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Influence of dust on the galactic structure Dust distribution models

Influence of dust on the galactic structure Dust distribution models

Dust in galaxies
The effects of absorbing material in galaxies were recognized before the physical nature of galaxies became clear. A study by H.D. Cur tis published in 1918 compared photographs of spirals in an obvious inclination sequence, showing that a band of obscuring material lies in the disk plane.

· Screen model Take a foreground screen of optical depth . Then the observed surface brightness is I = I 0 e- , where I 0 ­ true surface brightness (i = 90o ). The face-on extinction in the apparent mag. scale is A = -2.5 lg II0 = 1.086 . · Slab model Uniform density well-mixed slab of stars, gas and dust of physical depth H , volume emissivity (total luminosity of stars per unit of volume) and with a mean free path to its own stellar radiation of l . We can calculate the face-on optical surface brightness by integrating the contributions from elements at diferent depths x as

Influence of dust on the galactic structure Dust distribution models

Influence of dust on the galactic structure Dust distribution models

H

I (i = 0 ) =
0

o

e

- x /l

dx = l 1 - e

-

,

For the optically thick case, I (i ) = I (i = 0o ) = l , which is independent of i . But, for the optically thin slab, I (i ) = H seci = I (i = 0o ) seci , which increases as seci . Last formula can be rewritten as µobs = µface-on - 2.5 lg seci . 0 0 seci =1/cosi , thin disk: cosi =b/a, therefore, we obtain standard a correction to "face-on" orientation ­ µobs = µface-on - 2.5 lg b . 0 0 Face-on extinction in the mag. scale: A = -2.5 lg l [1 - e H
- -

where = H /l is the total optical depth of the slab to optical radiation. In the optically thin limit ( << 1) we therefore have I (i = 0o ) = H , while in the optically thick limit ( >> 1) I (i = 0o ) = l . When inclined (i = 0o ) H Thus I (i ) = l 1 - e
- seci

]



H seci seci .

= -2.5 lg

1-e

.

Compared with a screen, a given slab extinction corresponds to a significantly greater optical depth, because not all of the dust in a slab obscures all of the stars.


Influence of dust on the galactic structure Dust distribution models

Influence of dust on the galactic structure Dust distribution models

For instance, = 5 = A = 5.m 4 (screen), A = 1.m 75 (slab). · Sandwich model

As a preliminary, consider an optically thick ( >> 1) sandwich seen from the pole. The lowest layer will be totally hidden; the upper crust will be quite unobscured and we will also see a distance l into the dusty layer. So, the surface brightness is I (i = 0o ) H (1 - )/2 + l . In the absence of extinction ( = 0) I (i = 0o ) = H . Therefore, A = -2.5 lg[(1 - )/2 + / ] ( >> 1). The observed surface brightness of an inclined sandwich: 1- (1 + e 2 (1 - e seci

Total optical depth = H /l , = 1 slab model.

I (i ) = H seci

- seci

)+

- seci

).

Influence of dust on the galactic structure Dust distribution models

Influence of dust on the galactic structure Dust distribution models

Thus, for an opaque sandwich ( >> 1 or e- << 1) with = 0.5: I (i ) H seci /4 = I (i = 0o ) seci /4. The surface brightness behaves just as it would in an optically thin slab as deep as the unobscured upper crust (H /4). The face-on extinction: A = -2.5 lg 1- (1 + e 2
-

) + (1 - e

-

).

Face-on extinction (i = 0o ) vs. optical depth.


Influence of dust on the galactic structure Dust distribution models

Influence of dust on the galactic structure Dust distribution models

· Triple exponential model More realistic model: radial distributions of stars and dust are exponential with the same scale length value h, ver tical exponential scale height of stars ­ z , dust ­ zd = z . The problem is not simple (we must solve the radiative transfer equation). There is a good analytical approximation to the observed surface brightness, valid for thin (z << h) and not exactly edge-on (i 80o ) disk (Disney et al. 1989): I (r ) = 2I (0, 0)z where =e
-

= zd /z = and

cosi sini + h z =

/

sini cosi + h zd

e cosi

- r /h

,

0 - r /h e cosi (0 ­ central optical depth of the disk at i = 0o ).

1+

4 2 + ... , ( + 1)( + 2) ( + 1)( + 2)( + 3)( + 4)

Influence of dust on the galactic structure Dust distribution models

Influence of dust on the galactic structure Dust distribution models

· Numerical modelling Byun et al. (1994): the radiative transfer including both scattering and absorption has been computed for a range of model spiral galaxies with immersed dust layers.

Sumulations results according to analytical formula for triple exponential model: (1) transparent, dust-free exponential disk; (2) disk with 0 = 1 and i = 0o ; (3) 0 = 1 and i = 40o ; (4) 0 = 1 and i = 75o .


