Question

V value Determine the B - The y-axis contain stars that are in distance as the cluster.) of the turnoff (TO) and the age of each of the clusters in Figure 22.4. the images, but not part of the cluster. Thus, they may not be at the same is the measured V apparent magnitude. (These plots represent real data, and may Pleiades M 67 10 S 12 6 10 트 14 15 16 0 0.5 1 1.5 B-V Color Index 1.5 0.5 B-V Color Index NGC 2384 12 16 4. 20 0 0.5115 B-V Color Index FIGURE 22.4

Answer 1

Solution:-

Pleiades NGC 2682 0 0.5 10 15 B-V(mag) 05 L0 1 B-V(mag) B-V(ma Figure 22.4. Actual color-magnitude diagrams of three open clusters; what real data look like. The main sequence (which runs from right-bottom to left-top in a typical CMD diagram) is marked in orange in the above three diagrams. The leftmost top point of the main sequence denotes the Turn off point. The age of a star in the main sequence is calculated as MS T-1010 years Mstar (Lstar 1/4 Msun Lsun Lstar 10-04(star's absolute magnitude-4.85) Lsun Mstar 10-01 1(star's absolute magnitude-4.5)solar masses Msun Lstar = 10-04(star's absolut e magnitude-4.25) Lsun

Mstar 10 Msun 10-0.1(star's absolute magnitude-4.85) 0.1 (star's absolute magnitude-4.85)c In the CMD diagrams above, the apparent magnitude is provided. To the actual magnitude (the color index ys absolute magnitude graph provided at this reference,

15. B-V Turnoff-value = 0 star's absolute magnitude (m) = 1.2 Age = 8.035*10·years 16. B-V Tucnoff value 0.5 ster's absolute magnitude (m) 4 Age 5.559*10 veacs 17. B-V Tucnoff value 0.75 star's absolute magnitude (m)5.5 Age 6.38 10s years 18. Star clusters can be defined as groups of stars that appear concentrated in small regions of the sky It can be safely assumed that all the star members of a cluster have formed at the same time instant from a single primordial cloud of gas and dust, thus those individual stars achieve the following common features (a) They lie at the same distance from us (b) They have the same chemical composition and therefore,stellar clusters become ideal specimens to study the evolution of stars Generally H-R (Hertzsprung-Rusell) Diagrams are used to study star clusters, but a great simplification to these diagrams are the CMDs (Color Magnitude Diagrams). The horizontal variable is the radiation difference measured fromtwo different wavelengths (the colour index) and the vertical axis denotes the Luminosity/Magnitudes, Luminosity or absolute magnitude values implies the actual distance to the stars needs to be known, which is often not possible. Thus, often an apparent magnitude (often some color index), which does not depend on distance, is used as the vertical axis in CMDs. For stars lying at the same distance from us (as it certainly is the case for stellar clusters), their apparent magnitudes share a common factor of proportionality with their absolute magnitudes. Thus with a proper calibration chart the apparent magnitudes can be converted to absolute magnitudes and used for analysis. Lwnich is often not posible. Thus ohe verical aCMDs. For sars les

The formulae mentioned above can be used to calculate the age of stars using CMDs. All stars evolve with time; some do it veryfast, some very slowly, essentially depending on their masses. The more massive a star is, the lesser is its lifetime. Also, the mass defines the kind of process to perform in its final period of life. Almost independently of its mass, from birth up to 90% of its lifetime all stars evolve in a very similar fashion. They spend most of their lives burning hydrogen slowly in a state of stable equilibrium, and this is the reason why a typical H-R diagram does not show randomly scattered points over the entire graph, but mostly concentrated on a band stretching diagonally from right-bottom to left-top. This band is called the Main Sequence, and goes from the upper left (hot, luminous, blue stars) to the lower right (cool, dim, red stars) When the hydrogen supply in the core of the star is depleted, hydrogen burning is not possible anymore. This ends the main sequence phase of the star's life, and thereafter it moves out towards the upper right in a CMD. This new accessed region is known as the Red Giant Branch,and signifies the initial stages of the helium burning phase