PHYS 3650 Observational Astronomy Observations of Stars Learning

PHYS 3650: Observational Astronomy Observations of Stars

Learning Objectives u Stars: - definition - physical parameters - Hertzsprung-Russell (H-R) diagram - main categories u Energy Generation: - hydrostatic equilibrium - internal structure - nuclear fusion - energy transport u Measuring Stellar Parameters: - mass - radius - temperature - luminosity - composition

Learning Objectives u Stellar Classification: - Harvard classification scheme - Morgan-Keenan system - effective temperature - size u Stellar Evolution: - mass-luminosity relationship - main-sequence - post-main-sequence - star clusters

Learning Objectives u Stars: - definition - physical parameters - Hertzsprung-Russell (H-R) diagram - main categories u Energy Generation: - hydrostatic equilibrium - internal structure - nuclear fusion - energy transport u Measuring Stellar Parameters: - mass - radius - temperature - luminosity - composition

Stars u Much of astronomical research is concerned with the formation of stars (and their by-products such as planets) from interstellar gas, their subsequent evolution, and their often spectacular demise. u What two conditions must an object satisfy to qualify as a star? - what do all the object shown below share in common? - what single property distinguishes the Sun from the remaining objects shown?

Brown Dwarfs u The distinction between stars and planets has been complicated by the discovery of brown dwarfs. u Image below shows the first brown dwarf discovered in a survey of nearby M dwarf stars. Gliese 229 is an M 1 dwarf star located at distance 5. 8 pc.

Brown Dwarfs u Unlike stars, the spectrum of brown dwarfs show strong methane absorption lines just like gas giant planets (e. g. , Jupiter), indicating a low surface (photospheric) temperature.

Brown Dwarfs u Brown dwarfs with masses ≲ 13 MJ cannot achieve a core temperature sufficiently high to ignite nuclear fusion, and shine by the release of gravitational contraction energy. u Brown dwarfs with masses >13 MJ can achieve a core temperature sufficiently high to fuse deuterium (2 H) such as in Gliese 229 B, and those with masses ≳ 65 MJ can achieve a core temperature sufficiently high to also fuse lithium. Deuterium is a stable isotope of hydrogen comprising a nucleus with one proton and one neutron, and was produced during the Big Bang (0. 01% by constituent).

Brown Dwarfs u Brown dwarfs with masses ≲ 13 MJ cannot achieve a core temperature sufficiently high to ignite nuclear fusion, and shine by the release of gravitational contraction energy. u Brown dwarfs with masses >13 MJ can achieve a core temperature sufficiently high to fuse deuterium (2 H) such as in Gliese 229 B, and those with masses ≳ 65 MJ can achieve a core temperature sufficiently high to also fuse lithium. u Stars are defined to be objects which can achieve a core temperature sufficiently high (≳ 3 x 106 K) to fuse hydrogen. Deuterium is a stable isotope of hydrogen comprising a nucleus with one proton and one neutron, and was produced during the Big Bang (0. 01% by constituent).

Physical Parameters u Physical parameters of stars are usually expressed by comparison to the Sun. u Physical parameters of the Sun: Mass (M ) 1. 99 x 1030 kg Symbol for Sun Radius (R ) Mean density (ρ ) Effective temperature (T ) Luminosity (L ) Core temperature (Tcore) Age (t ) 332, 000 M� Symbol for Earth 6. 96 x 105 km 109 R� 1. 4 g cm-3 0. 25 ρ� 5780 K 3. 90 × 1026 W 1. 5 x 107 K ~5 x 109 year (20 × 1012 W via radioactive decay)

Physical Parameters u Size of the Sun compared to the Planets.

Physical Parameters u Size of the Sun compared to other stars.

Physical Parameters

Hertzsprung-Russell Diagram u Once the physical parameters of stars have been determined, one parameter can be plotted against the other to see whether any pattern emerges that provide clues to the nature of stars. u E. g. , a plot of absolute magnitude (luminosity) versus color (photospheric temperature) is known as the Hertzsprung-Russell (H-R) diagram.

Hertzsprung-Russell Diagram u HR-diagram constructed from the Hipparcos catalog of 22, 000 stars and Gliese catalog of 1000 nearby stars. u Hipparcos satellite (1989 -1993) measured trigonometric parallaxes for 118, 218 stars.

