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Massimo Capaccioli » 4.Photometry of late-type galaxies

Photometry of spiral galaxies

Images of spiral galaxies look much more complex and patchy than early-type galaxies. There the surface brightness does not fade smoothly and monotonically from a bright center outwards, as in E types; the spiral arms stand out prominently with the bright patches, where gas is hot and stars are young, and with the intricate labyrinth of the dust filaments and clouds.

Face-on late type spirals do not even show the disk underlying the spiral pattern (which is instead quite apparent in edge-on systems). Under these conditions it is hard to imagine that these galaxies may have a common photometric behavior. But it is not so: as ellipticals do, spirals can be categorized into very few classes according to the way the surface brightness varies with radius.

Grand spiral NGC 1232. Note the complex texture and the change in colors. Credit: ESO.

Photometry of spiral galaxies: differences with ellipticals

There are though some important differences with ellipticals.

The first is that spiral galaxies, as already Hubble pointed out, are two component systems: they have a central bulge and a disk.

Moreover, due to the mixture of cold (old) with hot (young) components, the parameters and even the trend of the light profiles may depend significantly on color.

A third difference is in the amount of internal extinction, which makes spatial deprojections quite hard if not impossible for quasi edge-on spirals.

The spiral 4013 seen on edge. Credit: NASA (HST).

Examples of bulge-disk decomposition

Major axis light profiles of spirals according to Freeman's classification into the types I and II.

Photometry of spiral galaxies: cont. (1)

The breakthrough in the field came again with the 1959 paper by Gérard de Vaucouleurs in the Handbuck der Physik. There, he showed that the light profiles of spirals can be modeled with the sum of two photometric [does it mean that they are also physical?] components: an elliptical-like bulge, following a $R^{1/4}$ law, and an exponential disk, so called because the trend of the surface brightness versus radius is:

$I(R) = I_0 e^{-(R/h)},$

or:

$-2.5\log I(R) = -2.5\log I_0 + 2.5h^{-1} \log(e^R)$

where $I_0$ and $h$ are a scale lengths.

Note the above formula is identical to Sersic’s with $n = 1$ .

Major axis means light profiles of NGC 2683 in four color bands: U, V, R, I, with exponential interpolations.

Photometry of spiral galaxies: cont. (2)

More recently two disk components have been recognized, a “thin” one, signed by the layer of neutral hydrogen, and a “thick” one, the nature of which is unclear. It could be the collection of accreted fragments or just an old disk popped up by interactions. Of course spiral galaxies, as well as all other galaxies, possess another important component, the “dark halo”, which is however not relevant photometry-wise. The luminosity integrated with the radius $R$ is: $L(R)= 2\pi I_0\int_0^R R^\prime e^{-R^\prime/h} dR^\prime= 2\pi I_0 h^{2} f(R/h)$

where: $f(x) = 1-(1+x)e^{-x} \le 1.$

[What is the relation between h and the effective radius?] At RHS the major axis light profiles of NGC 1433 in three color bands, and the trends of the corresponding two color indexes.

NGC 1433 photometry. Buta et al., A.J., 121, 225, 2001.

Examples of bulge-disk decomposition

Decomposition of the major axis light profiles of spiral galaxies into the exponential (disk) and R^1/4 (bulge) components after Kent (Ap.J.S.S., 59, 115, 1985). You may note the different relative importance of the two components.

Disk-bulge separation

How do you disentangle the disk component from the bulge? A better posed question is: how do you fit the major axis light profile of a spiral with the composite formula (with two free parameters):

$I(R)=I_e\mbox{exp}\left\{-7.67\left[(R/R_e)^{1/4}-1\right]\right\} +I_0 \mbox{exp}\left(-R/h\right),$

or any other combination of laws (e.g. Sersic with exponential)? The answer is by minimizing the $\chi^2$ of the $(O - C)$ :

$\chi^2=\frac{1}{N}\sum_{x=1}^{nx}\sum_{y=1}^{ny}\frac{\left( \mbox{galaxy}_{x,y}-\mbox{model}_{x,y}\right)^2}{\sigma_{xy}^2},$

where $\sigma$ is the local error, in an iterative process starting with a reasonable guess of the input parameters (fit of just the bulge with the de Vaucouleurs formula and of the outer profile with an exponential).

