/ ![[Star_Life_Cycle_Chart.jpg|align:center|700]] ## Protostar A **protostar** is the center of a collapsing gas in which the central mass begins accreting matter and radiating protostellar winds. It will continue to do this until hydrogen fusion is initiated. Before this, a star can achieve [[Deuteron Fusion|deuteron fusion]]. **Deutron Fusion in Protostars** Deuteron is the most easily fused nucleus available to accreting protostars when temperatures exceed $10^{6} \; {\rm K}$. The reaction rate is so sensitive to temperature that the temperature does not rise very much above this. The energy generated by fusion drives convection, which carries the heat generated to the surface. Deuteron fusion allows further accretion of mass by acting as a thermostat that temporarily stops the central temperature from rising above about $10^{6} \; {\rm K}$, a temperature not high enough for hydrogen fusion, but allowing time for the accumulation of more mass. If the core is in a stable state, the rate of energy generation will be constant. Therefore, it would require very large changes in either the deuteron concentration or the protostar density to result in even a small change in temperature, given the temperature is raised to such a high power. ${\rm (energy \ generation) \propto (deuteron \ concentration) \times (density) \times (temperature)^{11.8}}$ If there were no deuteron available to fuse, then stars would gain significantly less mass in the pre-main-sequence phase, as the object would collapse faster, and more intense hydrogen fusion would occur and prevent the object from accreting matter. Due to the scarcity of deuterium in the Universe, a protostar's supply of it is limited. After a few million years, it will have effectively been completely consumed. After this point, gravity will begin to overtake the protostellar radiation pressure, and the energy transport mechanism slows and switches from convective to radiative ([[Hertzsprung-Russell Diagram#Hayashi Track]] to [[Hertzsprung-Russell Diagram#Henyey Track]]) as ionization increases and opacity decreases. This allows the temperature to rise and hydrogen fusion to take over in a stable and sustained way. Hydrogen fusion will begin at $10^{7} \; {\rm K}$. **Protostellar Wind** The stellar wind originating from a [[Stellar Classes#Protostar|protostar]], prior to thermo-nuclear ignition. ## Dwarf Stars ### Black Dwarf *(stellar remnant)* A **black dwarf** is a theoretical stellar remnant, specifically a white dwarf that has cooled sufficiently to no longer emit significant heat or light. ### Brown Dwarf *(stellar remnant)* A **brown dwarf** is a star that was not massive enough ($M < 0.08 \; {\rm M_{\odot}}$) to burn hydrogen, but large enough to be powered by deuteron burning ($M > 0.05 \; {\rm M_{\odot}}$), which has a lower ignition temperature. - The lifetime of the deuteron burning phase can last $\sim 10^{6} - 10^{7} \; {\rm yr}$. - Mass Range: $0.013 \; {\rm M_{\odot}} \; \lesssim M \lesssim \; 0.8 \; {\rm M_{\odot}}$ - Maximum mass of [[Planetary Classes#Hot Jupiters]] ($M < 13 \; {\rm M_{\rm J}}$) defines the lower limit of brown dwarfs. Often, a brown dwarf is defined by the deuteron burning occurring at some point in its evolutionary development. Without this, it would be defined as a planet versus a star. That said, it is hard to define an astrophysical object by this standard with current observational methods, given they are very dim objects. Therefore, they are mostly defined by mass in practicality. > [!note] > Objects above the deuterium-fusion minimum mass (deuterium burning minimum mass, DBMM) will fuse