Star Formation

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Some of the research papers that you will be reviewing are very technical and probably understandable only by astrophysicists doing similar theoretical modeling or observations. One of the goals of this exercise is to get you all into the literature and help you start to develop skills in reading and filtering out information from such high-level papers. It won't take long until you realize how important the abstract, introduction, conclusion, and figures with their captions are. Well written, these parts of a paper may be all you (and anyone reading your papers) need to read.

The second note is that the following steps provide a deeper probe into the material covered in Secs. 12.2 and 12.3 of C&O An Introduction to Modern Astrophysics. It is highly desirable and strongly recommended that you read those sections before, or along with, working through this exercise.

The collapse and fragmentation of a large molecular cloud

Highlights from Chapter 12 of Carroll & Ostlie (2nd ed.)

Forces on volume element

The equation of motion for this volume element [Böhm-Vitense, Vol. 3, p. 246, Eq. (20.1)]:eqn (20.1)

For any given interstellar cloud to collapse, it must have enough gravity to overcome the gas pressure. Gravity can be helped along if the cloud experiences a density perturbation (nearby supernova explosion, the increased density of a spiral arm, for example).

Beyond the short highlights above, it is recommended that you study Carroll & Ostlie, Ch. 12, starting with Sec. 12.2, for more information on star formation. The following is a brief summary of that chapter.

Jeans mass and Jeans length

Review the derivation of the Jeans criterion as given in C&O, starting on p. 412. For a cloud to spontaneously collapse, it must have more than a minimum mass: Mc > MJ . The criterion may also be expressed in the minimum readius necessary to collapse a cloud of density ρ0: Rc > RJ, where

Jeans M and R Carroll & Ostlie Eqs. (12.14) and (12.16)

are the Jeans mass and Jeans length.

Homologous collapse and free-fall timescale

01. (2 pts) List two synonyms for homologous and then substitute one of them here: "___________ collapse." How does an inside-out collapse differ from a homologous one? (See also C & O, p. 414 - 417.)

A homologous collapse, although hardly realistic, gives us a rough idea of how an interstellar cloud becomes a star. The model assumes that throughout the collapse, in free-fall, the temperature remains nearly constant. To make this happen, the cloud must be optically thin and the gravitational potential energy created by the collapse must be efficiently radiated away. The cloud should become centrally denser and denser as the collapse progresses. Since the free-fall time is inversely proportional to the density, the central areas will collapse faster than the far edges.

Free-fall time Carroll & Ostlie Eq. (12.26)

An extremely simple series of sketches representing the formation of stars, including fragmentation.

A slightly more complicated representation from Sterzik, Durisen, and Zinnecker, A&A 411, 91-97 (2003):

Formation binary stars

02. (4 pts) After reviewing the introduction to the Sterzik et al paper, read through Sec. 2 and summarize briefly what is happening at the stages a, b, c and d. Do your best to relate the content to what the figure depicts.

For additional reading giving a summary of the current status of the theory of star formation, see "From clouds to stars - Protostellar collapse and the evolution to the pre-main sequence I. Equations and evolution in the Hertzsprung-Russell diagram," Wuchterl & Tscharnuter, A&A 398, 1081-1090 (2003).

03. <1 pt> The caption to Fig. 1 of the Wuchterl & Tscharnuter refers to optical depth τRoss = 2/3. What is the optical depth that is being characterized in this part of the paper?

04. <1 pt> Scan through the paper (so that you obtain a general essence of the goals) until you get to Sec. 3.2. How have the authors defined "stellar zero age"?


To quote C&O: "The process of fragmentation that segments a collapsing cloud is an aspect of star formation that is under significant investigation." (2007, p. 417) Clouds don't just form one massive star. Stars appear to form in groups, whether it is a binary or multiple-star system or star clusters of hundreds to thousands of stars. Observations seem to show that only about 1 percent of the molecular cloud actually forms stars. Is there some kind of "shut-off" mechanism? On pages 418 - 419, C&O argue that there is a minimum mass that is determined by when the collapse goes from being predominantly isothermal to adiabatic.

In addition, observations provide ample evidence that there are more low-mass than high-mass stars born when an interstellar cloud fragments. The implication is that the number of stars that form per unit area in the Milky Way's disk is strongly mass dependent (ibid. p. 430).