Main Stellar Categories u Astronomers separate stars into four main categories: - protostars (those still accreting mass) - pre-main-sequence (PMS) stars (those that have accreted the bulk/all of their mass and contracting onto the main sequence) - main-sequence stars (stably fusing hydrogen into helium) - post-main-sequence stars (shell hydrogen fusion, and/or fusing helium and heavier elements into even heavier elements)

Learning Objectives u Stars: - definition - physical parameters - Hertzsprung-Russell (H-R) diagram - main categories u Energy Generation: - hydrostatic equilibrium - internal structure - nuclear fusion - energy transport u Measuring Stellar Parameters: - mass - radius - temperature - luminosity - composition

Hydrostatic Equilibrium u Stars are bound together by their own gravity, an attractive force directed inwards. u What force prevents the star from collapsing? Gravity pulling inward to make the star more compact.

Hydrostatic Equilibrium u Gravity confines gas in the star against pressure expansion. u Pressure supports the star against gravitational collapse. u When there is exact balance between the two forces, a star is in hydrostatic equilibrium (no expansion or contraction). Gravity pulling inward to make the star more compact. Pressure pushing outward to expand the star.

Hydrostatic Equilibrium u What happens if the internal energy generated by nuclear fusion at the center of the star increases? Gravity pulling inward to make the star more compact. Pressure pushing outward to expand the star.

Hydrostatic Equilibrium u What happens if the internal energy generated by nuclear fusion at the center of the star increases? The star expands, as happens when they evolve away from the main sequence.

Internal Structure u Most stars (except white dwarfs and neutron stars) obey the ideal gas law P ρT, where P is the pressure, ρ the density, and T the temperature of the gas in the star. u To support the overlying layers, the inner layers of the star must be at progressively higher pressures; i. e. , higher densities or temperatures, or both (as is the case in stars). Gravity pulling inward to make the star more compact. Pressure pushing outward to expand the star.

Internal Structure u Internal structure of a star separated into two parts: - dense, hot, compact core where nuclear fusion takes place - lower density and temperature extended envelope through which radiation/heat from the core propagates (diffusion/convection) u Sun’s Core: size ~0. 25 R , T ~ 1. 5 x 107 K, ρ ~ 150 g cm-3 (× 105 air density). u Sun’s Envelope: outer layer (photosphere) T ~ 5800 K, ρ ~ 10 -7 g cm-3 (× 10 -3 air density). Air density ~ 1 g cm-3 Average density Earth ~5 g cm-3

Nuclear Fusion u Two main sources of stellar energy: - gravitational contraction (Kelvin-Helmholtz) - nuclear fusion at the hot stellar core (the Sun converts 3 x 10 -19 M from protons to helium nuclei every second) u For main-sequence stars, energy generation dominated overwhelmingly by nuclear fusion, which is extremely temperature sensitive. (Explanation why requires a course in quantum mechanics. ) u When core temperature Tcore < 1. 8 x 107 K (M*<1. 3 M ), the proton-proton chain reaction path dominates (rate ∝T 4). u When core temperature Tcore > 1. 8 x 107 K (M*≳ 1. 3 M ), the CNO cycle catalytic reaction path dominates (rate ∝T 17).

Nuclear Fusion Proton-Proton (pp) Chain u Relies on proton-proton reactions. u Main intermediary products are deuterium (2 H) and Helium-3 (3 He). u Net result is that two protons are converted into one helium atom plus particles/radiation. u Energy released as γ-rays, neutrinos, positrons, and in protons.

Nuclear Fusion Proton-Proton (pp) Chain u In brown dwarfs that fuse deuterium, reaction starts from the second step. u Net result is that two deuterium nuclei are converted into one helium atom plus particles/radiation. u Energy released as γ-rays and in protons.

Nuclear Fusion CNO Cycle u Carbon acts as a catalyst. u Net result is four protons converted into one helium atom plus particles/radiation. u Energy released as γ-rays, neutrinos, and positrons.

Nuclear Fusion u Energy generation rate by nuclear fusion as a function of stellar core temperature.

Energy Transport u Three ways for energy generated in core to be transported to the surface (photosphere) - Radiation (by photons) - Convection (by bulk motion of gas) - Conduction (by random motion of gas) u For main-sequence stars, energy is transported by a combination of radiation and convection (density is too low for energy to be as effectively transported by conduction).

