PHYS 3380 - Astronomy The second exam will be next Monday, November 9 at the regular class time. It is closed book but you may bring in one 8 1/2 X 11.

PHYS 3380 - Astronomy

The second exam will be next Monday, November 9 at the regular class time. It is closed book but you may bring in one 8 1/2 X 11 inch “cheat sheet” with writing on both sides. It will cover everything I have covered in class up through last Wednesday’s class (excluding what I covered on the first exam – i.e., starting with the class on 9/28/15). It will not cover anything from today’s or Monday’s class. The homework solutions up to assignment #8 are on line.


Homework Set #911/4/15

Due 11/16/14Chapter 12

Review Questions6,8Problems3, 7Learning to look1

Chapter 13Review Questions 2, 6Problem1


ALMA - an astronomical interferometer of radio telescopes in the Atacama desert of northern Chile

- on the Chajnantor plateau at 5,000 meters altitude - high and dry site - crucial to millimeter wavelength operations- 66 12-meter , and 7-meter diameter radio telescopes - up to 16 km baseline

Atacama Large Millimeter/submillimeter Array (ALMA)

PHYS 3380 - AstronomyThe principal sources of atmospheric attenuation are molecular resonances of water vapor, oxygen and ozone. The resonances of water vapor and oxygen are pressure broadened and cause attenuation far from the resonance frequencies. Below 30 GHz the absorption is dominated by the weak transition of H20 at 22.2 GHz, and rarely exceeds 20% in the zenith directions. The oxygen bands in the 53-67 GHz band are considerably stronger, and no astronomical observations can be made from the ground in this band. A similar effect happens with the isolated 118 GHz O2 line, which makes observations impossible in the 116-120 GHz band. There is a series of strong water vapor lines at 183, 325, 380, 448, 475, 557, 621, 752, 988 and 1097 GHz and higher. Observations can be made in the windows between these lines at dry locations like the Chajnantor plateau.


Composite image of the young star HL Tauri and its surroundings using data from ALMA (enlarged in box at upper right) and Hubble (rest of the picture). This is the first ALMA image where the image sharpness exceeds that normally attained with Hubble.


Incredible fine detail never been seen before in the planet-forming disc around a young star. These are the first observations that have used ALMA in its near-final configuration and the sharpest pictures ever made at submillimetre wavelengths. Show substructures within the never been seen before - possible positions of planets forming in the dark patches within the system.

PHYS 3380 - Astronomy Star Clusters

47 Tuc – Globular clusterNGC3293 - Open cluster

10 - 1000 starsAbout 25 pc in diameterOpen, transparent appearance - stars are not crowded together

105 - 106 stars10 - 30 pc in diameterNearly spherical and much closer together than open clusters


•MS turn off point varies massively, lowest is consistent with globulars•Maximum luminosity of stars can get to Mv-10

•Very massive stars found in these clusters

•MS turn-off points in similar position. Giant branch joining MS•Horizontal branch from giant branch to above the MS turn-off point•Horizontal branch often populated only with variable RR Lyrae stars

Open Cluster HRD Globular Cluster HRD


Differences are interpreted due to age – open clusters lie in the disk of the Milky Way and have large range of ages. The Globulars are all ancient, with the oldest tracing the earliest stages of the formation of Milky Way (~ 12 109 yrs)

Open vs. Globular Clusters

Globular clusters are old and metal poor - produce a horizontal branch

• Mass-loss dependent on metallic content - drives bluewards evolution

Open clusters are metal rich - produce a red clump

• More metal rich stars appear towards red

• Clump stars extreme red end of HB


PHYS 3380 - Astronomy Modelling star clusters

Best way to check stellar evolutionary calculations is to compare calculated and observed tracks. But can’t observe stars as they evolve - need to use star clusters.

Isochrones:

A curve which traces the properties of stars as a function of mass for a given age.

Be clear about the difference with an evolutionary track - which shows the properties of a star as a function of age for a fixed mass.

Isochrones are particularly useful for star clusters - all stars born at the same time with the same composition. Consider stars of different masses but with the same age . Make a plot of Log(L/L) vs. LogTeff for an age of 1Gyr. The result is an isochrone. Important - When we observe a cluster, we are seeing a “freeze-frame” picture at a particular age. We see how stars of different masses have evolved up to that fixed age (this is not equivalent to an evolutionary track).


NGC6231 young cluster

Age~ 6Myrs

Pleiades young open cluster

Age~ 100Myrs

47 Tuc : globular cluster. Age= 8-10Gyrs

NGC188: old open cluster . Age= 7Gyrs

PHYS 3380 - AstronomyEvidence for Stellar Evolution: Variable StarsSome stars show intrinsic brightness variations not caused by eclipsing in binary systems.Most important example: d Cephei

Cepheid stars - oscillate between two states1. star is compact - large temperature and

pressure gradients build up in the star. These large pressures cause the star to expand.

2. When the star is in its expanded state, there is a much weaker pressure gradient in the star. Without the pressure gradient to support the star against gravity, the star contracts and returns to its compressed state.

