READ: Chapter 11.1, 11.2 (11.2.1, only), 11.3(

HW READ: Chapter 11.1, 11.2 (11.2.1,11.2.2 only), 11.3( 11.3.1,11.3.2 only), 11.4,11.5 Question 11.2(HW#15) Problems 1(HW#16) (part a: recall: basic KE=1/2mv 2,Part tb: recall momentum conservation M f v f =M i v i), 2(HW#17)( use equation 1.2b) 7(HW#18). (hint: if KE =GPE then the V is the escape velocity..eq 1/2 mv 2 =GMm/R) M=neutron star mass m=particle mass computer problem 1(HW#19)(see example 11.3 for g at surface and page 198 for dg/dr set up a spread sheet with formulas hand in and also show formulas used!)

Iron absorbs energy from gravitational energy Released during the collapse And Fe breaks apart releasing p+ that combine with e- of the star

Collapses in one second what happens next is not completely understood

(in LMC) Called a TYPE II supernova TYPE 1 are in Binary systems with a WD companion Explosion speeds up nuclear reactions, create elements more massive than iron. Enriched material spreads out and goes to the next generation of Stars

Energy output ~10 53 ergs which can exceed that of an entire Galaxy Only 1% as the K.E. of the expanding shell & 0.1% as light Most of the energy leaves as the escaping Rapid increase and fades over months

Supernova Remnants Products of Nucleosynthesis are dispersed into the interstellar medium (atoms heavier than Iron) Glowing Shells are characteristics of the Remnants enrich The metallic nature of space. Newer stars always have a higher amount of these elements Why do Ancient stars appear to be only made of H and He?

Guess where we find Black Holes and Pulsars?

High energy e - are relativistic and the spiral motion creates this highly directional radiation

Properties of Synchrotron radiation 1. Electron s spiral 2. Constant acceleration in circular Motion gives off radiation 3M 3.Most radiation is admitted d In a small cone in the direction of motion Note other properties See figure 11.6 and the discussion of the Crab Nebula

BH & Neutron Stars formation

Properties of Neutron Stars Typical size: R ~ 10 km Mass: M ~ 1.4 3 M sun Density: ~ 10 14 g/cm 3 a piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!! A neutron star (more than the mass of the sun) would comfortably fit within Staten Island!!!

Neutron Degeneracy Pressure Neutron spin properties are similar to electrons hence they obey the The same Pauli exclusion principle x p >=h/2 Hence P =2(h/2 ) 2 n 5/3 n n /m n eq 11.2a Compared with the Electron DP P e =2(h/2 ) 2 n 5/3 e /m e since the star is all neutrons there is only P n to support it And in this case =n n m n or P n =2(h/2 ) 2 5/3 /m 8/3 n eq 11.2b in problem 11.3 for HW you use this and get the radius of a neutron star ~15km Example 11.1 What is the density g/cm 3 of a neutron star of mass 1.4 M sun compared to the density Of a single neutron. Given radius of N star= 15Km M sun =2 x 10 33 gm r n = 10-13 cm m n =1.7 x10-24 Example 11.2 using the neutron star density above and calculating a white dwarf density p g y g y (one solar mass roughly at a radius 1/100 of the sun see example 10.2 Compare the P n /P e

Example 11.3 calculate g on the neutron star and the value of the tidal effect ie dg/dr Ie g =GM/R 2 G=6.67 x 10-8 dyn cm 2 /g 2 Calculate l in class both! ->>>>>> Prone approach a neutron star? Rotation Rotation is characterized by how fast an angle moves ie. s= r or =s/r radians if s =2 r then =? =? degrees t is the angular rotation rate = rad /sec-> v= r Total time for one rotation called period P (from rate x time =distance) ->vp=2 r -> =P=2 r v =2 angular momentum J which is conserved by the stars core In the collapse to a neutron star For rotating sphere J=(2/5)MR 2 is called the moment of inertia for the sphere r s Consider the sun collapsing to a neutron star how fast is it rotating and what is the Period of rotation? J conservation J sun = J ns -> R sun2 sun =R ns2 ns -> ns/ sun =(R sun/r ns) ) 2 R sun = 7x 10 10 cm calculate ratio and since the sun rotates in 30days What is angular velocity and the period of the neutron star? Calculate now!!!

After considering star pulsation and orbits WHICH CANNOT GIVE THE TYPE OF PERIOD CALCULATED ONLY ROTATION WORKS! SEE KUTNER SEC 11.3.2 FOR ARGUMENTS ON PULSAR NATURE Discovered in radio range by Antony Hewish and Jocelyn Bell Burnell 1967. P=1.337301s for the first one..hundreds known today. SOUNDS! => Rapidly pulsed (optical and radio) emission from some objects interpreted as spin period of neutron stars with an interesting Light House model that will follow.

