Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.astro.spbu.ru/staff/resh/Lectures/lec1.pdf Äàòà èçìåíåíèÿ: Mon Jan 26 21:19:19 2009 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 23:40:14 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: zodiacal light

Surface photometry is a technique to measure the surface brightness distribution of extended objects (galaxies, HII regions etc.).

Surface Photometry of Galaxies
Vladimir Reshetnikov resh@astro.spbu.ru
St.Petersburg State University, Russia

Surface photometry: distribution of light (mass), global structure of galaxies, geometrical characteristics of galaxies, spatial orientation, stellar populations, characteristics of dust... Surface photometry and spectroscopic observations ­ two major observational methods of extragalactic astronomy.

Plan 1. Introduction 2. Methods of surface photometry 3. Presentation of surface photometric data 4. Standard models for early-type galaxies 5. Standard models for disk galaxies 6. Multicomponent galaxies 7. Influence of dust 8. Results: spirals, ellipticals 9. Sky surveys and deep fields 10. High-redshift galaxies

Literature
J. Binney, M. Merrifield "Galactic Astronomy", Princeton University Press, 1998 L.S. Sparke, J.S. Gallagher "Galaxies in the Universe: An Introduction", Cambridge University Press, 2000 D. Mihalas, J. Binney "Galactic Astronomy", W.H. Freeman and Company, 1981 S. Okamura "Surface photometry of galaxies", PASP, v.100, p.524, 1988 B. Milvang-Jensen, I. Jorgensen "Galaxy surface photometry", Baltic Astronomy, v.8, p.535, 1999


Introduction Standard definitions

Introduction Standard definitions

Definitions
Surface brightness ­ radiative flux per unit solid angle of the image (I f /). To a first approximation, the s.b. of an extended object is independent of its distance from us since f and are propor tional to 1/r2 (flat, static Universe). Optical astronomers measure s.b. in magnitudes per square arcsecond [m /arcsec2 or m / ]: µ = -2.5 lg I + const.

Definitions
The surface brightness in magnitude units is related to the surface brightness in physical units of solar luminosity per square parsec by I (L /pc2 ) = (206265)2 · 100
.4(M -µ-5)

= 4.255 108 · 100

.4(M -µ)

,

where M is the absolute magnitude of the Sun. In the B passband M
,B

= +5.48 =

µ(B ) = 27.05 - 2.5 lgI (B ). µ(B ) 27m /


corresponds to I 1 L,B /pc2 .

Introduction Shor t history of surface photometry

Introduction Shor t history of surface photometr y

Shor t history
One of the oldest techniques in modern astronomy. The first attempt at surface photometry of galaxies dates back to Reynolds (1913).
Reynolds (1913) ­ circles Walterbos & Kennicutt (1987) ­ solid line

Shor t history
Hubble (1930) ­ first systematic study of the light distribution in ellipticals. Main conclusions: elliptical galaxies 1) have no definite edge, I 2) have all the same standard luminosity profile I (r) = (r+0a)2 , 3) are relaxed self-gravitating systems in equilibrium. Redman & Shirley (1936­1938) ­ first systematic discussion of some of the technical difficulties of the photographic surface photometry. In par ticular they discussed the effect of the point spread function (PSF) on the apparent luminosity distribution. Oor t (1940) ­ joint photometric and dynamical analysis of NGC 3115 and NGC 4494.


Introduction Shor t history of surface photometry

Methods of surface photometry Main steps

Shor t history
Seyfer t (1940) ­ first quantitative study of optical color distribution in the disks of 7 spirals. Patterson (1940) ­ surface brightness in the disk of M 33 decays exponentially with distance from the center; first detailed intensity matrix maps of 14 spiral and irregular galaxies. Lindblad (1941-42) ­ detailed studies on the luminosity and color distributions in several large spirals; detection of reddening in the dust lanes between spiral arms; luminosity­color asymmetry along the minor axis of the image. G. de Vaucouleurs (1948) ­ "de Vaucouleurs law" for elliptical galaxies.

Main steps of surface photometry
Surface photometry is currently done using CCDs (charge-coupled devices).

