# How smooth is the Sun?

### Science Nugget: June 22, 2001

### Introduction

Theoretically, the Sun's apparent surface is really smooth. The layer we see (the photosphere, the point at which radiation decouples from matter) has a known temperature, and the Sun has a known mass and size. These facts suffice to determine that the thickness of the solar atmosphere at this point should be about 0.02% of the solar radius. This corresponds to a 2-mil tolerance on a ten-inch part, in machinist's parlance, not a bad job. But this is not the whole story, just the theoretical beginning of it. We know of many potential causes of solar roughness, including (on the largest scale) the fact of solar rotation. This will cause some oblateness, which in fact theoretically would be less than the 0.02% estimated above. But there are other things.

The study of solar roughness has an interesting history and many implications. It is a difficult art for an astronomer, because it involves the 3rd dimension (in this case height above some reference point, e.g. a layer specified by its opacity to a given wavelength - often 5,000 A as an arbitrary choice). Beyond that all is relative. Only advanced techniques such as modeling the limb darkening profile or by looking for little wiggles at the actual limb (edge) of the Sun could one make much progress. Studying the limb directly requires telescopes of high resolution, and to date X-ray telescopes have not had the needed resolution. Hence, we turn to desperate measures such as making maximum use of a solar eclipse.

### Using an eclipse as a knife-edge: predictions

Eclipses of the Sun by the Moon, as seen from low Earth orbit, have fascinating geometrical properties. Please see our earlier science nuggets on various eclipses in the past (get them from the nugget search engine, or from the topical index, or in particular look at this one. The limb of the Moon moves across the solar features (inexorably!), and because the Moon is cold and solid, its limb is exceedingly sharp. There are of course mountains on the Moon, which give rise to the phenomenon known as "Bailey's Beads".

Yohkoh had great timing for the eclipses that took place June 21 (also a solstice, of course, making it all the more appropriate that the Moon should execute a "stillstand"). We'll repeat the prediction we made last week, based upon M. Soma's calculations:

Java Script (2 Mbyte) -- MPEG (295 kbyte)

This cunning movie shows that the limb of the Moon hovers just above the limb of the Sun, and moves slowly back and forth across the limb. We have worked out the detailed timing of these phenomena

### Using an eclipse as a knife-edge: results

The following movies show the actual event, in close-up detail since we had to sacrifice the full-Sun images to get more data

Java Script (1.1 Mbyte) -- MPEG (177 kbyte) -- GIF (1.1 Mbyte)

More quantitatively, we can plot the signal as a function of time. The timing of the events in the eclipse is the first concern; eventually we will study the rapidity of the eclipse effects to measure or set limits on the extent of photospheric roughness - not a lightweight analysis task, especially because of the low signal-to-noise level.

The plot below simply shows the brightness of the central rows of the images above, but starting much earlier - the initial drop in signal shows the arrival of the Moon over the SXT field of view; the peak later on shows the peek at the corona below the lunar "knife-edge".

In the plot above the dotted line shows the half-signal level, and the times the signal intersects this are roughly 12:45:08 and 12:47:52 UT. These can be compared with the contact times read from the graph in the detailed plot we made of Soma_san's ephemeris. It shows a 10-15 second discrepancy, entirely consistent with the known imprecision of our knowledge of Yohkoh's orbit.

### Conclusions

Wheee! We did it! This was one of the trickier observing programs for Yohkoh, rivaling the Mercury transits, and as usual we thank R. Kano, T. Sakao and T. Watanabe in particular for help with hexadecimal commands to the spacecraft, as well as for general counsel. Now we look forward to some serious data analysis. From our present knowledge, we do not expect that the accuracy we'll achieve here will successfully detect an extended solar atmosphere, but the fact that we really don't know, and that this is the very first observation of its kind, means that we will look. Perhaps if TRACE did the same experiment, its superior data flow and angular resolution would lead more easily to a good measurement. It all depends upon celestial mechanics.

June 22, 2001