Lyman α intensities in a polar coronal hole from a 2D model

Adv. Space Res. Vol. 30, No. 3, pp. 523-528,2002 0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-l 177/02 $22.00 + 0.00 PII: SO273-1177(02)00331-9

Pergamon www.elsevier.com/locate/asr

LYMAN

a INTENSITIES FROM L. Zangrilii’

‘Dipartimento

4Dipartimento

IN A POLAR CORONAL A 2D MODEL

2, G. Poletto3,

HOLE

P. Nicolosi2 4, G. Noci’

di Astronomia e Scienza dello Spazio, Universitci di Firenze, I-50125 Firenze, Italy 21stituto Nazionale per la Fisica della Materia, Unit4 di Padova, Italy 30sservatorio Astrofisico di Arcetti, I-50125 Firenze, Italy di Ingegneria Elettronica ed Infonatica, Universitci di Padova, I-35131 Padova, Italy

ABSTRACT We simulate the coronal H I Lyman CYintensity for heliocentric distances between 1.5 and 2.5 Ra, and latitudes between 90” (North pole) and 30”, making use of a 2D semiempirical coronal hole model. Observations are made with the Ultraviolet Coronagraph Spectrometer (UVCS) on board the ESA-NASA solar satellite SOHO (Solar and Heliospheric Observatory). Model electron densities are derived from the collisional part of the 0 VI X1037.6 A line and the proton outflow speed is calculated from mass flux conservation along the magnetic field lines. The expansion factor and the direction of the magnetic flux tubes have been derived by adopting a simple analytical magnetic field configuration. The intensities of the Ly (Y line predicted by the model are compared with the observed intensities. 0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.

INTRODUCTION In this study we simulate the intensity of the H I Lyman (Y line between 1.5 and 2.5 Ra of heliocentric distance, and between 90” (North pole) and 30’ of latitude. To this end we developed a semiempirical coronal hole model in two dimensions, latitude and distance, making use of observations of coronal emission lines from the UVCS experiment (Kohl et al. 1995). Electron densities are derived from the collisional part of the 0 VI X1037.6 A line and the proton outflow speed is calculated from mass flux conservation along the magnetic field lines. The expansion factor and the direction of the magnetic flux tubes have been derived by adopting a simple analytical magnetic field configuration. In the coronal hole model, perpendicular kinetic temperatures, TL, have been derived from the observed widths of the line profiles, while parallel kinetic temperatures, TI, are assumed to range between the electron temperature, T,, and Tl. Simulations of the H I Ly (Y X1215.6 A line, are obtained by taking into account Doppler dimming effects (see e.g. Withbroe et al., 1982) and integrating along the line of sight (LOS) the predicted emissivities. The results are then compared with UVCS observations. The values of model parameters, such as the magnetic field configuration, kinetic temperature distribution, and proton flux at 1 a.u., have been selected to minimize differences between predicted and observed data. The data have been acquired during a week of observations in August 1996, making observations with both the Ly cr and 0 VI channels. We used data of the daily synoptic program, which gives information on the solar corona intensity in different UV spectral lines, and offers a good coverage at relatively low spectral resolution (in the 0 VI channel) over heliocentric distances from 1.5 to - 3 Ro. We identified the positions along the slit corresponding to latitudes 10 degrees apart from 30” to 90’ and summed up data over 30 pixels centered around these locations, in order to obtain a set of spectra ranging from 1.5 to N 2.6 Ro, along radials passing through different latitudes. To improve the statistics we summed up data of the entire week. F’rom these spectra we derived the intensity vs. heliocentric distance profiles for the H Ly cy and 0 VI X 1031.9 and X 1037.6 A lines, at fixed latitudes.

523

524

L. Zangrilli ef al.

LINE FORMATION IN THE EXTENDED SOLAR CORONA The intensity of UV coronal emission lines is the sum of a component due to the resonance scattering of the solar disc radiation, and one originating from collisional excitation of coronal ions: It,,,(s) = JLos Jx (&,II + jr,) dXdz (e.g. Withbroe et al., 1982). The emissivity of the resonance component, which is a function of the local outflow speed of the solar wind, is given by the following expression:

h&z jr&, n’) = -n(X+y Linus

J%

p(S * n”)cAd

+03 lD(V’, w)dv’ J -CO

where vs is the rest frame frequency, n(Xfm) is the number density of the ground state ion of the element X m - times ionized (the number density of H I in the case of Ly o), Br2 the Einstein coefficient of absorption, ID(!J’, W) the disc intensity at frequency v’, a the outflow speed of the wind, n’ the LOS direction, n” the direction of propagation of the disc radiation, p the angular dependence of the scattering process, and R. is the solid angle subtended by the solar disc. The emissivity of the collisional component is jcoll(~)

