Star Clusters, Stellar Evolution, & Interstellar...

Star Clusters,Stellar Evolution, &

Interstellar DustThe final stages of stellar evolutionOpen and globular stellar clusters

Extinction, reddening, polarization of starlightComposition of dust grains

February 27, 2020

University of Rochester

Star Clusters, Stellar Evolution, & Interstellar DustI Shell hydrogen fusion and subgiantsI Late stellar evolution: the giant branch,

horizontal branch, and asymptotic giant branchI Evolution of high mass stars: the iron

catastropheI Type II (core-collapse) supernovaeI Open and globular clusters as stellar clocksI Extinction and reddening of starlightI Scattering and optical depthI Polarization of starlightI Dust composition, size, and origin

Reading: Kutner Sec. 14.2–14.3, Ryden Sec. 16.1, ShuCh. 11

“Pillars of Creation,” Eagle Nebula (M16), NASA/ESA/HST.February 27, 2020 (UR) Astronomy 142 | Spring 2020 2 / 47

https://www.nasa.gov/content/goddard/hubble-goes-high-definition-to-revisit-iconic-pillars-of-creation

Shell hydrogen burning & the subgiant phase

Eventually, a star will exhaust the hydrogen at the very center.

The temperature is insufficient to ignite helium fusion but is high enough just outside thecenter for a shell of hydrogen fusion to provide support for the star. Thus,I T is nearly constant in the core (isothermal helium core), which keeps increasing in

mass due to hydrogen depletion.I There is increased luminosity and further expansion of the envelope of the star.I There is a decrease in effective temperature.

This is called the subgiant phase. The star moves off the main sequence, upwards and tothe right on the H-R diagram.

February 27, 2020 (UR) Astronomy 142 | Spring 2020 3 / 47

Observational H-R diagram

I Observational H-R diagram showingabsolute magnitude vs. color index.

I Made using distances from the Gaia mission


https://sci.esa.int/s/wKdy4dW

Degeneracy in the isothermal coreThe subgiant phase ends when the mass of the isothermal He core becomes too great forsupport of the star.I Reason for a maximum weight that can be supported by pressure in the core:

electron degeneracy pressure.I The core is like a white dwarf, except with additional external pressure.I The maximum mass in the core (Schonberg & Chandrasekhar 1942) is

Miso. core

Mtotal= 0.37

(µenvelope

µiso. core

)2

≈ 0.37(

0.621.32

)2

= 0.08 for the Sun

At this point comes the red giant phase.


http://adsabs.harvard.edu/abs/1942ApJ....96..161S

The red-giant phase

After the maximum mass of the core isexceeded, the star moves up and to the rightin the H-R diagram.I The core collapses, causing a rise in ρc

and Tc.I The convection zone extends inward

(“dredge-up”).I Stellar radius dramatically increases due

to the increase in radiation pressure fromthe interior, which now dominatessupport against gravitational collapse.


https://en.wikipedia.org/wiki/Dredge-up

The triple-α processThe core temperature reaches 108K and the triple-α process

342He→ 8

4Be∗ + 00γ + 4

2He→ 126 C + 20

0γ

begins helium fusion. The onset isvery rapid in stars with M ≥ M,leading to a phenomenon called thehelium flash.

The half-life of 8Be is 10−16 s and itdecays back into two 4He nucleiunless it interacts with a third 4Henucleus to form 12C. Some of the12C will then fuse with another 4Heto form 16O.


https://en.wikipedia.org/wiki/Triple-alpha_process

https://en.wikipedia.org/wiki/Helium_flash

Explanation of solar elemental abundances

The triple-α process explains why C and O are so abundant (in a relative sense) comparedto the other heavy elements.


A 1M star as a Red GiantRed giant structure: extremely dense He core and extremely tenuous and cool H envelope (ρ = 10−4 g/cm3).

Images from ATNF.


http://www.atnf.csiro.au/outreach/education/senior/astrophysics/stellarevolution_postmain.html

Late stages of stellar evolution

I The horizontal branch is the phase aftertriple-α onset.

I Interior: core He burning, shell Hburning. The core is on the He mainsequence.

I Note the differences and similaritiesbetween a 1M, 5M, and 10M star.

