Download D1 Stellar quantities (PPT)

Solar System
http://atropos.as.arizona.edu/aiz/teaching/nats102/mario/solar_system.html
Any model of Solar System formation must explain the following facts:
1.
All the orbits of the planets are prograde (i.e. if seen from above the North
pole of the Sun they all revolve in a counter-clockwise direction).
2.
All the planets (except Pluto) have orbital planes that are inclined by
less than 6 degrees with respect to each other (i.e. all in the same plane).
3.
Terrestrial planets are dense, rocky and small, while jovian planets are
gaseous and large.
▪ Solar system formed about 4.6 billion year ago, when gravity pulled together
low-density cloud of interstellar gas and dust (called a nebula)
http://ircamera.as.arizona.edu/NatSci102/
NatSci102/lectures/solarsysform.htm
▪ Initially the cloud was about several light years across. A small
overdensity in the cloud caused the contraction to begin and the
overdensity to grow, thus producing a faster contraction
▪ Initially, most of the motions of the cloud particles were random,
yet the nebula had a net rotation. As collapse proceeded, the rotation
speed of the cloud gradually increased due to conservation of angular momentum.
▪ Gravitational collapse was much more efficient along the spin axis, so the rotating ball collapsed
into thin disk with a diameter of 200 AU (0.003 light years) (twice Pluto's orbit), aka solar nebula
with most of the mass concentrated near the center.
▪ As the cloud contracted, its gravitational potential energy was converted into kinetic energy of the
individual gas particles. Collisions between particles converted this energy into heat (random motions).
The solar nebula became hottest near the center where much of the mass was collected to form the
protosun (the cloud of gas that became Sun).
▪ At some point the central temperature rose to 10 million K. The collisions among the atoms were so
violent that nuclear reactions began: the Sun was born as a star, containing 99.8% of the total mass
▪ Around the Sun a thin disk gives birth to the planets, moons, asteroids and comets.
▪ The great temperature differences between the hot inner regions and the cool outer regions of the
disk determined what of condensates were available for planet formation at each location from the
center. The inner nebula was rich in heavy solid grains and deficient in ices and gases. The outskirts are
rich in ice, H, and He (gas even at very low temp.).
Solar System
Asteroid belt situated between Mars and Jupiter, contains millions of asteroids.
Kuiper belt, beyond Neptune, much larger;
In addition to asteroids it is the source of short-period comets and contains dwarf planets
About 4.5 billion years ago, the
Earth’s moon is believed to have
been formed from material ejected
when a collision occurred between
a Mars-size object and the Earth.
Jupiter is the biggest planet in
terms of mass and volume.
Mercury is the smallest.
Asteroids and comets are both celestial bodies orbiting our Sun, and they both can have unusual
orbits, sometimes straying close to Earth or the other planets. They are both “leftovers” — made
from materials from the formation of our Solar System 4.5 billion years ago
Asteroids consist of metals and
rocky material. Those of size less
than 300 km have irregular shape
because their gravity is too weak
to compress them into spheres.
Comets are irregular objects a few kilometres across comprising
frozen gases (ice), rocky materials, and dust. Observable comets
travel around the Sun in sharply elliptical orbits with periods
ranging from a few years to thousands of years. As they draw near
to the Sun the gases in the comet are vaporized, forming the
distinctive comet tail that can be millions of kilometres long and
always points away from the Sun.
Stars
Stars initially form when gravity causes the gas in a nebula to condense.
As the atoms move towards one another, they lose gravitational PE that is converted into KE.
This raises the temperature of the atoms which then form a protostar.
When the mass of the protostar is large enough, the temperature and pressure at the centre will be sufficient
for hydrogen to fuse into helium, with the release of very large amounts of energy – the star has “ignited”.
The stability of a star depends on the equilibrium between two opposing forces. The equilibrium depends
