Stellar - PowerPoint Presentation

Slide1

Stellar atmospheresa very short introductionPart I

Ewa Niemczura

Astronomical

Institute

,

UWr

eniem@astro.uni.wroc.plSlide2
Slide3

Stellar spectraSlide4
Slide5

Stellar spectra

One picture is worth 1000 words, but

one spectrum is worth 1000 pictures!

Ivan

HubenySlide6

What is a Stellar Atmosphere?Stellar

atmosphere

:

medium

connected

physically to a star; from

this

medium

photons

escape to the surrounding space

region where the radiation observable by a distant

observer

originatesSlide7

What is a Stellar Atmosphere?Stellar

atmosphere

:

u

sually

, a

very

thin

layer

on the surface of the starlate stars

: photosphere, chromosphere, coronaSlide8

What is a Stellar Atmosphere?Stellar

atmosphere

:

u

sually

, a

very

thin

layer

on the surface of the starlate stars

: photosphere, chromosphere, coronaearly stars: photosphere, expanding regionsSlide9

Why study stellar atmospheres?„

Why

in the

world

would

anyone

want to

study

stellar atmospheres? They contain

only

10

-10 of the mass of a typical star! Surely such

a

negligible

fraction

of a star mass

cannot

possibly

affect

its

overall

structure

and

evolution

!”

Question

to D.

Mihalas

,

about

50

years

ago

From the

lecture

of Ivan

HubenySlide10

Why study stellar atmospheres?

Atmospheres

are

all

we

see

;

we

have

to use this information in the fullest.Stars:

Stellar

atmospheres:

Determination of atmospheric parameters.Slide11

Stellar spectraWhat can we obtain?

Spectral

classification

Atmospheric

parameters

Effective

temperature

TeffSurface

gravity

logg

Chemical abundancesMetallicity [m/H]

Microturbulence

,

macroturbulence

Chemical

peculiarities

Stratification

of

elements

Rotation

velocity

VsiniStellar wind parametersMagnetic field parametersSlide12

Stellar spectraWhat can we obtain?

Stellar

classification

Atmospheric

parameters

Chemical

peculiarities

Stratification of elements

Rotation

velocity

Stellar wind parameters

Magnetic

field

parameters

Multiple

systems

Variability

in

spectral

lines

Radial velocitiesOrbit determinationCluster membershipPulsations …Slide13

Why study stellar atmospheres?

Stars:

Stellar

atmospheres

:

Determination

of

primary

(

T

eff, logg, chemical composition) and secondary atmospheric parameters (rotation velocity

,

turbulence

etc.)Stellar

structure and evolution:Determination of basic stellar parameters

(

M

,

R

,

L

)

Determination

of the

detailed

physical

state

;

Boundry

for the

stellar structure/evolution models;Atmospheres do influence the stellar evolution after all (mass loss from the atmosphere).

 Slide14

Why study stellar atmospheres?Global

context

:

Galaxies

are

made

of

stars

(special case:

very bright stars in distant galaxies);Sources of chemical species;

(…)Slide15

Why study stellar atmospheres?Methodological

importance

:

Radiation

determines

the

physical

structure

of the

atmosphere, and this structure is probed

only

by the

radiation;

Sophisticated modeling approach needed – stellar atmospheres are

guides

for

modeling

other

astronomical

objects

(

e.g

. accretion discs, planetary nebulae, planetary atmospheres etc.).Slide16
Slide17

Models: typical assumptionsGeometry

Plane-parallel

symetry

very

small

curvature

(

e.g

.

main-sequence stars);Typically for stellar photospheres:

Sun:

km

Photosphere

: km;

Chromosphere

:

km;

Corona

:

 Slide18

Models: typical assumptionsGeometry

Plane-parallel

symetry

very

small

curvature

(

e.g

.

main-sequence stars);Spherical

symetry

significant curvature (

e.g

.

giants

,

supergiants

);

…

 Slide19

Models: typical assumptionsHomogeneityWe

assume

the

atmosphere

to be

homogeneous

.

