### Abstract

We find that all classes of galaxies, ranging from disks to spheroids and from dwarf spheroidals to brightest cluster galaxies, lie on a two-dimensional surface within the space defined by the logarithms of the half-light radius, r_{e}, mean I-band surface brightness within r_{e}, I _{e}, and internal velocity V^{2} ≡ (1/2)v _{c}^{2} + σ^{2}, where v_{c} is the rotational velocity and σ is the velocity dispersion. If these quantities are expressed in terms of kpc, L_{⊙} pc^{-2}, and km s ^{-1}, then this surface is described by the equation log r_{e} - log V^{2} + log I_{e} + log Y_{e} + 0.8 = 0, where we provide a fitting function for Y_{e}, the mass-to-light ratio within re in units of M_{⊙}/L_{⊙}, that depends only on Vand I_{e}. The scatter about this surface for our heterogeneous sample of 1925 galaxies is small (<0.1 dex), and both the scatter within one of the galaxy subsamples (1319 disks) and the analysis of subsamples with independently derived mass-to-light ratios suggest that the intrinsic scatter could be as low as ∼0.05 dex, or 10%, prior to any correction for observational errors. This small scatter has three possible implications for how gross galactic structure is affected by internal factors, such as stellar orbital structure, nuclear activity, or mass loss history, and by external factors, such as environment or accretion history. These factors either (1) play no role beyond generating some of the observed scatter, (2) move galaxies along the surface, or (3) balance each other to maintain this surface as the locus of galactic structure equilibria. We cast the behavior of Y_{e} in terms of the fraction of baryons converted to stars, η, and the concentration of those stars within the dark matter halo, ξ ≡ R_{200}/r_{e}, where R_{200} is the standard estimate of the virial radius. We derive expressions for η and ξ, use an independent measurement of η to evaluate leading constant terms, obtain η = 1.9 × 10 ^{-5}(L/L*)Y*V^{-3} and ξ = 1.4Vr _{e}^{-1}, and relate these to each other via log η + log ξ = -log Y^{e} + log Y* + const. Finally, we present the distributions of η and ξ for the full range of galaxies and conclude that the high Y_{e} of dSph's are due to low η, rather than any differences in ξ, that η is similar for spheroids and disks of a given V, and that η decreases with increasing V for systems with V > 30 km s ^{-1}. For systems with internal velocities comparable to that of the MilkyWay (149 km s^{-1} < V < 163 km s^{-1}), η = 0.14 ±- 0.05, and ξ is, on average, ∼5 times greater for spheroids than for disks.

Original language | English (US) |
---|---|

Pages (from-to) | 68-80 |

Number of pages | 13 |

Journal | Astrophysical Journal |

Volume | 682 |

Issue number | 1 |

DOIs | |

State | Published - Jul 20 2008 |

### Fingerprint

### Keywords

- Galaxies: formation
- Galaxies: structure

### ASJC Scopus subject areas

- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*682*(1), 68-80. https://doi.org/10.1086/529577

**Toward equations of galactic structure.** / Zaritsky, Dennis F; Zabludoff, Ann I; Gonzalez, Anthony H.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 682, no. 1, pp. 68-80. https://doi.org/10.1086/529577

}

TY - JOUR

T1 - Toward equations of galactic structure

AU - Zaritsky, Dennis F

AU - Zabludoff, Ann I

AU - Gonzalez, Anthony H.