on the gravitation which can collapse the star and the radiation pressure which can make the star expand.
This equilibrium is gained through nuclear fusion which provides the energy the star needs to keep it hot
so that the star's radiation pressure is high enough to oppose gravitational contraction.
When this is balanced the star is in a state of hydrostatic equilibrium and will remain stable for up to
billions of years.
This applies to all layers of the Sun.
Gravity pulls outer layers in, gas and
radiation pressure pushes them out.
It is pretty hot at the center!!!!
The fusing of hydrogen into helium takes up the majority of a star’s lifetime and is the reason
why there are far more main sequence stars than those in other phases of their life-cycle.
At the beginning of a star's life cycle the star consists mainly of hydrogen; 98% hydrogen.
All stars follow a simple “hydrogen burning”: hydrogen fuses into helium, in order to maintain an
equilibrium between gravity and pressure.
As the hydrogen is used up the star will eventually undergo changes that will move it from the
main sequence. During these changes the colour of the star alters as its surface temperature
rises or falls and it will change size accordingly. The original mass of material in the star
determines how the star will change during its lifetime.
Nuclear Fusion within stars: “hydrogen burning”: hydrogen fuses into helium.
Stars consist mainly of hydrogen, which is used for the fusion reactions that produce almost all of
their energy.
For Sun-like stars the process advances
through the proton–proton chain
1.
Two protons fuse to form a deuterium,
and releases a positron and a neutrino.
Each positron is annihilated to
create 2γ ray photons.
2. The deuterium nucleus fuses with another
proton, and produces a helium-3 nucleus.
3.
For stars of greater than four solar masses
undergo CNO cycle.
Again, four protons are used
to undergo the fusion process;
carbon-12 is both one of the
fuels and one of the products.
Two positrons, two neutrinos
and three gamma-ray photons
are also emitted in the overall
process.
Two helium-3 nuclei fuse to produce the
helium-4 nucleus. Two protons are released
Story about
our sun
Thus, in order to produce a helium nucleus, four
hydrogen nuclei are used in total (six are used in the
fusion reactions and two are generated).
The fusing of hydrogen into helium takes up the majority of a star’s lifetime and is the reason
why there are far more main sequence stars than those in other phases of their life-cycle.
• Star is a massive body of plasma/gas held together by gravity, with fusion going
on at its center, giving off electromagnetic radiation. There is an
equilibrium between radiation/gas pressure and gravitational pressure called
hydrostatic equilibrium
Groups of stars
Despite the difficulties in assessing whether stars exist singly or in groups of two
or more, it is thought that around fifty per cent of the stars nearest to the Sun are
part of a star system comprising two or more stars.
Binary stars consist of two stars that rotate about a common centre of mass. They
are important in astrophysics because their interactions allow us to measure
properties that we have no other way of investigating. For example, careful
measurement of the motion of the stars in a binary system allows their masses to
be estimated.
• Clusters: Gravitationally bound system of galaxies/stars.
• Stellar cluster is a group of stars held together by gravitation in same
region of space, created roughly at the same time from
the same nebula.
Open clusters consist of up to several hundred stars that are younger than
ten billion years and may still contain some gas and dust. They are located
within our galaxy, the Milky Way, and so lie within a single plane.
Globular clusters contain many more stars and are older than eleven billion
years and, therefore, contain very little gas and dust. There are 150 known
globular clusters lying just outside the Milky Way in its galactic halo.
Globular clusters are essentially spherically shaped.
The Pleiades is a stellar
cluster of about 500
stars that can be seen
with the naked eye
The galactic halo is an extended, roughly spherical component of a galaxy
which extends beyond the main, visible component. Several distinct