But

it’s

not

always the case,

e.g. sunspots, granulations, non-radial pulsations, magnetic Ap-stars (stellar spots), clumps

and

shocks

in hot star winds etc.Slide20

Models: typical assumptionsStationarityWe assume

the

atmosphere

to be

stationary

In most

cases

this

assumption can be accepted

Exceptions: pulsating stars, supernovae, mass transfer in close binaries etc.Slide21

Models: typical assumptionsConservation of momentum and mass

We

assume

hydrostatic

equilibrium

;

plane-parallel

geometry:

s

pherical

geometry

:

Exceptions

:

effects

of

magnetic

fields

,

interaction

in

binary

systems

etc.

no hydrostatic equilibrium:

 Slide22

Models: typical assumptionsConservation of energy

Nuclear

reactions

and

production

of

energy

:

stellar

interiorsStellar

atmospheres: negligible production of energy We assume that the energy flux is

conserved

at any radius:

 Slide23
Slide24

Different stars – different atmospheresTemperature

:

MS

stars

,

T~2000 – 60,000K

Brown

dwarfs

,

T < 2000K

Hot, degenerate

objects, T~104 – 108 KWhite dwarfs, T < 100,000K

Neutron

stars

, T~10

7KDensity:MS stars,

N~10

10

– 10

15

cm

-3

WD

,

N~10

21

– 1026 cm-3Slide25

Basic Structural EquationsStellar atmosphere:

plasma

composed

of

particles

(

atoms

,

ions, free electrons,

molecules, dust grains) and photons. Conditions: temperatures: ~103

– ~10

5

K; densities

: 106 – 1016 cm-3

.

Starting

point for

physical

description

:

kinetic

theory

Distribution

function

(most general quantity which describes the system):

-

number

of

particles

in a volume of the phase space at position , momentum , and time t.

 Slide26

Basic Structural EquationsKinetic (Boltzmann)

equation

(

describes

a development of the

distribution

function

):

–

nabla

differential

operators

with

respect

to the

position

and

momentum

components

–

particle

velocity

–

external

force

–

collisional

term (describes creations and destructions of particles of type

with the

position

(

) and

momentum

(

).

Kinetic

equation

–

complete

description

of the system

Problem

–

number

of

unknowns

(

e.g

.

different

excitation

states

of

atoms

etc.)

Simplification

–

moments

of the

distribution

function – integrals over momentum weighted by various powers of

 Slide27

Basic Structural EquationsMoment

equations

:

(moment

equations

of the

kinetic

equation

,

summed

over

all

kinds of particles;h

ydrodynamic

equations

):

Continuity

equation

(1):

Momentum

equation

(2):

Energy

balance

equation

(3):

–

m

acroscopic

velocity

–

total

mass

density

–

pressure

–

external

force

–

internal

energy

,

–

radiation

and

conductive

flux

 Slide28

Basic Structural EquationsAdditional equation

(

zeroth

-order moment

equation

):

conservation

equation

for particles of type

:

–

number

density

(

or

occupation

number

,

or

population

)

of particles of type .

 Slide29

Basic Structural EquationsSignificant simplification

of the system:

Stationary

,

static

medium (

), 1-D (

all

quantities

depend on one coordinate

):

Statistical

equilibrium equation

(0):

Hydrostatic

equilibrium

equation

(2

;

assumption

):

Radiative

equilibrium

equation (3; assumption):

 Slide30

Basic Structural EquationsConvection:

transport of

energy

by

rising

and

falling

bubbles

of

material

with properties different

from the

local

medium; non-

stationary and non-homogeneous process.

In 1-D

stationary

atmosphere

,

simplification

–

mixing-length

theory

;

Radiative

equilibrium equation with convection:

–

convective

flux

;

specified function of basic state parameters Slide31

TE and LTETE – thermodynamic equilibrium: s

implification

;

particle

velocity

distribution

and the

distribution

of

atoms

over excitation and ionisation

states

are specified by two

thermodynamic

variables

:

absolute

temperature

and

total

particle

number density (or the electron number

density

).

s

tellar atmosphere is not in TE – we see a star – photons are escaping – there are gradients of state parameters.

