HELIOSTAT II - MEASURING THE SOLAR ROTATION

Transcription

1 HELIOSTAT II - MEASURING THE SOLAR ROTATION SYNOPSIS: In this lab you will map sunspots, and from the movement of the spots over several days, you will determine the rotation rate of the Sun. EQUIPMENT: The heliostat, sunspot record forms, Stonyhurst disk overlays, protractor, ruler, and a pencil. WARNING: The intense solar light from the heliostat can cause instant eye damage! Do NOT look back up the beam of sunlight! Part I. Mapping Sunspots Mapping and counting sunspots is a principal method for studying solar activity. I.1 Your instructor will use the heliostat (solar telescope) to focus an image of the Sun on the wall chart holder. Position your sunspot record form in the holder so that the Sun's image is centered on the circle. Carefully trace with a pencil all of the sunspots that are visible. The diameter of the circle on your sunspot record corresponds to the average apparent size of the Sun as seen with our heliostat. Since the 's orbit is somewhat elliptical, the solar image will appear larger or smaller than the circle at different times of the year due to our changing distance from the Sun. I.2 Are we nearer or farther from the Sun than our average distance (one astronomical unit)? Explain your answer. I.3 North is not necessarily at the top of the image. You can determine direction by noting which way the image shifts when the heliostat is driven in a known direction. Without disturbing your drawing, drive the heliostat briefly in the west direction, using the direction toggle on the heliostat control box. Since the field of view is now westward of its original position, the solar image appears to have shifted to the east. Follow the motion of a single sunspot. When the spot clears the disk circle, make an "X" at its new position and label it "earth east" (see the attached example).

2 I.4 Remove the form from the holder. Record the date, time, and the name(s) of the observer(s) on the form. I.5 Draw a line from the original position of the selected sunspot to its final location. This line is parallel to the 's equator. Use a protractor to draw a second line perpendicular (90 ) to the equatorial line and through the center of the solar disk. The new line marks the projection of the 's axis of rotation onto the disk of the Sun. Label the upper end of the line N earth (for "earth north") and the lower end S earth (for "earth south"). The 's and the Sun's axes of rotation are not aligned with each other: the 's north pole is aimed approximately towards Polaris in Ursa Minor, while the Sun's north pole is oriented about 26 away towards the star Delta Draconis. As a result, when we view the Sun from the at different times during the

3 year, the Sun's north pole may appear tilted eastward or westward of the 's, or tipped towards or away from us. The number of angular degrees of tilt and tip are defined by two angles, P and Bo, as described below. The angle P describes how much the north pole of the Sun is tilted, in the plane of the sky (or the plane of your paper), towards the east (or west) from north. A positive angle P means the Sun's north pole lies to the east of N earth. N sun P North + - Looking towards the Sun from the East Sun West Plane of sky and drawing paper South S sun

4 The angle Bo describes how much the north pole of the Sun is tipped towards (or away from) you, the observer on. A positive angle Bo means that the north pole of the Sun is tipped towards the (so that the north pole of the Sun would, at least theoretically, appear on your drawing). B o - + N sun North Sun Looking sideways at the Sun and South S sun Plane of sky and drawing paper I.6 On your form, record the orientation angles P and Bo for the day of your observation. The angles are listed in Section C of the Astronomical Almanacfor each day of the year. I.7 Use a protractor to draw a line through the center of the solar image at an angle P from the N earth -S earth line; remember, the line should lie to the east (left) of north if P is positive, and to the west (right) if negative. This line marks the solar meridian, the north-south line dividing our view of the Sun into eastern and western hemispheres. Mark the upper end of the solar meridian N sun (solar north) and the lower end S sun (solar south). The Stonyhurst disk overlay will help you find the latitude and longitude of the sunspots. The grid is marked every 10 in latitude north and south of the solar equator, and every 10 east or west of the solar meridian line. I.8 Choose the Stonyhurst overlay with a Bo closest to the actual value corresponding to your observation. Center the circle of the Stonyhurst disk over your circular drawing, with the axis aligned with the solar meridian. Be sure that the correct sign (+ or -) for Bo appears at the top of the overlay. I.9 Number the prominent sunspots (see the attached example). Estimate, to the nearest degree, the solar latitude (N or S of

5 the solar equator) and solar longitude (E or W of the solar meridian) of every numbered spot. Part II. The Sunspot Cycle The number of sunspots is observed to grow and decline over a period of approx-imately 11 years; this phenomenon is known as the sunspot cycle. (The polarities of the sunspot magnetic fields reverse with each visible cycle, so the true cycle actually takes 22 years to repeat.) At the beginning of a new 11-year cycle, sunspots first appear at high latitudes (approximately 40 north and south of the solar equator). As the cycle progresses, the average latitude of sunspot occurrance slowly shifts to lower latitudes, so that near the end of the cycle, the majority of the sunspots appear around 10 north or south of the equator. The chart below shows the latitudes at which sunspots have occurred over the past 80 years. Although spots can appear at nearly any latitude, note the trend from high to low latitudes in each cycle; the appearance of the distribution has given the chart its name: the butterfly diagram.