Energy Transport u Transportation of energy from the center of a star depends on the gas opacity and temperature gradient at a given radius. u There are four sources of opacity in stellar atmospheres: - bound-bound transitions (i. e. , excitation of atoms/ions by photons) - bound-free transitions (i. e. , photo-ionization) - free-free transitions (i. e. , bremsstrahlung when emission is involved) - electron scattering < 0. 5 M 0. 5 – 1. 5 M > 1. 5 M

Energy Transport u Transportation of energy from the center of a star depends on the gas opacity and temperature gradient at a given radius. u When the gas opacity is low, how can energy be effectively transported? < 0. 5 M 0. 5 – 1. 5 M > 1. 5 M

Energy Transport u Transportation of energy from the center of a star depends on the gas opacity and temperature gradient at a given radius. u When the gas opacity is high, how can energy be effectively transported? < 0. 5 M 0. 5 – 1. 5 M > 1. 5 M

Energy Transport u Stars with masses < 0. 5 M are completely convective. These stars have relatively high densities and low temperatures, and hence have high gas opacities. u Stars with masses >1. 5 M have convective interiors and radiative envelopes. Because their nuclear energy fusion rate is ∝T 17, the temperature gradient in the stellar interior is very steep, promoting convection. In the envelope, hydrogen is strongly ionized and the gas opacity is low, promoting diffusion of radiation. < 0. 5 M 0. 5 – 1. 5 M > 1. 5 M

Energy Transport u Stars with masses 0. 5− 1. 5 M have radiative interiors and convective envelopes. Because their nuclear energy fusion rate is (only) ∝T 4, the temperature gradient in the stellar interior is not as steep as for more massive stars. Hydrogen is ionized and thus the gas has a low opacity, promoting diffusion of radiation. In the envelope, hydrogen is mostly neutral and the gas opacity is high. < 0. 5 M 0. 5 – 1. 5 M > 1. 5 M

Learning Objectives u Stars: - definition - physical parameters - Hertzsprung-Russell (H-R) diagram - main categories u Energy Generation: - hydrostatic equilibrium - internal structure - nuclear fusion - energy transport u Measuring Stellar Parameters: - mass - radius - temperature - luminosity - composition

Stellar Mass u How is the mass of the Sun (1. 99 x 1030 kg) measured?

Stellar Mass u First step is to determine the distance from the Earth to the Sun. This was first accomplished with high accuracy through observations of the transit of Venus.

Stellar Mass u Second step makes uses of Newton’s laws of motion and law for gravitation. u Assuming that Earth has a circular orbit about the Sun and negligible mass compared with the Sun, equate centrifugal with gravitational force (implicit assumption is that the Earth orbits the Sun rather than both orbiting their common center-of-mass) G M M�/a 2 = M� v 2/a where v = 2πa/T to derive the equation M = 4 π2 a 3 / G T 2 where a is the Earth-Sun distance (i. e. , orbital radius) and T the orbital period to derive M = 1. 99 x 1030 kg.

Stellar Mass u How are the masses of other stars measured? u Only direct method is through observations of stars in binary systems. u Fortunately, many stars are members of binary systems (e. g. , ~2/3 of all solarmass stars are members of binary systems). u Binary stars orbit about their center of mass. If we measure the period and linear separation (which requires knowledge of the distance, as well as orbital inclination) of the stars, we can determine total stellar mass. If we also measure the position of the center of mass, we can determine individual stellar masses.

Stellar Mass u For resolved binaries (component stars can be separated), center-of-mass can be measured by observing binary motion with respect to “fixed” background stars. center of mass

Stellar Mass u Most binary systems have elliptical orbits, complicating the determination of stellar masses. u In practice, all orbital parameters can be derived for resolved binaries. u One of primary science drivers for building optical interferometers is to resolve binary systems so as to measure stellar masses.

Stellar Mass u In spectroscopic binary systems (component stars cannot be separated), orbital inclination not known except in eclipsing binary systems. u As a consequence, can only derive lower limits for stellar masses. observer

Stellar Radius u Very few stars can be resolved even with the largest telescope; e. g. , the largest angle subtended in the sky by any star is ~0. 60, roughly comparable with the typical seeing at the summit of Mauna Kea, Hawaii. u The angular diameters of many hundreds of stars have been measured using optical interferometry. Knowledge of actual physical diameters requires knowledge of their distances.

