preliminaries & language

Extragalactic Astronomy Ac. Yr. 2003 / 2004

1

Preliminaries & Language

Part of what we deal with in this lecture may be known already from other courses. On the other hand it is essential to have a common language and a common knowledge on the quantities and units we use in Astronomy.We will deal mainly with flux, Luminosities, magnitudes and colors with reference to stars since these (stars) are one of the main components of a galaxy.We will very briefly mention about the system of coordinates used to locate a galaxy in the sky.See also the presentation prepared by the student Danieli Minelli (? Name TBC) on the color index.


2

Photometric units

• Fluxes at optical wavelengths are measured in logarithmic units, while in the X ray and other bands are measured in CGS units.

• We define the magnitude at a given wavelength (mλ) or in a selected wavelengths range (from λ1 to λ2) or over the whole electromagnetic spectrum (mbolometric = mbol) with the relation:

,obs 10 ,obs ,obs

f S dm 2.5 log f C where f

S d

S d,obs ; S is the passband

S d

λ λλ λ λ

λ

λλ

λ

λ

λ

λ λλ

λ

= − + =

=

∫∫

∫∫

i

i


3

The Absolute magnitude

• The absolute magnitude is defined as the apparent magnitude an object would have if located at a distance of 10 parsecs (1 parsec = 1 pc = 3.09 1018 cm).

• We can also write, since we measure all the fluxes at a distance of 10 pcs:M = -2.5 log10 L + const

Where L i sthe Luminosity of the object.From the previous definition of apparent magnitude we have (always w/o

considering the presence of dust absorption:

( ) ( )

2,obs ,d

10 2,10

f L 4

Modulus o

10m M m M 2.5 log 2.5 logf 4 d L

m M 5log d par sf dis tanc

ec 5 5log d Megapar see

c 25

λλ λ

λ

ππ

− = − = − = −

− = − = +

i


4

1544604750M

3.25.172814723450L

3.28.826363902190K

3.321.8110203071630H

3.642.4915702131220J

4.084.712420149806I

4.426.943060138658R

4.834.64360088551V

5.484.67400094445B

5.611.86178066365U

/1025 WA0V,V=0nm

MsunLsunFx JyFVHMΛ nmBand


5

3000 4000 5000 6000 7000 80000

0.2

0.4

0.6

0.8

1


6

T = 52500

0 2000 4000 6000 80000

1×1017

2×1017

3×1017

4×1017

5×1017

6×1017


7

T = 6000

0 2500 5000 7500 10000 12500 150000

5×1013

1×1014

1.5×1014

2×1014

2.5×1014

3×1014


8

T=5770 - Normalization

0 2000 4000 6000 8000 10000 12000 140000

5×1013

1×1014

1.5×1014

2×1014

2.5×1014


9

T = 2640

4000 6000 8000 10000 12000 14000 16000 180000

1×1012

2×1012

3×1012

4×1012

5×1012


10

The Color Index

• CI ª mλ1 - mλ2 This is a measure of the Energy distribution. See the student lecture.

See the student presentationIn

Class \ Extragalactic \ Indice di colore


11

Bolometric Correction

• We indicate the Bolometric Correction for the apparent magnitude at λas BCλ.

• BCλ=mbol - mλ

• The correction for the Sun in the V filter is zero. That is BCV (ü) = 0.0. • However a different definition gives: BCV (ü) = -0.19.• By definition all the Bolometric corrections are negative.

bolBC m mλ λ= −


12

MS stars HR Diagram

Sp TypeO3 O5 O8 B0 B3 B5 B8 A0 A5 F0 F5 G0 G5 K0 K5 M0 M5 M7 M8

Mv

-10

-5

0

5

10

15

20


13

Bolometric Correction Dwarfs

Teff0 10000 20000 30000 40000 50000 60000

BC

v (m

ag)

-5

-4

-3

-2

-1

0


14

Dwarfs - Bolometric Correction Visual

Sp TypeO3 O5 O7 O9 B0 B2 B3 B5 B7 B8 A0 A5 F0 F5 G0 G2 G5 K0 K5 M0 M5 M8

BCv

-7

-6

-5

-4

-3

-2

-1

0

1


15

Luminosity versus Type


Log

(L/L

sun)

-4

-2

0

2

4

6

8


16

Mass of MS Stars


Log(

M/M

Sun)

-2

-1

0

1

2

3


17

Luminosity versus Mass - Main Sequence

(M/MSun)0.01 0.1 1 10 100 1000

Log(

L/L Su

n)

-4

-2

0

2

4

6

8


18

Type versus Radius


R/R

sun

0

2

4

6

8

10

12

14

16


19

Contraction to Main Sequence

Mass (In soolar Masses)0 2 4 6 8 10 12 14 16

Tim

e (in

Yea

rs)

1e+4

1e+5

1e+6

1e+7

1e+8

1e+9


20

The Color Excess or Reddening• Along the line of sight light will be, in presence of interstellar – dust for

instance - or intergalactic material, absorbed and scattered. The scattering and absorption is wavelength dependent so that the color of the object will also be modified appearing generally redder since the absorption is stronger at shorter wavelengths.

