Homework #12 11/30/15 Due 12/7/15 Chapter 14 Review questions 4, 6, 12 Problem 8.

Homework #1211/30/15

Due 12/7/15

Chapter 14

Review questions 4, 6, 12

Problem 8

PHYS 3380 - Astronomy

Black Holes

Just like white dwarfs (Chandrasekhar limit: 1.4 M), there is a mass limit for neutron stars (neutron degeneracy):

Neutron stars cannot exist with masses > 3 M

We know of no mechanism to halt the collapse of a compact object with > 3 M.

It will collapse into a single point – a singularity:

=> A Black Hole!

PHYS 3380 - Astronomy Black Holes

Black holes are completely collapsed objects - radius of the “star” becomes so small that the escape velocity approaches the speed of light

Escape velocity for particle from an object of mass M and radius R

If photons cannot escape, then vesc>c. Schwarzschild radius is

Nothing (not even light) can escape from inside the Schwarzschild radius- we have no way of finding out what’s happening inside the Schwarzschild radius - the “event horizon”

€

vesc =2GM

R

€

R < RS ≡2GM

c 2 = 3 km

M

MSol


Object M (M) Rs

Star 10 30 km

Star 3 9 km

Sun 1 3 km

Earth 3x10-6 9 mm

Size of black holes determined by mass. Example Schwarzschild radius for various masses given by:

The event horizon is located at Rs - everything within the event horizon is lost. The event horizon hides the singularity from the outside Universe.

If the entire mass of the Earth was confined to 9mm, it would be a black hole - can’t collapse spontaneously into black hole because mass < 3 M


Black Holes in Supernova RemnantsSome supernova remnants with no pulsar / neutron star in the center may contain black holes.

Composite X-ray/optical/radio image of the supernova remnant W49B. The structure and composition of this remnant hints that it was a gamma ray burst and likely harbors a black hole at its center.


“Black Holes Have No Hair”

Matter forming a black hole is losing almost all of its properties.

Black Holes are completely determined by 3 quantities:

Mass

Angular Momentum

Electric Charge

PHYS 3380 - Astronomy Types of Black Holes

Schwarzschild - Non-rotating black hole -simplest black hole, in which the core does not rotate- only has a singularity and an event horizon

Kerr - Rotating black hole-probably the most common form in nature,- rotates because the star from which it was formed was rotating. When the rotating star collapses, the core continues to rotate, and this carried over to the black hole (conservation of angular momentum).-Has an Ergosphere - egg-shaped region of distorted space around the event horizon

-caused by the spinning of the black hole, which "drags" the space around it.)

-Static limit - The boundary between the ergosphere and normal space


At a distance, the gravitational fields of a black hole and a star of the same mass are virtually identical.

At small distances, the much deeper gravitational potential will become noticeable.

Black Hole Gravity Well


General Relativity Effects Near Black Holes

An astronaut descending down towards the event horizon of the BH will be stretched vertically (tidal effects) and squeezed laterally - friction would heat the astronaut to millions of degrees emitting x-rays and gamma rays.

“Spaghettification”



Time dilation

Event Horizon

Clocks starting at 12:00 at each point.

After 3 hours (for an observer far away from

the BH): Clocks closer to the BH run more slowly.

Time dilation becomes infinite at the event horizon.



Gravitational Red Shift

Event Horizon

All wavelengths of emissions from near the event horizon are stretched

(red shifted).

Frequencies are lowered.

PHYS 3380 - AstronomyRemember: General Theory of Relativity predicted gravity could bend space - confirmed during a solar eclipse when a star's position was measured before, during and after the eclipse.

An object with immense gravity (like a galaxy or black hole) between the Earth and a distant object could bend the light from the distant object into a focus, much like a lens can.

Einstein ring -the deformation of the light from a source into a ring through gravitational lensing of the source's light by an object with an extremely large mass (such as another galaxy, or a black hole).


Animated simulation of gravitational lensing caused by a going past a background galaxy.