 Slide32

TE and LTE LTE – local thermodynamical equilibrium:

s

implification

;

standard

thermodynamical

relations

are

employed

locally for local values of

,

or

,

despite

of the

gradients

that

exist

in the

atmosphere

.

equilibrium

values of distribution functions are assigned to massive particles, the radiation field can depart from equilibrium (Planckian) distribution function.

 Slide33

LTELTE is characterised by three

distributions

:

1.

Maxwellian

velocity

distribution

of particles:

–

particle

mass and

velocity

–

B

oltzmann

constant

 Slide34

LTE2. Boltzmann excitation equation

statistical

weight

of

levels

–

level

energies

(

measured

from the

ground

state

)

 Slide35

LTE3. Saha ionisation equation

–

total

number

density

of

ionisation

stage

–

ionisation

potential

of the

ion

–

p

artition

function

defined

by

(

cgs

)

In LTE the same

temperature

applies

to

all

kind

of

particles

and to

all

kinds

of

distributions

.

 Slide36

LTEMaxwell, Saha, Boltzmann equations – LTE from macroscopic

point of

view

Microscopically

– LTE

is

hold

if

all

atomic processes are in detailed balance the number of processed

is

exactly

balanced by the number of inverse processes

,

–

any

particle

state

between

which

there exists a physically reasonable transition.e.g. – is an atom in an excited state , the same atom in another state , etc.

 Slide37

LTE vs. non-LTEnon-LTE (NLTE) – any state that

departs

from LTE

(

usually

it

means

that populations of some

selected energy levels of some selected atoms/ions are allowed to depart

from

their

LTE value, but velocity

distributions of all particles are assumed to be Maxwellian, with the same kinetic

temperature

).

 Slide38

LTE vs. non-LTEWhen we have to take non-LTE into

account

?

LTE

breaks

down

if

the

detailed

balance of at least one

transition breaks downRadiative transitions – interaction

involves

particles and photonesCollisional

transitions – interactions between two or more

massive

particles

Collisions

tend

to

maintain

LTE (

their

velocities

are Maxwellian)Validity of LTE depends on whether the radiative transitions are in detailed balance or not. Slide39

LTE vs. non-LTEDepartures from LTE:Radiative rates in an

important

atomic

transition dominate

over

the

collisional rates and

Radiation is not in equilibrium (intensity does not have Planckian distribution)

Collisional

rates are

proportional to the particle density – in high densities departures from LTE will be small.

Deep

in the

atmosphere

photons

do not

escape

and

intensity

is

close to the equilibrium value – departures from LTE are small even if the radiative rates dominate over the collisional rates.Slide40

LTE vs. non-LTEnon-LTE if: rate of photon absorptions

>>

rate

of

electron

collisions

LTE

if

:

low

temperatures and high densitiesnon-LTE if: high temperatures

and

low

densitiesSlide41

LTE vs. non-LTELTE if: low

temperatures

and high

densities

non-LTE

if

:

high

temperatures

and

low

densities

R.

Kudritzki

lectureSlide42

Transport of energyMechanisms of energy transport:radiation:

(

most

important

in

all

stars

)

convection

:

(important especially in cool stars)conduction: e.g. in the transition between solar chromosphere and

corona

radial

flow of matter: corona and stellar wind

sound and MHD waves: chromosphere and corona

 Slide43

Intensity of Radiation

specific

intensity

of

radiation

at

position , travelling in direction

, with

frequency

at time

– the

amount

of

energy

transported

by

radiation

in the

frequency

range , across an elementary area into a solid angle in a time interval :

–

angle

between

and the

normal

to the

surface

.