• The measured magnitudes, or fluxes, must therefore be corrected for this effect since they might appear fainter not because of the distance but because of the absorption.

• Indeed it is because of the ignorance about the absorption that in the past the model of the Galaxy and the distance scale was completely wrong.

( ) ( )( ) ( ) ( ) ( ) ( )

( )

abs 0 ,0.

1 2 for ins tance obs no Dust

1 2 1 2 0 , 1 0 , 2 1 2 1 2obs 0

1 2 1 2

m observed magnitudem A m m

m magnitude in absence of dust

E m m E B V CI CI

E m m m m m m or m m m m

E m m A A and m M A 5log d 5

λλ λ λ

λ

λ λ

λ λ λ λ λ λ λ λ λ λ

λ λ λ λ λ λ λ

∆

≡ = −

− ≡ − = −

− = − − − − − −

− = − = + + −


21

From the observed extinction curve

( )

( ) ( )( ) ( ) ( ) ( )

( )( ) ( )

V VV

B V

0

A AR 3.1 depends on grain sizeE B V A A

E U BQ U B B V U B 0.72 B V

E B V

E U B0.72; B V 0.332 Q

E B V

= =− −

−= − − − − − −

−

−≈ − =

−i

For early type stars I can estimate theIntrinsic color index without observing

The spectrum.


22

Q versus Sp

Sp

O5 O6 O8 O9 B0 B0.5 B1 B2 B3 B5 B6 B7 B8 B9 A)

Q

-1.0

-0.8

-0.6

-0.4

-0.2

0.0


23

Intergalactic (& ISM) Medium• Observational evidence exists that the column density of

Hydrogen is related to the color excess (HI & Dust). The empirical relation:

• Near the Sun we have: nH =106 m-3 so that for a distance d through the disk we have:

• NH= 3.09 1025 (d/kpc) m-2; E (B-V) = 0.53 (d/kpc) and AV = 1.6 (d/kpc)

25 2 1

225

5.810 ( )

( )5.810

Htot

Htot

N E B V m magNE B V m

− −

−

= −

− =

1 m2

1 kpc

nH


24

Standard ISM Extinction

3.253.283.323.644.084.424.835.485.61MŸ

47503450219016301220806658551445365

λeff/nm

.748-0.78R

.052-2.93N

.023-3.02M

.058-2.91L

.112-2.74K

.175-2.55H

.282-2.22J

.482-1.60I

1.0V1.3241.B1.5311.64U

(AX/AV)(EX-V/EB-V)Band X


25

Toward the GC• AM ~ 0.6 ; AB = 34.5

• The Probability for a B photon to reach us is:

• 10 –0.4 (34.5) = 10 –13.8 = 1.6 10 -14


26

M.S.-Zero Age,Dwarfs,E(B-V)=0.2,E(U-B)=0.14

B-V-1 0 1 2

U-B

-2

-1

0

1

2


27

H-K versus J-H; Red for E(B-V)=0.2

J-H-0.4 -0.2 0.0 0.2 0.4 0.6 0.8

H-K

-0.1

0.0

0.1

0.2

0.3

0.4


28

MS Stars / m-M = 15 / MS stars in Class Sony

B-V

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

U-B

-1

0

1

2

E(B-V) = 0.9E(U-B) = 0.9 * 0.72


29

Standard M.S,

(B-V)0

-0.5 0.0 0.5 1.0 1.5 2.0

Mv

-10

-5

0

5

10

15

Obsxerved at m-M=15

(B-V)obs=(B-V)0+E(B-V)=(B-V)0+0.9

0.0 0.5 1.0 1.5 2.0 2.5 3.0

V obs=

Mv+

0.9*

3.1+

15

10

15

20

25

30

35


30

Timetable for Formation – May be

Z ~ 1Superclusters, walls and voidsZ ~ 1Thin disks of spiral galaxiesZ ~ 2Rich clusters of galaxiesZ ì 3Cosmic magnetic fieldsZ ì 3The first 10% of the heavy elementsZ ~ 5Angular momentum of rotation of galaxies Z ~ 5Dark halos of galaxiesZ ì 5Dark MatterZ ~ 10The intergalactic mediumZ ì 10The first Engines for active galactic nucleiZ ~ 20Spheroids of GalaxiesZ ì 103Gravitational potential fluctuations


31

Luminosity & Surface Brightness Bias

Here a galaxy would look like a star

Not visible against the sky background

Zwicky Compact Galaxies


32

Colors of GalaxiesColor versus GdV Type

Morphological Type-6 -4 -2 0 2 4 6 8 10 12

Col

or

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0


33

Preliminaries on the Luminosity Function

• The Luminosity Function of Galaxies will be re visited and use extensively in the Cosmology course where we will also see the distribution function for the AGN and other objects.