= ~~(x+m)necd?Mv

-

vo)

where n, the electron density, C&1(!&) is the collisional coefficient, coronal line profile. To take into account the possibility of anisotropic the velocity distribution is described with a bi-maxwellian function.

which is a function kinetic temperatures

of Te; & is the of coronal ions,

DETERMINATION OF THE ELECTRON DENSITY To determine the electron density in the corona, we identify the collisional component of the observed 0 VI line at 1037.6 A, which is given by IcOll = KS L0s nzdx (see eq. 2), where the constant K depends on T, (via the 0 VI ionization equilibrium and the collisional coefficient C&,ll), the oxygen abundance, and other atomic parameters. Once the collisional components have been identified, we evaluate bosn!dz, assuming that the dependence of n, on the heliocentric distance can be expressed by n,(r) = CiZ1 air *a , with N = 3. The parameters ai, bi are derived by a best fit technique, minimizing the differences between calculated and observed values. Because the percentage &l/1 (I = IcOll + I,, is the total intensity) depends on the 0 VI outflow speed, vg VI, and the intensity ratio R = 1~0~~.~/1~0~~.~ is essentially a function of vg ~1, we separated the collisional part of the 0 VI 1037.6 A line as a function of the observed ratio R using a Doppler dimming technique. at a latitude 90” and for heliocentric distances To this end we built the I,,~~/1 us. R curve adopting, and two electron density profiles, taken from 1.5 Q 5 r 5 3 Ro, the observed kinetic temperatures, Guhathakurta & Holzer (1994) and Guhathakurta et al. (1999), being representative of a coronal hole during the minimum of solar activity phase. For each of the two adopted n,(r) profiles, we separated the IcOll component, and evaluated a new radial law for n,(r). Then, we averaged the two resulting density radial laws, and repeated the above procedure using the n,(r) from the previous step until a convergence is found. We then applied this technique at lower latitudes, adopting as initial profile that of the adjacent latitude. This method relies on the knowledge of the oxygen abundance, which may change from open to closed field line regions (see e.g. Raymond at al., 1997). Hence, we limited our analysis to regions outside the equatorial streamer, assuming a constant oxygen abundance (7 x 10m4, normalized to the H abundance; von Steiger et al., 1995). The radial profile of density us. heliocentric distance at latitude 90”, in the range 1.5 to 4 b, is shown in Fig.(l-a), together with other profiles taken from the literature and obtained from white light observations. The latitudinal profiles of n, at constant altitudes are shown in Fig.(l-b) in the range 1.5 5 T 5 3R,,,. In both figures, the uncertainties in the n, profiles are derived from the estimates of the errors in the fitting parameters, based on the Poissonian statistics of the 0 VI line intensities. OUTFLOW SPEED ALONG THE MAGNETIC We adopted the magnetic field model of Bansszkiewicz In this model an azimuthal current sheet in the equatorial

FIELD LINES et al. (1998) to describe the topology of flux tubes. plane is combined with an &symmetric multipole

Lyman a Intensities in a Polar Coronal Hole From a 2D Model

1.1 -

525

(b)

4.“““‘.

.I”’

00

10

00

100

from

the collisional

e(deg)

Fig. 1. (a) Radial profiles the 0 VI doublet intensity. represent

the uncertainty

(40” - 50”)

because

of n,

at latitude

(b) Latitudinal

90’.

in the determination

of the lower number

The solid curve

profiles

is the n8 profile

of n, at different

of n,.

of observations

In panel

(b)

at different

distances.

The dotted

the uncertainty distances

part

of

lines in both figures

is larger

at mid

latitudes

at these latitudes.

field (a dipole plus a quadrupole). We derived the expansion factor by using the magnetic flux conservation. In this model the strength of the quadrupolar component changes as a function of a parameter Q: Q = 0 corresponds to a pure dipole plus a current sheet, Q = 1.5 corresponds to the maximum contribution of the quadrupolar component. To perform the simulations presented in this work, we selected the intermediate case Q = 1, after having explored the topology given by different geometries. The absolute outflow speed of protons in the solar wind can be obtained from the conservation of particle flux along a field line. Assuming at 1 a.u. a constant value for the particle flux, F = nPw z 2 x lo* cm-*s-i (see Goldstein et al. 1996), where the proton density for a fully ionized plasma with 10 % helium is nP = 0.8n,, the proton outflow speed is given by V(r,e) =

F(la.u.)(215 0.8ner2

Ra)2 f(1 A.U.,0)

f (7-y 0)