The Initial Mass Function and Current Day Mass Function

Rana IMF Rana CDMF

The above images are from "Mass function of stars in the solar neighbourhood," Rana, N. C., Astronomy and Astrophysics, vol. 184, 104-118, 1987. From his abstract: "It is found that the classical views such as near constancy of star formation rate, an IMF having a simple power law in mass, no appreciable infall of matter from the halo, and no exotic amount of dark remnants or brown dwarfs, are still able to offer a consistent view of the chemical evolution of the solar neighbourhood."

05. (4 pts) In 1987, there was no confirmed observational evidence of any brown dwarfs whatsoever. How many brown dwarfs have been observationally confirmed to date? How would this number change either of the graphs shown above? How is the initial mass function (IMF) figured out?

Massive stars: They form first and wreak havoc on the star formation process

We suspect that the most massive stars take only around 50,000 years to collapse into a zero-age main sequence stars, while stars like our sun may take 1,000 times longer. This means that as the temperature of the massive star increases it will start to produce more and more ultraviolet radiation, dissociating the molecules first and then ionizing the hydrogen atoms. This will create an HII region inside of an HI region. There is ample observational evidence where several O and B stars have formed first. Their high luminosity leads to significant radiation pressure that will seemingly "blow" mass out of the cloud, halting further star formation. Here is a series of images and related web sites that demonstrate this scenario.


Stellar Snowflake Cluster

Newborn stars, hidden behind thick dust, are revealed in this image of a section of the Christmas Tree Cluster from NASA's Spitzer Space Telescope, created in joint effort between Spitzer's Infrared Array Camera (IRAC) and Multiband Imaging Photometer (MIPS) instruments.

Object name: Snowflake Cluster
Object type: Star cluster, Star forming region
Position (J2000): RA: 06h 41m 0.00s Dec: 9° 36' 22.00"
Distance: 2,700 light-years
Constellation: Monoceros

Spitzer Data
Image Credit: NASA/JPL-Caltech/P.S. Teixeira (Center for Astrophysics)
Instrument: IRAC + MIPS
Wavelength: 3.6 microns and 4.5 microns (blue), 5.8 microns and 8.0 microns (green), and 24 microns (red)
Image scale: 33x56 arcmin
Orientation: North is 1.6 degrees clockwise from up
Release Date: 2005/12/2

06. (3 pts) Take a look at video Snowflake Cluster (Gallery Explorer). Especially noticeable is the star that has a number of stars seemingly radiating from it. Based on your reading here, what kind of process could create such stellar radiating structures, if real? What might have been the structure of that part of the molecular cloud preceding star formation? (See also "Making Elephant Trunks" below.)

The Trifid Nebula

SF2 sf7

"Three huge intersecting dark lanes of interstellar dust make the Trifid Nebula one of the most recognizable and striking star birth regions in the night sky. The dust, silhouetted against glowing gas and illuminated by starlight, cradles the bright stars at the heart of the Trifid. This nebula, also known as Messier 20 and NGC 6514, lies within our own Milky Way Galaxy about 9,000 light-years from Earth, in the constellation Sagittarius. This image from NASA's Hubble Space Telescope, offers a close-up view of the center of the Trifid Nebula, near the intersection of the dust bands, where a group of recently formed, massive, bright stars is easily visible."

Credit: NASA, ESA, and The Hubble Heritage Team (AURA/STScI)


For more information on the massive-star-forming region that we know as the Trifid, see " Spectacular Spitzer Images of the Trifid Nebula: Protostars in a Young, Massive-Star-forming Region," Rho & Reach, The Astrophysical Journal, 643:965-977, 2006.

07. What are the Class 0 protostars that the authors Rho & Reach discuss? Are they related to young stellar objects (YSOs) in any way (older, younger, etc.)?

08. In the last paragraph of the discussion section (before the thank-you paragraph), the authors ask three questions. Pick one of the questions and state whether or not they were able to answer it. Include the "how" or the "why not."


A Star's Close Encounter

The potential planet-forming disk (or "protoplanetary disk") of a sun-like star is being violently ripped away by the powerful winds of a nearby hot O-type star in this image from NASA's Spitzer Space Telescope. At up to 100 times the mass of sun-like stars, O stars are the most massive and energetic stars in the universe. The system is located about 2,450 light-years away in the star-forming cloud IC 1396.

09. There is a related article linked from the web site titled, "Planets Prefer Safe Neighborhoods." We know that spectral type O and B stars don't live long enough for life, even simple microorganisms, to form. What are the hazards for any protoplanetary disks that try to form or happen to blunder near an O star?