CCD detectors When a photon hits the detector, it sets free electrons, generating a current. This current is collected and amplified, and the signal produced should be linearly propor tional to the number of incident photons. The surface of a CCD is divided into individual picture elements, or pixels. It is possible to do photometry (the image recorded is then a por tion of the sky/star/galaxy) or spectroscopy (the light is dispersed by using a grating into its colors).

Methods of surface photometry Main steps

Methods of surface photometry Main steps

Main steps of surface photometry
There are some common problems with CCDs, which need to be taken into account in every observational program: ­ read-out noise (random fluctuations in the count rate: 3­10 e/pixel) ­ dark counts (failure to respond to currents, or electrons without an incident signal cooled down to 100­200 K) ­ cosmic rays (energetic par ticles hit the detector and produce a signal which is not related to the astronomical object under study). They appear as "stars", but if the same por tion of the sky is imaged more than once, it's unlikely a cosmic-ray will fall in the same pixel. Hence they can be corrected for.

Main steps of surface photometry
· Flat-fielding. Pixels do not respond uniformly. Need to measure the individual response of the pixels by observing a diffuse screen or black twilight sky. · Sky background subtraction. The background local sky level IS (x, y ) is determined and subtructed from IG+S (x, y ), leaving IG (x, y ), the intensity distribution of only the galaxy. This is the most impor tant step in surface photometry. · Stack of frames. · Photometric calibration. Need to observe some standard stars of known brightness to determine how many counts correspond to a given flux or magnitude. · Presentation of surface photometric data. · Detailed interpretation, modelling.


Methods of surface photometry Problems and accuracy

Methods of surface photometry Problems and accuracy

Sky background subtraction
The brightness of the moonless sky is made up of 4 components: · Air glow: Photochemical processes in the upper atmosphere. It depends on the position on the sky. Changes by as much as 20% on timescales of tens of minutes. · Zodiacal light: Sunlight scattered off par ticles in the solar system. Makes the largest contribution. · Faint unresolved stars in our Galaxy. · Diffuse extragalactic light ­ distant, faint, unresolved galaxies. Relative impor tance of these components, and total intensity from them vary from site to site and with position in the sky. The Ear th's atmosphere contributes only about 30% of the ground-based night sky brightness.

Sky background subtraction
Brightness of the moonless night sky:

The night sky is rather red; it has a color index near B-V = +0.9, similar to that of a fairly red galaxy.

Methods of surface photometry Problems and accuracy

Methods of surface photometry Problems and accuracy

Sky background subtraction
Inaccurate subtraction of the background contribution can mislead the following interpretation.

Effect of Seeing
One impor tant aspect in the study of the surface brightness of galaxies is the characterization of their surface brightness profiles, that is the dependence of the surface brightness on the projected distance from the center of the galaxy. However, turbulence in the upper atmosphere degrades the quality of an image since, due to changes in the refractive index, the light-rays from a point-like object that reach the detector have to travel slightly different paths, and hence arrive at slightly different places on the detector. The shape on the detector of an otherwise point-like source is called the Point Spread Function (or PSF), and depends both on the seeing of the site, and on the proper ties of the telescope-detector assembly.

The effects of errors in the subtracted sky level on the typical profiles of E and S galaxies (dashed line ­ the background was overestimated by 1%, dotted line ­ underestimated by 1%).


Methods of surface photometry Problems and accuracy

Methods of surface photometry Problems and accuracy

Seeing
The effect of the seeing is to blur an otherwise sharp image. If in absence of seeing the surface brightness of an object at a position R is It (R ), the measured brightness at a location R will be: Iapp (R) = d2 R P (R - R )It (R ),

Seeing
It is possible to show that:


Iapp (R) =
0

dR R It (R ) I0 (

RR ), 2

where I0 is a modified Bessel function of order zero. For R the measured surface brightness is smaller than the true s.b., for R ­ is larger than the real s.b. since the light removed from the smallest radii has to emerge at slightly larger radii. The overall effect of seeing is to introduce into a featureless power-law profile an apparent core, that is, a central region of nearly constant apparent s.b.

where P (d) is the PSF. In the simplest case, the PSF can be treated as a circularly symmetric Gaussian P (d) = 1 d2 exp(- 2 ). 2 2 2