6 SUNSPOT NUMBER SOLAR LATITUDE DATE The lower chart shows the annual average sunspot number; it clearly illustrates the cyclical nature of solar activity. The number is computed as follows: { (# of Spots) + (# of Groups x 10) } x Correction Factor = Sunspot Number. Every visible spot is counted, including each tiny individual spot as well as those appearing in groups. To this is added the number of distinct sunspot groups, which count as an additional 10 spots each. The sum is multiplied by a correction factor which takes into account the size of the telescope, the location, and the experience of the observer. II.1 Analyze the distribution of today's sunspots with latitude. What is the highest latitude (in either hemisphere) at which a spot occurs? The lowest latitude? Estimate the average latitude of all sunspots, regardless of northern or southern hemisphere.

7 II.2 Estimate the sunspot number according to the formula; assume a correction factor of 2.0. Compare your sunspot number with the official count from the previous day (your instructor will show you how to get this data from the GOES satellite link in the classroom). Although a single day's (or even month's) data is insufficient to characterize the solar activity, it is frequently possible to get a rough estimate of the current phase of the sunspot cycle from a single observation. II.3 What do you estimate is the current phase of the 11-year sunspot cycle, based upon the observation and drawing you have just made? Critically analyze your data and defend your assessment in writing, taking into account both the latitude distribution of spots and the sunspot number. Do the observations agree with what you would expect for this date, based an extrapolation of the trends in the above diagrams? Part III. Solar Rotation Over the course of several days, sunspots are observed to move across the disk of the Sun. By observing the day-to-day motion of the sunspots, we can determine the solar rotation rate. III.1 III.2 Obtain a copy of a Solar Record Form from your lab instructor that contains sunspot observations of the Sun made about two to three days ago. The two maps must have several recognizable sunspots in common. Repeat steps I.5 through I.9 for the previously-made drawing in order to establish the lines of latitude and longitude (be sure to check the Astronomical Almanac for the P and Bo values on that date). Identify sunspots that appear on both maps, and assign them the same spot label; use the appearance, relative location, and latitudes of the spots to aid in the identification. Measure the latitude and longitude of these spots as before, using the appropriate Stonyhurst overlay.

8 III.3 III.4 III.5 Confirm that individual sunspots do not shift significantly in latitude over time, suggesting that any apparent change in longitude is due to the rotation of the Sun rather than random spot movement. For each sunspot, determine the angle that it appears to have rotated between observations (treat E longitudes as negative, W longitudes as positive, and subtract the first longitude measurement from the second). Average your measurements from the different spots to produce your best estimate of the observed rotation angle. Determine the number of hours between the two observations, and convert the time interval into fractional days. Divide the observed rotation angle by the elapsed time in days to determine the apparent solar rotation rate in degrees per day. The orbits around the Sun at a rate of 360 in one year (365 days), or an average motion of almost exactly 1 per day (this is probably not a coincidence; it is generally assumed that ancient astronomers/mathemeticians divided the circle into 360 parts for just this reason!). Since we orbit the Sun in the same direction that it rotates, our motion "chases after" the sunspots; thus, the apparent movement of spots is less than their actual rotation by about 1 per day. III.6 Compensate for the orbital motion of the by adding 1 to your computed apparent daily rotation. III.7 Use your daily solar rotation rate to compute the average rotational period of the sunspots: the number of days that it takes for a sunspot to travel 360 around the Sun. Compare your measurement of the rotational period of the Sun with the textbook. Discuss known or suspected sources of error in your measurement.

9 SUNSPOT RECORD FORM Observers Names: EXAMPLE (Finished Drawing) N sun N earth Date Time P B o August 18th, :45 am MDT o o P East #1 #4 #3 #2 Major Sunspots S earth S sun o 25 N 12 o W 1 o 12 o S 38 E o S o 16 S 11 o W 41 o W

10 SUNSPOT RECORD FORM Observers Names: Date Time P B o Major Sunspots

11 SUNSPOT RECORD FORM Observers Names: Date Time P B o Major Sunspots