Diagram from ATNF.


http://www.atnf.csiro.au/outreach/education/senior/astrophysics/stellarevolution_postmain.html

Nomenclature: Spectral type

The “Harvard” spectral type of a star is a classification based on the strength ofabsorption lines of several molecules, atoms, and ions (Cannon & Pickering 1901).I Generally, types A–M correspond to steady decreases in the strength of hydrogen

lines. Type O is weaker still.I Type P for planetary nebulae and Q for miscellany. N not used.I In 1925 Cecilia Payne showed that the spectral type sequence OBAFGKM is a

sequence of decreasing temperature from roughly 35000K to 3500K (Payne 1925).I Numbers 0–9 add a further refinement of temperature within the spectral classes (0 =

hottest, 9 = coolest).I L, T, and Y recently added for cooler brown dwarfs.

Examples: Vega is an A0 star; the Sun is a G2 star; Pollux is a K2 star; Betelgeuse is an M2star.


http://adsabs.harvard.edu/abs/1901AnHar..28..129C

https://en.wikipedia.org/wiki/Stellar_classification

http://adsabs.harvard.edu/abs/1925PhDT.........1P

Harvard spectral classification

Class Te [K] M [M] R [R] L [L] Frac. MS Pop. [%]O ≥ 30000 ≥ 16 ≥ 6.6 ≥ 30000 0.00003B 10000− 30000 2.1− 16 1.8− 6.6 25− 30000 0.13A 7500− 10000 1.4− 2.1 1.4− 1.8 5− 25 0.6F 6000− 7500 1.04− 1.4 1.15− 1.4 1.5− 5 3G 5200− 6000 0.8− 1.04 0.96− 1.15 0.6− 1.5 7.6K 3700− 5200 0.45− 0.8 0.7− 0.96 0.08− 0.6 12.1M 2400− 3700 0.08− 0.45 ≤ 0.7 ≤ 0.08 76.45

Table of spectral classes O through M for the Main Sequence. From wikipedia. See also Habets & Heintze (1981) andLedrew (2001).


https://en.wikipedia.org/wiki/Stellar_classification

http://adsabs.harvard.edu/abs/1981A%26AS...46..193H

http://adsabs.harvard.edu/abs/2001JRASC..95...32L

Nomenclature: Luminosity class

At Yerkes Observatory in the 1940s, Morgan, Keenan, and Kellman added anotherdimension to classification with luminosity classes (Morgan et al. 1943).

V main sequence or “dwarf” stars (the Sun)IV “subgiants”, brighter than V by 1 or 2 magnitudes for the same spectral typeIII normal “giants”, another few magnitudes brighter

II, I “bright giants” and “supergiants,” even brighter (Antares, Betelgeuse)VI, VII “subdwarfs” and “white dwarfs” (Sirius B). Subdwarfs are metal-poor MS

stars. White dwarfs are degenerate stellar remnants.Examples: Vega is an A0V star; the Sun is G2V, Pollux is K2III, and Betelgeuse is M2I.


http://adsabs.harvard.edu/abs/1943assw.book.....M

H-R diagram


After the horizontal branch: M < 2M

I Isothermal C-O core forms as He isexhausted.

I Not enough weight to overcomedegeneracy pressure.

I Core cannot collapse and ignite C-Ofusion (requires 500 MK!)

I H/He burning in outer core, ejection ofrest of stellar envelope, forming aplanetary nebula (few 1000 yrtimescale).

The core becomes a 0.6M C-O white dwarfwith T0 ∼ 108 K. It lasts forever unless it hasa close stellar companion.


After the horizontal branch: M > 2M

I Asymptotic giant branch(ABG/supergiant) evolution

I Repeated core collapse after fuelexhaustion, up to Si fusion to produceFe-peak elements.

I R and L steadily increase while Tedecreases.

I Each successive fuel is exhausted fasterthan the last. For a 15M star (Woosley& Janka 2006):

Fuel H He C NeTime 107 yr 106 yr 103 yr 0.7 yr

O, Mg Si, . . . Fe . . .2.6 yr 18 dy 1 s


http://adsabs.harvard.edu/abs/2005NatPh...1..147W

http://adsabs.harvard.edu/abs/2005NatPh...1..147W

What happens after the nuclear fuel is exhausted?

For most M > 2M stars:I During burning of the heavier elements and radiative support of the stellar envelope,

stars tend to be hydrodynamically unstableI This leads to the loss of large fractions of the stellar mass.I Oscillations: note that evolution takes stars across the instability strip, which is

nearly vertical at Te ∼ 5000 K.I Stellar winds can also remove significant amounts of material.

These processes can keep a star’s core mass below the SAC limit, so the final states of thestar are like those of lower-mass objects: planetary nebula phase and white dwarfremnant.


What happens after the nuclear fuel is exhausted?