specific

intensity

,

proportionality

factor

;

dimention

: erg cm

-2

sec

-1

hz

-1

sr

-1

dSSlide44

Intensity of RadiationPhoton distribution

function

–

number

of

photons

per unit

volume

at

location

and

time

, with

frequencies

in the

range

propagating

with

velocity

in the

direction

.Number of photons crossing

an

element

in

time

is:

Energy

of

photons

:

where

:

 Slide45

Intensity of RadiationFrom the comparison of

energy

of

photons

:

w

ith

defined

before

:

Relation

between

specific

intensity

and

photon

distribution

function

:

Using

this

relation

we

define

moments

of the

distribution

function

(

specific

intensity

):

energy

density

,

flux

and

stress

tensor.

 Slide46

Intensity of RadiationEnergy density

of the

radiation

(

is

the

number

of

photons

in an elementary

volume, is the energy of photon):

Energy

flux

of the

radiation

(

is

the

vector

velocity

);

how

much

energy flows trough the surface element:

Ratiation

stress

tensor:

Photon

momentum

density

(

momentum

of

an

individual

photon

is

):

 Slide47

Absorption and Emission CoefficientThe

radiative

transfer

equation

describes

the changes

of the

radiation

field

due to its interaction

with the matter.Absorption coefficient – removal of energy from the radiation field by matter:

Element of

matterial

of cross-

section

and

length

remove from a

beam

of

specific

intensity

an

amount

of

energy

The dimention of

is

cm

-1

 Slide48

Absorption and Emission CoefficientThe

radiative

transfer

equation

describes

the

changes

of the

radiation

field due to its

interaction with the matter.Absorption coefficient – removal of energy from the radiation field by

matter

:

–

dimention

of

length

;

measures

a

characteristic

distance

a

photon

can

travel

before

it

is absorbed – a photon mean free path.  Slide49

Absorption and Emission CoefficientEmission

coefficient

– the

energy

released by the

material

in the form of

radiation

.Elementary amount

of material of cross-section and length releases into a solid angle

in

direction

within a frequency band

an

amount

of

energy

:

The

dimention

is

erg cm

-3

hz-1 sec-1 sr-1

dSSlide50

Absorption and Emission CoefficientMicroscopic physics

–

all

contributions

from microscopic

processes

that give rise to

an absorption or emission of photons with specified properties.True absorption and scattering:

True (

thermal

) absorption – photon

is removed from a beam and is destroyed.Scattering –

photon

is

removed

from a

beam

and

immediately

re-

emitted

in a

different direction with slightly different frequency.

 Slide51

Absorption and Emission CoefficientQuantum theory of

radiation

–

processes

that give

rise

to

an absorption or

emission of a photon:Induced absorption – an absorption of a photon and transition of an

atom/

ion

to a higher energy state

;Spontaneous emission – an emission of a photon and a spontaneous

transition

of

an

atom/

ion

to a

lower

energy

state

;Induced emission – an interaction of an atom/ion with a photon and an emission of another photon with identical properties (negative absorption).Slide52

Radiative Transfer EquationBasicRadiative transfer

equation

:

We express

conservation

of the

total

photon

energy when a radiation

beam passes through an elementary volume of matter of cross-section and

length

(measuread along

the direction of propagation):

The

difference

between

spectific

intensity

before

and

after

passing

through

the

elementary

volume

of

path

length

is

equal

to the

difference

of the

energy

emitted

and

absorbed

in the

volume

.

 Slide53

Radiative Transfer EquationBasic

The

differences

of

intensities

:

General form of the

radiative

transfer

equation

:

 Slide54

Radiative Transfer EquationBasicSpecial

case

:

one

dimentional

planar

atmosphere

:

–

angle

between

direction of propagation of radiation and the normal

to the

surface

Time independent RTE:

dz

zSlide55

Radiative Transfer EquationBasicSpecial

case

:

spherical

coordinates

Time independent:

 Slide56

Radiative Transfer EquationOptical Depth, Source function1-D transfer

equation

:

Elementary

optical

depth

:

Source

function

:

