---
abstract: 'We present a visual determination of the number of bright points (BPs) existing in the quiet Sun, which are structures though to trace intense kG magnetic concentrations. The measurement is based on a 01 angular resolution G-band movie obtained with the Swedish Solar Telescope at the solar disk center. We find 0.97 BPs Mm$^{-2}$, which is a factor three larger than any previous estimate. It corresponds to 1.2 BPs per solar granule. Depending on the details of the segmentation, the BPs cover between 0.9% and 2.2% of the solar surface. Assuming their field strength to be 1.5 kG, the detected BPs contribute to the solar magnetic flux with an unsigned flux density between 13 G and 33 G. If network and inter-network regions are counted separately, they contain 2.2 BPs Mm$^{-2}$ and 0.85 BPs Mm$^{-2}$, respectively.'
author:
- 'J. Sánchez Almeida, J. A. Bonet, B. Viticchié, D. Del Moro'
title: Magnetic bright points in the quiet Sun
---

Motivation {#intro}
==========

Our understanding of the quiet Sun magnetic magnetic fields has turned over during the last decade. Traditional magnetograms showed magnetic signals only at the network boundaries, occupying only a small fraction of the solar surface, and mainly produced by spatially unresolved kG magnetic concentrations [e.g., @bec77b; @sol93]. Nowadays magnetic signals are detected almost everywhere [e.g., @dom03a; @har07; @lit08], and there is no doubt on the presence of a volume filling component of dG and hG fields as inferred from the Hanle depolarization signals [e.g., @fau93; @tru04]. The intra-network (IN) magnetic fields have passed from hardly delectable signals in long-integration low spatial resolution magnetograms [e.g., @mar88; @wan95], to ubiquitous features [e.g., @lin99; @san00].The abundance of new magnetic structures makes them potentially important to understand the global magnetic properties of the Sun [@san04; @tru04], and also makes it unlikely that the quiet Sun magnetism results from the decay of active regions [e.g., @san03b]. Since the quiet Sun magnetic fields do not seem to be debris from active regions, they are not automatically generated by the dynamo responsible for the solar cycle. A different production mechanism seems to be at work, probably an efficient turbulent dynamo driven by granular convection [@pet93; @cat99b], an hypothesis corroborated by the latest numerical simulations of granular magneto-convection [@vog07; @pie10]. The sensitivity of the current polarimeters allow us to detect weak linear polarization signals produced by the transverse component of the magnetic fields [@har07; @lit08], and to find out that they often emerge as short loops pooping up from the sub-photosphere [@cen07; @mar09]. In agreement with the turbulent dynamo scenario, quiet Sun magnetic fields come with strengths in the full range from basically zero to 2kG [@san00; @dom06]. Even if they only fill a small fraction of the quiet photosphere, the part having strong kG fields may be particularly important from a physical point of view. Magnetic flux and magnetic energy scale as powers of the field strength, therefore, depending on their (uncertain) area coverage, kGs may surpass the contribution of the more common but weaker fields [@san04]. Moreover, buoyancy makes kG concentrations vertical [e.g., @sch86] and so, they can provide a mechanical connection between the photosphere and the upper atmosphere [e.g., @bal98; @san08]. Theoretical studies support the traditionally-ignored but potentially-important influence of the quiet Sun photosphere on the chromosphere, transition region, and corona [e.g. @sch03b; @goo04; @jen06]. Despite all these (and other) significant advances, our understanding of the quiet Sun magnetism is still incomplete. Each observational improvement reveals more magnetic structures, in a process showing no sign of having converged yet.

As a part of this movement to characterize the properties of the quiet Sun magnetism, we discovered the ubiquitous presence of bright points (BPs) in the intergranular lanes of the quiet Sun [@san04a]. The plasma in the lanes is cold and therefore dark, but the BPs look bright because they trace intense kG magnetic concentrations [@spr77]. The magnetic field provides most of the pressure required to maintain the structure in mechanical balance, which reduces the gas pressure, the density and, thus, the opacity. The kG concentrations resemble holes carved on the solar surface which allow us to peep up into the sub-photosphere, where deeper usually means hotter and brighter. This picture is confirmed by realistic numerical simulations [e.g., @car04; @kel04], and thus BPs are regarded as proxies for kG magnetic concentrations. The presence of BPs everywhere on the quiet Sun has been verified in several works, e.g., @dew05 [@dew08; @bov08; @san08]. However, none of these works find as many BPs as @san04a [0.3 BPsMm$^{-2}$]. This is partly due to the angular resolution of the images, taken with small telescopes, and also due to the use of automatic algorithms for BP identification which can hardly detect the faintest BPs. In an effort to calibrate with visual detection one of these methods [@bov01; @bov07], we repeated the tedious but otherwise accurate analysis carried out by @san04a. This time we use a G-band image of much better quality. The result of such detailed analysis is surprising, and we report it here. We find three times more G-band BPs than in the original study and, therefore, far more than the numbers reported in all the previous studies cited above. Our density implies that the quiet Sun has more BPs than granules, and at least 1% of the quiet solar surface is covered by BPs.

