Transcript Gamma Ray Bursts: The biggest bang since the big one!

Black holes
science fact, fiction of fantasy
Chris Done, University of Durham
Gravity: warped spacetime
• Straight paths on curved
space!!
• NOT a spooky, action at a
distance force (Newtonian)
• Space(time) warped by
mass(energy)
Gravity: warped spacetime
• Matter tells space how to
curve, curvature tells
matter how to move
Gravity: warped spacetime
• So light is affected too!
• Lightbending – light travels in straight lines over curved
surface so path looks curved!
• One of first tests of GR …
True position
Apparent position
Gravity: warped spacetime
• More gravity, deeper
hole in spacetime, higher
velocity to escape more mass or smaller
size
• Black hole – escape
velocity is faster than
light so can’t get out!
• No change in curvature
at Earths orbit – black
holes don’t suck
inexorably! Unlike bad
SF movies…
Gravity: warped spacetime
• Utterly extreme. Need
mass of earth
squashed down to
1cm! Or mass of sun
squashed into size of
London.
• Impossible!!!!!!!!?
• How to get such
extreme compression?
Black hole recipe: I
• Take 1 massive star (at least
10 bigger than Sun)
• Stars fuse 4H to He
• Lose mass, gain energy via
Einstein’s E=mc2
• Hydrogen bomb! in its
stable life – outward
pressure of hot gas (fusion)
balanced by inward pull of
gravity
• Cook until all hydrogen
fuel eventually exhausted.
Chemistry!
Black hole recipe: I
• Take 1 massive star (at least
10x bigger than Sun)
• Stars fuse 4H to He
• Lose mass, gain energy via
Einstein’s E=mc2
• Hydrogen bomb! in its
stable life – outward
pressure of hot gas (fusion)
balanced by inward pull of
gravity
• Cook until H all gone.
Black hole recipe: II
• Run out of H but gravity
never runs out – contracts
core so higher temperatures
• then fuse higher atomic
number elements…
• Builds up all the chemical
elements of the periodic
table!
Chemistry!
• He core pulled in by gravity, temperature increases. If high enough fuse 3He to C
• C core pulled in by gravity temperature increases. If high enough fuse C+He to O
• O core pulled…….
Black hole recipe: II
• Builds up all the chemical
elements of the periodic
table!
• But get less and less energy!
• Iron is crossover between
fusion and fission! No more
energy!
• Iron core builds up as iron
‘ash’ sinks down from
layers above. pulled in by
gravity but no other energy!
Black hole recipe: III
• Fe core pulled in by
gravity. How far can
material be compressed?
• Electron degeneracy
pressure – wave-particle
duality in quantum
mechanics. Smaller box,
smaller wavelength,
higher energy, faster!
• Can’t go faster than c!
Black hole recipe: IV
• Hit this when Fe core is 1.4x
mass of Sun
• e- + p+ > n + n
• Neutrons have higher mass,
shorter wavelength so fit in
MUCH smaller box! Floor
drops away.
• Dramatic supernovae
explosion!
• Neutron star core left held up
by degenerate neutrons.
• mass of sun, size of London.
A digression…..
• Outer layers blasted
across interstellar space
• Contains all heavy
elements needed for life
(C, N, O, Fe etc)
• Where slams into
molecular gas then
triggers next generation
of stars/planets(/life?)
Black hole recipe: V
• But core being hit by
infalling layers from above
• Neutrons get squashed into
smaller and smaller box,
going faster and faster
• Hit c at 1.4-3x mass of sun
(depends on rotation rate)
• no known state of matter can
hold up complete collapse
• Event horizon only factor of
3 smaller than a neutron star
Observing black holes?
• How to test this ?
• The thing about a black
hole, its main
distinguishing feature is its
black! And the thing about
space, your basic space
colour is its black! So how
are you supposed to see
them ? Red Dwarf
Disc Accretion
• Single particles orbit
• Gravitational orbits inner ones faster
• Continuous ring of gas Frictional viscosity
dissipates energy as
material can fall inwards
• BRIGHT accretion discs
glowing X-ray hot
• Characteristic spectral lines
• Electron wave fits exactly
only at certain
distance=energy
Energy
Atomic lines
Doppler shift
• Doppler shift!