- secondary image of the galaxy can be seen within the black hole Einstein ring on the opposite direction of that of the galaxy. - secondary image grows (remaining within the Einstein ring) as the primary image approaches the black hole. - surface brightness of the two images remain constant, but their angular size varies

- produces an amplification of the galaxy luminosity as seen from a distant observer. The maximum amplification occurs when the background galaxy (or in the present case a bright part of it) is exactly behind the black hole.

Lensing by a Black Hole


Brightening of MACHO-96-BL5 happened when a gravitational lens passed between it and the Earth. When Hubble looked at it, it saw two images of the object close together - indicated a gravitational lens effect - intervening object was unseen.

- conclusion that a black hole had passed between Earth and the object.


Stephen Hawking showed that black holes are not entirely black but emit small amounts of thermal radiation.

- applied quantum field theory in a static black hole background. - result - a black hole should emit particles in a perfect black body spectrum.

- Hawking radiation.

Virtual particle pairs constantly created near the horizon of the black hole, as they are everywhere - quantum fluctuations. Normally, they are created as a particle-antiparticle pair and they quickly annihilate each other. But near the horizon of a black hole, it's possible for one to fall in before the annihilation can happen, in which case the other one escapes as Hawking radiation.

- removes energy from black hole - evaporation

Temperature of the emitted black body spectrum is proportional to the surface gravity of the black hole.

- large black holes are very cold and emit very little radiation- black hole of 10 solar masses would have a Hawking temperature of several nanokelvin, much less than the 2.7K produced by the Cosmic Microwave Background. - micro black holes on the other hand could be quite bright producing high energy gamma rays.


Compact Objects with Disks and Jets

Black holes and neutron stars can be part of a binary system.

=> Strong X-ray source!

Matter gets pulled off from the companion star, forming an accretion disk.

Heats up to a few million K.


Cygnus X-1

Wide-field radio image of the environment of the black hole system Cygnus X-1. The cross marks the location of the black hole. The bright region to the left (East) of the black hole is a dense cloud of gas existing in the space between the stars, the interstellar medium. The action of the jet from Cygnus X-1 has 'blown a bubble' in this gas cloud, extending to the north and west of the black hole.


Observing Black Holes

No light can escape a black hole

=> Black holes can not be observed directly.

If an invisible compact object is part of a binary, we can estimate its mass from the orbital period and radial velocity - the same way we have discovered extra-solar planets.

Mass > 3 M

=> Black hole!


How to Determine Compact Object Masses

P = orbital period

Kc = semiamplitude of companion star

i = inclination of the orbit to the line of sight (90o for orbit seen edge on)

MBH and Mc = masses of invisible object and companion star

Keplers Laws give:

This gives us a firm lower limit on BH mass from relatively simple measurements

€

PKc3

2πG=

MBH3 sin3 i

MBH + Mc( )2

NameBHC Mass (solar

masses)Companion Mass (solar masses)

Orbital period (days)Distance from Earth

(light years)

A0620-00/V616 Mon 11 ± 2 2.6–2.8 0.33 about 3500

GRO J1655-40/V1033 Sco 6.3 ± 0.3 2.6–2.8 2.8 5000−11000

XTE J1118+480/KV UMa 6.8 ± 0.4 6−6.5 0.17 6200

Cyg X-1 11 ± 2 ≥18 5.6 6000–8000

GRO J0422+32/V518 Per 4 ± 1 1.1 0.21 about 8500

GRO J1719-24 ≥4.9 ~1.6 possibly 0.6 about 8500

GS 2000+25/QZ Vul 7.5 ± 0.3 4.9–5.1 0.35 about 8800

V404 Cyg 12 ± 2 6 6.5 about 10000

GX 339-4/V821 Ara 5–6 1.75 about 15000

GRS 1124-683/GU Mus 7.0 ± 0.6 0.43 about 17000

XTE J1550-564/V381 Nor 9.6 ± 1.2 6.0–7.5 1.5 about 17000

4U 1543-475/IL Lupi 9.4 ± 1.0 0.25 1.1 about 24000

XTE J1819-254/V4641 Sgr 7.1 ± 0.3 5–8 2.82 24000 – 40000

GRS 1915+105/V1487 Aql 14 ± 4.0 ~1 33.5 about 40000

XTE J1650-500 9.7 ± 1.6 [17] . 0.32[18]


Candidates for Black Hole

Compact object with > 3 M must be a black hole!

