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Introduction to Astronomy & Astrophysics

OrWhat Astrophysicists do?

Monday 27 April 2015

The constellation Orion

What is the universe made up of?

% by mass


Astronomy : Most ancient science

Jantar Mantar in JaipurIndias legacy in astronomy


The windows to the universe

Electromagnetic radiation Neutrinos Gravitational waves


molecular, atomic excitations & ionizations

(a) O3 : UV(b) H2O : IR(c) ionosphere reflection : Radio(d) photoelectric absorption : Xray


Two windows to do astronomy from earth

1.Optical (and some IR)

2.Radio

The rest of the EM spectrum from space


Mauna Kea, Hawaiisee http://www.ifa.hawaii.edu/mko/

A dormant volcano, 4.2km above sea level


2m Himalayan Chandra Telescope (HCT) at Hanle, Leh, Ladak


Thirty meter telescope(artist impression)

Planned to be constructed


The sizes of various telescope mirrors


Hubble Space Telescope


a planetary nebula

a spiral galaxy

a cluster of galaxies

Many forms of wonders


Very Large Arrayradio telescope,

New Mexico, USA


Indias GMRT

30 dishes, 45m diameter each


Radio observations (left) of galaxy M 87 in comparison with its optical observations (above)


The center of our Galaxy,viewed in radio wavelength (VLA, 90cm)


Xray Astronomy

The Chandra xray telescope orbits the earth while looking at the high energy sky


Chandra image of an elliptical galaxy


Galaxy M 10623.5 Million

Light year away from us

Multiwavelength Astronomy

This image is a composite of images taken in multiple wavelengths (optical+xray+radio). You can see the spiral arms of this spiral galaxy in red & white shades (also some blue stars are visible). That is the optical image. Notice the diffuse structure in blue & purple. Blue is x-ray and purple is radio. This structure is not visible in optical. Views through multiple observational windows are required to build up complete picture of an astronomical object.


RCW 86, SNR.

In 185 AD the Chinese Astronomers seem to have observed this explosion. This is the remnant of the explosion visible even now. This is another composite image of different wavelengths. Blue and green colors are from the x-ray image. Yellow & red are part of the infrared image.

Multiwavelength Astronomy

ps : Images in both previous slide and this are false-colored.


Locations in the sky

Celestial sphere : Imaginary sphere with earth as centre


Coordinate system

Celestial (a.k.a Equatorial) coordinate system


Its all about angles

smaller angles are measured in arcminutes ()and arcseconds ()


Convince yourself by checking how long does sun take to cross your fingers...

Or whether you can block moon with your little finger...


Why do we have total solar eclipse?

Total solar eclipse is possible only because the angular sizes of Sun and moon are same.

Moon 3.8x105 km away from earth

Diameter : 3474 km

Sun 1.5x108 km away from earth

Diameter : 1. 4 x106 km


Angular ResolutionAbility to see distinctly

Eyes : 1

What decides the limiting angular resolution ?

Diffraction introduces a certain fuzziness in the image.

A telescope mirror of D diameter

~ /DMonday 27 April 2015

Constellation Gemini

CastorAlpha gemenorium

a visual binaryin fact 4 stars!


Angular resolution

The spatial resolution of a telescope depends on

(i) the size of its lenses or mirrors and (ii) the size of the pixels in its detectors (iii) and by the smoothness of a telescope's mirrors or lenses.(iv) the resolution is also limited by air turbulence (for ground based observatories)

Andromeda : (a)10 (b)1 (c)5 (d)1

A simulation of the same region, how it will be viewed through three different Infrared telescopes. From left to right IRAS, ISO and

Spitzer telescopes.


Stars rise & set


Local sky


Arches national park, Utah, USA


Local sky


Distance in Astronomy1. Parallax

d = 1/pAssumed :-1. sun is fixed2. stars are fixed

In arcseconds, the parallax angle,p = 1 AU . (180/pi) . 3600


Luminosity, Flux, Stellar Spectra, HR diagram


Luminosity, L(power)

dE/dt

Flux, F(energy/time/unit-area)

dE/(dt dA)

d

L/4.Pi.d2


basicastro4 October 26, 2006

12 CHAPTER 2

Figure 2.1 Flux per wavelength interval emitted by different types of stars, at their sur-

faces, compared to blackbody curves of various temperatures. Each black-

bodys temperature is chosen to match the total power (integrated over all wave-

lengths) under the the corresponding stellar spectrum. The wavelength range

shown is from the ultraviolet (1000 A= 0.1 m), through the optical range(3200-10,000 A), and to the mid-infrared (105 A= 10 m). Data credit: R.Kurucz.