Observation and analysis procedure {#description}
==================================

Figure \[fullfov\] shows the image selected for in-depth analysis. It is the best in a series of quiet Sun disk center images taken with the Swedish Solar Telescope [SST; @sch02] in the G-band (a 10.8 Å wide filter centered at 4305.6 Å). The $68\farcs 5\times 68\farcs 5$ field of view (FOV) was observed on September 29, 2007. The series was restored using multi-frame blind deconvolution [@noo05] to have an angular resolution close to the diffraction limit of the SST at the working wavelength ($\simeq$01). Each snapshot results from combining 125 images, rendering a mean cadence of one snapshot every 15 s. The dataset includes simultaneous CaH line-core images, which we use to determine network boundaries. Further details are given by @bon08.

![image](f1.ps){width="90.00000%"}

The BPs were selected in a way similar to that described by @san04a. The reference image was segmented into locally bright features and background using the algorithm by @str94. We flick on the computer screen the segmented image and the true image, selecting as BPs bright structures coinciding with one of the segmented patches.

![Illustration of the visual selection procedure. (a) Low contrast image of a small subfield of the FOV (see the box in Fig. \[fullfov\]). It is used to select the brightest G-band BPs. (b) Same image as (a) shown with high contrast. Used to identify fainter BPs. (c) Binary map with the selected structures. (d) Time series (see the insets) illustrating how an uncertain BP in the reference image (time 0 sec, the arrow) was actually a clear and conspicuous BP a few minutes before (time -165 sec, the arrow). The subfield shown in the time series is marked as a box in (a). []{data-label="zoom"}](f2.ps){width="40.00000%"}

We first pinpoint obvious BPs in the intergranular lanes of the best image. In case of doubt, we play back and forth the animation with snapshots around it. We then select as BPs in our image those that along the time sequence show up as clean BPs (see the example in Fig. \[zoom\]d). Doubtful identifications were discarded. Moreover, we also include BPs that were conspicuous before or after, but which remain as faint brightenings in the reference snapshot because of evolution. The procedure was repeated using two different saturation levels for the true image. The low contrast (between 0.8 and 1.5, in units of the mean quiet Sun intensity) was used to select the brightest BPs, whereas the high contrast (between 0.7 and 1.1) was used for dimmer BPs. Figure \[zoom\]a and b contain a small part of the full FOV shown with these two different contrasts. (A box outlines the subfield in Fig. \[fullfov\].) The disk center was not fully devoid of magnetic activity during the observation. There was a small nearby active region (AR NOAO 10971[^1]), that the telescope pointing avoided. We discard the influence of this AR on the observed region with the following arguments: (1) a simultaneous [*Hinode*]{} SOT/NB Na[i]{}5896Åmagnetogram including the outskirts of the AR and the SST FOV shows that the two of them are well separated. (2) The average unsigned magnetic flux density in our FOV (29G) is within the low range of values of the signals in a magnetogram of the quiet Sun taken under the same conditions ten days later, when no AR was present. This reference magnetogram yields a signal of 34$\pm$5G, with the error bar representing the standard deviation among the signals in randomly chosen subfields with the size of the SST FOV.

Results
=======

Figure \[fullfov\] shows the result of our selection. The original G-band image has been enhanced in those segmented structures identified as BPs. One can recognize super-granulation and meso-granulation scales, although BPs are found throughout the FOV. We identify 2380 BPs, which correspond to 0.97 BPs Mm$^{-2}$. In the segmentation employed for BP selection, these BPs cover 0.89% of the surface (the so-called filling factor $f$). However, the filling factor is an uncertain parameter. (The number density of BPs is far more robust.) If the segmentation algorithm is used dilating the kernel by one pixel (roughly speaking, increasing the size of the individual BPs by 1 pixel), then the surface coverage becomes 2.2%. This other segmentation is as good as the original one as judged from visual inspection. The segmentation algorithm underestimates the area covered by the large BPs. They are split into several individual objects, and the empty space left between them does not contribute to $f$ (compare the bright continuous filaments in Fig. \[zoom\]b with the corresponding broken segmentation in Fig. \[zoom\]c). The splitting of one large object into several small pieces also enlarges our BP number density. However, this bias does not have a big impact because large obsjects are mostly in the network, and when network and IN are treated separately, the resulting number densities turn out to be very similar (see below).

