Spiral galaxies

Global relations for spirals: the Tully-Fisher relation

• same sort of global scaling relations as the fundamental plane is observed in spiral galaxies - for spirals, the relation is that $L\propto v_{max}^4$, known as the Tully-Fisher relation. Here, $v_{max}$ is the maximum rotation velocity observed in a spiral disk; sometimes observed via HI line widths, and sometimes via optical rotation curves. Note that this relation doesn't explictly include surface brightness, so family of spirals may be even further restricted than elliptical (which fell on a plane in 3D space of luminosity, velocity, surface brightness); however, may partly be artifact of selecting spirals with higher SB (see more below).

• naive explanation is similar to that for the fundamental plane, namely the virial theorem. Here we have
  
  $$L = c_1 I_0 r_e^2$$
  
  
  
  
  $$M = c_2 {v_{max}^2 r_e\over G}$$
  
  
  With a bit of algebra, we derive
  
  $$L\propto {v_{max}^4\over I_0 (M/L)^2}$$
  
  
  .

• Problems with the explanation:
  • to get the TF relation, we require the process of galaxy formation/evolution to give $I_0 (M/L)^2$ approximately constant at fixed $L$ and $v$. So far, there has been no clear reason for this to occur. We know that disk galaxies have a range of surface brightnesses and a trend of surface brightness with luminosity. Again, this $M/L$ include dark matter, so it's not just stellar populations.

  • Another indication that the TF relation may be more complex is that the observed slope of the relation is not exactly 4, and in fact, depends on the bandpass and the nature of how the velocity is measured. The IR relation is closest to the nominal slope, and often, this result is interpreted as implying that extinction is important in the optical bandpasses. However, some work has shown that the derived slope depends on the aperture used, and the IR results are from small aperture measurements; when mags are extrapolated to total mags, the slope becomes shallower. So the simple explanation may not be much of an explanation.

• For most studies of the TF relation, only high SB galaxies are considered, suggesting M/L independent of L for these. However, on closer inspection, the TF relation shows some curvature at fainter mags. This nonlinearity suggests that (M/L) increases at lower luminosity.

• In spirals, luminosity is not a direct tracer of mass because of differences in stellar populations, and also in gas content. This has led to the measurement of the baryonic TF relation. This provides some clues about ratio of baryonic to total mass in galaxies.

• Given potentially simpler kinematics in spirals (dominated by rotation), can trace distribution of mass, via rotation curves:
  • Rotation curves probe dark matter content and profile
  • general observation that rotation curves are $\sim$ flat implies that $M \propto r$, $\rho \propto r^{-2}$.
  • however, shape of the rotation curve is moderately well-correlated with the luminosity, in the sense that one gets steeper RCs for lower L galaxies (Persic and Salucci Fig 4). However there is significant variation at each luminosity.
  • Note variety of RC shapes - there is no disk-halo conspiracy required to make all RC flat, because all RCs aren't flat!
  • Comparing rotation profile with luminosity profile allows one to determine whether the luminous mass is able to produce the rotation profile, and one finds that dark mass is required, that the fraction of dark mass increases with radius, and also that the DM fraction increases at fixed radius with decreasing luminosity.

  • to determine the amount of dark matter in disk galaxies requires knowledge about the M/L of the stellar population, which we don't know (it depends on the star formation history).
    • given luminosity profile, shapes of the RC curves tell us that DM is there, because there's no way to get high enough stellar mass-to-light ratios in the outer region
    • can't derive the stellar M/L from the rotation curve because of the presence of dark matter for which we don't know the density distribution.
    • common assumption is the ``maximum-disk'' hypothesis, in which one assumes that the innermost parts of the rotation curve are driven by the luminous mass alone - these regions then give a M/L, which is assumed constant as a function of radius. Combined with the outer rotation curve, mass profiles for the luminous and dark components are derived (Kent 1a ,Kent 1b.
    • However, applicability of maximum disks is debateable.

  • RCs of LSB galaxies confirm the high M/L of LSB galaxies. Compare 2 galaxies at identical positions in TF relation and see that LSB galaxy much more DM dominated (e.g. de Blok & McGaugh Fig 3). Universal RC might need to be 2D with SB and luminosity.
    • Shapes of LSB rotation curves currently under active debate, as to what they imply for dark matter distribution.
    • Numerical models predicts cuspy distribution of dark matter, with $\rho \propto r^{-1}$ in the inner parts (Navarro-Frenk-White NFW profile).
    • Some observations suggest more of a core
    • However, interpretation of relatively low velocities in LSB centers can be complicated by a variety of effects, e.g. projection, beam smearing, non-circular velocities, etc.

Stellar populations and star formation in spiral disks

• want to know the star formation history of spirals and see if they are correlated with any global properties such as Hubble type, environment, etc.