ROTATING Neutron stars->pulsars We saw Angular momentum conservation => Collapsing stellar core spins up to periods of ~ a few milliseconds. Magnetic fields are amplified up to B ~ 10 9 10 15 G. (upto2x10 9 to 10 12 times the average magnetic field of the sun) Magnetic flux is constant on a surface goes as BR 2 or BR 2 =constant in collapse Ie B -> 1/R 2 other arguments bring in dynamo s, super fluid, Hard crusts etc for neutron stars

I = MOMENT OF INERTIA = ANGULAR VELOCITY P IE. I NS ns = I sun sun ie conservation of Angular momentum as before

Pulsars / Neutron Stars Neutron star surface has a temperature of ~ 1 million K. Cas A in X-rays Wien s displacement law, max = 3,000,000 nm / T[K] i i l th f 3 gives a maximum wavelength of max = 3 nm, which corresponds to X-rays.

Light Curves of the Crab Pulsar

Lighthouse Model of Pulsars Some think that Hot spots on the surface Some think that Hot spots on the surface Creates beams of Particles but the ideas are still fuzzy! A Pulsar s magnetic field has a dipole structure, just like Earth ie off-axis. A rough model is that Synchrotron Radiation which is in a tight beam from particles spiraling in the field is emitted mostly along the magnetic poles. But a good model does not exist except for the concept of a lighthouse like sitiuation!

Images of Pulsars and Other Neutron Stars The vela Pulsar moving through interstellar space Th C b The Crab nebula and pulsar

The Crab Pulsar (2) Visual image X-ray image

CRAB NEBULA

Pulsar Winds Pulsars are emitting winds and jets of highly energetic particles. These winds carry away about 99 9 % of the These winds carry away about 99.9 % of the energy released from the slowing-down of the pulsar s rotation.

The Crab Pulsar (the most studied) Pulsar wind + jets Supernova 1054 About 200,000 pulsars are estimated for our galaxy

Pulsar Periods Over time, pulsars lose energy and angular momentum see sec 11.3.3 and Example 11.4 Nebula gains the Lost energy hence Is maintained! => Pulsar rotation is gradually slowing down. PERIOD INCREASES! Implies faster rates Are younger pulsars! GLITCHES (see Ex 11.5..SUPPORT NEUTRON STAR MODEL OF PULSARS? STARQUAKES (SOLID BULGING SURFACE CRACKS BECOMES ROUNDER AND SPEEDS UP THE ROTATION! Esp CRAB but not all!

Proper Motion of Neutron Stars Some neutron stars are moving rapidly through interstellar space. Thi i ht b lt f This might be a result of anisotropies during the supernova explosion forming the neutron star

Binary Pulsars Some pulsars form binaries with other neutron stars (or black holes). Radial velocities resulting from the orbital motion lengthen the pulsar period when the pulsar is moving away from Earth... and shorten the pulsar p period when it is approaching Earth.

Neutron Stars in Binary Systems: X-ray Binaries Example: Her X-1 2M sun (F-type) star Star eclipses neutron star and accretion disk periodically Neutron star Orbital period = 1.7 days Accretion disk material heats to several million K => X-ray emission

Pulsar Planets Some pulsars have planets orbiting around them. Just like in binary pulsars, this can be discovered through variations of the pulsar period. As the planets orbit around the pulsar, they cause it to wobble around, resulting in slight changes of the observed pulsar period.

Measuring Distance to Pulsar by Dispersion Sec 11.4 and the Last part of Pulsar lab Electromagnetic waves slow down in medium (not a vacuum) which is opposite of Mechanical waves like sound The speed in the medium of the E&M wave depends on the wavelength (or f) The measure of the slowdown is expressed by the Index of Refraction n( ) n( ) = c/c(n)= c/c(n( )) ie c is speed of light and c(n) speed in the medium And clearly n>1 for media E h l h h Each wavelength has a different index of refraction

Using dispersion to separate wavelengths of light

Examples of pulse dispersion Two different wavelengths from each pulsar arrive at separate times Because their speed in the Interstellar Medium (mostly electrons) is different

The Difference in time of arrival can be used to determine the distance To the Pulsar see section 11.4 Since the rate x time =distance c( ) t =d and c )=c/n ) for and t 1 =d/c( 1 ) t 2 = d/ c 2 ) *** From which h the text t gives us 11.21 t 1 =dn( 1 )/c and t 2 = dn( 2 )/c 11.22 t =d/c [n( 1 )-n( )] Since the speed or index of refraction of Radio waves changes because of the interaction with electrons in the Interstellar Mediu Section 11.4 relates the n( ) ton e (electron density) The lab exercise relates the speed directly to the electron density and shows c( ) =f 2 /124.5 f =frequency hence ***-> t 2 -t 1 =d/c( 2 ) d/(c( 1 )= d(1/v 2-1/v 1 ) (lab approach!) From which the lab exercise shows (be sure to follow the logic) Lab uses L for d! t 2 -t 1 d * = --------------------------------- 124.5 [ (1/f 2 ) 2 -(1/f 1 ) 2 ]