Introduction to Astronomy: Stars PDF

 Contents   Introduction.  Observational Evidences  Distances in astrophysics.  Luminosity.  Star Color (photometry)  Spectral type (spectroscopy).  Star Radius  Star Mass.  The Hertzsprung-Russell diagram ...

 Contents   Introduction.  Observational Evidences  Distances in astrophysics.  Luminosity.  Star Color (photometry)  Spectral type (spectroscopy).  Star Radius  Star Mass.  The Hertzsprung-Russell diagram  Stellar Evolution  Introduction  The birth of Stars  Stellar Maturity and old age.  The deaths of stars.  Neutron stars and black holes  Introduction   A star is a luminous sphere of plasma (ionized gas) held together by its own gravity.  Thermonuclear reactions happen in the core of the star, releasing energy that traverse the star’s interior and then radiates into outer space.  Astrophysicists have developed methods to determine how far are Image from NASA the stars, their sizes, masses, chemical compositions….  The combination of theoretical models and experimental evidences provided a global picture of star evolution (from birth to death).  Main questions   What are the stars made of ?  Where does the light/energy of the stars come from ?  What are the typical sizes, masses, colors, temperatures, and composition of the stars?  Is the Sun a “normal” star or is it special ? When will the Sun die ?  From birth to death …. What are the typical phases in the life of a star ? How long can they live ?  Preliminary concepts: Black Body   Black body: physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.  A black body in thermal equilibrium emits electromagnetic radiation according to Planck’s law: 2ℎ𝜈 3 1 𝐵𝜈 = 2 ℎ𝜈Τ𝑘 𝑇 𝑐 𝑒 𝐵 −1 where 𝐵𝜈 is the spectral radiance (J/m2)  Preliminary concepts: Black Body   If the spectral radiance is integrated for all the frequencies and over the solid angles corresponding to a hemisphere above the surface, one finds the Stefan-Boltzmann law 𝑃 = 𝜎𝑇 4 , 𝜎 ≡ 2𝑘𝐵4 𝜋 5 Τ15𝑐 2 ℎ3 ≈ 5.67 × 10−8 𝐽Τ𝑠𝑚2 𝐾 4 where P is the total power emitted per unit area at the surface of the black body.  The wavelength at which the intensity per unit wavelength reaches its maximum is given by Wien’s law: 2.9 × 10−3 𝑚𝐾 𝜆𝑚𝑎𝑥 = 𝑇(𝐾) Distances in Astrophysics Distances in Astrophysics  Object Length units in astrophysics:  Astronomical Unit: mean distance between the Earth and the Sun (1AU is 206265AU about 150 million of kilometres ). 1”  Parsec: distance at which one AU subtends an angle of one arcsecond (1pc is about 206265 AU ) Sun 1AU Earth  Light-year: distance that light travels in vacuum in one Julian year (1 light-year is about 0.3 parsec) Image from “The Essential Cosmic Perspective “ Bennet et al Distances in Astrophysics   Radar: a radio pulse is sent towards a nearby body and, by measuring the time for the partially reflected signal to return the Earth, the distance is calculated.  Parallax: apparent displacement of an object because of a change in the observer's point of view  Fitting to models or experimental evidences: main-sequence fitting or period-luminosity relation for Image from Wikipedia cepheids Distances in Astrophysics   Standard Candles example: if we know the intrinsic brightness of an object and measure the apparent one, we can determine the distance (see next slides). Ex1: white dwarf supernovae -> explosion after reaching the Chandrasekar limit (1.44 𝑀⊙ ) due to mass accretion in a binary system. Ex2: Tully-Fisher empiral relation between the luminosity of a spiral galaxy and its maximum rotational velocity, which can be found by measuring the width of the 21cm hydrogen line Luminosity  Luminosity   Luminosity (L): amount of energy emitted by the star each second (measure in W).  Apparent brightness: The amount of energy per m2 and time arriving at a imaginary sphere of radius r is 𝐿 𝑏= 4𝜋𝑟 2  Instead of using J/m2s, astronomers measure the brightness using a dimensionless number called “magnitude”, which dates back to the days of ancient Greek astronomy.  Absolute magnitude (M), apparent magnitude (m) and distance (d) in pc are related by 𝑀 = 𝑚 − 5 log10 𝑑 − 1 From ESA Educational Support  Luminosity  Experimental procedure: 1. Measure the total amount of energy that comes from the star per unit time and determine the apparent magnitude m. 2. Measure the distance d in pc. 3. Compute the absolute magnitude by using the relation 𝑀 = 𝑚 − 5 log10 𝑑 − 1 4. Compute the luminosity from 𝐿 4.72 − 𝑀 log10 = 𝐿⊙ 2.5 with 𝐿⊙ = 3.846 × 1026 𝑊 the Sun luminosity Star Color  Star Color   Besides a different in brightness (magnitude), stars also exhibit different colors.  Radiation brings two types of information: 1.Total amount of energy (magnitude). 2. Energy distributed along wavelengths (color) Image from NASA/ESA Hubble Telescope Image courtesy of kstars. Star’s color is directly associated with its surface temperature  Color  Experimental procedure: 1. Photometry: measure intensity of the starlight detected by a light sensitive device at the focus of a telescope with three standardized set of colored filters: ultaviolet (U), blue (B), and central yellow (V). 