all their deuterium in a very short time, whereas objects below this limit will burn little, and hence, preserve their original deuterium abundance. ### Red Dwarf *(Also known as **M Dwarf Stars**)* ![[HR_redDwarfs.jpg|align:center|500]] **Red Dwarfs** or **M Dwarfs** are low mass and low luminosity stars that can fuse hydrogen, but not helium. In the [[Hertzsprung-Russell Diagram|HR-Diagram]], the populate the low temperature end of the [[Hertzsprung-Russell Diagram#Main Sequence (MS)]]. That said, they are also classified as *flare stars* with significant stellar variability due to magnetic field fluctuations. > [!measure] Typical Parameters > These parameters overlap with some [[#Brown Dwarf]] stars and [[Spectral Classes#K]] stars. There are various definitions for the cutoff values for these stars. > - $M \sim 0.08 - 0.45 \; {\rm M_{\odot}}$ > - $L \lesssim 0.08 \; {\rm L_{\odot}}$ > - $T_{\rm eff} \sim 2000 - 3900 \; {\rm K}$ Given they cannot exceed the helium burning threshold ($M \gt 0.45 \; {\rm M_{\odot}}$), they will continue burning hydrogen in throughout the remainder of their lifetime. If the star is fully convective ($M < 0.3 \; {\rm M_{\odot}}$), the star will be well-mixed allowing the star to completely fuse all available hydrogen until it becomes a helium star. ### White Dwarf *(Also known as a **degenerate dwarf**)* A **white dwarf** is a stellar remnant composed mostly of electron-degenerate matter after a star has transversed the [[Hertzsprung-Russell Diagram#Post-Asymptotic Giant Branch (Post-AGB)|post-AGB]] sequence. With the envelope shed through stellar winds, the remaining white dwarf is effectively the exposed core of the star. They are though to be the final evolutionary state of all stars whose [[Hertzsprung-Russell Diagram#Zero-Age Main Sequence (ZAMS)|ZAMS]] mass is not high enough to become a [[neutron star]] ($M\lesssim 8\,M_\odot$). Hence, they are supported by electron degeneracy pressure, in contrast to the neutron degeneracy pressure that support [[Neutron Star|neutron stars]]. These stellar remnant cannot fuse carbon, such that they cool down over time (potentially to the theoretical [[#Black Hole|black dwarf]]?). Depending on their progenitor star, the composition of the white dwarf composition can be variable. | Type | White Dwarf Mass | Progenitor Mass | | ------------------------ | :----------------------------: | :--------------------------: | | He White Dwarf | $0.1 - 0.4 \; {\rm M_{\odot}}$ | $\lt 0.5 \; {\rm M_{\odot}}$ | | C-O White Dwarf | $0.5 - 1.3 \; {\rm M_{\odot}}$ | $0.5 - 8 \; {\rm M_{\odot}}$ | | O-Ne-Mg White Dwarf \*\* | $1.0 - 1.3 \; {\rm M_{\odot}}$ | $6 - 8 \; {\rm M_{\odot}}$ | (\*\*rare population, seems to be evaded by mass loss) > [!measure] Typical Parameters > > More than $95 \%$ of stars become white dwarfs. > > - $M \sim 0.1 - 1.3 \; {\rm M_{\odot}}$ > - $R \sim 0.01 - 0.02 \; {\rm R_{\odot}} \sim {\rm R_{\oplus}}$ > - $\rho \sim 10^{4} - 10^{7} \; {\rm g/cm^{3}} \quad \left( \ll \rho_{\rm neutron\ star} \sim 10^{14} \; {\rm g/cm^{3}} \right)$ **Evolutionary Process:** 1) A low to intermediate mass star will begin fusing hydrogen on the [[Hertzsprung-Russell Diagram#Main Sequence (MS)|main sequence]] 2) Once fusible hydrogen is exhausted, the star will travel the [[Hertzsprung-Russell Diagram#Subgiant Branch (SGB)|subgiant branch]] and [[Hertzsprung-Russell Diagram#Red Giant Branch (RGB)|red giant branch]] until it helium fusion ignites through the [[Triple-Alpha Process|triple-alpha]] and [[Alpha Process|alpha process]]. - This creates an inert carbon-oxygen core. 3) As carbon-oxygen ash builds up in the core, the star heats and travels the [[Hertzsprung-Russell Diagram#Horizontal Branch|horizontal branch]] before expanding and cooling along the [[Hertzsprung-Russell Diagram#Asymptotic Giant Branch (AGB)|asymptotic giant branch]]. 