For the most massive stars (M & 8M):I Mass loss is insufficient to keep the core in the white dwarf phase; maximum mass of

Fe white dwarf is 1.26M.I Result: further collapse and neutronization (and creation of signicant number of

neutrinos).I When the collapsing core reaches tens of km in size, neutron degeneracy pressure

sets in, which can stop or slow the collapse.I However, since the collapse has been from white-dwarf to neutron-star dimensions,

infalling material from the stellar envelope is going very fast (a large fraction of c).I Result: envelope rebounds off the stiff neutron-degenerate material and blows up the

rest of the star.This is called a core collapse or Type II supernova.


Core-collapse (Type II) supernovaNomenclature: Type II or CCSN. Remnant is a NS or more rarely a BH, depending oncore mass (M = 1.3− 2.2M).

Image from NASA/CXCFebruary 27, 2020 (UR) Astronomy 142 | Spring 2020 19 / 47

https://www.nasa.gov/missions/science/f_supernovae.html

Observation of stellar evolution: Star clusters

I Stars tend to form in clusters at about the same age (within 1− 2 Myr of each other)and are nearly the same distance from us.

I H-R color-magnitude diagrams for stars in the cluster make it very easy to infer thestars’ location on the main sequence.

I If we make an H-R diagram of a cluster we tend to see a turnoff point.I The turnoff is caused by stars exhausting their H supply and moving along the

horizontal branch.I Higher-mass stars move off the MS first, so the turn off starts on the

high-mass/high-Te end of the H-R diagram (upper left) and moves down aslower-mass stars age and exit the MS.

I In other words, the turnoff point acts like a clock, telling us the age of stars in thecluster with very good accuracy.


https://en.wikipedia.org/wiki/Turnoff_point

The turnoff point

Left: H-R diagram for two open clusters, from wikimedia commons.Right: Cartoon of turnoff points for several clusters. From P. Eskridge.


https://commons.wikimedia.org/wiki/File:Open_cluster_HR_diagram_ages.gif

http://frigg.physastro.mnsu.edu/~eskridge/astr101/week9.html

Open and globular clusters

Stars are classified into open (young) or globular (old) clusters.

Properties of open clusters:I Low density, irregular, lots of blue starsI Low random velocities (few km/s)I Hundreds of thousands of stars, not

always gravitationally boundArchetypes: Pleiades (M45), Hyades, h andχ Persei

Properties of globular clusters:I High density, spherical, few blue starsI Higher random velocities (tens of km/s)I Millions of stars, gravitationally bound

Archetypes: ω Centauri, M3, M13, 47Tucanae


Open clusters: the Pleiades (M45)The Pleiades are about 135 pc away and are roughly 110 Myr old.

Left: Optical image of the Pleiades cluster with the brightest stars highlighted.Right: H-R diagram of X-ray sources in the cluster (Stauffer et al. 1994).


http://adsabs.harvard.edu/abs/1994ApJS...91..625S

Globular clusters: M3M3 is about 12 Gyr old, like all Galactic globular clusters, and it is 10.4 kpc away.RR Lyrae stars are not plotted (note gap in HB).

Left: M3, from P. Challis (APOD).Right: H-R diagram from Montgomery et al. 1993.


http://antwrp.gsfc.nasa.gov/apod/ap980719.html

http://adsabs.harvard.edu/abs/1993AJ....106..181M

Size and composition of interstellar dust

Size More like cigarette smoke than household dust: < 0.1 µm in most darkclouds, ranging from 10 nm (50-100 atoms) in diffuse and UV-illuminatedclouds to ∼ 1 µm in the darkest molecular clouds.

Amount About 1% by mass of the interstellar medium.

Composition Silicates (“rock”), carbon, and probably metallic iron, just like terrestrialplanets.

Temperature T = 10− 100 KI Heated by UV starlightI Cooled by blackbody emission; radiation from interstellar grains can be

seen at IR wavelengths.


Origin and life of interstellar dust grains

Grains are born primarily in the winds of late type (giant, AGB) stars, condensing as thewind material cools; and perhaps secondarily in the interstellar medium (ISM),condensed from cold gas and perhaps conglomerated with other grains.I Dust is often seen to be crystalline in giant stars, yet it is not crystalline in the

interstellar medium.

I But the average dust grain lives billions of years in the ISM, enough time fororiginally crystalline grains to become shattered and amorphotized by UV photonsand cosmic rays.