2. This procedure gives three apparent magnitudes, which are denoted by U, B, V. 3. Compute the differences (B-V) and (U-B), which are called the color indexes and give information about how much brighter or dimmer a star is in one wavelength band than in another. Image courtesy of kstars. 4. Bonus: using Black Body Radiation model, find the temperature of the star. Spectral Type  Spectral Type   A continuous spectrum of radiation, following a nearly perfect black body, is produced deep within star atmosphere (hot and dense gas)  This light moves outward through a cooler and less dense layers of the star’s upper atmosphere, where atoms absorb radiation at specific wavelengths (spectral lines).  Astronomer created spectral classes and classified the stars according to their spectra: OBAFGKM (Oh, Be A Fine Girl, Kiss Me )  The classification was refined and they added a number from 0 to 9, for instance G9…K0 Image from “Universe” Freedman-Geller-Kaufmann  Spectral Type   Spectra have information about the chemical composition of the stars.  In 1920, Payne and Saha showed that star’s spectrum is affected by the star’s surface temperature (ionization and excitation of the atoms responsible of the line).  Moreover, spectral lines shape (core+wings) contains relevant information such as the rotation speed of the star.  Line shifts with respect to the ones measured in the lab give information about the velocity (Doppler effect). Harvard Classification System for Spectral Types  Spectral Type  Experimental procedure: 1. Using spectroscopy technique, get a detailed spectrum of the star. 2. From the analysis of the lines, get the following information:  Spectral type OBAFGKM (by identifying the presence and strength of certain lines).  Star Temperature: (by using the spectral classification and theoretical models).  Chemical composition (presence or absence of lines)  Velocity (by measuring Doppler shifts ).  Rotational velocity of the star (line profiles). Star Radius  Star Radius  Method 1:  1. Using photometry (apparent magnitude), and known the distance, we can determine the luminosity (L) of the star. 2. Using spectroscopy the star temperature T is determined. 3. For a Black Body, one has the theoretical relation 1 𝐿 𝐿 = 4𝜋𝑅2 𝜎𝑇 4 ⇢ 𝑅= 𝑇2 4𝜋𝜎  Method 2: 1. Some stars are not isolated but form multiple-star systems in which two or more star orbit around each other. 2.Sometimes, an apparently single star yields spectra in which two complete sets of spectral lines shift back and forth (double-line spectroscopic binaries). 3.If the binary system is also eclipsing from the Earth, then the radius and masses can be determined by analyzing the spectra and the light curve (see next slides) Star Mass  Star Mass   Some binary systems are oriented in such a way that the two stars eclipse each other periodically, as seen from the Earth.  The light curve (see figure below) gives the orbital period P.  Parallax measuremen can provide the semimajor axis a  Kepler Third law provide the sum of the masses 𝐺(𝑀1 + 𝑀2 )/4𝜋2 = 𝑎3 Τ𝑃2.  From center of mass determination and spectroscopy analysis (velocities), the masses can be separated Ophiuchi Orbit. J. B. Kaler, Image from “Universe” Freedman-Geller-Kaufmann HarperCollins. The Hertzsprung-Russell diagram The H-R diagram   Stars are not scattered randomly in a Luminosity- Temperature diagram.  There is a diagonal band, named the principal sequence, that extends from upper-left corner (hot bright, and bluish stars) from the lower-right corner (cool, dim, redish stars).  The Sun belongs to the main sequence. Credit from ESO  The H-R diagram   The relation 𝐿 = 4𝜋𝑅2 𝜎𝑇 4 can be used to plot the radii in the diagram.  Beside the main sequence, the following important regions are identified: Giants stars: 10 to 100 times larger than the Sun and temperature between 3000 and 6000 K). Stars of this region with temperature between 3000-4000 K are called Red Giants. Supergiants: 100 to 1000 times larger than the Sun. White Dwarfs: mass similar to the Sun but size of the Earth. Luminosity comes from stored thermal energy (not from nuclear reactions) Image from “Universe” Freedman- Geller-Kaufmann  The H-R diagram   The H-R diagram opens the following questions: Why are stars organized in few regions ? Why do most of the stars belong to the main sequence ? What are White Dwarfs ? Are they really stars ?  The answers to these questions come from the history of “star evolution” Introduction  Introduction   Since star emit huge amount of energy they should evolve.  They look unchanged for humans because their time scales are between millions to billions of years.  The different populated regions in the H-R diagram correspond to different stellar phases.  Astrophysicists have developed a theory of stellar evolution by combining observations and theoretical models.  The theory explains how the stars are born in huge clouds of interstellar gas, they mature, grow old, and die while enriching the space with new material for future star generations The birth of stars  The birth of stars   Interstellar space is not empty but filled with tenuous matter (gas and dust)  Photographies, spectroscopy, and interstellar extinction provide evidences about the existence of this matter.  