4) As the star begin to exceed the [[Luminosity#Eddington Limit]], it will shed its outer layers to form a [[Nebulae#Planetary Nebula|planetary nebula]], leaving behind its exposed core. 5) The remnant core is the new white dwarf. Usually, white dwarfs are composed of carbon and oxygen through the above process. Since the white dwarf can no longer undergoes fusion reactions, the star has no source of energy and it no longer supported against gravitational collapse. It is only supported by electron degeneracy pressure, causing it to be extremely dense. A non-rotating white dwarf has a maximum mass limit, beyond which it can no longer be supported through electron degeneracy pressure, known as the [[Chandrasekhar limit]] ($M_{\rm WD} \lesssim 1.4 \; {\rm M_{\odot}}$). When a carbon-oxygen white dwarf that approaches this mass limit, either by accretion of mass from a companion star ("single-degenerate" progenitor) or via a WD-WD merger ("double-degenerate" progenitor), may explode as a [[Stellar Explosions#Type Ia]] supernova. **Open Questions:** 1. What is the maximum [[Hertzsprung-Russell Diagram#Zero-Age Main Sequence (ZAMS)|ZAMS]] mass for star to become WD? We know below 8-10 solar masses they become a WD, but don't know the maximum. 2. What are the properties of their magnetic fields? 3. Planets around WDs (Andrew Vanderburg here at MKI) 4. Binary WD physics (Kevin Burdge here at MKI) 5. Details of type 1a supernova progenitors ## Main Sequence *See the [[Hertzsprung-Russell Diagram#Main Sequence (MS)]] section of [[Hertzsprung-Russell Diagram]].* ## Giant Stars ### Red Giant !UNFINSIHED - See [Wikipedia](https://en.wikipedia.org/wiki/Red_giant) ### Red Supergiant !UNFINSIHED - See [Wikipedia](https://en.wikipedia.org/wiki/Red_supergiant) ### Blue Giant !UNFINSIHED - See [Wikipedia](https://en.wikipedia.org/wiki/Blue_giant) ### Blue Supergiant !UNFINSIHED - See [Wikipedia](https://en.wikipedia.org/wiki/Blue_supergiant) ## Neutron Star *See the [[Neutron Star]] note in "D. Compact Objects".* ## Black Hole *See the [[Black Hole]] note in "D. Compact Objects".* ## Variable Stars The stellar variability is thought to be caused by a variety of factors, each outlined in the below "Variability Tree" showing how variable stars are classified. ![[variableStar_classification.png|align:center]] [Here](https://www.aavso.org/sites/default/files/Variable%20Star%20Classification%20and%20Light%20Curves%20Manual%202.1.pdf) is a good source for details about the different types of variable stars. ### Cepheids ![[cepheid_period-luminosity.gif|align:center|400]] **Cepheid Variable Stars** are supergiants that [[Pulsation|pulsate]] in both diameter and temperature, changing their [[Luminosity|brightness/luminosity]] with a well-defined [[Pulsation#Pulsation Period|period]] and amplitude. Because of this, Cepheids are used by astronomers as standard candles. > [!measure] Typical Parameters > - $M \sim 4 - 20 \; {\rm M_{\odot}}$ > - $L \sim 10^{3} - 10^{5} \; {\rm L_{\odot}}$ > - $R \sim 50 \; {\rm R_{\odot}}$ > - $P \sim 1 - 50 \; {\rm day}$ There are two classes of Cepheids: 1) *Classical Cepheids* - [[Stellar Populations#Population I (Pop. I)]] stars with very regular periods on the order of days to months. ([[Spectral Classes#F]][[Luminosity Classes|6]] - [[Spectral Classes#K]][[Luminosity Classes|2]]) 2) *Type II Cepheids* - [[Stellar Populations#Population II (Pop. II)]] stars that pulsate with periods between 1 and 50 days. *(many subclasses) The [[Pulsation|pulsations]] are driven through the [[Pulsation#Kappa Opacity Mechanism]] and act as sound waves resonating in the stellar interior. From this mechanism, **denser stars resonate and pulse faster.