(3)

where T is the heliocentric distance and 8 is the latitude. Once V(T, 0) along field lines is known, we evaluate v us. latitude at different heliocentric distances by interpolating between adjacent field lines. In Fig(2) the profile of the velocity of protons vs. latitude for different heliocentric distances is shown, for three different magnetic field geometries (Q = 0, 1, 1.5). Looking at the case Q = 1, we see that the outflow speed is about 100 - 120 kms-i in the polar region between 1.5 - 1.75 Q, reaching about 350 kms-’ at 2.5 &. In all three cases, a steep decrease of the velocity shows up in the range of latitudes 60’ - 80”, at high heliocentric distances. The dip in the velocity profile at about 70” and the peak at N 50” are mainly due to the waviness of the density profile. Errors in the density determination suggest us to look at this behaviour with some caution. However, we can be confident in saying that the steep velocity decrease from the pole towards lower latitudes levels in between 50” - 70°, then declines steeply hereafter. SIMULATION OF CORONAL HOLE Lyman a INTENSITIES In this section we compute the Ly a line intensity, ILK Q, using the coronal hole model previously developed, and we compare the predicted II+ (I values with the observed ones. In order to investigate the impact of different choices of different parameters, we illustrate the results we obtain when they take different values. In Fig.(3-a) the simulated ILL o1 values at 0 = 90 ’ are shown together with the observed intensities. The

L. Zangrilli er al.

526

Fig.

2.

Latitude

heliocentric

profiles

distances,

of the wind outflow

for three geometries

speed for protons

of the magnetic

field.

derived

from mass conservation

The dotted

bracketing

at different

lines are derived from

estimates of the errors in n8.

assumed parameters are F(l a.u.) = 2 x lo8 cm-2s-1, the kinetic temperature is isotropic, TY = lo6 “K. The relative deviations between simulated and observed data, lAIl/Iot,s, are given in Fig.(S-b), which demonstrates how the geometries with a poorer capability of reproducing the observations are the dipole plus quadrupole case (Q = 1.5) and the intermediate case Q = 1. For Q = 0 (pure dipole) lAI(/&-,, is always lower than 40 %, with the larger deviations from observations at high heliocentric distances. The effects of an anisotropic kinetic temperature of protons on the modelled intensities are shown in Fig.(3-c), where we adopted a kinetic parallel temperature equal to the electron temperature (ql = Te), F(l a.u.) = 2 x lo8 cm-2s-1, Q = 0. The simulations refer to the polar direction (0 = 90’). From Fig.(3-d) we deduce that the isotropic case tends to give better results, while the fully anisotropic model strongly deviates from the observations by about 50 - 60 %, for distances higher than 2 Ra. While 2 x lo8 cm-2s-1 is the value most commonly used for the wind flux at 1 a.u., higher values are also reported (see e.g. McComas et al., 2000). The effect of varying the proton flux value at 1 a.u. is to modify by a constant factor the whole outflow speed field determined by the mass conservation. The way in which this affects the predicted 1~~ Q is a function of the coronal absorption profile width. Basically, increasing the value of F(l a.u.) causes a steeper radial gradient of the calculated intensities. Figs.(S-e), (3-f) show that F(l a.u.) = 2 x lo8 (with Q = 0) gives results more consistent with the observed intensities. The model parameters which turned out to yield the best simulations of observed IL,, D are: Q = 0; isotropic kinetic temperatures; F(l a.u.) = 2 x lo8 cm- 2s -l. Using these values we calculate (Fig.4 a-f) the radial profiles of IL,, D at latitudes 10” apart within the coronal hole. Predicted 1~~ Q is represented by open squares, the observed one by asterisks. The relative deviations between simulated and observed data are also shown (full squares). The only variation with latitude which can be seen in Fig.(4 a-f) is a gradual increase of the intensity towards the equatorial regions, at distances higher than 2 Ra: while the intensity measured at 1.5 b is approximatively constant (- 1.53 erg s-l cmw2 sr-r at 90”, N 1.38 erg s-l cmm2 sr-r at 40”), the value measured at 2.25 Ra at 40”, N 4.52 x 10e2 erg s-l cmm2 sr-‘, is larger by 50 % than that

527

Lyman a Intensities in a Polar Coronal Hole From a 2D Model I”“I”“I”_.‘I”“I”“I”__‘I”“I”“l” ---g-O __ .mod. Iso. . .. ..q=1 “-4 c

P

. mod. bZ.0.W

__ ;-

mod. Mlso.

q_

mod. 1-1.1.1

:.. ‘... Q: ’ ‘...

\\I @I

d

‘b

0.8 _; 0.8 \ z 0.4

1.5

2

2.5

1.5

2

2.5

1.5

2

2.5

‘/%I

Fig.

(a) Intensity

3.

the case Q = 0 (solid and

Q

simulated

=

1.5

while

distance at 8 = 90”.

open squares

(dashed

line),

respectively.

and observed

data.