At RHS the GALFIT decomposition of NGC 221 (M32). Top: (a) original image, (b) and (c) residuals. Bottom: observed light profile, components, their sum, and geometrical parameters.

GALFIT decomposition of NGC 221 (M32). Credit: Peng et al., AJ, 124, 266, 2002.

Bulge-disk separation

But take care of removing seeing affected inner parts, removing defect and foreground stars, etc.

One may similarly decompose a complete image adding the information on the geometry of the isophotes (centers, orientations, and flattening).

Public domain software, such as GALFIT (cf. Peng et al., Detailed structural decomposition of galaxy images, A.J., 124, 266, 2002), may help us, provided these tools are used wisely. Computer programs provides always an answer. You must check that it is makes sense! How? By making experiments with simple cases with known answers, such as toy models.

Vertical structure of the disks

In a simplified model view, elliptical galaxies may be thought as spheroids seen at an inclination (angle between the line-of-sight and the symmetry axis of the galaxy) that remains usually undetermined for the lack of information on the intrinsic flattening of the system. This is not the case for spirals, where the dust lane on the principal plane allows us to declare when the system is edge-on. In these cases we may study the photometric vertical structure of disks. In 1981, using a self-gravitating isothermal sheet description for the vertical distribution (of matter) in exponential disks, Piet van der Kruit and Searle found that the 3-D light distribution [at M/L = const.; why?] could be described by the following expression:

$I(R,z)=I(R)\mbox{sech}^2\left(\frac{z}{z_0}\right)= I(0,0) e^{-R/h_R}\mbox{sech}^2\left(\frac{z}{z_0}\right)$

later modified into the parametric family:

$I(R,z)=I(R)\mbox{sech}^2\left(\frac{z}{z_0}\right)= I(0,0)e^{-R/h_R}\mbox{sech}^{2/n}\left(\frac{nz}{2h_z}\right)$ by dropping the isothermal assumption. The parameter $n$ ( $= 1$ for isothermal distribution, $= +\infty$ for an exponential function) has been measured to be: $n/2=0.54\pm 0.20.$ The scale height $h_z$ is constant with radius at least in the optical and IR and for late type spirals.

Disk of NGC 891. Credit: NASA (HST)

Disk scale height gradients as a function of the revised Hubble type from de Grijs and Peletier (AA, 320, L21, 1997).

Scale height of the S0 galaxy NGC 3115

Scale height as a function of the distance R from the center for the disk of the S0 NGC 3115 after Capaccioli et al. (MNRAS, 234, 335, 1988). Note the change of trend, which is flat only at intermediate radii.

Freeman law

Recently it has been realized how heavily selection effects have biased our discovery of galaxies. This bias, which will be clear later, has possibly induced the two following believes.

In the 1960’s and 1970’s two very popular laws with strong impact on this matter captured the attention of the community. They are related to the (extrapolated) peak brightness $\mu_0$ of both ellipticals and spirals, in both cases apparently independent of $L$ and confined within very narrow Gaussians:

1. the Fish (1964) law for spheroids: $\mu_0= 14.08 \pm 0.9\ \mbox {mag/arcsec}^2$ ;

2. the Freeman (1970) law for face-on disks of spirals: $(\mu_0)_c = 21.65 \pm 0.3\ \mbox{mag/arcsec}^2$ .

In the Freeman law, so named after the Australian astronomer who proposed it in 1970 (Ap.J., 160, 811), $(\mu_0)_c$ is the value that the extrapolated bright peak of the disk, $\mu_0$ , would have if the galaxy would be seen face-on. Assuming the galaxy to be a transparent spheroid, the correction is just the ratio $k$ between the apparent major and minor axes of the isophotes [Are they ellipses? Are they independent of R?]. Thus: $\left(\mu_0\right)_c = \mu_0 +2.5\log k -0.2\cosec b_BIID;$ the last term is an average correction of the Galactic extinction based on just the Galactic latitude $b_BIID$ of the object under study.

Freeman's (1970) law: constancy of the peak brightness with Hubble type.

Trend with the Hubble type of the disk scale length after Freeman (1970).

