a computer program which simulates how the flux
distribution N(f,t) of magnetic elements evolves with time in a unipolar or
mixed-polarity region, where N(f,t)*df is the number density of elements
with flux in the range [f,f+df]. The model includes the effects of emergence,
merging, cancellation, and break-up of magnetic elements. For example,
the merging of elements of flux f1 with elements of flux f2 removes
those elements but creates elements of flux (f1+f2). The rate of merging
is assumed to be proportional to the number density of elements f1 and f2:
dN/dt = C(f1,f2)*N(f1,t)*N(f2,t), where the coefficient C(f1,f2) depends
on the size and velocity of the magnetic elements. Starting from an
arbitrary initial distribution N(f,0), the flux distribution is evolved
in time until a stationary state is reached. Preliminary results indicate
that the flux distribution depends crucially on the value of the net flux:
if the net flux is close to zero, most of the flux is in small elements
(10^17 Mx), but for nonzero net flux most of the flux accumulates in larger
elements (10^18 - 10^19 Mx). We hope to use the MDI data to provide
observational constraints on such models.


Reference:

Jingxiu Wang, Haimin Wang, Frances Tang, Jeongwoo W. Lee, and Harold Zirin,
"Flux Distribution of Solar Intranetwork Magnetic Fields",
Solar Physics 160, 277, 1995