components of galaxies comprise the halo: the galactic spheroid (stars) the
galactic corona (hot gas, i.e. a plasma) the dark matter halo.
Constellation is a pattern formed by stars that are in the same general direction
when viewed from the Earth. Such stars are not held together by gravity.
Nebula
Regions of intergalactic cloud of dust and gas are called nebulae.
As all stars are “born” out of nebulae, these regions are known as stellar
nurseries. There are two different origins of nebulae. The first origin of
nebulae occurred in the “matter era” around 380 000 years after the Big
Bang. Dust and gas clouds were formed when nuclei captured electrons
electrostatically and produced the hydrogen atoms that gravitated
together.
The second origin of nebulae is from the matter which has been ejected
from a supernova explosion. The Crab Nebula is a remnant of such a
supernova.
Other nebulae can form in the final, red giant, stage of a low mass star
such as the Sun.
• Galaxy is a huge group of stars, dust, and gas held together by gravity,
often containing billions of stars, measuring many light years across.
Some galaxies exist in isolation but the majority of them come in clusters
containing from a few dozen to a few thousand members.
The Milky Way is part of a cluster of about 30 galaxies called
the “Local Group” which includes Andromeda and Triangulum.
Regular clusters consist of a concentrated core and are spherical in shape.
Irregular clusters have no apparent shape and a lower concentration of galaxies
within them.
The Andromeda galaxy with
Since the launch of the Hubble Space Telescope it has been observed that even two smaller satellite galaxies.
larger structures, superclusters, form a network of sheets and filaments;
approximately 90% of galaxies can be found within these.
In between the clusters there are voids that are apparently empty of galaxies.
Spiral galaxies the most common class of galaxies (both The Milky Way and Andromeda).
They have a flat rotating disc-shape with spiral arms spreading out from a central galactic
bulge that contains the greatest density of stars. It is increasingly speculated that, at the
centre of the galactic bulge, there is a black hole.
The spiral arms contain many young blue stars and a great deal of dust and gas.
Other galaxies are elliptical in shape, being ovoid or spherical – these contain much less gas
and dust than spiral galaxies; they are thought to have been formed from collisions between
spiral galaxies. Irregular galaxies are shapeless and may have been stretched by the presence
of other massive galaxies – the Milky Way appears to be having this effect on some nearby
dwarf galaxies.
Astronomical distances
Resulting from the huge distances involved in astronomical measurements, some unique,
non-SI units have been developed. This avoids using large powers of ten and allows
astrophysicists to gain a feel for relative sizes and distances.
1 light-second = (3.0 × 10 m/s)(1.0 s) = 3.0 × 108 m = 3.0 × 105 km
1 light-minute = 18 × 106 km
1 light-year (ly) 1 ly = 9.46 × 1015 m ≈ l013 km.
The Earth—Moon distance is 384,000 km = 1.28 light-seconds.
The Earth—Sun distance is 150,000,000 km = 8.3 light-minutes.
The astronomical unit (AU): the average distance between the Sun and the Earth. It
is really only useful when dealing with the distances of planets from the Sun.
1 AU= 1.50 × 10 11 m ≈ 8 light minutes
1 parsec (pc): This is the most commonly used unit of distance in astrophysics.
1 pc= 3.26 ly = 3.09 × 10 16 m
Distances between nearby stars are measured in pc, while distances between distant
stars within a galaxy will be in kiloparsecs (kpc), and those between galaxies in
megaparsecs (Mpc) or gigaparsecs (Gpc).
Parallax Method relies on the apparent movement of the nearby star against
the background of further stars as the earth orbits the sun.
• It is the most direct measure of distance.
• two apparent positions of a close star with respect to position
of distant stars as seen by an observer in both January and July
are compared and recorded to find angle p
• tan 𝑝 =
𝑆𝑢𝑛 − 𝐸𝑎𝑟𝑡ℎ 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 1𝐴𝑈
=
𝑆𝑢𝑛 − 𝑠𝑡𝑎𝑟 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑑
For small angles: sin p  tan p  p
1𝐴𝑈
𝑑=
𝑝
when talking about stars, parallax is very, very small number.
Parallaxes are expressed in seconds.
p  rad 