(since the solid angle of a full sphere is 4pi steradians). The intensity of blackbodyradiation is therefore

I =c

4piu =

2h3

c21

eh/kT 1 B . (2.4)

In cgs, one can see the units now are erg s1 cm2 Hz1 steradian1. We have keptthe product of units, s1 Hz1, even though they formally cancel out, to recall theirdifferent physical origins: one is the time interval over which we are measuring

the amount of energy that flows through a unit area; and the other is the photon

frequency interval over which we bin the spectral distribution. I of a blackbody isoften designated B.Now, let us find the net flow of energy that emerges from a unit area (small

enough so that it can be presumed to be flat) on the outer surface of a blackbody

(see Fig. 2.2). This is obtained by integrating I over solid angle on the half spherefacing outwards, with each I weighted by the cosine of the angle between theintensity and the perpendicular to the area. This flux, which is generally what one

actually observes from stars and other astronomical sources, is thus

f = pi/2=0

I cos d = I2pi12= piI =

c

4u =

2pih3

c21

eh/kT 1 . (2.5)

Blackbody spectrum. x-axis is wavelength, y-axis is the power emitted per unit wavelength per unit area of the blackbody. The body emits in all wavelengths. But in a given wavelength, it always emits more if its temperature is more. In other words, Temperature is the only quantity that determines the power/area (== flux) of a blackbody.

Stellar spectrum. Spectra of different stars are plotted. x-axis is wavelength, y-axis is the power emitted per unit wavelength per unit area of the star. Solid curves are fits to the spectrum using blackbody models (of various temperatures). We can see how it is remarkably similar to the blackbody spectrum at the right side.

Stellar Spectrum & Blackbody Spectrum

Power, L = 4R2 T4

Energy/area/time = surface flux = T4

max T = constMonday 27 April 2015

Hertzsprung-Russell Diagrams

Hertzsprug & Russell

When total luminosity (==power) emitted by stars are plotted vs their surface temperature, the plot didnt look random. Instead some patterns started appearing.

Both the plots are same. HR diagram is a plot of Luminosity vs surface Temperature of stars. Ignore the right y-axis and bottom x-axis of the plot above.


M(r)

P+dP

P

r+dr r

What makes stars stable?


M(r)

P+dP

P

r+dr r

Gravitational force on the cylinder



M(r)

P+dP

P

r+dr r

Gravitational force on the cylinder

To be equal & opposite to the diff. in pressure



Equation of hydrostatic equilibrium

Stellar matter ideal gas

Boyles law : P = kB T (2/mH)Special cases where P = P() alone

An order of magnitude estimate : Solar core temperature

What energizes the Sun?


Replace with averages

Substitute for Ms and Rs, Pc ~ 6 x 1014 N/m2 And use Pc = n kB Tc to get Tc ~ 107K


Main sequence star

big gas cloud of hydrogen gets heated up to ~107K by gravitational contraction

Nuclear fusion reaction (hydrogen to helium) starts

Thus a main sequence star (stars that burn H to He) is formed. Its luminosity is a sole function of its mass


Stellar Evolution in a Nutshell


How to produce huge amount of energy?

Mass & energy are not two separate entities.One could be traded for the other.

How to practically achieve this?

Binding energy per nucleon curve.

See that the curve has a maximum around A=60. Most stable element is the one with maximum BE/nucleon. To disrupt it, relatively more energy has to be provided. On both sides of this element, BE is lesser (ignore some fluctuations in between, like for 4He).


If you have Z protons and (A-Z) neutrons forming a nucleus, the mass of the nucleus

mnuc < Z mp + (A-Z) mn

ie., There is a mass deficit. Energy equivalent of this mass deficit is the BE. (noted as negative conventionally)

BE = [ Z mp + (A-Z) mn - mnuc ] c2

So if you fuse nucleons and get a nucleus, this energy can be released.

4 protons 4He : releases energy of 0.007 mp c2

Hence if we have 2x1030kg of hydrogen, we can get ~1047 J of energy. Sun can shine for 1011 years!

While going from a lower BE/nucleon state to a higher BE/nucleon state energy can be released.Because the curve in the previous page has a maximum, this can happen in two ways : either from A > 60 side (fission) or from A< 60 side (fusion).