34

Mass to Luminosity Ratio

We usually refer to the Luminosity in the B (LB) or V (LV) filters normalized to the Sun. In most stellar system and in galaxies the luminosity is dominated by massive stars while the mass is dominated by low mass stars. This is essentially the consequence of the Initial Mass Function (IMF) and stellar evolution. During star formation the number of small mass stars is much larger that the number of high mass stars and the stellar evolution makes massive stars to evolve quickly while the low mass stars evolve slowly and about in the age of the Universe or may even take longer. From previous graphs (students make fits):

MMSun 1 by definitionL L

MM 10L LMMStars log 3.8 log ; M 0.5 M

ML L M 0.1L L

=

≈ = ⇒

=


35

Values for “normal” galaxies”

V , B ,

B

M MM 6 10L L L

with a max imum range ofM

2 20L

≤ ≤

We observe similar values for the mean stellar population in the solar neighborhood. In general population that are older have a larger value (the bright massive stars are all evolved and lost luminosity). Populations with high metal content also tend to have high M/L. Younger and metal-poor populations tend to have lower values of M/L.


36

GALAXIES• The Luminosity Function describe the Number of galaxies per unit Volume

and between Luminosities L and L+dL. I can also define it as the Number of galaxies brighter than the Luminosity L, Integral Luminosity Funcion, and the is the integral of the previous one from L to Infinity.

• Schechter gives the perused analytical formula for the total Luminosity Function, while, as we will see, when we distinguish between Morphological types, we can either fit by a Gauss function or by a Schechter Function. Furthermore I can define the Functions either in Luminosities or in Magnitudes.

* * *

( L,x, y,z )dLdV N( x, y,z ) ( L )dLdV

N L LN( x, y,z ) ( L )dL Exp dLL L L

α

Φ ϕ

ϕ

=

= −


37

Typical values

Ho=50 km/s/MpcL*=3.2 1010 LŸ

α = -1.25MvŸ=-26.78Mbol=-26.85

φ* = (N/L*) ~ 0.01 Mpc-3h3

[ ][ ]

0B

B,

H km / s / Mpc Lh & M 2.5log 5.48100 km / s / Mpc L

= = − +


38

Transforming in Magnitudes

( ) ( ) ( )( ) ( )* *1

0.4 M M 0.4 M MM 10 Exp 10α

φ+

− − − ∼

And the Gauss distribution.

( ) ( )2

2

MM Exp

2µ

φσ

−

∼


39

An Example

• How many objects do I have within the solid angle ∆Ω and redshifts z1 and z2? What is the hypothesis I do?

– Where L1 is the faintest Luminosity I can detect at a given z assuming my sensitivity is limited to a flux flim corresponding to a limiting magnitude ml.

( ) ( )2

11

2cz

1 2 Lo ocz

cz czN z ,z dz L dLH H

∆Ω ϕ∞

=

∫ ∫

( )

( ) ( )

1

l

1

2

11 1* * *L

o

20.6 m

Lo o0

fczL LL dL N 1 , ; 4L L H L

cz cN 0, dz L dL 10 NormalizationH H

ϕ Γ α π

∆Ω ϕ

∞

∞∞

= + =

∞ = = =

∫

∫ ∫


40

Functions used

( ) ( )

( )

( )

( ) ( )

x 1 x

0 0

x 1

y

Tot 0

Tot 0

e x dx; 1 e x dx

, y e x dx

N L dL N ( 1)

L L L dL N L* 2

α α

α

Γ α Γ α

Γ α

ϕ Γ α

ϕ Γ α

∞ ∞− − −

∞ − −

∞

∞

= + =

=

= = +

= = +

∫ ∫∫

∫∫


41

The Gamma Function


42

The Plot

Cou

nts

z

• This is only indicative since we used non cosmological relations and these must be used for z¥0.1. The student practice using the cosmological relation for Luminous distance. In addition look at the counts of galaxies and the redshifts surveys. Compare the redshift distribution of various samples with the distribution expected for the limited magnitude of the sample. See also later slides.


43

How α works

−1.25

-1

-0.75

M

Φ(M

)


44

Gauss ~ Virgo

Spirals +Im

dE – M*= -17.4Alpha =-1.35

E + S0


45

The composite L.F.


46


47

See also Zucca et al.

preliminaries & language

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