180  60  60 p  sec 
d  m 
1
648000 1
→ p rad  
p  sec 
 
1 149597870691 648000  3.08  1016 m

p  sec 
p  sec 
d  pc  
1
p  sec 
1 AU = 149597870691 m
1 pc = 3.09 X 1016 m
“Parsec” is short for
parallax arcsecond
‘One parsec is a distance corresponding to a parallax of one arc second'
• Even the nearest star has a tiny parallax!
► First measured in 1838
► The closest bright star Alpha Centauri
4.3 light-year
0.75 pc
The farther away an object gets, the smaller its
shift. Eventually, the shift is too small to see.
Parallax has its limits…
http://www.astronomy.ohiostate.edu/~pogge/Ast162/Movie
s/parallax.gif
There is a limit to the distance that can be measured using stellar parallax – parallax
angles of less than 0.01 arcsecond are difficult to measure from the surface of the Earth
because of the absorption and scattering of light by the atmosphere. Turbulence in the
atmosphere also limits the resolution because it causes stars to “twinkle”.
1
Using the parallax equation, gives a maximum range of 𝑑 = 0.01 = 100 pc
In 1989, the satellite Hipparcos (an acronym for High Precision Parallax Collecting Satellite)
was launched by the European Space Agency (ESA). Being outside the atmosphere,
Hipparcos was able to measure the parallaxes of 118 000 stars with an accuracy of 0.001
arcsecsond (to distances 1000 pc); its mission was completed in 1993.
Gaia, Hipparcos’s successor, was launched in 2013 and is charged with the task of
producing an accurate three-dimensional map showing the positions of about a
billion stars in the Milky Way. This is about one per cent of the total number of stars
in the galaxy! Gaia is able to resolve a parallax angle of 10 microarcsecond
measuring stars at a distance of 100 000 pc.
limits because of small parallaxes:
d ≤ 100 pc from Earth
d ≤ 1000 pc from Hipparcos
d ≤ 100 000 pc from Gaia
To understand the nature, to interpret many beautiful phenomena you have to have a
tool. We are introducing something that we know all about and then we’ll compare
the nature with that ideal case!!!!!!!
A black body is a theoretical object that absorbs 100% of the
radiation that
that is incident
uponhas
them
it. found
Because
In practice
no material
been
to there is no
reflection or
transmission
it appears
perfectly
black. in its
absorb
all incoming
radiation,
but carbon
graphite
absorbsas
allperfect
but about
3%. Itofis radiation, emitting the
Such bodies
wouldform
also behave
emitters
a perfect
emitterpossible
of radiation.
maximumalso
amount
of radiation
at their temperature.
This type of radiation consists of every wavelength possible but containing
different amounts of energy at each wavelength for a particular temperature.
• Black bodies in thermal equilibrium emit energy to balance the energy
they absorb and remain at a constant temperature.
The only parameter that determines how much EM radiation the black body
radiates for the given wavelength is its temperature.
That is why the radiation emitted by an blackbody is often called thermal radiation.
The hotter the blackbody, the more EM radiation at all wavelengths.
• Black body emits energy according to Planck’s and Wien’s law
Although stars are not perfect black-bodies they are capable of emitting
and absorbing all wavelengths of electromagnetic radiation.
Blackbody radiation
Planck's Law predicts the radiation of a blackbody at
different temperatures.
It gives intensity of radiation as a function of wavelength.