** $ T \; \propto \; \frac{1}{\sqrt{\rho}} \hspace{1cm} \text{where} \hspace{1cm} \begin{aligned} T &= \text{Period} \\ \rho &= \text{density} \end{aligned} $ > [!note] Cepheids can be 100 times more luminous than [[#RR Lyrae]] stars. > [!space] Leavitt's Law > > Henrietta Swan Leavitt established a period-luminosity relation (**Leavitt's Law**) in Cepheids by studying thousands of stars in the LMC and SMC. > > $ > M_{V} = -2.81 \log_{10} P - 1.43 \hspace{1cm} \text{where} \hspace{1cm} > \begin{aligned} > &M_{V} = \text{magnitude in V-band} \\ > &P = \text{period in days} > \end{aligned} > $ > > The above equation for **Leavitt's Law** quoted from *"Bradley/Ostlie, Introduction to Modern Astrophysics, 2nd Edition (pg 486)"*. This expression disagrees with the expression on [Wikipedia](https://en.wikipedia.org/wiki/Period-luminosity_relation) and in Megan Masterson's notes. I am guessing it has to do with how the [[Photometry#UBVRI Filters|V-band]] was historically defined (i.e. what bandpass filters were being used), but I am uncertain on the details. > $ > \begin{alignat}{3} > &\text{Wikipedia:} &\hspace{1cm} M_{V} &= -2.43 \left( \log_{10} P - 1.0 \right) - 4.05 \\ > &&&= -2.43 \log_{10} P - 1.62 \\ > \\ > &\text{M. Masterson:} &\hspace{1cm} M_{V} &= -2.43 \log P - 4.05 > \end{alignat} > $ > > This relationship allowed the measurement of [[Magnitude#Absolute Magnitude|absolute magnitudes]] from pulse periods and distances by comparisons with the [[Magnitude#Apparent magnitude|apparent magnitude]]. The relationship was further calibrated with Cepheids that had known distances via parallax. Biggest source of uncertainty in the calibration comes from metallicity dependence and obscuration in the interstellar [[Interstellar Medium#Dust|dust]]. > > This *standard candle* acts as a relatively local distance estimator in the [[Cosmic Distance Ladder]], because you need to be able to resolve a single star and reliably measure period. Furthest such object is NGC 3370 at $\sim 29 \; {\rm Mpc}$. ### RR Lyrae **RR Lyrae Variable Stars** are periodic, [[Stellar Populations#Population II (Pop. II)|Pop. II stars]] found in [[Stellar Clusters#Globular Cluster|globular clusters]] on the [[Hertzsprung-Russell Diagram#Horizontal Branch]]. They [[Pulsation|pulsate]] in both diameter and temperature, changing their [[Luminosity|brightness/luminosity]] using a similar [[Pulsation#Kappa Opacity Mechanism|mechanism]] to [[#Cepheids]]. > [!measure] Typical Parameters > - $M \lesssim 1.0 \; {\rm M_{\odot}}$ (started with $\sim 2.5 \; {\rm M_{\odot}}$ before mass loss) > - $L \sim 50 \; {\rm L_{\odot}}$ > - $P \sim {\rm hours\ to\ days}$ They are used as [[Cosmic Distance Ladder|standard candles]] to measure extra-galactic distances since they are more common than [[#Cepheids]]. However, they tend to be more unstable and less reliable pulses. > [!space] Differences between [[#Cepheids]] > - Shorter Periods > - Less Luminous > - Arise from lower mass stars > - Not a reliable period luminosity relation like with [[#Cepheids]] (except with [[Electromagnetic Spectrum|K band]]) > - harder to calibrate due to inconsistencies > - Occupy a smaller luminosity space of the [[Hertzsprung-Russell Diagram|HR diagram]] > - An observer needs to measure apparent luminosity + know the absolute magnitude get distance > - Follow the same [[Pulsation#Kappa Opacity Mechanism|pulsation mechanism]] as [[#Cepheids]] ### T Tauri Stars *(abbreviated as **TTS**)* **T Tauri stars (TTS)** are a class of variable, [[Hertzsprung-Russell Diagram#Pre-Main Sequence|pre-main sequence]] stars on the [[Hertzsprung-Russell Diagram#Hayashi Track]] in the process of contracting onto the [[Hertzsprung-Russell Diagram#Main Sequence (MS)|main sequence]]. They are identified by their [[Electromagnetic Spectrum|optical]] variability and strong chromospheric lines. The stellar variability of T Tauri Stars is thought to be caused by: - large areas of starspot coverage (leading to violent activity in the stellar atmosphere) - Intense and variable [X-ray](https://en.wikipedia.org/wiki/X-ray "X-ray") and [radio](https://en.wikipedia.org/wiki/Radio "Radio") emissions - Extremely powerful protostellar winds - Ejecta gas in high-velocity [[#Bipolar Flows|bipolar jets]] - Obscuration from clumps ([protoplanets](https://en.wikipedia.org/wiki/Protoplanet "Protoplanet") and [planetesimals](https://en.wikipedia.org/wiki/Planetesimal "Planetesimal")) in the disk surrounding the stars There are two classes of T Tauri Stars: 1) *Classic T Tauri stars (CTTS)* - possess extensive disks that result in strong emission lines 2) *Weak-lined T Tauri stars (WTTS)* - surrounded by either a very weak disk or no disk at all - WTTS are good sites for studying early stellar evolution and planetary formation since the star is unencumbered by nebulous material. **Characteristics:** - Found near molecular clouds - They are powered by gravitational contraction and heating ([[Timescales#Thermal Timescale|thermal timescale]]) - Central temperatures at too low for hydrogen fusion - Oten have large accration disks left over from star formation - Typically representative of [[Spectral Classes#F]], [[Spectral Classes#G]], [[Spectral Classes#K]], [[Spectral Classes#M]] spectral types - strong emission lines and broad absorption lines - Spend $\sim 100 \; {\rm Myr}$ on the [[Hertzsprung-Russell Diagram#Pre-Main Sequence|pre-main sequence]] during its collapse - Many TTS are in binary systems - This class is named after the prototype, T Tauri, a young star in the Taurus star-forming region. > [!measure] Typical Parameters > - Age: $\lesssim 10 \; {\rm Myr}$ > - Period: $\sim 1-10 \; {\rm day}$ > - Mass: lt;2 \; {\rm M_{\odot}}$ ## Other Objects ### Blue Straggler Star that appears to be younger and more massive than the other stars in its cluster or galaxy. They are called "blue" stragglers because they are hotter and bluer in color than other stars of similar age. Blue stragglers are thought to form through stellar mergers, but they challenge our understanding of stellar evolution. Since blue stragglers appear to be younger and more massive than other stars in their surroundings, they should have already evolved off the [[Hertzsprung-Russell Diagram#Main Sequence (MS)|main sequence]] and become [[Stellar Classes#Red Giant|red giants]]. ### Wolf-Rayet Star ![[wolf_rayet.jpg|aling:center|400]] A **Wolf–Rayet (WR) Star** is a massive stellar type with very strong stellar winds as evolved descendants of very massive stars ([[Spectral Classes#O]]) that have blown off abut half their mass and now emit highly-ionizing radiation as dying supergiants. They are distinct from other stellar types because lack hydrogen lines in their spectra, due to their hydrogen envelope being expelled by stellar winds. Instead their spectra are dominated by broad emission lines of highly ionized elements in their outer layers. - This includes helium (the exposed