• since we see star formation ongoing in disks, the situation is usually interpreted in a different way than in E galaxies, where we assumed some simple combination of SSPs was probably correct (or even a single SSP!). Information on detailed age distributions in spirals is quite limited; difficult in MW because of unknown distances to stars and extinction, and difficult to probe far down the LF in M31. Note Hipparcos results on solar neighborhood, and HST/ground results on the bulge.

• since SF is ongoing in spirals, it's generally assumed that it has been ongoing since the age of the disk, and the SF history is often simply parameterized by an exponential rate, $R(t) = \exp(-t/\tau)$, which very possibly is a poor representation! The exponential time scale is often characterized by the birthrate, $b$, which gives the rate of current SF to the past SFR averaged over the age of the disk.

• current SF can be estimated from a variety of techniques
  • H$\alpha$ observations, which gives the number of ionizing photons if one assumes that all ionizing photons are used and eventually re-emitted - a limitation is extinction, and the assumption that HII regions are ionization bounded.
  • far-IR flux (but beware heating from IS radiation field)
  • radio continuum emission (beware non-thermal components)
  • far-UV flux (UIT, Galex) (beware extinction)

• relation between the H$\alpha$ EW and the broadband color can be used to estimate the IMF if the exponential SFH is assumed, e.g. Kennicutt et al Fig 2,
  • birthrate parameter can be estimated either by comparison with the models, or more directly by using the H$\alpha$ luminosity to determine the current SFR and then estimating the past SFR by measuring the mass of the disk. This latter involves determining a stellar M/L for the disk. Comparison of methods (Kennicutt et al Fig 4).
  • mild indication that the IMF of high-mass stars in external galaxies appears to be somewhat shallower than that of our own galaxy but the uncertainties/assuptions in the method may lead to substantial systematic problems.
  • Results suggest systematic variation of star formation history with Hubble type (Kennicutt et al Fig 6); but note classification issues.

• metallicities of spirals: present Z distribution derived from ISM. Stellar distribution harder to determine - complicated by age and extinction effects (see Gallazzi et al MNRAS 362, 41 (2005)).
  • Present day metallicities are correlated with galaxy luminosity, e. g. Tremonti et al ApJ 613, 898 (2004), Fig 4
  • Correlation even clearer with stellar mass
  • Probably not just due to slower evolution at lower masses (i.e. closed box model), but to mass loss in lower mass galaxies
  • Similar trends seen in stellar metallicities and ages, albeit with larger scatter (some from observational technique)
  • Gradients appear to exist, but do not seem be to well correlated with anything (gradients flatter in more luminous galaxies??)

Gas in spirals and correlation with SFR

• Spirals provide a good laboratory to study processes which affect star formation. Especially important given lack of understanding of star formation; galaxy formation models need to parameterize it.
  • Star formation rates vary significantly from galaxy to galaxy.
  • Strongly star forming galaxies called starburst galaxies
  • Very strongly star forming galaxies often produce high ratio of far-IR radiation to optical radiation, and are called ultra-luminous infrared galaxies (ULIRGs)

• Is SFR correlated with amount of gas in galaxy? When normalized by galaxy mass, find good correlation with HI mass, but poor correlation with CO (Kennicut Fig 3). This is peculiar; possible explanation include real lack of correlation with molecular content, or variations in conversion factor from CO to $H_2$, or importance of local distribution.

• Distribution of gas within spirals: molecular gas more centrally concentrated. In some galaxies, CO traces H$\alpha$ well, but not in others (Kennicut figs 4 and 6). H$\alpha$ in general traces CO better than it traces HI, in contradiction to the global properties. In general, it seems that SF is more directly coupled to total gas density, atomic+molecular, rather than to any particular phase. Note that SF essentially shuts off in outer regions of disk, even though there's plenty of gas there.

• Star formation laws.
  • Schmidt law, which has $SF\propto \rho^n \propto \Sigma^N$.

  • Measured relations show a more complex behavior (Kennicutt Fig 8).

  • slope in regions of high gas density roughly comparable between galaxies (Schmidt law), but different galaxies have different thresholds for SF. Kennicutt SF law.

  • threshold density is expected from consideration of stability of disks - below critical density, disks are stable against large scale perturbations; for a thin isothermal gas disk, $\Sigma_c(r) = \alpha \kappa(r) \sigma / 3.36 G$, where $\sigma$ is the gas velocity disperions, and $\kappa$ is the epicyclic frequency, which is related to the rotation curve. The critical density depends on rotation profile and velocity dispersion.

  • density of gas in spirals matches reasonably well the profile of critical density (Figs 10 & 11). In this model, the threshold surface density is a function of radius (Fig 14). Suggests threshold as f(r) then Schmidt law with $N\sim 1.3$ - with several possible systematic uncertainties (extinction, other factors which vary with r). However, behavior near the threshold is significantly steeper - and most regions of most galaxies appear to be near the threshhold!

• global star formation law. Star forming galaxies show range of current star formation rates from $\sim$ 1 Msun/yr to hundreds of Msun/yr; what sets the SFR? Results from a sample of normal galaxies (Kennicutt Fig 2), starburst galaxies(Kennicutt Fig 5), and all galaxies combined (Fig 6). Remarkably tight relation is seen over wide range of densities and star formation rates.