It depends only upon the temperature of the black body.
• The hotter the blackbody the more energy
emitted per unite area at all wavelengths.
Stars’ and planets’ radiation spectrum is approximately the same as black-body radiation.
Except for their surfaces, stars behave as blackbodies.
Wien’s law: Wavelength at which the intensity
of the radiation is a maximum λmax, is:
2.9×10-3
max (m) 
T(K)
• The peak emission from the blackbody moves to shorter wavelengths as the
temperature increases (Wien’s law)
Note that the peak shifts with temperature.
Luminosity of a star is the total power radiated by a star.
(total energy per second)
If we regard stars as black body, then luminosity is
L = A σT4 (W)
Stefan-Boltzmann’s law
A is surface area of the star, T surface temperature (K), σ is Stefan-Boltzmann constant.
When we assume that a star is spherical we can use this equation in the form:
L = 4πR2σT4
(W)
R is the radius of the star
(Apparent) brightness (b) is the power from the star received per
square meter of the Earth’s surface
L
b = 4π𝑑2
(W/m2)
L is luminosity of the star; d its distance from the Earth
Can be measured, for example, by using a telescope and a charge-coupled device ? IB
Photometer!!! Internet
Some data for the variable star Betelgeuse are given below.
Average apparent brightness = 1.6 × 10–7 Wm–2
Radius = 790 solar radii
Earth–Betelgeuse separation = 138 pc
The luminosity of the Sun is 3.8 × 10 26 W and it has a surface temperature of 5800 K.
(a) Calculate the distance between the Earth and Betelgeuse in metres.
(b) Determine, in terms of the luminosity of the Sun, the luminosity of Betelgeuse.
(c) Calculate the surface temperature of Betelgeuse.
For a star, state the meaning of the following terms: (a) (i) Luminosity (ii) Apparent brightness
(i) The luminosity is the total power emitted by the star.
(ii) The apparent brightness is the incident power per unit area received at the surface of the Earth.
(b) The spectrum and temperature of a certain star are used to determine its luminosity to be
approximately 6.0×1031 W. The apparent brightness of the star is 1.9×10-9 Wm-2. These data can be used
to determine the distance of the star from Earth. Calculate the distance of the star from Earth in parsec.
L
L
b=
→
d
=
=
4π𝑑2
4π𝑏
6.0 × 1031
= 5.0 × 1019 𝑚
−9
4𝜋 × 1.9 × 10
5.0 × 1019
5.0 × 1019
𝑏 = 5.0 × 10 𝑚 =
𝑙𝑦 =
𝑝𝑐 = 1623 𝑝𝑐
9.46 × 1015
3.26 × 9.46 × 1015
19
𝑏 ≈ 1600 𝑝𝑐
(c)Distances to some stars can be measured by using the method of stellar parallax.
(i) Outline this method.
(ii) Modern techniques enable the measurement from Earth’s surface of stellar parallax angles
as small as 5.0 × 10–3 arcsecond. Calculate the maximum distance that can be measured
using the method of stellar parallax.
(i) The angular position of the star against the
background of fixed stars is measured at six
month intervals. The distance d is then found
using the relationship d = 1/p
𝑖𝑖 𝑑 =
1
= 200 𝑝𝑐
5 × 10−3
Suppose I observe with my telescope two red stars A and B that are part of a binary star system.
Star A is 9 times brighter than star B.
What can we say about their relative sizes and temperatures?
Since both are red (the same color), the spectra peak at the same wavelength.
By Wien's law
2.9×10-3
max (m) 
T(K)
L = 4π R2 σ T4
then they both have the
same temperature.
(W)
Star A is 9 times brighter and as they are the same distance away from Earth.
Star A is 9 times more luminous:
LA 4RA2TA4