These candidates are all members of X-ray binary systems in which the compact object draws matter from its partner via an accretion disk.


Black Hole and Neutron Star Masses from Binary Systems

From J. Caseres, 2005, astro-ph/0503071


A black-hole-powered jet of electrons and other sub-atomic particles streaming out from the center of M87 at nearly the speed of light -the blue jet contrasts with the yellow glow from the combined light of billions of unseen stars and the yellow, point-like clusters of stars that make up this galaxy. - the monstrous black hole at center of M87 has swallowed up matter equal to 2 billion times our Sun's mass. M87 is 50 million light-years from Earth.

Black Holes at the Center of Galaxies


Active Galactic Nuclei (AGN) often have black-hole-powered jets - highly collimated and fast outflows that emerge from close to the disc - of electrons and other sub-atomic particles

• production mechanism and jet composition are not known at present

observations cannot distinguish between the various theoretical models that exist.

• have the most obvious observational effects in the radio waveband but radiate in all wavebands from radio to gamma-ray

synchrotron radiation

Relativistic Jets

Jets streaming out from the center of M87 observed at various wavelengths-


Superluminal speed illusion created by the finite speed of light and rapid motion • clouds move towards Earth at speeds very close to that of light, in this case, more than 98 percent of the speed of light - nearly keep pace with the light they emit as they move towards Earth. When the light finally reaches us, the motion appears much more rapid than the speed of light.


Apparent superluminal motion when the radiating source is moving so fast that it nearly “catch up” with its own radiation.

A source component is moving at velocity v and at an angle θ(φ relative to the line-of-sight. Consider the emission of photons at two different times t =0and t = tc. Photons emitted at t= tc will reach theobserver at Δt = tc(1 − βcosφ) later than those emitted at t=0.

Motion of a

plasma co

mponent

The apparent separation of the two source components then is Δr = vtcsinφ

Yielding an apparent velocity on the sky of: vapp = Δr/Δt = vsinφ/(1 − βcosφ

PHYS 3380 - Astronomy Death Star Galaxy

Jet from a black hole at the center of a galaxy striking the edge of another galaxy• composite image - X-rays (purple), optical and ultraviolet (red and orange), and radio (blue) • jet from the main galaxy on the lower left is striking its companion galaxy to the upper right. • jet impacts the companion galaxy at its edge and is then disrupted and deflected


M84 - a massive elliptical galaxy in the Virgo Cluster, about 55 million light years from Earth.

• composite X-ray (blue), radio (red), and visible (yellow and white)• number of bubbles visible in hot gas, outlined with blue X-ray emission.

blown by relativistic particles generated by the central supermassive black hole in M84 - travel outwards in the form of a two-sided jet.

• smaller bubbles are found inside large bubbles provide clear evidence for repeated outbursts from the central black hole.

PHYS 3380 - AstronomySpectroscopic Observations of Black Hole at the Center of M84

Indicate a rapidly swirling disk of trapped material encircling the black hole. Rapid dramatic swing to the left (blueshifted or approaching gas) and then an equivalent swing from the right (redshifed)Measured velocity 400 km/s within 26 LY of the galaxy's center, where the black hole dwells - gives a black hole mass of at least 300 million solar masses.


M31 Andromeda


Triple nucleus of M31

40 Light - Years

Two nested disks in Keplarian rotation around a supermassive black hole.

http://ftp.seds.org/pub/images/hst/m31.jpg


Zoom into the nucleus of the M31 then dissolve into animation of a concentration of red stars and a disk of young blue stars swirling around a black hole.

-revealed by Hubble's Space Telescope Imaging Spectrograph (STIS) -Astronomers not sure how the pancake-shaped disk of stars could form so close to a giant black hole

- tidal forces should tear matter apart, making it difficult for gas and dust to collapse and form stars.


high-resolution spectrum obtained with the Faint-Object Camera on board HST, • change in Doppler shift of the [O II] emission line at 372.7 nm clear from both the spectral images and intensity crosscuts.• plot of the measured velocities compared to a model with a massive central object shows very good fit with a central mass of 3 billion solar masses confined within a radius of 3.5 parsecs or less - almost completely requires that this mass be a black hole.