I Cold-gas condensation and conglomeration naturally produce amorphous grains.See, e.g., Draine (2006).


http://adsabs.harvard.edu/abs/2006IAUJD..11E...8D

Evidence for interstellar dust

How do we know that there is interstellar dust?Extinction Dark markings on the Milky Way (dark clouds) are generally caused by

absorption and/or scattering of background starlight rather than holes in thestellar distribution.

Reddening Stars associated with dark markings are much redder in color in theircontinuum emission than one would infer from their spectral type (classifiedby line emission). This selective emission is naturally explained by thewavelength dependence of scattering and absorption of light by sub-µmparticles.

Polarization of originally unpolarized lines by starlight is naturally explained byselective absorption by nonspherical, aligned, sub-µm solid particles.


Extinction vs. wavelengthDust extinction as a function of wavelength, normalized to AV = 1. The bump at 0.22 µm is likely caused bygrains of graphite (e.g., soot).

0.2 0.4 0.6 0.8 10

1

2

3

4

λ ( m)

A λ (m

agnit

udes)

VisibleUV Infrared

μ

Copyright © 2010 Pearson Education, Inc.February 27, 2020 (UR) Astronomy 142 | Spring 2020 28 / 47

Dark clouds

ρ Oph

Antares (α Sco)

Trifid Nebula (M 20)


Dark clouds

Good modern images reveal filamentary cloudlike structures in the dark mark-ings. This makes it more plausible that they are dark absorbing clouds ratherthan holes in the distribution of stars.


A hole in the sky

NGC 1999 in Orion: an exception thatproves the rule.I Long thought to be a dark globule

overlying a more diffuse cloud andextinguishing background starlight.

I The star would lie farther from us thanthe globule, nearer than the diffusecloud.

Visible image from NASA/HST/STScI


http://hubblesite.org/newscenter/archive/releases/2000/10/image/a/

A hole in the sky

The “globule” turns out to be dark even atvery long IR and sub-mm wavelengths.I An ordinary globule would emit

brightly at these long wavelengths.I So in this case the hole really is a hole.

Image: blue = 4.5 µm, green = 70 µm, red = 160 µm. FromHerschel Space Observatory (Stanke et al. 2010)


http://adsabs.harvard.edu/abs/2010A%26A...518L..94S

Proof of the existence of extinction

Trumpler’s experiment on open clusters(Trumpler 1930): plot sum of fluxes from allstars in cluster versus solid angle occupiedby the cluster.I If all open clusters had the same

diameter D then Ω = π(D

2r

)2∝ r−2.

I Since flux scales like r−2 one should geta straight light through the origin.

I Scatter: clusters do not all have thesame D.

I Curve does not pass through origin:flux falls faster than r−2; impliesextinction. Solid angle ( )µ1 2r


http://adsabs.harvard.edu/abs/1930PASP...42..214T

Rayleigh scatteringScattering by non-absorbing dielectric spheres with number density N, index of refractionn and radius a λ. If f0 is the flux without extinction, then the observed flux f is givenby the Beer-Lambert Law:

f = f0e−αx = f0e−τs

where

α =

(32π3(n− 1)2

3N

)1

λ4 =1`

is the volume scattering coefficient and

τs = αx =∫ x

0α(x′) dx′

is the optical depth in scattering.

*

x

f

Star

Dustcloud


Rayleigh scattering and the “blue sky effect”

I You will derive these expressions in an intermediate E&M course. The point toremember is the very strong wavelength dependence τs ∼ λ−4.

I Large τs means more light is scattered out of the line of sight, and therefore less lightis transmitted to you.

I Note that short-wavelength light is scattered more effectively than long-wavelengthlight because of the λ−4 dependence.

I Thus the sky is blue, as are reflection nebulae like NGC 1999, because blue light isside-scattered efficiently.

I By the same token, what gets transmitted is more red because the blue light isscattered out of the direct line of sight. Thus, sunsets are red, as is extinguishedstarlight.

I Note that long-wavelength light (IR, radio) can penetrate dust.


Rayleigh scattering

I The Trifid Nebula (M20) exhibitssignificant effects of scattering (Malin2017).

