LIFETIME OF INTRANETWORK MAGNETIC ELEMENTS
1
JUN ZHANG1 , GANGHUA LIN1 , JINGXIU WANG1 , HAIMIN WANG2 and
HAROLD ZIRIN3
Beijing Astronomical Observatory, Chinese Academy of Sciences, Beijing 100080, China
2
Big Bear Solar Observatory, New Jersey Institute of Technology, U.S.A.
3
Solar Astronomy, 264–33 Caltech, Pasadena, CA 91125, U.S.A.
(Received 28 July 1997; accepted 29 August 1997)
Abstract. Using a 10-hour time sequence of very deep magnetograms of Big Bear Solar Observatory,
we have studied the lifetime of Intranetwork Magnetic Elements for the first time. The analysis reveals
the following results:
(1) The lifetime of intranetwork elements ranges from 0.2 hr to 7.5 hr with the mean of 2.1 hr.
There appears to be a quasi-linear dependence of the lifetime on the total flux of elements.
(2) Most intranetwork elements appear as a cluster of mixed polarities from an emergence center
somewhere within the network boundary and are destroyed by three mechanisms: merging with
intranetwork or network elements of the same polarity, cancellation of opposite polarity elements, or
separation and disappearance at the position where they appear.
(3) We estimate that the total energy released from the recycling of IN elements is
1:6 1028 ergs s,1 , which seems to be comparable to the energy required to heat the corona.
1. Introduction
The Intranetwork (IN) magnetic fields are weakest in field strength and smallest in
flux in the photosphere. They were first observed by Livingston and Harvey (1975)
and Smithson (1975). In recent years progress was made in IN’s morphology
dynamics and some quantitative aspects from time sequences of deep magnetograms obtained at the Big Bear Solar Observatory (BBSO) (Martin, 1984; Wang,
Zirin, and Shi, 1985; Zirin, 1985; Wang et al., 1995, Paper 1, and references herein;
Wang et al., 1996, Paper 2). IN fields are difficult to observe because they are so
weak. Recent studies of IN fields are based on observations obtained at Big Bear
and Huairou (Beijing, China) Solar Observatories. Keller et al. (1994) and Lin
(1995) have found an upper limit on the intrinsic strength of IN fields at 1000 G
and with 68% probability at 500 G. The lifetime is an important parameter of IN
magnetic elements. Yet no reliable measurements of IN element lifetimes have
been made so far.
The magnetograms on 4 June 1992 are the best ever obtained for a quiet region
at BBSO for the study of IN elements. The magnetograms were acquired by
integrating 4096 video frames, and recording them in 16-bit memory. The 10-hour
sequence consists of 83 images with an average time resolution of 7.2 min. The
whole field of view (FOV) is 310 240 arc sec2. The pixel resolution is 0:3700 in
the X direction and 0:3800 in the Y direction. The detection limit of magnetic flux
is 1016 Mx, spatial resolution is 200 , and the sensitivity of apparent flux density is
Solar Physics 178: 245–250, 1998.
c 1998 Kluwer Academic Publishers. Printed in Belgium.
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2 G. The calibration coefficient is 0.0122 G per pixel value. Additional information
has been given in Papers 1 and 2.
2. The Lifetime of Intranetwork Elements
2.1. SAMPLE AND DEFINITION
We selected 528 intranetwork elements by identifying and tracking each of them
from birth to death (see Paper 1 on the identity of IN elements). We classified the
evolution of intranetwork elements into four possible categories:
(1) Merging of same polarity elements.
(2) Breakup into smaller elements.
(3) Cancellation of opposite polarity elements.
(4) Decaying into weak fields below the noise level (2:5 0:2 G, Paper 1).
From the sequence of magnetograms studied, we can see that most IN elements
appear as clusters of mixed polarities. Some elements are born as small ephemeral
regions, and a few are generated by separating from other IN or network elements.
If an element diffuses into weak fields below the noise level, we define it as a death.
Similarly, if an element emerges into strong fields over the noise level, it is defined
to be born. On the other hand, when an element A breaks into elements B, C and D,
A is said to die, while B, C and D are born. When elements E and F merge together
and form another element G, E, and F die, G is born. The lifetime of an element is
the duration from its birth to death over the noise level.
2.2. LIFETIME DERIVED BY THE STATISTICAL METHOD
From the 10-hour sequence of observations, we were able to follow 528 intranetwork elements from birth to death. Figure 1 shows a histogram of the lifetime of
these elements. The lifetimes of these elements range from 0.2 hr to 7.5 hr with a
peak distribution at 1.5 hr. The mean lifetime is 2.1 hr with a standard deviation of
1.4 hr.
We also measured the flux of each element. Figure 2 shows the relationship
between the flux and lifetime. As one can see, the larger the flux, the longer the
lifetime, and there appears to be a quasi-linear dependence of lifetime on flux.
The IN magnetic elements emerge mainly in clusters of mixed polarities from a
localized area within a network cell. We call such an area a flux-emergence center.
In Figure 3, an example of a cluster emergence is shown. The letter ‘A’, labelled
at 15:35:16 UT, indicated the site of an emergence center, as judged from the time
sequence of magnetograms. A pair of IN elements emerged at 15:47:10 UT (within
the brackets). The positive polarity element (white) disappeared at 17:00:43 UT
without interaction with other elements; the negative polarity element (black) ‘cancelled’ with a positive one of another couple of emergent IN elements on the right
LIFETIME OF INTRANETWORK MAGNETIC ELEMENTS
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Figure 1. The histogram showing the distribution of intranetwork element lifetime.
and merged with the negative element at 17:00:43 UT. Then the merged negative
polarity element cancelled with a network element at 18:43:48 UT.