We have tried to separate the contribution of network and IN. This separation is based on the Ca H images taken simultaneously with the G-band images. They are smoothed with a 4 kernel, with the bright patches above a threshold representing the network. The threshold was tuned to get a 10% area coverage, which is the kind of network surface coverage during solar minimum [e.g., @fou01; @san04]. Number densities and filling factors were separately re-computed for the pixels inside and outside the network thus defined. The number density of BPs and the filling factor of the IN are slightly smaller than the ones for the full FOV, but not so much. One gets 0.85 BPs Mm$^{-2}$ and $f=0.77$% when the full FOV rendered 0.97 BPs Mm$^{-2}$ and 0.89%, respectively. This small difference is due to the fact that BPs are found throughout, rather than being concentrated in the network. The density in the network patches is 2.2 BPs Mm$^{-2}$, whereas $f=2.2$%.

As we explain in § \[intro\], our work was originally motivated to calibrate the automatic procedure by @bov01 [@bov07]. A detailled comparison goes beyond the scope of this Letter, but the algorithm systematically underestimates the number of BPs, so that it yields 0.18 BPs Mm$^{-2}$. The patches associated to these BPs are substantially larger than those inferred here, so that $f$ remains $\simeq2$%.

Discussion
==========

According to the current paradigm, the BPs trace intense magnetic concentrations so, our observation constrains the fraction of quiet Sun plasma having kGs. Our measurement should be regarded as a lower limit since we only include secure BPs (§ \[description\]), the area of large BPs is underestimated (§ \[results\]), and diverse arguments suggest that some kGs are not bright [e.g., @san01; @vog05; @bec07]. Moreover, we miss BPs since the detectability of the small ones critically depends on the resolution [e.g. @tit96], and quiet Sun BPs are often at the resolution of the observation [e.g., @san04a; @bov08]. In fact, differences of angular resolution partly explain the lower number density of BPs previously reported in the literature (§ \[intro\]). Another part of the difference is due to the use of automatic algorithms based on single frames to detect the BPs, which are still unable to identify the smallest and dimmest BPs in the images (§ \[results\]).

Even a 1% filling factor in the form of kG fields represents a big challenge. They are not yet produced by the current turbulent solar dynamo simulations [@vog07], and they are overlooked in recent studies of the quiet Sun magnetic field strength distribution based on Stokes spectro-polarimetry [e.g., @oro07; @ase09]. Assuming that typical BPs have 1.5 kG field strengths, they contribute to the solar magnetic fields with an unsigned flux density between 13 G and 33 G depending on whether we adopt 0.9% or 2.2% for their filling factors. However, @oro07 report only 9.5 G, with field strengths dominated by hG rather than kG fields. The solution to this double puzzle may also have to do with insufficient spatial resolution. On the one hand, the amount of kG fields created by magneto-convection simulations increases with increasing spatial resolution [e.g., @bus08]. On the other hand, the standard procedure of interpreting Stokes profiles does not acknowledge the existence of unresolved structuring. When it is acknowledged, then kG fields with filling factors compatible with the limits posed here are found [@vit10].

Figure \[fullfov\] shows BPs throughout. Their abundance can be emphasized by comparison with the number of granules. There are some 0.82 granules Mm$^{-2}$ [e.g., @mul00], which implies that the quiet Sun has more BPs than granules, i.e., our image has 1.2  [BPs per granule.]{} Yet another revealing reference to compare with is the largest sunspot-group ever photographed on the Sun. It seems to correspond to a complex active region observed on April 7, 1947, which occupied $4.3\times 10^3$ millionths of solar hemisphere [@hog47]. This record-braking large sunspot yielded only $f\simeq 0.2$%, i.e., one would need several ARs like this one to carry the same unsigned flux as the quiet Sun BPs have at any time if they uniformly cover the solar surface.

The SST is operated in the Spanish Observatorio del Roque de los Muchachos by the Institute for Solar Physics of the Royal Swedish Academy of Sciences. [*Hinode*]{} is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ, NASA (US) and STFC (UK) as partners. We thank A. de Vicente for his support on the Condor[^2] workload management system used during image restoration. The work has been partly funded by the Spanish Ministries of Education, and of Science and Innovation (projects AYA2007-66502, AYA2007-63881 and ESP2006-13030-C06-04), and by the EC (SOLAIRE Network – MTRN-CT-2006-035484). [*Facilities:*]{} ,

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[^1]: It never developed fully, producing only a few pores during its peak activity.

[^2]: http://www.cs.wisc.edu/condor/