Methods of surface photometry Problems and accuracy

Methods of surface photometry Standard packages

Seeing

Standard packages
ESO-MIDAS (http://www.eso.org/midas/) European Southern Observatory - Munich Image Data Analysis System The MIDAS system provides general tools for image processing and data reductions with emphasis on astronomical applications including special reduction packages for ESO instruments at La Silla and the VLT at Paranal. In addition it contains application packages for stellar and surface photometry, image sharpening and decomposition, statistics and various others. IRAF (http://iraf.noao.edu/) Image Reduction and Analysis Facility IRAF includes a good selection of programs for general image processing and graphics applications, plus a large number of


Methods of surface photometry Standard packages

Presentation of surface photometr y data Graphic methods

Standard packages
programs for the reduction and analysis of optical astronomy data. Some packages are also available for the analysis of HST, XRAY and EUV data. ESO-MIDAS and IRAF are freely available on many platforms (VMS, UNIX...). Both systems include a complete programming environment for scientific applications, which includes a programmable Command Language scripting facility. IDL (http://idlastro.gsfc.nasa.gov/) Interactive Data Language (commercial package) The IDL Astronomy Users Library ­ repository for low-level astronomy software written in the commercial language IDL. Not an integrated package, but a collection of procedures from which users can pick and choose for their own use.

Presentation of surface photometric data

Final result of modern digital surface photometry is the calibrated surface brightness distribution, I (x, y ), in units of m / , in the form of a digital data array. It consists of a huge amount of numbers ( 106 - 107 ), which do not allow any easy physical interpretation. The most natural way is to present a gay-scale map or a false-color map. Also, more conventional, way is to plot a map of isophotal contours ­ isophotes.

Presentation of surface photometry data Graphic methods

Presentation of surface photometr y data Graphic methods

Graphic methods

Graphic methods
2D data are often reduced to a 1D brightness profile ­ I (r). Widely used profiles are the following:

1. Photometric cuts
Original s.b. distributions along specific P.A. (e.g., major/minor axis) of a galaxy. Shor tcomings: twist of isophotes, non-axisymmetric structures (bars, spiral arms, HII regions...).

Elliptical galaxy NGC 3379 (right), NGC 3384 (top) and NGC 3389


Presentation of surface photometry data Graphic methods

Presentation of surface photometr y data Graphic methods

Graphic methods
2. Azimutally-averaged profile
is the profile obtained by averaging the brightness distribution I (r, ) over on an ellipse with semimajor axis r and an axial ratio . ( is usually defined by the isophotes in the faint outer region.)

Graphic methods
A plot of the s.b. as a function of the equivalent radius r is the equivalent profile. Very smooth profile even for galaxies whose isophotes have considerable irregularities! But equivalent profile is affected by the change of geometry due to the inclination.

3. Equivalent profile (de Vaucouleurs 1948)
Let S be the area included in an isophote of a s.b. level I . If the isophotes consist of several "islands", S includes the area of all such islands. The equivalent radius, r , is defined as the radius of a circle which has the same area as S , that is, r = (S/ )1/2 .

4. Ellipticity and orientation profiles

P.A. and b/a vs. a for NGC 3379

Presentation of surface photometry data Graphic methods

Presentation of surface photometr y data Graphic methods

Graphic methods

Graphic methods
5. Isophotal shapes
Dot-dashed and broken curves ­ mean profiles along the major and minor axes, solid curve ­ azimutally-averaged profile, solid curve with circles ­ equivalent profile. Isophotes are not perfect ellipses. There may be an excess of light on the major axis (disky), or on the "corners" of the ellipse (boxy):

Disky (left) and boxy (right) isophotes


Presentation of surface photometry data Graphic methods

Presentation of surface photometr y data Graphic methods

Isophotal shapes
The diskiness/boxiness of an isophote is measured by the difference between the real isophote (R()) and the best-fit elliptical one (Rell ()):

Isophotal shapes
() = 0 + 1 (an cos n + bn sin n), n= where the terms with n < 4 all vanish (by construction), and a4 > 0 is a disky galaxy, while a4 < 0 corresponds to a boxy isophotes. Normalized coefficient a4 /a ­ standard characteristic for the shapes of the isophotes.