Light curve of d Cephei


Pulsating Variables: The Valve Mechanism

Partial He ionization zone is opaque and absorbs more energy than necessary to balance the weight from higher layers.

=> Expansion

Upon expansion, partial He ionization zone becomes more transparent, absorbs less energy => weight from higher layers pushes it back inward. => Contraction.

Upon compression, partial He ionization zone becomes more opaque again, absorbs more energy than needed for equilibrium => Expansion

PHYS 3380 - AstronomyCepheid Variables: The Period-Luminosity Relation

The variability period of a Cepheid variable is correlated with its luminosity

- most recent empirical formula produced using data from the Hipparcos satellite, to calculate the distances to many Galactic Cepheids via trigonometric parallax.

(P is in days)

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Mv = -2.81 log(P) - (1.43 ± 0.1)

Cepheids have masses between five and twenty solar masses. More massive stars are more luminous and have more extended envelopes. Because these envelopes are more extended and the density in their envelopes is lower, their variability period, which is proportional to the inverse square root of the density in the layer, is longer. the more luminous it is, the more slowly it pulsates.

PHYS 3380 - AstronomyPopulation I - Type I Cepheids - metal-rich stars

• common in the spiral arms of the Milky Way galaxy• extreme Population I - youngest stars found farther in • intermediate Population I stars are farther out, etc. • Sun is considered an intermediate Population I star • have regular elliptical orbits of the galactic centre, with a low relative velocity• more likely to possess planetary systems, since planets, particularly terrestrial planets, thought to be formed by the accretion of metals• intermediary disc population - between the intermediate populations I and II

Population II - type II Cepheids - metal-poor stars • more primitive. formed during an earlier time of the universe• intermediate Population II - common in the bulge near to the centre of the galaxy• halo Population II - in the galactic halo • believed that Population II stars created all the other elements in the periodic table, except the more unstable ones.

Type II Cepheids not as opaque as type I • energy escapes more easily• less luminous for same period of pulsation


Population III - metal-free stars • hypothetical population of extremely massive and hot stars with virtually no metal content, except for a small quantity of metals formed in the Big Bang, such as Lithium-7• believed to have been formed in the early universe.

RR Lyrae - older, less massive, and fainter (~45 L) than Cepheids• little over half the Sun’s mass• from speed at which RR Lyraes pulsate (~0.2 - 2 days) know that size cannot be changing enough to cause the change in brightness that we see.

- surface of the star would have to move in and out so fast that the star would blow itself apart.

• as the RR Lyrae shrinks and expands, the surface heats up and cools down.

-change in brightness accounted for by temperature change• often found in globular clusters - allow better determination of distance and metallicity

PHYS 3380 - Astronomy Cepheid Distance MeasurementsMeasuring a Cepheid’s period, we can determine its absolute magnitude. Comparing absolute and apparent magnitudes of Cepheids, we can measure their distances.

The Cepheid distance measurements were the first distance determinations that worked out to distances beyond our Milky Way.

Cepheids are up to ~ 40,000 times more luminous than our sun

can be identified in other galaxies - Edwin Hubble first identified some Cepheids in the Andromeda galaxy, thus proving its extragalactic nature


Pulsating Variables: The Instability Strip

For specific combinations of radius and temperature, stars can maintain periodic oscillations.

Those combinations correspond to locations in the Instability Strip

Cepheids pulsate with radius changes of ~ 5 – 10 %.


Period Changes in Variable Stars

Periods of some Variables are not constant over time

because of stellar evolution.

Another piece of evidence for stellar evolution.

PHYS 3380 - Astronomy The End of a Star’s LifeWhen all the nuclear fuel in a star is used up, gravity will win over pressure and the star will die.

High-mass stars will die first, in a gigantic explosion, called a supernova.

Less massive stars will form planetary nebula and die as white dwarfs or in a less dramatic event than a supernova, called a nova


The Final Breaths of Sun-Like Stars: Planetary Nebulae

The Helix Nebula

Remnants of stars with ~ 1 – a few M

Radii: R ~ 0.2 - 3 light years

Expanding at ~10 – 20 km/s (Doppler shifts)

Less than 10,000 years old

Have nothing to do with planets.


The Formation of Planetary Nebulae

The Ring Nebula in Lyra

Two-stage process:

Slow wind from a red giant blows away cool, outer layers of the star

Fast wind from hot, inner layers of the star overtakes the slow wind and excites it

=> Planetary Nebula

PHYS 3380 - Astronomy Planetary NebulaeOften asymmetric, possibly due to

• Stellar rotation• Magnetic fields• Dust disks around the stars

The Butterfly Nebula

Globe

The Ring Nebula

The Helix Nebula

Knots in theHelix Nebula

Knots in theHelix Nebula



The Remnants of Sun-Like Stars: White Dwarfs

Sunlike stars build up a Carbon-Oxygen (C,O) core, which does not ignite Carbon fusion.