• Period and velocity
give distance and
gravity strength
Doppler Shift
Susan
cruisin' down
the freeway
seventy-eight,
And assuming
the policeman
is doing
standing
in range His gun tells him all
go
speedracing,
go speedracing
about
the frequency
change
She
justSusan's
likes towalking,
drive fast,
it's notHer
thatspeed
she's racing
late (nodays
tail-gating,
Then
walking
are doneno tail gat
Goes
overlight
a hilltop
what
surprise
(toofar,
latelightspeed's
sister, you're
for itthe
now
They're
yearsand
away,
anda that's
pretty
theinlimit,
Blue
and red flashing lights right in front of her eyes Nee nee nah nah
big speedlimit
Now
Susan'splenty
standing
sidefrom
of her
But there's
we by
canthe
learn
thecar,
light of a star (split it with a
show
methere's
your licence,
you're
prism,
little lines
in it)in big trouble
Trucks
blowing
right
by her but
she's
notthat's
going
far
By looking
at the
spectrum
at the
light
glowing
(wavelengths of
(they're
stillmeasured
cruisin', Susan's
losin') its Doppler Shift will tell us if it's
emission,
with precision)
She's
beenorcaught
by a doo
speed trap, and now she can hear,
coming
going Doo
here
comes
the physics,
now,
That's
the Doppler
Shiftyou're
- you in
seeforit,itit's
true Doppler Shift - to the red
Sound
the Doppler Shift right in her ear Eeee-oww
or theof
blue
That's
Doppler
Shift - you've
heard
it I know,
Doppler
Shift - first it's
Whenthe
a star
is approaching
and it's
coming
our way
Its spectrum
then
it's bluer,
low won't you hear what I say And when a star's retreating
seems
The
cop's
gunAnd
shoots
out only measures
radar Andits
thefrequency
beam bounces
back
off
waygood
out of
range
the scientist
change
Well
Susan's
that's acar
redshift, If the star is moving away
By gravity – all they possess!
• Gravitational effect on
nearby stars
• Stars in GC get to
within a lightday, but
this is 2000x event
horizon. Not probing
the REALLY curved
BH spacetime.
• Hard to detect
By gravity – all they possess!
• Gravitational effect on
nearby stars
• Stars in GC get to
within a lightday, but
this is 2000x event
horizon. Not probing
the REALLY curved
BH spacetime.
• Hard to detect
Supermassive black holes!
• In the centers of galaxies
• Bright accretion discs (and
jets) powering intense
activity from nucleus – AGN
• Can outshine host galaxy –
quasi-stellar object - QSO
galaxy
quasar
star
Conclusions
•
•
•
•
•
•
black holes – ultimate test of Einstein General Relativity
Can form astrophysically from death of massive stars
Most stars are in binaries – X-ray bright accretion
Measure mass from binary orbit – BH or NS
Supermassive black hole in centre of our Galaxy
And in most other galaxies too – accretion of material
again gives X-rays, powers activity seen from Quasars
Disc Accretion
• Single particles orbit
• Gravitational orbits inner ones faster
• Continuous ring of gas Frictional viscosity
dissipates energy as
material can fall inwards
• BRIGHT accretion discs
glowing X-ray hot
• Differential velocity.
friction gravity  heat
• Thermal emission: L = AsT4
• Temperature increases
inwards as more
gravitational energy and less
area.
Log n f(n)
Spectra of accretion flow: disc
Log n
Behaviour of maximum…
• Newtonian orbits
• Gravity attractive – wants
to be closer in.
• but if closer then rotate
faster due to angular
momentum conservation
• Bigger outward centrifugal
force!
• Balance inward gravity with
outward angular momentum
to get stable orbit
• Can always orbit closer
energy
Angular
momentum,
barrier 1/r2
r
Newtonian
gravity  -1/r
Behaviour of maximum…
• Extra terms in GR potential
• (Rest mass energy)
• Term which is –ve so adds
to gravitational potential
and makes it
stronger
• Gravity will always
dominate if get to small
enough r!
energy
Angular
momentum,
barrier 1/r2
Rest mass energy
r
Newtonian
gravity  -1/r
Extra GR -1/r3
Behaviour of maximum…
• Extra terms in GR potential
• (Rest mass energy)
• Term which is –ve so adds
to gravitational potential
and makes it
stronger
• Gravity will always
dominate if get to small
enough r!
• Last stable orbit – gravity
so strong that no friendly
angular momentum barrier
to stop you falling
down……
energy
Angular
momentum,
barrier 1/r2
Rest mass energy
r
Newtonian
gravity  -1/r
Extra GR -1/r3
Speed limit c in SR
• Space-time curved by mass-energy
• All forms of energy gravitate!! Mass
• Increase v ie KE so increase
response to gravity.
• v<< c rest mass dominates
• v~c then KE dominates.
Increasing energy increases
response to gravity ie increases
inertial mass and harder to
increase speed!
c
v
• How far in can the disc go?
Obviously stops at event
horizon! But GR gravity is
stronger than Newtonian – there
is a point where stable orbits no
longer possible. Can’t just go
round (like fly-by-wire planes –
need engines to keep it stable!)
• Origin of ‘black holes suck’ scifi ideas.