Stellar Radius u Stellar radii can be inferred from eclipsing spectroscopic binaries. Such binaries are therefore particularly important in astronomy for inferring stellar parameters (mass, radius, and effective temperature). vs + vl (vs = velocity of small star, vl = velocity of large star)

Stellar Radius u Can be indirectly inferred from luminosity, L*, and effective temperature, T*: which requires a method 2 for inferring the effective temperature. 4 L*= 4πR* σT* u If the Sun was a perfect blackbody, the effective temperature of the Sun would be equal to the blackbody temperature of the Sun at its photosphere. u The Sun is not a perfect blackbody, and its effective temperature is the temperature a blackbody would have to produce the same luminosity as the Sun at its photosphere.

Stellar Temperature u Stars emit an approximate blackbody spectrum from the lowest visible layer called the photosphere. But stars are not perfect blackbodies …

Stellar Temperature u Cooler layer above that where much of the photospheric light is emitted absorbs light in spectral lines to produce absorption lines, as well as at the Balmer break. The relative strengths of these absorption lines provide a more accurate determination of the stellar effective temperature.

Stellar Luminosity u From photometry, we can measure the apparent brightness (flux) of a celestial object (star). u The luminosity of the object, L = 4πd 2 f, where f is the measured flux and d the distance. u For relatively nearby stars, we can use trigonometric parallax to determine distance. Distant Stars d ~ p/1 AU Sun Earth Nearby Stars

Stellar Luminosity u For more distant stars in the Galaxy, we can infer the kinematic distance.

Stellar Luminosity u Gaia is an ambitious mission to chart a three-dimensional map of our Galaxy, the Milky Way, in the process revealing the composition, formation, and evolution of the Galaxy. Gaia will provide unprecedented positional and radial velocity measurements with the accuracies needed to produce a stereoscopic and kinematic census of about one billion stars in our Galaxy and throughout the Local Group. This amounts to about 1% of the Galactic stellar population. Gaia was launched on 19 Dec 2013.

Stellar Composition u About 20 minutes after the Big Bang, the Universe comprised ~75% hydrogen nuclei (protons), ~25% 4 He nuclei, ~0. 01% 2 H (deuterium) nuclei, and trace amounts of 3 He, 7 Li, 6 Li, 3 H (tritium), and 7 Be nuclei in a sea of electrons. u Both 3 H and 7 Be are unstable isotopes: - 3 H ➝ 3 He with 12 -hr half life - 7 Be ➝ 7 Li with a 53 -day half life

Stellar Composition u All other elements are synthesized in stellar nuclear cores and then dredged up by convection and excreted by stellar winds or in supernova explosions, or nuclear reactions in material accreted on the surfaces of compact stars (white dwarfs, neutron stars). u Interstellar gas and hence stars, which form from interstellar gas, are composed primarily of hydrogen and helium, together with trace amounts of metals. u In astronomy, metals refer to elements heavier than helium (note: definition is entirely different from that used by physicists and chemists). Solar Abundance

Stellar Composition u The metallicity of a star indicates the amount of metals in a star (more precisely, at the stellar photosphere). u Usually, the metallicity of a star is specified by its iron abundance (number of iron to hydrogen atoms) relative to the Sun: u Iron lines are used because they are relatively strong in stellar spectra and hence easy to measure.

Stellar Composition u Determination of metallicity requires not only observations to measure the strength of iron absorption lines, but also theoretical modeling to infer the iron abundance (c. f. , Principles of Astronomy course). u For the Sun, log 10 (Fe_atoms / H_atoms) ≃ -4. 33. What is the metallicity, [Fe/H], of the Sun? 0. u What values of [Fe/H] do stars with lower metallicities than then Sun have? Negative. u Stars can span a wide range of metallicities, about -4. 5 < [Fe/H] < +1. 0. Stars in globular clusters and the Galactic halo have relatively low metallicities. Stars in the Galactic disk generally have similar or higher metallicities than the Sun. What does this tell you about when these stars were born? Stars with lower metallicities born earlier when the Galaxy was less enriched by metals, whereas stars with higher metallicities born later when the Galaxy was more enriched by metals.