Symbols

two different

F(l

of Ly (Y us. line),

values of the proton

a.u.) = 2.5 x lo8 cm-2s-1

two cases described

above.

(open

deviation

the observations

F(l

meaning

intensity

case (open

in the above

triangles are relative

represent

observations. as in (a).

ofLy circles

line).

(d) Relative

a vs. distance and dotted

simulated

intensities

to the case Q = (b)

Relative (open

deviations

1 (dotted

deviation

(c) Ly CYintensity

a.u.) = 2.0 x lOa crne2se1

circles and dotted

(e) Simulated

and fully anisotropic

represent

the same

flux at 1 a.u.:

and solid line) from

Asterisks have

Open

and open circles

Asterisks

from observations refer

for

and solid line),

at 19 = 90” in the isotropic

line).

between

VS. distance

squares

in line)

to data.

in the

(open squares (f)

Relative

two cases.

at 90”, N 2.93 x 10T2 erg s-l cmm2 ST- ‘. The Ly cr intensity is reasonably well reproduced at all latitudes and distances (within 30 - 40 %), except at a few points at high distances at latitudes between 40” - 60”. In this study we have shown that the predictions of Ly Q intensities based on the semiempirical model we developed are in agreement with the observations made with the UVCS experiment. As a consequence, the model outflow speeds can be assumed to represent the proton outflow speed vs. distance and latitude from polar coronal holes. The decrease of the proton speed from high to low latitudes we inferred from the model, is consistent with the decrease with latitude of solar wind speed observed by Ulysses (Phillips et al., 1995). We also showed that our results favour an isotropic distribution of H atoms kinetic temperatures. ACKNOWLEDGEMENTS LZ and GP acknowledge support mission of international cooperation

from Agenzia Spaziale Italiana between ESA and NASA.

for the UVCS experiment.

SOHO is a

REFERENCES Banaszkiewicz M., Axford W. I., McKenzie, J. F., An analytic solar magnetic field model, A&A, 337, 940, 1998. Goldstein, B. E., Neugebauer, M., Phillips, J. L., Bame, S., Gosling, J., et al., ULYSSES plasma parameters: latitudinal, radial, and temporal variations, A&A, 316, 296, 1996. Guhathakurta M., Holzer T. E., Density structure inside a polar coronal hole, ApJ 426, 782, 1994.

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L. Zangrilli ef al.

-3

Fig. 4. (a-f) Radial profiles of Ly CYintensity. asterisks.

The relative

deviations

Simulated

between simulated

intensity

is represented

by open squares, observed by

and observed data are shown with full squares.

Guhathakurta M., Fludra A., Gibson S. E., et al., Physical properties of a coronal hole from a coronal diagnostic spectrometer, Mauna Loa Coronagraph, and LASCO observations during the Whole Sun Month, J. Geophys. Res., 104, 9801, 1999. Kohl, J. L., Esser, R., Gardner, L. D., Habbal, S., Daigneau, P. S., et al, The Ultraviolet Coronagraph Spectrometer for the Solar and Heliospheric Observatory, Solar Phys., 162, 313, 1995. McComas, D. J., Barraclough, B. L., Funsten, H. O., Gosling, J. T., Santiago-Muiioz, E., et al., Solar wind observations over Ulysses’ first full polar orbit, J. Geophys. Res., 105, 10419, 2000. Phillips J.L., Bame S.J., Barnes A., et al., Ulysses solar wind plasma observations from pole to pole, Geophys. Res. Lett., 22, 3301, 1995. Raymond, J. C., Kohl, J. L., Noci, G., Antonucci, E., Tondello, G., et al., Composition of Coronal Streamers from the SOHO Ultraviolet Coronagraph Spectrometer, Solar Phys., 175, 645, 1997. Saito, K., Makita, M., Nishi, K., Hata, S., A non-spherical &symmetric model of the solar K corona of the minimum type, Ann. Tokyo Astron. Obs., 12, 51, 1970. von Steiger, R., Schweingruber, R. F. Wimmer, Geiss, J., Gloeckler, G., Abundance variations in the solar wind, Adv. Sp. Res., 15, 3, 1995. Withbroe, G. L., Kohl, J. L., Weiser, H., Munro, R. H., Probing the solar wind acceleration region using spectroscopic techniques, Space Sci. Rev., 33, 17, 1982. Zangrilli, L., Poletto, G., Nicolosi, P., Noci, G., Latitudinal Dependence of the Outflow Speed of the Solar Wind from UVCS Observations. In: J.-C. Vial & B. Kaldeich-Schiirmann (ed.) Proc. Eigth SOHO Workshop, ESA Publications Division, The Netherlands, p. 721, 1999.