The

emission

and

absorption

coefficients

are

local

quantities

,

so

the

definition

of

source

function

is

good for all geometries.

zSlide57

Radiative Transfer EquationOptical Depth, Source functionPhysical

meaning

of

optical

depth

:

RTE in the

absence

of

emission

:

With the

solution

:

the

optical

depth

is

the e-

folding

distance

for

attenuation

of the

specific intensity due to absorption; the

probability

that

a

photon

will travel an optical distance is:

 Slide58

Radiative Transfer EquationOptical Depth, Source function

Physical

meaning

of

source

function

:

number

of

photons

emitted

in

an

elementary

volume

to

all

direction

(

comes from

integration over the all solid angles, and transforms energy to the number of photons).

he

source

function

is proportional

to the

number

of

photons

emitted

per unit

optical

depth

interval

.

 Slide59

Radiative Transfer EquationElementary Solutions

1. No

absorption

, no

emission

,

Radiation

intensity

remains

constant

.2. No

absorption, only emission,

Outcoming

radiation

from

an

optically

thin

radiative

slab (

e.g

.

forbidden

line

radiation from planetary nebulae, radiation from solar transition region or/and corona).3. No emission, only absorption

 Slide60

Radiative Transfer EquationElementary Solutions4.

Absorption

and

emission

,

General

formal

solution

of the transfer

equation

– formal because

it

is assumed

that both and

a

re

specified

functions

of

position

and

frequency

:

5.

Semi-infinite

atmosphere

–

emergent

radiation

(

observed

intensity

is

a weighted average of the source function along the line of sight.

 Slide61

Radiadive Transfer EquationMoments

Moments

of

specific

intensity

(of the

photon

distribution

function): photon energy density, radiation flux, radiation

stress

tensor.

Integration of transfer

equation

(

kinetic

equation

) – relations

between

these

moments

:

Structure

of the moment

equations

of the

kinetic

equation

:

 Slide62

Radiadive Transfer EquationMomentsIn astrophysics

:

moments

are

angle

averaged

, not

angle-integrated

quantities:

In the

plane-parallel

approximation

moments

of

specific

intensity

are

scalar

quantities

:

 Slide63

Radiative transfer equationMomentsThe moment

equations

of RTE:

Eddington

factor

:

Combination of

two

moment

equation

:

There

is

no

dependence

on the

angle

;

useful

in

numerical

solution

.

 Slide64
Slide65

Model atmosphereDefinition and terminologyModel atmosphere

–

S

pecification

of

all

atmospheric

state

parameters as function of

depth.Table of values of the state parameters in the discrete depth points.State

parameters

: depend on the type of the model (on the

basic assumption under which the model is constructed)

M

assive

particle

state

parameters

– from

this

we

can

determine the radiation field by a formal solution of the transfer equation.Slide66

Basic equationsClassic stellar atmosphere

problem

Radiative

transfer

equation

First order form:

Second order form:

NA x NF vs. NF

NA –

number

of

angle

points

NF –

number

of

frequency

points

 Slide67

Basic equationsClassic stellar atmosphere

problem

Hydrostatic

equilibrium

equation

:

– mass in the

column

of a cross-

section

of 1 cm

2

above

a

given

point in the

atmosphere

 Slide68

Basic equationsClassic stellar atmosphere

problem

Total

pressure

:

The

hydrostatic

equilibrium

equation

–

effective

gravity

acceleration

:

true

gravity

acceleration

(

acting

downward

) – the

radiative

acceleration

(

acting

upward

).

 Slide69

Basic equationsClassic stellar atmosphere

problem

Radiative

equlibrium

equation

:

the

total

radiation flux is conserved

using

the

radiative

transfer

equation

:

 Slide70

Basic equationsClassic stellar

atmosphere

problem

Statistical

equilibrium

eqations

=

rate

equations

The conservation equation for a particle :

Explicitly

:

and

–

radiative

and

collisional

rate

;

Total

number

of

t

ransitions

out of

level

=

total

number

of transitions into level ;Radiative rates depend on radiation intensity;Collisional rates

depend

on

temperature

and

electron

density

.