Coulomb BarrierBefore two protons to be able to collide, they have to overcome their electrostatic repulsion

10-15 mkinetic energy of the colliding nucleons are required to overcome this barrier

Hence, nuclear fusion can happen only at high temperatures.

Classically not possible to tunnel through this barrier.


After hydrogen burning

If the core temp is high enough He -> C -> O -> Fe (stops)

Stars like sun never reach such high temperatures. They are left with CO core where no fusion happens (white dwarf).

Red giant : H burns in an outer shell. Blue super giant : CO burning core, He shell, H envelope White dwarf, CO core resist gravity due to degeneracy

pressure (pressure arising in fermions due to Paulis exclusion principle)


Mass increases, radius decreases If mass increases beyond a limit, the

degeneracy pressure of free electrons can not support the gravity.

This is the Chandrasekar limit Initial mass of the star is 1.4M_sun White dwarfs small luminosity (note

that it occupies the left bottom corner of the HR diagram, it has very low luminosity) originates from its residual heat

Chandrasekhar and White dwarf mass limit


Higher mass stars


Neutron stars & Supernovae

Higher mass stars have an Fe core.

No more fusion (Fe of A~60 is the most stable element -- remember the BE/nucleon curve). Core collapses to become a neutron star.

Lot of gravitational potential energy is released. Causing an SN explosion

Above : (perhaps) An ancient SN happened in Milkyway seen by our ancestors in the American southwest.

Below : A modern SN, happened at the edge of a far away galaxy.


Pulsars


Type Ia Supernovae


Keplers laws & Astrophysics

stellar mass from binaries planetary orbits dark matter


Keplers laws Orbit of a planet is an ellipse. Sun at one of the focii

Equal areas at equal time

P2 = k a3 (P is period of the planet, a is semi-major axis of its orbit, k is a constant.)

k(M), where M is the mass of Sun


Keplers 3rd law in solar system

Note : this plot is in log-scale. Hence it is linear


Binary stars

-Algol (the Demon)-Alpha-centauri-Beta-Lyrae-Rigel-Sirius-Spica

Some examples


Mass measurement in binaries

Only from binary stars can we accurately determine masses of individual stars

M1 a1 = M2 a2

a = a1 + a2

a2 = M1 a /(M1+M2)

P = 2 pi/;

2 = G(M1+M2)/a3If we can map each orbits & if we know distance & if we know P, we get M1 & M2

We assumed circular orbits in the above calculation.a1 and a2 are the distances of the two masses M1 and M2 respectively from the center of mass (magenta point). In the circular orbit, of both stars are the same. You can convince yourself of this by looking at the animations at http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)


Milkyway : Our home

Artists image


What is a galaxy?

Stars Diffuse matter

(gas & solid particles that do not self-gravitate)

Dark Matter


Diffuse gas & solid particles : Nebulae


And what about dark matter?

We need to understand a bit more before getting into that.


Rotation curve of spiral galaxies

Vera Rubin. Pioneer of galaxy spectrum studies. Thanks to her, world realized there may be matter that can not be seen (because it does not interact with photons, ie., it does not interact via electromagnetic forces*). Matter that is Dark. Presence of such material can only be inferred via its gravitational interactions.

* There are 4 known type of forces in the nature. Electromagnetic, Weak, Strong, and Gravitational.


How does galaxy spectrum studies help in knowing the presence of Dark Matter?

spectral lines can tell the velocity with which material is moving in the galaxy. [How? : see next section on doppler shift]

velocity of the material carries information of the gravitational potential in which the material moves.


Velocity of light source from doppler shift


The background(blue) is the sketch of a galaxy. Concentric circles are drawn to represent different radii (from the galactic center). At different radii, the material has different rotational velocities.

The red curve is the velocity of material vs its distance from the galactic center.

Such a curve is called Rotation Curve


Rotation curve of spiral galaxies

Both M33 galaxy and our galaxy rotation curves show that velocity is much larger than expected at large distances from the centre. At these large distances, there is very less visible matter. Velocities should behave like in our solar system (like in slide-51), because all the mass is concentrated at smaller radii. Velocity should fall off with distance. That doesnt happen implies that there is matter that is not emitting light.

Our galaxy rotation curve


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optical image

chandra image

xray image

infrared image

radio observations

blue purple

earth diameter

blue stars