Name:Partner(s):Lab #8 The Crab NebulaIntroductionOne of the most fascinating objects of the winter night sky is the famous Crab nebula,located near the tip of one of Taurus the Bull’s horns. The nebula was discovered by thewell known French astronomer, Charles Messier, in 1758. It is the first object in his catalogof nebulous objects of the night sky that he began compiling in 1764. The Crab nebula is infact the remnants of the bright supernova of 1054. This supernova was recorded by Chineseastronomers to have been visible during the day for 23 days and in the nighttime sky for twoyears.In 1968 , radio astronomers Staelin and Reifenstein found the stellar remnant at the core ofthe nebula - a neutron star! This neutron star spins on its axis 30 t imes a second. The star’smagnetic field causes it to emit beams of light from its magnetic polls. These twin spotlightbeams sweep by the Earth, causing the neutron star to app ear to blink on and off. Becauseof this flickering, the neutron star is also called a “pulsar.”The purpose of this lab is to learn about a number of fascinating properties of the CrabNebula, including its appearance, radiation mechanisms, expansion rate, age, distance, andsome of its spectral properties.Finding the Crab Nebula’s AgeFo r this par t of the lab, you will need t he photographs taken of the Crab nebula in 1973 and2000 so that you can find the rate of expansion (both of these photographs are negatives so thebrightest spots appear dar k). The location of the pulsar is indicated in the following image:Astronomy 101 8 – 1 Introduction to Astronomy1 (2 pts). To estimate how long the Crab Nebula has been expanding, you must first obtainthe scale for each photograph (at the end of the lab). In both cases, measure the distancebetween t he two marked stars in millimeters, estimating to the nearest 0.1mm (in otherwords try to judge the distance in between each millimeter tick mark). Knowing that theangular distance between the stars is 385 arcseconds, find the scale of each photo in units of[arcseconds/mm].DateDistance Between MarkedStars (mm)Photographic Scale(arcseconds/mm)197320002 (2 pts). ( a) Carefully locate the pulsar as indicated in the diagram above.(b) Identify 10 relatively well-defined knots in the filaments around the peripheryof the Crab on both photos. Be sure to distribute your selections ar ound the nebula as muchas possible, and select at least f our knots near the edges of the minor axis of the nebula.The term minor axis is used to refer to the shortest dimension across the nebula. Clearlynumber the knots you select on both photos so you don’t confuse them.3 (5 pts). Now use a millimeter ruler to measure the distance of each knot, to the nearest0.1 mm, from the pulsar on both photos. Note: knots are fainter and fuzzier than starswhich are darker and circular. Write yo ur results in Table 2 under the columns labeled r1973 and r 2000 (r stands for radius).4 (2 pts). Use the correct scale from step (1) to obtain the angular distances of the knotsfrom the pulsar, q, by converting r into q and fill in the corresponding spaces in Table 2.5 (2 pts). We will now calculate the average speed of the ejected material in the knotsrelative to the central pulsar. The angular velocity of any knot, w, is given by the expressionw = dq/dt (1)where dq is the angular change in position of a knot, and dt is the interval in time betweenthe two photos (i.e. 27 years). Using this formula, calculate w for each knot in units of[arcseconds/year] and enter the results in Table 2.6 (2 pts). Knowing the angular speed, w, and the angular position, q, of each knot in 1973,we can solve for the tota l time, T since the explosion using the simple relationT = q/w (2)Find the estimated time since the explosion for each knot a nd place the results in Table 2.7 (2 pts). The mean scatter in dq, where dq is the change in the angular distance of eachknot from the pulsar, gives an indication of the random errors in your distance measurements.Indicate the mean error in the space provided below Table 2.Astronomy 101 8 – 2 Introduction to AstronomyKnot #r 1973(mm)q 1973(”)r 2000(mm)q 2000(”)dq (”)w(”/yr)T (yr)123456789108 (3 pts). Calculate the mean of the 1 0 T values you obtained, then use this to calculatethe date of the supernova occurred.(a) The mean T is(b) Thus, the date of the explosion, a ccording to your results, was9 (2 pts). Use your spread in values of T (and the following equation) to estimate yourandom uncertainty:∆T =largest time − shortest time2(3)The uncertainty in T is.10 (2 pts). When calculating the date of the supernova explosion, what have you assumedabout the velocity of the gaseous knots?11 (3 pts). Compare your value fo r the date of the supernova event to the accepted valueof year 1054. What does this suggest about t he expansion velocity of the nebula? Explain.Astronomy 101 8 – 3 Introduction to AstronomyFinding the Distance to the NebulaIn terms of the velocity of expansion, v [km/sec], and the expansion rate, w [arcseconds/yr],measured between 197 3 and 2000, we can compute the distance to the Crab nebula.To do this, recognize that in its actual motion, v, across the plane of the sky, a knot can beconsidered as having traversed a tiny f r action of the circumference of the celestial sphere.(The total circumference is 2πd, where d is the distance from the observer to the nebula.)This fraction is just a portion of a complete 360◦angle that has been swept out by theangular motion of the knot. Thus we can set up a relation between the angular and spacialvelocities:w/365◦= v/2π (4)From the above formula, we can solve for the distance, d, in units of light years. Modifying theexpression appropriately so that v has units of [km/sec] and w has units of [arcseconds/year](along with knowing that one light year is equal to 9.46 × 1012kilometers), the distance ofthe nebula is given byd = 0.69v/w (5)So far we have found the angular rate of expansion, w, of the Crab Nebula. To obtainits distance, the equation above shows that we need to measure the linear velocity, v, bysome other method. To accomplish this, you will learn some of the spectral properties of asup ernova remnant, and use the same technique that astronomers use to measure velocitiesfrom sp ectral lines.Look at the spectrum of the Crab Nebula on the following page. In this negative image, thebright emission lines of the nebula and laboratory comparison spectra above and
View Full Document
Unlocking...