Low Surface Brightness galaxies

In his 1976 letter to Nature on the Visibility of galaxies, Mike Disney disputed the above laws, showing that they might result from selection effects discriminating low surface brightness (LSB) galaxies. And these latter began to be seen in galaxy surveys. In the 1980’s, the Virgo Cluster photographic survey of Sandage et al. provided the basis to apply a photographic technique that allowed the serendipitous discovery of Malin 1, a giant LSB disk galaxy beyond the Local Supercluster (at $cz \sim 25000\ km/s$ ).

To-day extensive surveys have found many LSB galaxies; most of them are late-type spirals and often very gas rich; some are early spirals or dwarf ellipticals.

Most LSB galaxies are fit well by an exponential radial profile: $I(R) = I_0 e^{-R/h}$ (out to $r \sim 3\div 6h$ ).

A few have even prominent bulges, usually well fit by a $r^{1/4}$ law. This question will be taken back in the section on Luminosity Functions.

Note, in the figure at RHS, the excess of low surface brightness (LSB) galaxies at the left of the diagram.

Space density of galaxies as a function of central surface brightness, after Bothun et al. (PASP, 109, 745, 1997).

The prototype of LSB galaxies

The giant LSB galaxy Malin 1, barely visible but for the bright center. Credit: The Encyclopedia of Science on the Web.

Colors and color gradients for disks

Spiral galaxies are bluer than ellipticals due to the presence of bright young stars (which can be very blue). Old stars are red [why?]. The color index $(B-V)$ decreases from $0.75$ to $0.5\ mag$ with increasing Hubble type. From a SDSS large sample we learn that almost all but the smallest galaxies show negative disk color gradients:

$\Delta (g-r) = -0.006\ mag/kpc$ and $\Delta (r-z) = -0.018\ \mbox{\it mag/kpc},$

which are independent of the morphological types but strongly dependent on the disk surface brightness $\mu_d$ , with lower surface brightness galactic disks having steeper color gradients: $\Delta (g_r) = -0.011\mu_d + 0.233.$

In dwarf galaxies the gradient is instead positive: they become redder in the outer parts. The fact is interesting in view of the different histories of these objects with respect to the brighter galaxies. It has been found recently that most (90%) of the disk are broken exponentials, with truncated (Type II) and anti-truncated (Type III) light profiles (these “types” have nothing to do with Freeman’s). Colors have a minimum at truncation in Type II, and a plateau in Type III. However, the mass profiles calculated using colors resemble those of the pure exponential (Type I) galaxies for the truncated profiles, suggesting that the origin of the break is likely due to a radial change in stellar population.

Disk Types I, II, and III, with color and mass profiles. Credit: Bakos et al., Ap.J., 683, L103, 2008.

M51 and early type-companion in enhanced colors. Credit: SDSS

Colors and color gradients of bulges

According to Balcells and Peletier (1993), colors of bulges are predominantly bluer than those of ellipticals (independently of the differences in total luminosity). The result indicates that bulges are younger and/or more metal-poor than elliptical galaxies. Most bulges do not reach solar metallicities. Bulges show predominantly negative color gradients (bluer outward) that increase with bulge luminosity. The similarity with ellipticals suggests that the formation of the disk did not affect the stellar populations of the bulge in a major way.

The figure shows the colors of bulges versus the total magnitudes of the bulges themselves and of the entire galaxy, for objects not affected by dust reddening.

Credit: Balcells and Peletier, A.J., 107, 135, 1994.

Bulges of spirals

A recent study based on a large SDSS sample (Oohama et al., 2009) shows that bulge properties change systematically along the Hubble sequence from early to late types; the size becomes somewhat smaller, while the surface brightness and the luminosity get fainter. In contrast, disks remain similar irrespective of the morphology from S0 to Sc (as Freemam claimed). Then the systematic change of the bulge to disk ratio B/D is not due to the disk, but rather to the bulge. It is also argued that bulges do not form a unique sequence with ellipticals. The figure shows the correlation between effective radius and effective surface brightness for the bulges of a large sample of S0s and spirals. Dashed lines mark the loci of equal total luminosity. The solid line holds for ellipticals.