## 3. Determination of the magnetic modulation from two-wing observationsAlthough the data between January 19, 1996 and April 1, 1996 are
perturbed by a variety of commissioning activities, it represents the
only period during which both the blue and red wings of the Na D lines
were observed from space with the GOLF system which includes the
magnetic modulation. The classic resonance scattering helioseismometer
yields an observable designated as The use of the modulated electromagnet permits a monitoring of the
net solar line profile as averaged by the instrument. The amplitude of
magnetic modulation can be found in addition through the use of the
orbital changes in the sun-spacecraft velocity. The magnetic
modulation combined with the wing selection by the rotating polarizers
provides four measurable quantities:
. These can be combined to yield a
number of different expressions for If the scattering process included only one term instead of three,
the difference between and
would be the same as would result
from a velocity shift equivalent to that implied by the separation
between the wavelengths of the two states of magnetic modulation. The
asymmetrically placed set of three scattering wavelengths causes the
centroid of the combination to be dependent on the scattering gas
temperature. We can estimate the effective value of the wavelength
separation by smoothing each
The value of which produces the
most exact agreement between the and
is uncertain due to irregularities
in the longer term trends of the two functions. The magnitude of this
uncertainty can be estimated by examining
as a function of
with
as a parameter. This comparison is
shown in Fig. 3. The value of
determines the average value of so
that if is too small,
is positive and if
is too large,
is negative. The correct
leaves the average of
near zero. A figure of the merit for
any choice of is
, the rms variation in
considered as a function of
. The best value of
is that which minimizes
. Due to the irregularities in the
function as shown in Fig. 3
this minimum is not precisely defined. The behavior of
versus
is shown in Fig. 4. The breadth
of the minimum in Fig. 4 provides an estimate for the uncertainty
of which is about
0.5 m s
In order to convert into an effective magnetic field modulation amplitude we use the derivative of Eq. (5) to obtain a relationship between the line intensity slopes and : Next we need to relate the amplitude of magnetic modulation
to
and this requires consideration of the interaction between the solar
line profile and the sodium scattering. Each scattering component has
a wavelength according to
Eq. (1). The sun-spacecraft velocity determines
where Eqs. (11) and (12) require knowledge of the line profiles over
some range in and using a linear expansion about the reference velocity we obtain: Two properties of these definitions are worth emphasizing: first, even though we have used a velocity scale for the argument of the line profile function, we have reversed the sign in order to account for the fact that the velocity appears with a negative sign in Eqs. (14 - 17); and second, the slopes are positive while the slopes are negative. We can now express the intensity change due to the magnetic modulation as Utilizing the fact that we can write as giving which can be inserted into Eq. (8) to obtain: Due to the temperature dependence of the scattering strengths
, the value of
also depends on the temperature as
well as the offset velocity. The total range in temperature as
indicated by the platinum probe is from 169.9 The derived corresponds to a magnetic modulation of gauss. Eq. (24) provides a precise determination of the magnetic modulation amplitude and is adopted for the remainder of this paper.
© European Southern Observatory (ESO) 2000 Online publication: January 29, 2001 |