• multiple explanations may give observed trend: consider two possible qualitative physical mechanisms behind observed relations.
  • star formation related to growth of instabilities suggests
    
    $$\rho_{SFR} \propto {\rho_{gas}\over (G\rho_{gas})^{-0.5} } \propto \rho^{1.5}$$
    
    

  • Alternatively, perhaps SF is related to the local dynamical timescale (e.g., SF triggered by passage through spiral arms). Then
    
    $$\Sigma_{SFR} \propto {\Sigma_{gas}\over (\tau_{dynamical})} \propto \Sigma\Omega_{gas}$$
    
    

  • Both give comparable SFRs (Kennicutt Figure 7).

• gas consumption ``paradox"
  • Mean time given by $M_{gas}/SFR$ (e.g. Kennicut et al Fig 7).
  • Possible resolutions:
    • Possibly resolved by considering recycling.
    • Missing gas-rich galaxies? Low SB galaxies may resolve the apparent paradox, since these have very high gas mass fractions. It appears that the gas fraction is correlated with the SB (McGaugh and de blok fig 1). Given significant numbers of LSB galaxies, paradox is resolved. LSBs as ``retarded" galaxies

Interaction of stars with the ISM

• Stars form from ISM, but also influence the structure of the ISM in return.

• ISM is a multi-phase medium, with molecular clouds, cold atomic gas, diffuse ionized gas, HII regions, hot coronal gas; distribution of gas in the ISM is notably chaotic. Often, ``three-phase medium'' (cold, warm, hot) is discussed. Gas is not uniformly distributed, and the different phases are interspersed with each other.

• some effect of stars on the ISM is expected from the processes of supernovae and mass loss from stars.
  • supernovae clear out ``superbubbles'' in the ISM; it is possible that these superbubbles even propagate to the vertical edges of the disks and allow for mass outflow from the disk into the halo. If this is the case, one might expect this gas to eventually fall back down onto the disk, leading the the ideas of galactic fountains and chimneys.

  • also possible that the shocks from supernovae act to compress gas clouds, possibly trigering further star formation in nearby regions.

  • Significant galactic winds (outflows) are observed in starburst galaxies, e.g. M82

• These processes are important for understanding:
  • feedback mechanisms by which star formation may be self-regulating
  • chemical evolution of galactic disks
  • the existence of gas halos around galaxies
  • the escape of ionizing radiation from galactic disks.

AGN

• Additional feedback may come from activity in nucleii of galaxies. This has recently become popular for considering the comparison of model mass functions and observed luminosity functions for high luminosity galaxies.

• Quick AGN review (see book by Peterson, 1997)
  • Seyfert galaxies: types 1 (broad lines) and 2 (narrow lines)
  • BL Lac objects
  • LINERS
  • QSOs/quasars
  • Radio galaxies.
    • Energy source may be same, but don't generally directly see nuclear activity.
    • Fanaroff-Riley (FR) types 1 (low radio luminosity, edge-darkened) and 2 (high radio luminosity, edge-brightened).

• Frequency of Seyfert phenomenon; 1-2% but all(?) galaxies may harbor activity at some level.

• Generally considered to be powered by accretion onto nuclear black hole. Arguments for existence of BH:
  • timing arguments,
  • broad Fe line (see review by Fabian).
  • BH masses from reverberation mapping, and comparison with dynamical measurements of BH masses.

• Unified model; physical picture and differences as a function of viewing geometry. Accretion rates and accretion rate differences (review by Pogge?). Differences from variations in gas supply (quantity and/or efficiency of infall) and/or from different BH masses?

• Current idea that feedback from AGN may be important in limiting masses/luminosities of most massive galaxies

Bulges

• Understanding bulges may be important in understanding nature of Hubble sequence

• Structural properties of bulges:
  • surface brightness profiles (Sersic indices): some deVaucoleurs bulges, but many exponential profiles
  • Possible correlation between bulge and disk scale lengths (e.g. Macarthur, Courteau, Holtzman ApJ 582, 689 (2003), Fig 20))?

• Stellar population properties of bulges:
  • Recall MW bulge (and halo) thought to be primarily old (bulge CMD and LF); M31 halo may be younger (Brown et al results).
  • Mg-$\sigma$ relation similar to that of ellipticals and corresponding implications for early bulge formation.
  • Colors: Peletier and Balcells observations (Fig 2) of similar disk and bulge colors
  • Stellar populations from line strengths
    • Central line strengths
    • Correlation between bulge and disk populations?

• Kinematical properties of bulges: variation of degree of rotational support, but generally more rotational support than ellipticals

• Formation possibilities:
  • monolithic collapse
  • secular evolution; pseudobulges
  • minor mergers, major mergers (before disk formation).
  • Plausibly two (or more?) formation mechanisms for bulges.