He-burning shell keeps dumping C and O onto the core. C,O core collapses and the matter becomes degenerate.

Formation of a White Dwarf


Equation of State of a Degenerate Gas

At high densities, gas particles may be so close, that interactions between them cannot be neglected.

What basic physical principle will become important as we increase the density and pressure of a highly ionised ideal gas ?

The Pauli exclusion principle - the e– in the gas must obey the law:

No more than two electrons (of opposite spin) can occupy the same quantum cell

The quantum cell of an e– is defined in phase space, and given by 6 values:

x, y, z, px, py, pz

The volume of allowed phase space is given by

The number of electrons in this cell must be at most 2

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ΔxΔyΔzΔpxΔpyΔpz = h3


White Dwarfs

Degenerate stellar remnant (C,O core)

Extremely dense:1 teaspoon of WD material: mass ≈ 16 tons!!!

White Dwarfs:

Mass ~ M

Temp. ~ 25,000 K

Luminosity ~ 0.01 L

Chunk of WD material the size of a beach ball would outweigh an ocean liner!


White Dwarfs

Low luminosity; high temperature => White dwarfs are found in the lower left corner of the Hertzsprung-Russell diagram.


Example of WD discovered in Globular cluster M4

Cluster age ~ 12GyrsWDs represent cooling sequenceSimilar intrinsic brightness as main-

sequence members, but much hotter (hence bluer)


The Chandrasekhar Limit

The more massive a white dwarf, the smaller it is.

Pressure becomes larger, until electron degeneracy pressure can no longer hold up against gravity.

WDs with more than ~ 1.4 solar masses can not exist!


･ On Main Sequence, Sun evolves slowly due to the changing chemical composition of its core - the Sun gets hotter and increases in luminosity (moving to the left and up in the HR diagram).

･ After the hydrogen is used up in the core, the helium core contracts, and heats the hydrogen rich layer just outside of the core. The hydrogen ignites in the shell around the core and the Sun moves to the right in the HR diagram.

･When the outer layers of the Sun become convective, the luminosity of the Sun shoots up and the Sun becomes a Red Giant.

･ The core continues to contract until it reaches the ignition temperature for helium

･ At the point of helium ignition, the core of the Sun is supported by the hot (normal) gas of helium nuclei produced by the hydrogen burning and by degenerate electrons; the electrons already occupy many of the available energy levels up to very high energies - it will take a lot of heat in order to increase the energy of even 1 electron. The fractional increase in the kinetic energy of the electrons will be very small for a given amount of heat input. So, the pressure due to the electrons does not change very much for a given amount of heat input -the core of the Sun will not expand strongly in response to the ignition of the helium.

Summary of 1 M evolution


･ The temperature of the core rises (really the temperature of the helium nuclei gas rises) as the reactions turn-on - the reaction rate goes up - the temperature of the helium nuclei in the core goes up - the rate of reactions goes up - and so on.... Until ignition of helium burning - helium flash lasts for a few minutes or less with a peak core luminosity of up to 1 x1011 L.

･ The helium flash shuts down because, eventually, as you add enough heat to the gas, you can excite electrons to higher energy states and you eventually spread the electrons out over a large enough range of states to make the gas normal. (obey the perfect gas law).

･ The helium flash occurs in stars less massive than around 2.25 M.

･ After the helium flash, the star quiescently burns what is left of the helium in its core (for a time ~ 10 - 20 % as long as its Main Sequence lifetime).

･When the helium is converted into carbon and oxygen, the core again contracts, ignites helium burning in a shell around the core, expands, cools, and moves to the right in the HR diagram.


･When the star becomes convective, it moves up the AGB greatly increasing in luminosity at roughly constant temperature. Low mass stars are not, however, massive enough to reach the ignition temperature of carbon before the core becomes completely supported by degenerate electron pressure (which halts the contraction).

･ The nuclear evolution of the Sun ends at this point and the star is now ready to enter into its final stages of evolution; at this time the star is AGB star characterized by a carbon-oxygen core, surrounded by a helium burning shell and a hydrogen burning shell.

• For stars whose mass is greater than 2.25 M, the electrons in their cores are not

degenerate at the time of helium ignition and so there is no helium flash and they settle into a stage of quiescent helium burning before they approach the AGB.

•Star cools and moves left on the H-R diagram possibly generating a planetary nebula

•He-burning shell keeps dumping C and O onto the core. C,O core collapses and the matter becomes degenerate.

•Star becomes a white dwarf


Summary of 1 M evolution

Approximate typical timescales

Phase (yrs)

Main-sequence 9 x109

Subgiant 3 x109

Redgiant Branch 1 x109

Red clump 1 x 108

AGB evolution ~5x106

PNe ~1x105

WD cooling >8x109

PHYS 3380 - Astronomy The second exam will be next Monday, November 9 at the regular class time. It is closed book but you may bring in one 8 1/2 X 11.

Documents

alma image

astronomical observations

mondays class

wednesdays class

observations impossible

regular class time

massive stars

chajnantor plateau