Log n f(n)
Spectra of accretion flow: disc
Log n
• This point depends on SPIN
• Spinning black hole drags
spacetime around with it
• Disc not rotating so fast with
respect to spacetime so can get
in closer
• a=0 Rlso = 3Rs horizon Rs
• a=1 (maximal Kerr)
Rlso = 0.5 Rs horizon 0.5 Rs
• Can get in closer to spinning
black hole. More energy to
dissipate over smaller area: disc
temperature 3x higher for same
luminosity for a=1
Log n f(n)
Spectra of accretion flow: disc
Log n
• Spinning black hole drags
spacetime around with it
• Disc not rotating so fast with
respect to spacetime so can get
in closer
• a=0 Rlso = 3Rs horizon Rs
• a=1 (maximal Kerr)
Rlso = 0.5 Rs horizon 0.5 Rs
• Spinning black hole has more
energy to dissipate over smaller
area: disc temperature 3x higher
for same luminosity for a=1
Log n f(n)
Spectra of accretion flow: disc
Log n
Speed limit c in SR
• Travelling at constant speed c through spacetime!
• ds2=c2dt2 –dx2
• Normally v<<c so all motion is through TIME
• If v~c then more and more of speed goes through
space so less to go through time – time dilation!
ct
x
Speed limit c in SR
• Travelling at constant speed c through spacetime!
• ds2=c2dt2 –dx2
• Normally v<<c so all motion is through TIME
• If v~c then more and more of speed goes through
space so less to go through time – time dilation!
ct
x
Galactic Binary systems
• Huge amounts of data
• See accretion rate vary on
timescales of days-years
• Observational template of
accretion flow as a function of
L onto ~10 M BH
• Thermal disc L = AsT4 so
constant inner radius at last
stable orbit L T4 as accretion
rate changes
7 years
Disc spectra: last stable orbit
• Pick ONLY ones that look
like a disc!
• L/LEdd T4max (Ebisawa et al 1993;
Kubota et al 1999; 2001)
• Constant radius over factor
10-50 change in luminosity
• Last stable orbit!!! Looks
like Einstein GR (Gregory,
Whisker, Beckwith & Done 2004)
•
Proportionality constant
gives Rms i.e. a as know M
• Consistent with low to
moderate spin not maximal
Gierlinski & Done 2003
Disc spectra: last stable orbit
• Pick ONLY ones that look
like a disc!
• L/LEdd T4max (Ebisawa et al 1993;
Kubota et al 1999; 2001)
• Constant radius over factor
10-50 change in luminosity
• Last stable orbit!!! Looks like
Einstein GR (Gregory, Whisker,
Beckwith & Done 2004)
•
Proportionality constant
gives Rms i.e. a as know M
• Consistent with low to
moderate spin not maximal
• Matches theoretical spin from
supernovae collapse
Gierlinski & Done 2003
Conclusions
• GR black holes – event horizon, last stable orbit
• Can form astrophysically from death of massive stars
• Where these accrete then get observational tests of GR in
strong field from X-ray emitting gas lighting up regions
of strong spacetime curvature
• Simple disc spectra – luminosity can change by factor 50
with L T4max implies constant size scale
• Consistent with GR prediction of last stable orbit for
low/moderate spin black holes
• Corrections to GR from proper gravity must be smallish
• ASTROPHYSICS  PHYSICS
Disc spectra: last stable orbit
• Pick ONLY ones that look
like a disc!
• L/LEdd T4max (Ebisawa et al 1993;
Kubota et al 1999; 2001)
• Constant radius over factor
10-50 change in luminosity
• Last stable orbit!!! Looks
like Einstein GR (Gregory,
Whisker, Beckwith & Done 2004)
•
Proportionality constant
gives Rms i.e. a as know M
• Consistent with low to
moderate spin not maximal
Gierlinski & Done 2003
Bright accretion discs!
• Huge gravitational potential
energy of infalling material so
gas heated to X ray temperatures
and very luminous.
• Bright accretion disc GR gravity
stronger than Newton. Last
stable orbit at 6Rs.
• Newton: orbit closer in by going
round faster.
• Can’t go faster than c… 3Rs.
• GR gravity stronger….
Event horizon
• What happens at
r=Rs=2GM/c2?
• Speed is distance/time  c at
Rs no matter where dropped
from or how fast it was hurled
towards the hole…
• So must be infinite
accelerations (could drop
from rest just above horizon
and would still be at c at Rs)
• Can’t have fixed anything! So
no sense to make a fixed
radial grid…..
Gravity: warped spacetime
• No change in
curvature at Earths
orbit – black holes
don’t suck inexorably!
(Unlike bad SF
movies… but there is
something very odd
close to the event
horizon…..)
• But what happens at
horizon? And below??
Curved spacetime: black holes
• Black holes are just made up of curved spacetime!
• No surface, no distinguishing features…
Event horizon
• Horizon just the place where light can no longer get out
• Matter coming in can sail straight through…
r=0
r=Rs
r
t
r
Gravity: warped spacetime
• Below horizon
spacetime itself is
infalling!
• singularity at bottom –
all matter crushed to
infinite density in
infinitesimal point
• NEED QUANTUM
THEORY OF
GRAVITY!