Astronomy 490              Homework #10  (revised version!!)                       Spring 2007

 

 

Due date:   try to complete by class on Mon, April 30; accepted through Fri, May 4

 

Journal paper:  

   Faulkner et al. 2005, PSR J1756-2251: A New Relativistic Double Neutron Star

       System,  Astrophysical Journal Letters, 618, L119

 

Supplementary article:

 

   Winn 1999, The Life of a Neutron Star, Sky and Telescope, July 1999 (9 pages)

 

1.  Read the Sky & Telescope article first—it’s an excellent and easy-to-read article that provides very useful background for reading the journal article.  Note that the Sky&Tel article was not handed out in class, so you’ll need to print it yourself off the class web page (sorry about that).  Color printing is a plus (especially for the dP/dt vs. P graph).

 

2.  Read the Faulkner article carefully.  Record questions and comments on each section.

 

3.  As you learned from the Sky&Tel article, recycled pulsars are spun up by material that

     accretes onto them from a companion star.  The material, just before it hits the surface

     of the neutron star, is orbiting at circular velocity.

 

  (i)  Write down an expression for this circular velocity in terms of the radius and mass

       of the neutron star.

 

 (ii)  Compute the speed at which (the equator) of a neutron star can rotate before the star

        reaches “break-up” velocity.  (Hint:  equate the force of gravity on a mass m at the  

        equator to the centrifugal force acting on the mass, and solve for the velocity.)

        Compare this velocity to the circular velocity and comment.

 

(iii)  Find an expression for the minimum spin period (fastest spin) that a spherical object

        of mass M and radius R can have.

 

 (iv) Use the expression you derived in (iii) to compute how fast the following objects

        could spin, in principle, before breaking up (flying apart due to centrifugal force):

        a.  the Sun

        b.  the Earth

        c.  a white dwarf of mass 1.4 Msun and radius equal to that of Earth

        d.  a neutron star of mass 1.4 Msun and radius 15 km

        e.  an asteroid of radius 15 km and density equal to that of Earth 

 

Comment on the significance of your results in the context of the observed pulse periods of recycled pulsars.  What besides neutron stars could emit such rapid steady pulses?