A large sample of HII regions

Please visit this clickable map of HII nebulae that shows the locations in the Galaxy of star forming regions taken at visible wavelengths. View at least half of the nebulae (out of 16 shown), and answer these questions:

10. What one feature do you note that seems to be present in most or all of the images you examined? What question was conjured up in your mind as you reviewed these images?

11. Since we don't have exact distances to these HII regions, we don't know the actual sizes. Theoretically, however, we have the Strömgren radius to guide us. What assumptions go into the formulation of this radius and what parameters are involved? How would you observationally test the validity of the Strömgren radius?

Shock front morphology and triggering of star formation

A research area that has seen lots of activity recently has to do with the formation of stars in a molecular cloud, the effect the HII ionization fronts have on star formation, and why those "elephant trunk" and tall, skinny pillars form at the edge of the cavity hollowed out by radiation pressure from the OB associations.

Making elephant trunks

12. First, take a look at just one of the star forming regions where weird pillar-like structures are plentiful: the eta Carinae region. The explanation is given at "Carina in Context." Also interesting is Pillars Behind the Dust. You should make sure you take a look at All Pillars Point to Eta. If you had to describe what you see to a blind student, what would you say?



Although there are a number of places where theoretical work is going on with the intent of modeling the formation of such features, there is one publication that seemed to have at least one scenario that at least partially reproduces the observations: "Three-Dimensional Dynamical Instabilities in Galactic Ionization Fronts"; Whalen and Norman, The Astrophysical Journal 672 (2008) 287. The authors also bring in the relevance of their work to cosmological reionization by questioning whether "I-front instabilities" arise in the primordial clouds of primeval massive stars and protogalaxies (a welcome stellar astrophysics to cosmology linkage).

13. Review this article and especially some of the images of the results, and state whether or not you are convinced that the model(s) work. Which model seems to come the closest to replicating reality? What criteria did you use in your selection?

Triggering of star formation

SF10 14. Please review the abstract and introduction to the article: "Triggered Star Formation in the W5 H II Region," The Astrophysical Journal, 595:900-912, 2003. Summarize what you reviewed there. Take a look at the paper's Fig. 4 (reproduced here), and state whether you find the evidence (backed up by additional reading of the article) convincing. Explain why or why not.


The schematic drawing below shows a possible method for star formation triggering by a shock front. (Source of the figure is lost.)



Massive Young Stars Trigger Stellar Birth

This image seems to be the observational equivalent of the theory shown at the left. You should spend a few moments comparing the "theory" (such as I've been able to recover) and the observations as given on the Spitzer web site.

15. What if the theory that the initial formation of massive stars and the triggering of subsequent massive star formation results in a progressive series of star clusters being formed? That is, would it be possible to have "cigar-shaped" stellar regions in molecular clouds? The evidence could be provided through observation. What kind(s) of observations would you propose to test the possibility of a range of ages of the star clusters through space? For example, in the "hockey stick" image that follows, would you see if the star clusters highlighted had a range in ages?

16. Is there a possible relationship to this process and what you discerned from the star patterns in the snowflake cluster investigated above?



A Slice of Orion

This image composite shows a part of the Orion constellation surveyed by NASA's Spitzer Space Telescope. The shape of the main image was designed by astronomers to roughly follow the shape of Orion cloud A, an enormous star-making factory containing about 1,800 young stars. This giant cloud includes the famous Orion nebula (bright circular area in "blade" part of hockey stick-shaped box at the bottom), which is visible to the naked eye on a clear, dark night as a fuzzy star in the hunter constellation's sword.

Object type: Nebula, Star-Forming Region
Position (J2000): RA: 05h 35m 14.10s Dec: -5° 22' 23.00"
Distance: 1450 light-years
Constellation: Orion

Image Credit: NASA/JPL-Caltech/T. Megeath (University of Toledo)
Instrument: IRAC
Wavelength: 3.6, 4.5, 5.8 and 8.0 microns
Exposure Date: February 16 and 18, 2004, March 9, 2004, October 8, 12, and 27, 2004
Exposure Time: 41.6 seconds per position
Image scale: 4.6 x 1.6 deg
Orientation: North is 52 deg CW from up
Release Date: 2006/08/14

T Tauri Stars

T Tauri stars (named after the prototype, T Tauri) are a stage in the birthing of a star having a mass in between ~0.5 and 2.0 solar masses. It is thought (and some meteorites may contain shock evidence) that the Sun went through this stage.