I Dark lanes in upper, ionized, nebula:extinction

I Blue color of lower, reflection, nebula:scattering

I Many bright red stars in field:reddening


http://oldweb.aao.gov.au/images/captions/aat012.html

http://oldweb.aao.gov.au/images/captions/aat012.html

Scattering Regimes

a λ τ ∼ λ−4

a ∼ λ τ ∼ λ−1

a λ τ ∼ C


Color excess & extinction

Starting from the Beer-Lambert Law f = f0e−τ, we can express extinction in terms ofmagnitudes:

mobs = −2.5 log f = −2.5 log f0 − 2.5 log (e−τ)

= m0 + 2.5τ log e = m0 + 2.5τ(0.434)= m0 + 1.086τ

Thus we can define a wavelength-dependent extinction term A(λ) = 1.086τ(λ) such that

mobs(λ) = m0(λ) + A(λ) mobs −M = 5 log r− 5 + A

In other words, the effect of extinction is to make stars look fainter than they should giventheir distance.



The effect of extinction isto reduce the flux atshorter wavelengths. Thismakes the color of theobject redder, and itreduces the overallbrightness of the object(making it appear furtheraway).

103 104Wavelength [Å]

103

104

105

106

107

Flux

[erg/s/Å/cm

2 /sr]

OriginalExtinguished



For a color index such as B−V, the individual magnitudes will be shifted by apassband-dependent extinction term:

V = V0 + AV B = B0 + AB

Hence the observed color will be

B−V = (B−V)0 + (AB −AV) = (B−V)0 + E(B−V)

The term E(B−V) is called the color excess. In terms of optical depth, the color excess is

E(B−V) = AB −AV = 1.086(τB − τV) = 1.086τV

(τB

τV− 1)



The wavelength dependence of extinction is written in terms of R, the ratio of total toselective extinction:

R =AV

E(B−V)=

1τBτV− 1

Since τ ∼ λ−n with n > 0, extinction is larger at shorter wavelengths (reddening). Inother words, stars look redder than they should given their temperature. For particleswith size a ≈ λ, τ ∼ λ−1 and

R =1

τBτV− 1

=1

λeff,Vλeff,B− 1≈ 4.2

for λeff,B = 445 nm and λeff,V = 551 nm.

For diffuse dark clouds, R ≈ 3.06 and τV = 2.76E(B−V).


Extinction correction

Recipe:1. Reduce every B−V by the same

amount E(B−V)

2. Reduce every V by the visualextinction AV

3. The whole H-R diagram shifts tobluer and brighter values.

You will be applying these correctionsin future homeworks and recitations.


Extinction and reddening by real dust grains

Most interstellar grains are not just dielectric,they absorb light as well. Empirically,

τa ∼ λ−1.85 λ = 0.5− 20 µm

except for certain special wavelengths (seebelow).

Reddening, or differential extinction, is definedby color excesses E(U− B) and E(B−V) where

E(U− B)E(B−V)

≈ 0.72

Empirical color-color relation for unextinguishedzero-age main sequence stars.


The reddening correction

Take observations at three wavelengths (e.g., U, B, V). Compare the color-color plot tounextinguished stars. Shift the plots until they fit. The amounts by which the clustershifts are E(B−V) and E(U− B), in this case 0.32 and 0.18.


Polarization of light by nonspherical dust grainsInterstellar dust grains are actually not spherical; they tend to be needle-shaped orflake-like. Thus they can absorb or scatter light with some polarizations — thecomponents of the electric field E along the long axis of the grain — better than others.

Light

Dust grainseen fromside

Dust grainseen from top

Scattered light polarized along grain direction

Transmitted light polarized perpendicular to grain direction


Polarization of light by dust grainsInterstellar dust grains are often aligned with their long axes along some given direction.That direction can be determined by external magnetic fields and/or gas motions.I Most common alignment: B perpendicular to the long axis of spinning dust grains

(Davis & Greenstein 1951).

Stellar dust grain polarization in the Galaxy (T.J. Jones).February 27, 2020 (UR) Astronomy 142 | Spring 2020 46 / 47

http://adsabs.harvard.edu/abs/1951ApJ...114..206D

http://bgandersson.net/grain-alignment

Polarization of light by dust grains

Model of the Galactic magnetic field (Jansson & Farrar2012)

Top: Observed magnetic field of NGC 891 (Krause 2011)Bottom: Observed magnetic field of NGC 5775 (Soida et al.2011)


http://adsabs.harvard.edu/abs/2012ApJ...757...14J

http://adsabs.harvard.edu/abs/2012ApJ...757...14J

http://adsabs.harvard.edu/abs/2012mfu3.conf..155K

http://adsabs.harvard.edu/abs/2011A%26A...531A.127S

http://adsabs.harvard.edu/abs/2011A%26A...531A.127S

Star Clusters, Stellar Evolution, & Interstellar...

Documents

Transcript of Star Clusters, Stellar Evolution, & Interstellar...