shell), nitrogen, carbon, and sometimes oxygen. - These emission lines are often broad and asymmetric, and can be used to study the properties of the star's stellar wind. > [!measure] Typical Parameters > - Mass: Formed at $\sim 40 - 50 \; {\rm M_{\odot}}$, but lost about half of mass from stellar winds > - Temperature: $\sim 20000 - 200,000 \; {\rm K}$ ### Herbig–Haro (HH) Objects ![[HHo.png|align:center]] **Herbig Haro Objects** are bright patches of nebulosity around a [[#Protostar|protostar]] with narrow jets of emission (like [[#T Tauri Stars]]). This emission is partially ionized, and it excites the surrounding material as its ejected, similar to an [[Nebulae#Emission nebula|emission nebula]]. *(In fact, the first one discovered was classified as an emission nebula rather than a distinct class of object.)* **Characteristics:** - Typically found in molecular clouds and other star forming regions - When the excited gas relaxes/recombines, see strong emission lines in the [[Electromagnetic Spectrum|optical]] - Jets moving at $\sim 100\,\pu{km s^{-1}}$ probably formed due to presence of an accretion disk - These are transient phenomena lasts $\sim 10^4$ years, but can change on month to year timescales as jet encounters new media - First discovered in the Orion nebula ### Bipolar Flows ![[bipolarFlow.png|align:center]] **Bipolar flows** is the two-sided, polar outflows launched by protostars during their collapse or [[Hertzsprung-Russell Diagram#Post-Asymptotic Giant Branch (Post-AGB)|post-AGB]] stars during binary accretion. The flow is driven by either... 1) Dense, collimated jets composed of high-speed stellar winds and focused into two narrow streams. - $v_{\rm jet} \sim 100 \; {\rm km/s}$ - $T_{\rm jet} \sim 10^{4} \; {\rm K}$ - Shock materials emits in the [[Electromagnetic Spectrum|optical]] ([[#Herbig–Haro (HH) Objects]]) - Knots can be observed along the jets - The density of the jets which can make the outflow difficult to observe directly. 2) Broader wind cones of molecular outflows with more slowly moving gas. - $v_{\rm jet} \sim 10 \; {\rm km/s}$ - $T_{\rm jet} \sim 10 \; {\rm K}$ - Observed in the [[Electromagnetic Spectrum|milimeter]], through emission from molecular lines Though the mechanism for producing these collimated bipolar jets is not entirely understood, it is believed that interaction between the accretion disk and the stellar magnetic field For the young [[Stellar Classes#Protostar|protostars]] (younger than [[Stellar classes#T-tauri star|T-tauri]] stars), the flow can originate from the accretion of matter from the parent molecular cloud. For evolved stars, the flows can originate in the [[Nebulae#Planetary nebula|planetary nebulae]], with the jets driven by accretion from a [[Binary Stars|binary]] companion. ### OH Maser An astrophysical **maser** *("**M**icrowave **A**mplification of **S**timulated **E**mission of **R**adiation")* is a naturally occurring source of stimulated spectral line emission, typically in the microwave portion of the electromagnetic spectrum. An **OH maser** is an astrophysical object with significant OH (hydroxyl molecule) [[Einstein Coefficents#Stimulated Emission|stimulated_emission]] in the [[Electromagnetic Spectrum|milimeter wavelength]] ($\sim 1.6 \,\pu{GHz}$). - These objects have line intensities far above what would be expected of a blackbody. - Thought to be caused by enhanced [[Einstein Coefficents#Stimulated Emission|stimulated emission]] - Found near star forming regions, protostars, or evolved [[Hertzsprung-Russell Diagram#Post-Asymptotic Giant Branch (Post-AGB)|post-AGB]] stars. (similar to [[#bipolar flows]])