2.3. UNCERTAINTY
The lifetime we derived from the data contains uncertainties. We may have underestimated the lifetime of every IN element. For example, when an IN element diffuses
into weak field below the noise level, we define it as dead, but in fact it may still
exist. On the other hand, a lifetime shorter than 0.3 hr may be limited by the time
resolution and seeing conditions, and a lifetime longer than 7.5 hr may be limited
by the length of observation time. For this reason, perhaps we have excluded some
short-lived and long-lived IN elements. Looking at the distribution of the lifetime
from Figure 1, it is obvious that more than 80% of IN element lifetimes range from
0.5 hr to 5.5 hr, so our results about the lifetime of IN elements may be valid.
3. Discussion
In Paper 1, we derived the mean number density and the flux of IN elements. When
an IN element is pushed into the network, if it has the same magnetic polarity as the
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Figure 2. Plot of the relationship between flux of IN elements and lifetime.
network element, the IN element will simply merge with network and no energy
will be released. If it has the opposite polarity, it will ‘cancel’ with the network
element, likely by slow magnetic reconnection, and some magnetic energy will be
released due to the reconnection. In Paper 2, we estimated the amount of the energy
which might be released in IN-network encounters. With the new finding of the
lifetime of IN elements, we can make a better estimate of the energy. In Paper 1,
we found that the mean number density of IN fields is 3.5 per 100 arc sec2, i.e.,
N = 4:05 105 over the whole Sun, the mean lifetime is T = 2:10 hr, so the
replenishment rate of IN fields is then R = N=T = 53:6 element s,1 . Suppose
half of the IN elements ‘cancel’ with network elements and release energy. This
energy dissipation rate can be estimated to be
dE
dt
= B8 2NT V = 12 B 8F RH ;
2
(1)
where V is the volume and H is the depth of an IN element. For a conservative
reckoning, we adopt H as half the scale height of horizontal supergranular flows,
which was found to be 1200 km (November, 1994), B = 500 G (Lin, 1995;
Keller et al., 1994) and F = 2:5 1017 Mx (Paper 1). We then obtain dE=dt =
LIFETIME OF INTRANETWORK MAGNETIC ELEMENTS
249
Figure 3. Time sequence of magnetograms showing the evolution patterns of IN elements. The
letter ‘A’ labelled at 15:35:16 UT indicates the site of an emergence center. A pair of IN elements
emerged at 15:47:10 UT (within the brackets); the positive polarity element (white) disappeared at
17:00:43 UT and had no interaction with others; the negative polarity element (black) ‘cancelled’ with
a positive one of another couple of emergent IN elements on the right and merged with the negative
element at 17:00:43 UT. Then the merged negative polarity element cancelled with a network feature
at 18:43:48 UT.
1:6 1028 ergs s,1 . This is comparable to the energy needed to heat the corona,
i.e., 1:8 1028 ergs s,1 (Withbroe and Noyes, 1977).
In Paper 1, we found that, in this same region, 22% of total flux was in the form
of IN magnetic flux (6:3 1020 Mx) and 78% in the form of network magnetic
flux (2:2 1021 Mx). Liu et al. (1994) have given the mean lifetime of network
elements as 50 hr. We can deduce that, in this region, the average disappearance
(or birth) rate of total flux in IN elements is 7 times larger than that of network
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magnetic flux, i.e., 8:3 1016 Mx s,1 for IN elements and 1:2 1016 Mx s,1
for network elements. Furthermore, over the whole Sun the average disappearance
(or birth) rates are 1:3 1019 Mx s,1 for IN elements and 1:9 1018 Mx s,1 for
network elements, respectively.
Acknowledgements
We would like to thank Drs Yuanyong Deng and Yunchun Jiang for many useful
comments. This work is supported by the Major Project 19791090, funded by National Natural Science Foundation of China (NSFC), US NSF CAREER Award
ATM-9628862 to Wang and NSF China–US collaboration grant INT-9603534.
References
Keller, C. J., Deubner, F. L., Egger, U., Fleck, B., and Povel, H. P.: 1994, Astron. Astrophys. 286, 626.
Lin, H.: 1995, Astrophys. J. 446, 421.
Liu, Y., Zhang, H., Ai, G., Wang, H., and Zirin, H.: 1994, Astron. Astrophys. 283, 215.
Livingston, W. C. and Harvey, J.: 1975, Bull. Amer. Astron. Soc. 7, 346.
Martin, S. F.: 1984, in S. L. Keil (ed.), Small-Scale Dynamical Processes in Quiet Stellar Atmospheres,
Sunspot, NM, p. 30.
November, L.: 1994, Solar Phys. 151, 1.
Smithson, R. C.: 1975, Bull. Amer. Astron. Soc. 7, 346.
Wang, J., Zirin, H., and Shi, Z.: 1985, Solar Phys. 98, 241.
Wang, H., Tang, F., Zirin, H., and Wang, J.: 1996, Solar Phys. 165, 223 (Paper 2).
Wang, J., Wang, H., Tang, F., Lee, J. W., and Zirin, H.: 1995, Solar Phys. 160, 277 (Paper 1).
Withbroe, G. L. and Noyes, R. W.: 1977, Ann. Rev. Astron. Astrophys. 15, 363.
Zirin, H.: 1985, Australian J. Phys. 36, 961.