 Slide71

Basic equationsClassic stellar atmosphere

problem

Total

number

conservation

equation

(

or

abundance definition equation):

Only

a

limited

number

of

levels

of

an

atom/

ion

is

treated

explicitly

(the rate equation is written and solved, low-lying levels); remaining levels – approximations, and the abundance definition:

 Slide72

Basic equationsClassic stellar atmosphere

problem

Charge

conservation

equation

:

global

electric

neutrality of the medium

is

the

charge

associated

with

level

(0 for

levels

of

neutral

atoms

, 1 for

once ionised atoms etc.); summation extends over all levels of all ions of all species. Slide73

Additional equationsClassical

stellar

atmosphere

problem

D

efinition

equations

of the

absorption

and emission coefficients:

Bound-bound

transitions

(i.e.

spectral

lines)

Bound-free

transitions

(continua)

Free-free

absorption

(

inverse

brehmstrahlung

)

Electron

scattering

Another

equations

:

relevant

cross-

sections

,

definition

of LTE

populations

, etc.

 Slide74

Basic equations: summary

Equation

State

parameter

Radiative

transfer

Mean

intensities

,

Radiative

equilibriumTemperature, Hydrostatic

equilibrium

Total

particle density,

Statistical equilibriumPopulations,

Charge

conservation

Electron

density

,

Equation

State

parameter

Radiative

transfer

Radiative equilibriumHydrostatic equilibriumStatistical equilibrium

Charge

conservationSlide75

Types of model atmosphereStatic models: assumption of hydrodynamical

equilibrium

a

pplies

only

to

atmospheric

layers

that are

close

to

hydrodynamic

equilibrium, i.e. the macroscopic

velocity

is

small

compared

to the

thermal

velocity

of

atoms

–

stellar photospheresbasic input parameters: effective temperature, surface gravity and chemical composition, additional

parameters

:

microturbulence

, and in

case

of convective models: mixing length.Slide76

Types of model atmosphereStatic LTE models: LTE assumption,

two

state

parameters

,

temperature

and

density

(or electron

density) describe the physical state of the atmosphere at any given depth.standard

models

Example: Kurucz ATLAS9

codeSlide77

Types of model atmosphereStatic non-LTE models: model which

takes

into

account

some

kind

of

departure

from LTE:models solving

for the full structure (TLUSTY)restricted non-LTE problem: the atmospheric structure is

assumed

to be

known from previous calculations

(LTE or simplified non-LTE), radiative transfer and statistical equilibrium for a chosen

atom/

ion

is

solved

simultaneously

(DETAIL/SURFACE).

n

on-LTE

line-blanketed

models: non-LTE is considered in most energy levels and transitions between them – lines and continua – that influence the atmospheric structure. number of such lines may go to millions. Slide78

non-LTE modelsWhen departures from LTE may be important

in

stellar

atmospheres

?Slide79

non-LTE modelsFor a star of any spectral type, there

is

always

a

wavelength

range

, and of

course a layer in the atmosphere,

where non-LTE effects are important.„important non-LTE effects” – arbitrary – it depends

what

precision do we want; e.g. for B stars, visual

part 10% - LTE will be OK, 2-5% - non-LTE is necessary; EUV, the same star – 10-20% requires non-LTE effects. Slide80

Types of model atmosphereUnified models:no assumption of

hydrostatic

equilibrium

in the

whole

atmosphere

ranging

from a static photosphere to a

dynamical outher parts.Slide81
Slide82

LiteratureD. Mihalas: „Stellar Atmospheres”I. Hubeny: „

Stellar

atmospheres theory: an

introduction

”

in: Stellar atmospheres: Theory and Observations, Lecture note in physics, J.P. De Greeve

,

R.Blomme

, H.

Hensberg (Eds.), SpringerD. Gray:

„The observations and analysis of stellar photospheres”