PY - 2008/7/20

Y1 - 2008/7/20

N2 - We find that all classes of galaxies, ranging from disks to spheroids and from dwarf spheroidals to brightest cluster galaxies, lie on a two-dimensional surface within the space defined by the logarithms of the half-light radius, re, mean I-band surface brightness within re, I e, and internal velocity V2 ≡ (1/2)v c2 + σ2, where vc is the rotational velocity and σ is the velocity dispersion. If these quantities are expressed in terms of kpc, L⊙ pc-2, and km s -1, then this surface is described by the equation log re - log V2 + log Ie + log Ye + 0.8 = 0, where we provide a fitting function for Ye, the mass-to-light ratio within re in units of M⊙/L⊙, that depends only on Vand Ie. The scatter about this surface for our heterogeneous sample of 1925 galaxies is small (<0.1 dex), and both the scatter within one of the galaxy subsamples (1319 disks) and the analysis of subsamples with independently derived mass-to-light ratios suggest that the intrinsic scatter could be as low as ∼0.05 dex, or 10%, prior to any correction for observational errors. This small scatter has three possible implications for how gross galactic structure is affected by internal factors, such as stellar orbital structure, nuclear activity, or mass loss history, and by external factors, such as environment or accretion history. These factors either (1) play no role beyond generating some of the observed scatter, (2) move galaxies along the surface, or (3) balance each other to maintain this surface as the locus of galactic structure equilibria. We cast the behavior of Ye in terms of the fraction of baryons converted to stars, η, and the concentration of those stars within the dark matter halo, ξ ≡ R200/re, where R200 is the standard estimate of the virial radius. We derive expressions for η and ξ, use an independent measurement of η to evaluate leading constant terms, obtain η = 1.9 × 10 -5(L/L*)Y*V-3 and ξ = 1.4Vr e-1, and relate these to each other via log η + log ξ = -log Ye + log Y* + const. Finally, we present the distributions of η and ξ for the full range of galaxies and conclude that the high Ye of dSph's are due to low η, rather than any differences in ξ, that η is similar for spheroids and disks of a given V, and that η decreases with increasing V for systems with V > 30 km s -1. For systems with internal velocities comparable to that of the MilkyWay (149 km s-1 < V < 163 km s-1), η = 0.14 ±- 0.05, and ξ is, on average, ∼5 times greater for spheroids than for disks.

AB - We find that all classes of galaxies, ranging from disks to spheroids and from dwarf spheroidals to brightest cluster galaxies, lie on a two-dimensional surface within the space defined by the logarithms of the half-light radius, re, mean I-band surface brightness within re, I e, and internal velocity V2 ≡ (1/2)v c2 + σ2, where vc is the rotational velocity and σ is the velocity dispersion. If these quantities are expressed in terms of kpc, L⊙ pc-2, and km s -1, then this surface is described by the equation log re - log V2 + log Ie + log Ye + 0.8 = 0, where we provide a fitting function for Ye, the mass-to-light ratio within re in units of M⊙/L⊙, that depends only on Vand Ie. The scatter about this surface for our heterogeneous sample of 1925 galaxies is small (<0.1 dex), and both the scatter within one of the galaxy subsamples (1319 disks) and the analysis of subsamples with independently derived mass-to-light ratios suggest that the intrinsic scatter could be as low as ∼0.05 dex, or 10%, prior to any correction for observational errors. This small scatter has three possible implications for how gross galactic structure is affected by internal factors, such as stellar orbital structure, nuclear activity, or mass loss history, and by external factors, such as environment or accretion history. These factors either (1) play no role beyond generating some of the observed scatter, (2) move galaxies along the surface, or (3) balance each other to maintain this surface as the locus of galactic structure equilibria. We cast the behavior of Ye in terms of the fraction of baryons converted to stars, η, and the concentration of those stars within the dark matter halo, ξ ≡ R200/re, where R200 is the standard estimate of the virial radius. We derive expressions for η and ξ, use an independent measurement of η to evaluate leading constant terms, obtain η = 1.9 × 10 -5(L/L*)Y*V-3 and ξ = 1.4Vr e-1, and relate these to each other via log η + log ξ = -log Ye + log Y* + const. Finally, we present the distributions of η and ξ for the full range of galaxies and conclude that the high Ye of dSph's are due to low η, rather than any differences in ξ, that η is similar for spheroids and disks of a given V, and that η decreases with increasing V for systems with V > 30 km s -1. For systems with internal velocities comparable to that of the MilkyWay (149 km s-1 < V < 163 km s-1), η = 0.14 ±- 0.05, and ξ is, on average, ∼5 times greater for spheroids than for disks.

KW - Galaxies: formation

KW - Galaxies: structure

UR - http://www.scopus.com/inward/record.url?scp=48749127975&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=48749127975&partnerID=8YFLogxK

U2 - 10.1086/529577

DO - 10.1086/529577

M3 - Article

AN - SCOPUS:48749127975

VL - 682

SP - 68

EP - 80

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1

ER -