T Tauri stars - Wild as dust


Figure 5: Positions of the observed stars in the HRD, assuming a distance of 460 pc. Black dots indicate classical T Tauri stars associated with IC 2118, crosses mark the other target stars and asterisks are for wTTS detected by ROSAT (Alcalà et al. 1996). Dotted lines indicate the isochrones of 106, 3 x 106, 5 x 106, 107, 5 x 107, and 108 years, and thin solid lines show the evolutionary tracks from Palla & Stahler's (1999) model. The dashed line corresponds to the birthline and thick solid line indicates the zero age main sequence.

Kun et al, " The IC 2118 association: New T Tauri stars in high-latitude molecular clouds," A&A 418, 89-98 (2004)

T Tauri stars are characterized by infrared excesses, a location above the zero-age main sequence on the HR Diagram, hydrogen emission, lithium absorption, P-Cygni profiles in their spectra (see Fig. 12.17 in C&O, p. 436), and fairly rapid irregular variations in luminosity (P ~ days). Many are associated with Herbig-Haro objects created by the jets from these stars plowing into the interstellar medium. The very young members of this class of stars may have an accretion disk that powers and collimates the jets (see C&O, p. 439).

17. a. Explain what causes a spectral line to have a P Cygni profile. b. The existence of forbidden lines in a spectrum is indicative of what? c. Herbig-Haro objects show emission-line spectra. Why?

Here is a star that has a lot going on: Optical and infrared properties of V1647 Orionis during the 2003-2006 outburst, D. Fedele et al A&A 472, 1, 2007, 207 - 217

18. Briefly highlight the results of their observations, listing which characteristics of a T Tauri or FU Orionis star this particular young star exhibits.

FU Orionis Stars - Wish you could observe them?

Review the abstract, introduction, and conclusion to the paper: "Spitzer IRS Observations of FU Orionis Objects," Green et al., The Astrophysical Journal, 648:1099-1109, 2006.

19. What conclusions do the authors give?

SF21 (Image from Embedded Outflow in HH 46/47.)
It appears that HH objects have very intriquing spectra.

What's new in T Tauri studies

The Spitzer Space Telescope has given us some wonderful insight into the reasons for the different classifications of T Tauri stars.


Spectra Show Protoplanetary Disc Structures

The top illustration represents the spectrum of a star with no circumstellar disc or other surrounding material. The distribution of light at any given wavelength follows a specific and well-known line, determined by the laws of physics and the temperature of the star. In the case of a star, most of the light is produced at shorter wavelengths (the left side of the diagram), due to the high temperature of the star's surface. Moving to the right-hand side of the diagram, the wavelengths increase to lower energies (indicating lower temperatures) and, the starlight drops off.

In the second diagram, we see the spectrum of a star with a disc of dust and gas around it. The warm dust and gas disc around the star produces its own infrared light, which changes the shape of the spectrum. The circumstellar material is cooler than the surface of the star, so it emits most of its light at longer infrared wavelengths, closer to the right-hand side of the diagram. Now, there is an excess of infrared emission, which can not be coming from the star itself. The disc is revealed.

Going a step further, in the third diagram we see the spectrum of a star with a circumstellar disc around it, but in this case, the inner part of the disc has been swept away, perhaps by the formation of a planet. The dust closest to the star was also the hottest, so its absence means that there is less emission from the disc at higher temperatures. The only dust producing infrared light is much cooler than the star, and radiates only at long wavelengths. This low temperature "bump" on the spectrum indicates a disc with a missing center, and may be the first clue that planets have formed inside the disc.

20. Classify the stars whose spectra are shown here according to whether you think they are "naked" (no disk), have a full circumstellar disk, or have a inner gap in their circumstellar disk. (Maybe somewhere in between these categories.) What surprised you about this work? Which one represents a Class I star? Class II? Class III? SF16
Spitzer Spectra of Protoplanetary Discs
Paper: The Astrophysical Journal Supplement Series, 154:391-395, 2004
Spitzer Spectrum of Ices in a Protoplanetary Disc

SF22Spectrum of AA Tauri: Observations versus Model

It is possible to model emission lines in a star, even in the infrared part of the spectrum where many of the lines are formed by molecules (each of which has thousands and thousands of lines per nanometer). One of the strongest emission lines belongs to hydrogen cyanide. Would you want to drink the water on AA Tauri? (No answer needed.)