LB 4RB2TB4
RA2
 9 2
RB
 RA  3 RB
So, Star A is three times
bigger than star B.
Suppose I observe with my telescope two stars, C and D, that form a binary star pair.
▪ Star C has a spectral peak at 350 nm - deep violet
▪ Star D has a spectral peak at 700 nm - deep red
What are the temperatures of the stars?
By Wien's law
 peak
3
2.9

10

T
3
3
2.9

10
2.9

10
TC 

 8300 K
 peak
350 10 9
 peak in m
T in K
3
3
2.9

10
2.9

10
TD 

 4150 K
 peak
350 10 9
If both stars are equally bright (which means in this case they have equal luminosities
since the stars are part of a pair the same distance away), what are the relative sizes of
stars C and D?
LC 4RC2 TC4

LD 4RD2 TD4
RC2 83004
RC2
4
 1  2

2
 
RD 41504
RD2
RD2  16 RC2  RD  4 RC
Star C is 4 times smaller than star D.
The Sun, our favorite star!
The Sun is the basis
for all of our
knowledge of stars.
Why?
WE CAN SEE IT REALLY WELL.
Today we will take a journey to the
center of the Sun, starting with what
we can see…
…and ending up
deep in the core.
Overview of Solar Structure
Main Parts:
The Sun is made of
mostly HYDROGEN and
HELIUM
The Corona
Mass is ejected
into space as the
solar wind
• Outer layer of the Sun
• Millions of degrees
but very diffuse
• Extends millions of
kilometers into space
• Hot and energetic,
gives off lots of x rays!
The solar wind streams off of the Sun in all
directions at speeds of about 400 km/s (about
1 million miles per hour). The source of the
solar wind is the Sun's hot corona. The
temperature of the corona is so high that the
Sun's gravity cannot hold on to it.
• The Sun has intense magnetic fields
• The magnetic fields release energy from the Sun
• Release seen in sunspots, flares, coronal mass ejections &
other phenomena
Flares
This twisting leads to the loopy
structures we see!
BE
BEAMAZED!
AMAZED!
Earth to scale.
Yes, really.
The Sun’s magnetic fields create
sunspots
The Sun has an 11-year solar cycle
Maximum
Minimum
Visible
Ultraviolet
Ultraviolet
Sunspots!
-284
-174
304nm
nm
nm
Ultraviolet
195
nm
temperature is about 5800 K…
• Remember how the temperature and
color of stars are related? The temperature
of our Sun gives it its yellowish color!
Our Sun is really
yellowish green,
but our
atmosphere
absorbs and
scatters some of
the blue light.
Sunshine = Energy from Fusion
E=
Energy
2
mc
Mass
Speed of
Light
Speed of light is BIG-- so a little
mass can turn into a LOT of energy!
review:
• Gravity compresses and heats the center of the sun
• At the core nuclear reactions take place
• The Sun is a giant nuclear reactor
• Energy flows from the core outward, but how
does it get out and end up as sunshine?
The next two layers of the Sun
are all about getting the
energy being made in the
core out into space!
It takes a lot of time, but we
get it eventually.
How does energy get from one place to another?
1.
2.
3.
Hot stuff rises…Cool stuff sinks!
BOILING
Convection
Metal of a pan heats by conduction…
…heat travels through the atoms of the pan
Not very important for stars!
Conduction
Radiation
•
•
•
Photons can “scatter” off of unbound electrons
When they scatter, the photons share their energy
with the electrons
Ionized
The electrons get hotter
gas
Convection and Radiation are most important for the
Sun!
Really high resolution spectrum of the Sun:
lots of absorption lines!
Hot source makes a continuous thermal
spectrum
Light passing through a cloud of cooler
gas gets some light absorbed out:
ABSORPTION SPECTRUM
 Outer layers of the Sun are cooler than interior
 Interior opaque part of Sun produces a thermal spectrum, while
cooler outer layers produce absorption lines!
How Much Fusion a
Second?
• Einstein’s formula
– E = m c2
• The luminosity of the Sun is
– 4 x 1026 Watts
• So …
The Sun loses
4 million tons
of mass per
second!
The Sun Takes About 4
Weeks to Rotate
•What is the sun made of?
• We know diameter & mass
• Density = mass / volume
– Density = 1.4 times water!
– Low density +
– Hot temperature
The Sun is a ball of gas!
• Determined from study of spectrum and
atomic spectra in the laboratory
• 74% Hydrogen
• 25% Helium
• 1% All other elements
Particles emitted by the sun detected
on the Earth confirm picture of the Sun
given in this power point. Good night.
Very important thing is the question of
mass
That question can be translating into question:
What are binary stars ????????
star
Binary Stars
A large ball of gas that creates and
emits its own radiation.
two balls – not necessarily gas,
not necessarily emitting radiation
Can be white dwarf, even black hole
>60% of Stars are in
Binary Systems
Contains two (or sometimes more)
stars which orbit around their common
center of mass.
Importance - only when a star is in a
binary system that we have the possibility
of deriving its true mass.
The more unequal the
masses are, the more
it shifts toward the
more massive star.
The period – watching the system for many years.
The distance between the two stars - if we know the
distance to the system and their separation in the sky.
→ the masses can be derived.
2 3
4

d
T 
G  M1  M 2 
2
The masses of many single stars can then be determined by
extrapolations made from the observation of binaries.
Visual binary: a system of stars that can be seen as two separate
stars with a telescope and sometimes with the unaided eye
Hubble image of the
Sirius binary system.
Sirius B can be clearly
distinguished (lower
left)
They are sufficiently close to Earth and the stars are well enough separated.
Sirius A, brightest star in the night sky and its companion first white dwarf star to
be discovered Sirius B.
Spectroscopic binary: A binary-star system which from
Earth appears as a single star, but whose light spectrum
(spectral lines) shows periodic splitting and shifting of
spectral lines due to Doppler effect as two stars orbit one
another.
have patience
Eclipsing binary: (Rare) binary-star system in which the two stars are too
close to be seen separately but is aligned in such a way that from Earth we
periodically observe changes in brightness as each star successively
passes in front of the other, that is, eclipses the other
Algol known colloquially as the Demon
Star, is a bright star in the constellation
Perseus. It is one of the best known
eclipsing binaries, the first such star to be
discovered.
NASA
An animation of an eclipsing binary
system undergoing mass transfer.
X-ray Binaries
A special class of binary stars is the X-ray binaries, so-called
because they emit X-rays. X-ray binaries are made up of a normal
star and a collapsed star (a white dwarf, neutron star, or black hole).
These pairs of stars produce X-rays if the stars are close enough
together that material is pulled off the normal star by the gravity of
the dense, collapsed star. The X-rays come from the area around
the collapsed star where the material that is falling toward it is
heated to very high temperatures (over a million degrees!).