Helioseismology has a recent past, when the 5-minute solar oscillations, first observed in the sixties by Leighton, Noyes and Simon, were identified theoretically and observationally as the evanescent photospheric counterpart of the acoustic modes resonating in the underlying convection zone. At present, the oscillation frequencies are used to get information on the Sun's interior, like the extension of the convection zone and the internal rotation velocity, whilst other oscillation properties, like phase differences, can be used to diagnose the atmospheric layers. The future, which the successful launch of SOHO makes closer, will be probably dominated by the study of low frequency modes, in particular g-modes.
Very recently the detection of a number of g-modes in solar wind
measurements done by Ulysses has been reported
(Thomson et al. 1995).
This kind of measurements needs
to be confirmed before being widely accepted.
In progress there are both ground
and space based experiments to measure solar global modes (see e.g.
Fig. 3 in Harvey 1995).
In particular we will refer here to the IRIS and GOLF experiments.
The IRIS (International Research on the Interior of the Sun)
ground-based network for full disk
helioseismology (e.g. Fossat 1991; Pallé et al.
1993) is measuring since 1991
the full disk line-of-sight velocity, from the Doppler shift of
the sodium 
line, over a range of frequencies
from 100 
, when the atmospheric conditions are good enough,
up to about 10 mHz, limited by the photon statistical noise
of the sodium resonance cell.
The GOLF (Global Oscillations at Low Frequency) experiment, on
board of the satellite SOHO (Solar and Heliospheric Observatory),
which was launched on December 2, 1995, will make a definite effort to
detect and identify the solar g-modes.
The measuring method involves an extension to space of the ground-based
technique used by IRIS (Gabriel et al. 1995). The data
will be collected continuously for a period of at
least two years (hopefully six) over a
range of frequencies from 
to 6 mHz, without limitations due to duty cycle and merging problems.
The possibilities of these experiments to detect solar oscillations in the low frequency domain and definitely identify the g-modes depend crucially on the contrast in power between the oscillation signal and other time dependent signals in the same frequency range. This "noise'' is partly instrumental and partly of solar origin, therefore the signal to noise ratio could be in principle increased by our ability to understand and remove solar sources of non-oscillatory signals.
Harvey (1985) made an estimate of the background Doppler-shift
noise of solar origin in full-disk measurements assuming
that it is due to the finite lifetime
(evolution) of four velocity fields:
granulation, mesogranulation, supergranulation and active regions.
The parameters of this model, whose values were derived from high
resolution observations, are the rms velocity amplitudes and the
lifetimes of
the motions. In this way, Harvey got a continuous noise spectrum in which
active regions and supergranulation
make the largest contribution to the power
in the g-mode frequency band
(
), whilst granulation dominates at higher frequencies.
In subsequent works, observed power spectra have been used to fit the
model parameters, getting different results according to the estimate
Of the instrumental contribution to the observed background
(Jiménez et al. 1988; Elsworth et al. 1993). A
similar noise model has been used by Harvey et al. (1993) to
study the solar noise spectrum of chromospheric oscillations, and a more
complex model of the irradiance background due to granulation,
mesogranulation and supergranulation, based on a numerical simulation of
their time evolution, has been proposed by Andersen et al.
(1994).
The solar noise spectrum has also a spectral line component.
Claverie et al. (1982) established the existence
of a 13.1 
day signal of amplitude
in measurements of the
mean Doppler velocity shift of the integrated solar disk.
This finding was confirmed by Isaak et al. (1984), who found
also a second less prominent peak at a period of 27.2 days,
and, later, by Jiménez et al. (1988) and Régulo et al.
(1993).
Claverie et al. in their paper suggested a possible explanation of this phenomenon in terms of a rapidly rotating solar core (see also Dicke 1983). On the other hand, taking into account the effect of active regions passing over the solar disk, several authors (Durrant & Schröter 1983; Andersen & Maltby 1983; Edmunds & Gough 1983) have been able to reproduce the observations sufficiently well to establish that active region modulation is almost completely responsible for the observed signal. However, it is not yet clear if the spots or other parts of the active regions make the largest contribution to the velocity signal. Indeed, different simulations of the signal have been based on the plage area (Durrant & Schröter 1983; Herrero et al. 1984), on the sunspot area (Andersen & Maltby 1983; Régulo et al. 1993), on spot and plage area (Edmunds & Gough 1983; Jiménez et al. 1988) and, finally, based on daily magnetograms (Ulrich et al. 1993) and GONG modulation images (Beck et al. 1995).
The agreement with the observations is generally good, but not enough to consider any of these models a completely successful correction of the integrated sunlight observations for the effect of active regions.
The active region noise arises because they may introduce real local
velocities contributing to the global average, and
because, through both their magnetic fields and thermal structure,
they change the integrated profile of the observed lines by an amount
that is set by the active region distribution and modulated by solar rotation.
In this paper, we model the latter effect, which originates from the
different line shapes in magnetic and quiet solar areas.
Both sunspots and plages appear darker than the quiet Sun
in the sodium
D lines at about 
from the line core, where the passbands
of the resonant cell are centered, therefore
Roger Ulrich has called this effect
magnetic darkening velocity.
We simulated the velocity and flux fluctuations
produced by different active region distributions,
using an analytical description of their action.
Such an approach has proved to be
successful in clarifying the formation of the spectral line component
of the noise attributed to solar active regions.
We have applied our model to ground based velocity measurements, comparing our results with the data obtained by the IRIS network, and we plan to extend the simulation for calibrating the data coming from the GOLF experiment, whose level of background noise is expected to be one order of magnitude lower than it is on ground based measurements.
Preliminary results of our simulation have been presented by Marmolino et al. (1995, hereafter Paper I). In this paper we complete the analysis started in Paper I discussing in details the dependence of the simulation results upon a number of model parameters. Specifically, in Sect. 2 we recall the methods and describe the data which our simulation is based on; in Sect. 3 we review briefly on the calibration methods necessary to get velocities out of the observed photometric ratios; in Sect. 4 we show and discuss the results, and in Sect. 5 we summarize our main conclusions.