Influence of dust on the galactic structure Dust distribution models

Influence of dust on the galactic structure Dust distribution models

Byun et al. (1994)

Some conclusions: · The minor-axis profiles in spiral galaxies with inclinations 0o < i < 90o show a characteristic asymmetry due to dust. · The apparent galactic center of inclined galaxies is displaced from its true position when there is dust present. · A color gradient is predicted in dusty spiral galaxies. · The inferred scale lenght of a dusty spiral galaxy is different in different bands. · The internal extinction of a galaxy in one band cannot be conver ted to that in another band by simply using an extinction law. · An optical depth of order 1 through the center of a face-on spiral galaxy implies that the galaxy is effectively transparent. However, if the same galaxy is seen edge-on it will exhibit a prominent dust lane.

Influence of dust on the galactic structure Dust extinction in spiral galaxies

Influence of dust on the galactic structure Dust extinction in spiral galaxies

Distribution of dust and value of
Two observational methods have produced relible measurements of disk opacity: occulting galaxy pairs and the calibrated number of more distant galaxies. · Distant galaxy counts The number of distant galaxies seen through the face-on foreground spiral is a direct indication of its opacity, after proper calibration using ar tificial galaxy counts. Holwerda et al. (2005): galaxy counts for a sample of 32 deep HST/WFPC2 fields. The main results are: (1) most of the disks are semi-transparent; (2) spiral arms are more opaque; (3) as are brighter sections of the disk.

Radial opacity profile from Holwerda et al. (2005)


Influence of dust on the galactic structure Dust extinction in spiral galaxies

Influence of dust on the galactic structure Dust extinction in spiral galaxies

· Occulting galaxies

Examples:

Ideal case: relatively face-on spiral (A) backlit by a par tly occulted, preferably early type, galaxy (B). Basic assumption: light from both the occulted galaxy and the foreground galaxy is sufficiently symmetric to characterize the contributions in the overlapping region from the unprojected par ts of the galaxies.

Influence of dust on the galactic structure Dust extinction in spiral galaxies

Influence of dust on the galactic structure Inclination corrections

Standard corrections
Main conclusions from various approaches: · Disks are more opaque in the blue and are practically transparent in the near-infrared. · Disks are practically transparent in the outer par ts but show significant absorption in the inner regions (0 (V ) 1 - 3). · The extinction correlates with galaxy luminosity ( L0.5 ). · Spiral arms are more opaque than the disk. · hdust /h
stars

· Total luminosity Ai = CL (T ) lg (a/b)25 , (RC3 catalog)

where CL depends on the wavelength and on the morphological type. In the B filter CL = 1.5 - 0.03 · (T - 5)2 (T 0), CL = 0 (T < 0). Example: Sc galaxy (T = 5) with b/a = 0.10 at edge-on orientation looks fainter by 1.m 5 than face-on. Tully et al. (1998) found dimming that was dependent on mass (luminosity) as well as on wavelength: CL (B ) = 1.57 + 2.75(lgW i - 2.5), where W i 2Vmax .

1 - 1.5, z

stars

/z

dust

2 (V passband).


Influence of dust on the galactic structure Inclination corrections

Influence of dust on the galactic structure Inclination corrections

Therefore, for Milky Way type galaxy with Vmax =220 km/s CL = 2.m 0.

· Disk central surface brightness Standard correction: µface 0
-on

a = µobs + 2.5 Cµ lg , 0 b

Unterborn & Ryden (2008): analysis of 78 230 galaxies in the SDSS ° survey (r -band, eff = 6250A). The dimming is well described by the relation Mr (lg b/a)2 , rather than standard Mr lg b/a.

where Cµ = 1 for transparent disk, Cµ = 0 for optically thick, opaque disk. Real galaxies ­ Cµ 0.5. · Color indices
The dashed red curve shows M
r

(B - V ) = Cc (T ) lg (a/b)25 , where Cc = 0.35 - 0.022 · (T - 3)2 Cc = 0

(RC3 catalog) (-1 T 7), (T -1, T 7).

=

-0.64 lg b/a, and

the solid blue curve shows Mr = 1.27 (lg b/a)2

Influence of dust on the galactic structure Inclination corrections

Therefore, Sc galaxy (T = 5) with b/a = 0.10 looks redder by (B - V ) = +0.26 at i = 90o than at i = 0o . · Inclination dependence of the isophotal radius Standard corrections: hi /h0 = 1 + lg (a/b), hi and h0 are exponential scale length values at arbitrary and zero inclinations and 0.3 - 0.4. R
23.5 23 Ri23.5 /R0 .5 = (a/b)CD , is the isophotal radius at µ(I ) = 23.5 and CD 0.2. 23.5 90 23 /R0 .5 1.6 for b/a = 0.10.

Example: R