Stars are formed from cold and dark clouds of interestellar medium named dark nebulae.  Typical dark nebulae contains few thousand solar masses of gas and dust spread over a volume of 103pc3 and temperature 10K.  The temperature (and the pressure) is Horsehead Nebulae so low that the cloud contracts under its own gravity.  Star formation can be triggered by nearby supernova explosions, collision of galaxies,…  The birth of stars  During the  contraction, the gravitational energy is converted into thermal energy and the gases heat up.  In few thousand of years of contraction, the surface temperature reaches 2000-3000K and it produces substantial luminosity.  Protostar contration follows until the core reaches few million of degrees, when hydrogen burning begins.  The thermonuclear process release enormous amount of energy, that increases the pressure and stops the Pre-main sequence tracks contraction.  If M> 60 𝑀⊙, the protostar is too hot and radiation pressure too high.  If M< 0.08 𝑀⊙ temperature is not high enough to burn hydrogen (brown dwarfs) The main sequence  The main-sequence   Stars spend most of their life in the main sequence, burning hydrogen into helium 4H → He + energy  There is a mass loss 4H = 6.693 × 10-27kg 1He = 6.645 × 10-27kg -------------------------------------- Mass loss = 0.048 × 10-27kg From NASA  According to Einstein’s formula E= mc2 = 4.3 × 10-12J  The main-sequence   It can be shown that, for star of mass M, the luminosity and its lifetime are 𝐿 ∝ 𝑀3.5 1 T ∝ 2.5 𝑀  Therefore, star with a large mass has a high luminosity but a short lifetime ! From NASA’s Cosmos Stellar Maturity  Stellar Maturity  From Main-Sequence to Red Giant  As hydrogen decreases, core has troubles to support the weight of the outer region.  The core contracts, the temperature Red Supergiant increases, and the region of hydrogen burning expands outward from the core → ↑ Luminosity  At some point there is no more hydrogen in the core, and hydrogen burning just Red Giant happens in a spherical shell around the core.  The core contracts, and the graviational energy comming from this contraction increases the temperature to 100 million of K.  Hydrogen burning in the shell is stimulated → ↑ Luminosity.  The outer layers of the star expand and cool.  The star size increases and its temperature decreases (Red Giant)  Stellar Maturity Red Giant Evolution   As the hydrogen-burning shell moves outwards in the Red Giant, it adds mass to the Helium core. Red Supergiant  The Helium core contract and its temperature reaches 100 Million, enough to ignite the thermonuclear reactions Red Giant 4He+ 4 He →8Be 8Be+ 4 He → 12C + γ 12C+ 4 He → 16O + γ  These reactions liberate energy that stops the core contraction.  The amount of time burning He is 20% of the one in the main-sequence.  Stellar Maturity Asymptotic Giant Branch   In the AGB, the main source of energy is helium and hydrogen fusions in shells around a core of Carbon and Oxygen. Red Supergiant  Helium produced in the hydrogen shell drops toward the center of the star. This produces that the energy of the helium shell varies periodicall (thermal pulse) Red Giant  “Mira Variables” are a class of pulsating variable AGB stars (periods longer that 100 days and amplitude greater than one magnitude).  They pulsate because the entire star expands and contract, changing the temperature (shifting energy output between infra-red and visual wavelengths) Stellar Death  Stellar Death 0.4 𝑀⊙ < M < 8 𝑀⊙   Temperature is not enough to ignite the carbon.  During a thermal oscillation,the outer layers of the star separate from the Carbon-Oxygen core.  The core has approximately the size of the Earth and the mass of the Sun (M 8 𝑀⊙   Gravitational compression increases the star temperature up to 600 Million Kelvin, enough to burn the Carbon (and produce Ne, Mg)  Ne can also burn to produce more O and Mg.  If the mass is large enough to reach 1.5billion K, then Oxygen burning starts to produce S, Si, P, Mg.  Silicon burning produces 56Fe. From Wikipedia  The proton and neutron in 56Fe are so tightly bound together that no further energy can be extracted by fusing more nuclei with iron.  The sequence of burning stage finishes with Fe.  Stellar Death M> 8 𝑀⊙   The electrons in the star core should support the pressure but the continuous deposition of Fe make the mass exceed the Chandrasekhar limit  The core collapses, the temperature raises to 5 billion K and the gamma- ray photons associated with this intense heat break down the Fe nuclei into He (photodisintegration).  As the density climbs, electrons and protons combined to produce neutrons and neutrinos Crab Nebula. From Wikipedia (neutronization).  A stellar explosion named supernova happens.  Stellar Death  For M< 25 𝑀⊙ , the final product is a neutron star:  Made by neutrons.  Gravitational collapse stopped by the neutron degeneracy pressure.  1.4 𝑀⊙