Consider a Schechter luminosity function of the form where a = 0.9, ΦΣ = -0 (L)dL = D(+) L e-(L/Lx)dL, L 0.012h3 Mpc3 and L - 1010h Lo. Calculate the total number density. Express the final answer in terms of h where h = Ho/(100 km s−¹Mpc¯¹) (Ho is the Hubble constant).

Question 2: apparent magnitude my 1 = 305.9, b = −44.9 and is d=4.5 kpc from the Sun. a.) The integrated light from the Milky Way globular cluster NGC 104 has an 4.03 mag and absolute magnitude My -9.52 mag. It is located at b.) = = Estimate the amount of extinction between the Sun and 47 Tucanae in magnitudes. What does this value of extinction mean for the amount of attenuation by dust between Earth and NGC 104?.

As a mass m of gas falls into a black hole, at most 0.1mc2 is likely to emerge as radiation; the rest is swallowed by the black hole. Show the Eddington luminosity for a black hole of mass M is equivalent to 2*10-9 Mc2yr-1. Explain why we expect the black hole's mass to grow by at least a factor of e every 5*107 years. Where Edding Luminicity is defined as LE=(4piGMmpc)/(sigmaT), where G is the gravitational constant, M is the mass of the black hole, mp is the mass of a proton, c is the speed of light, and sigmaT is Thomson scattering where sigmaT=6.653*10-25 cm2.

Suppose a quasar is shining with a luminosity L.  What is the approximate minimal mass of the black hole?  (If the black hole had a lower mass than this, the pressure in the material would overcome the gravity of the black hole and the material would be blown apart.) Give your answer in solar masses, in scientific notation to one significant figure (no decimal places). Value: L=1×10^12Lsun​ Suppose the quasar in the previous problem is 10% efficient at turning rest mass into energetic photons, according to Einstein's equation E=mc2.  What is the necessary rate of accretion of mass onto this black hole, to sustain its luminosity of 1* 1012 solar luminosities -- i.e. how much mass must be 'fed' to this black hole to keep the AGN shining so brightly?   Give your response in units of solar masses of material per year, with one decimal place.

A main sequence star of mass 25 M⊙has a luminosity of approximately 80,000 L⊙. a. At what rate DOES MASS VANISH as H is fused to He in the star’s core? Note: When we say “mass vanish '' what we really mean is “gets converted into energy and leaves the star as light”. Note: approximate answer: 3.55 E14 kg/s b. At what rate is H converted into He? To do this you need to take into account that for every kg of hydrogen burned, only 0.7% gets converted into energy while the rest turns into helium. Approximate answer = 5E16 kg/s c. Assuming that only the 10% of the star’s mass in the central regions will get hot enough for fusion, calculate the main sequence lifetime of the star. Put your answer in years, and compare it to the lifetime of the Sun. It should be much, much shorter. Approximate answer: 30 million years.

The visible section of the Universe is a sphere centered on the bridge of your nose, with radius 13.7 billion light-years. (a) Explain why the visible Universe is getting larger, with its radius increasing by one light-year in every year. (b) Find the rate at which the volume of the visible section of the Universe is increasing.

(a) Estimate the Eddington luminosity of a 0.072 M, star and compare your answer to the main-sequence luminosity given in Problem 21. Assume k = 0.001 m² kg¯'. Is radia- tion pressure likely to be significant in the stability of a low-mass main-sequence star? (b) If a 120 Mo star forms with log1o T. = 4.727 and log1o(L/Lo) = 6.252, estimate its Eddington luminosity. Compare your answer with the actual luminosity of the star.

A student wants to determine the Stefan-Boltzmann constant, o. The student then measures the 3) luminosity, surface area, and temperature of an object. The temperature of the object is changed several times. The student measures the new temperature and luminosity for each of the new cases. The surface area is assumed to be the same in each case. The data is then plotted to determine the Stefan-Boltzmann constant. The student knows that the relationship between these quantities is given by the Stefan-Boltzmann Law: L= GAT* (19) To determine the Stefan-Boltzmann constant we need to transform the data, that according to the theory will be a 4th degree polynomial, to form a straight line. How do we transform the data so that the graph will be linear? What is the slope of the line? What are the labels for the vertical and horizontal axis of the graph? Hint: Consider how we transformed the data in case 2 from a quadratic to linear.

For the Galactic Center black hole (Sag. A*), which has mass ~4.1 million solar masses, find the maximum luminosity that could be emitted via spherical accretion of ionized gas (i.e., the Eddington limit LEdd). Express your answer as a multiple of the Qmlaxy's total luminous output, = 2.5 x 1010 L. LMW (i.e., enter the ratio LEdd/LMw).

If a circular accretion disk around a 1.4 M, neutron star has a radius of 1.00 x 105 km as measured from the center of the neutron star to the edge of the disk, what is the orbital velocity (in km/s) of a gas particle located at its outer edge? (The mass of the Sun is GM 1.99 x 1030 kg. Hint: Use the circular orbit velocity formula, V, = ; make sure to express quantities in units of meters, kilograms, and seconds.) km/s