3,700 light-year-diameter dust disk encircles a 300 million solar-mass black hole in the center of the elliptical galaxy NGC 7052 - possibly a remnant of an ancient galaxy collision. Disk rotates 155 kilometers per second at 186 light-years from the center. strong source of radio emission and has two oppositely directed `jets' emanating from the nucleus.

PHYS 3380 - Astronomy The Hubble Expansion Law

Hubble constant H - one of the most important numbers in cosmology • may be used to estimate the size and age of the Universe• indicates the rate at which the universe is expanding• changes with time

H0 = v/d

where v is the galaxy's radial outward velocity, d is the galaxy's distance from earth, and H0 is the current value of the Hubble constant.

In 1929, Edwin Hubble announced that almost all galaxies appeared to be moving away from us.

• observed as a redshift of a galaxy's spectrum. • appeared to have a larger displacement for faint, presumably further, galaxies.

the farther a galaxy, the faster it is receding from Earth.


The Hubble Constant

Most recent calculation H0 used 2003 data from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite

• combined with other astronomical data yielded a value of: H0 = 70.1 ± 1.3 km/s/Mpc.

• agrees well with that of obtained in 2001 by using NASA's Hubble Space Telescope:

H0 = 72 ± 8 km/s/Mpc

• less precise figure obtained independently in August, 2006 using data from Chandra X-ray Observatory:

H0 = 77 km/s/Mpc with an uncertainty of ± 15%.

NASA summarizes existing data to indicate a constant of H0 =70.8 ± 1.6 km/s/Mpc

if spacetime is assumed to be flat, or H0 =70.8 ± 4.0 km/s/Mpc

otherwise

In 2012, Freedman et al. found H0 = 74.3 ± 2.1 (km/s)/Mpc after a re-calibration of the Cepheid distance relation based on Spitzer infrared data, combined with WMAP7 and Hubble cosmological data. Because Cepheid variables are used to determine galactic distances, this recalibration had a significant effect on the galactic distance scale and hence H0.

PHYS 3380 - AstronomyThe Age of the Universe

The age of the universe has been estimated by a number of methods:

Lower limit provided by observations - must be at least as old as the oldest thing in it.

• temperature of the coolest white dwarfs• turnoff point of the red dwarfs in globular clusters

typically yield ages in the range 14-18 billion years

Inverse of Hubble constant

€

1

H=d

v= T

T =1

70.8km /s /Mpc×

3.09 × 1019km

Mpc×

1yr

3.15 ×107s=13.8 ×1010 yr

PHYS 3380 - Astronomy QuasarsCertain objects emitting radio waves observed in 1960s had very unusual optical spectra.

• named Quasistellar Radio Sources (meaning "star-like radio sources") - contracted to quasars. • finally realized that the reason optical spectra were so unusual is that the lines were Doppler shifted by a very large amount, corresponding to velocities away from us that were significant fractions of the speed of light. • objects were thought to be relatively nearby stars, no one had any reason to believe they should be receding from us at such velocities.

First and brightest Quasar discovered• left image shows radio and optical composite of quasar and its jet. • right image superposes contours of radio frequency intensity. • sharp radial lines are optical spike artifacts because of its brightness

Quasar 3C273


Images show the three most distant quasars known. • redshift parameters are 4.75, 4.90, and 5.00 respectively, which places them at distances of about 15 billion light years

Quasars have very large redshifts, indicating by the Hubble law that they are at great distances.

• the fact that they are visible at such distances implies they emit enormous amounts of energy and are certainly not stars.

Now thought to be AGNs powered by supermassive rotating black holes at their centers.

• most luminous objects known in the universe - objects that have been observed at the greatest distances from us - most distant are so far away that the light we see coming from them was produced when the Universe was only one tenth of its present age.

Homework #12 11/30/15 Due 12/7/15 Chapter 14 Review questions 4, 6, 12 Problem 8.

Documents

Transcript of Homework #12 11/30/15 Due 12/7/15 Chapter 14 Review questions 4, 6, 12 Problem 8.