() = R() - Rell ()

Presentation of surface photometry data Graphic methods

Presentation of surface photometr y data Graphic methods

Isophotal shapes

Isophotal shapes
Disky/boxy shapes for E galaxies correlate with various other galaxy parameters: ­ Boxy galaxies are more likely to show isophotal twists (and hence be triaxial) ­ Boxy galaxies tend to be more luminous ­ Boxy galaxies have stronger radio and x-ray emission ­ Boxy galaxies are slow rotators ­ In contrast, disky galaxies are midsized ellipticals, oblate, faster rotators, less luminous in radio and x-ray Bender et al. 1988


Presentation of surface photometry data Graphic methods

Presentation of surface photometr y data Photometric parameters

Isophotal shapes
Kormendy & Bender (1996): revision of the Hubble sequence for elliptical galaxies

System of standard photometric parameters (G. de Vaucouleurs)
Basic parameter ­ total or asymptotic magnitide. For an ideal object with circular isophotes, the luminosity emitted between r and r + dr is 2 I (r)dr. The integrated luminosity emited between the center and r is
2 r r

L( r) =

I (r)rddr = 2
0 0 0

I (r )rdr .


Total (asymptotic) luminosity is LT = 2 0 I (r )rdr . The fraction of the total luminosity emitted between 0 and r is
Ellipticals are illustrated edge-on and at ellipticity b/a = 0.4.

k (r) =

L( r) . LT

Presentation of surface photometry data Photometric parameters

Presentation of surface photometr y data Photometric parameters

System of standard photometric parameters
k (r) vs. r (or µ) ­ relative integrated luminosity curve or growth curve.
1 Effective radius re is determined so that k (re ) = 2 , i.e., half the total luminosity is emitted within the circle of this radius.

System of standard photometric parameters
Effective surface brightness µe ­ surface brightness at r 1 or k (µe ) = 2 . Mean surface brightness inside µe (or re ): I e = 2LT 2 or µ e = mT + 5 lgre + 1.995, re where mT ­ total magnitude of galaxy. Concentration indices: k (r1 ) = 1/4, k (r3 ) = 3/4 and C21 = re /r1 , C32 = r3 /r (or r r ). More popular version: C = 5 â lg(r80 /r20 ), where r are the growth curve radii.
80 e e

If the isophotes are ellipses of semiaxes a, b, we can introduce effective semimajor and semiminor axes ae and be , and the equivalent effective radius re = ae be . When the isophotes an equivalent radius Then the equivalent ted luminosity curve effective radius re is are irregular, it always possible to define r (r = (S/ )1/2 ­ see previous sect.). luminosity profile and the relative integraare I (r ) and k (r ), and the equivalent defined by k (re ) = 1 . 2

and r

20


Presentation of surface photometry data Photometric parameters

Presentation of surface photometr y data Photometric parameters

Other parameters
· Rotational asymmetry parameter As = ij |Iij - IiR | j , ij Iij

Other parameters

where Iij ­ intensity in pixel (i, j ), and IiR ­ corresponding j intensity after image rotation by 180o about image center. As correlates with morphological type and color index. · Clumpiness (or smoothness) S ­ the ratio of the amount of light contained in high frequency structures to the total amount of light in the galaxy. S is similar to Asymmetry but one subtracts a smoothed version of the object from itself.
CAS vs. Hubble type for 44 isolated spirals (Hernandez-Toledo et al. 2007)

Presentation of surface photometry data Photometric parameters

Presentation of surface photometr y data Photometric parameters

Other parameters
· Lopsidedness Global low-order asymmetry:

Other parameters Also:
axial ratio (q = b/a) galaxy inclination (cos2 i = P.A. or P.A.(r) diameter (D25 )
2 q 2 -q0 2 1- q 0

)

Quantitative measure of lopsidedness is the average of the m = 1 to m = 0 azimuthal Fourier amplitudes between 1.5 and 2.5 scale lengths of the disk ­ A1 /A0 . 30% of field spiral galaxies exhibit significant lopsidedness ( A1 /A0 0.2) at large radii.

B /D ratio etc.