General model of vertical distribution of stars in the Milky Way using complete Jeans equations

ABSTRACT The self-consistent vertical density distribution in a thin, isothermal disc is typically given by a sech2 law, as shown in the classic work by Spitzer. This is obtained assuming that the radial and vertical motions are decoupled and only the vertical term is used in the Poisson equation. We argue that in the region of low density as in the outer disc this treatment is no longer valid. We develop a general, complete model that includes both radial and vertical terms in the Poisson equation and write these in terms of the full radial and vertical Jeans equations which take account of the non-flat observed rotation curve, the random motions, and the cross term that indicates the tilted stellar velocity ellipsoid. We apply it to the Milky Way and show that these additional effects change the resulting density distribution significantly, such that the mid-plane density is higher and the disc thickness (HWHM) is lower by 30–40 per cent in the outer Galaxy. Further, the vertical distribution is no longer given as a sech2 function even for an isothermal case. These predicted differences are now within the verification limit of new, high-resolution data for example from Gaia and hence could be confirmed.

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Stellar Population Studies with the SDSS. I. The Vertical Distribution of Stars in the Milky Way

The Astrophysical Journal ◽

10.1086/320647 ◽

2001 ◽

Vol 553 (1) ◽

pp. 184-197 ◽

Cited By ~ 248

Author(s):

Bing Chen ◽

Chris Stoughton ◽

J. Allyn Smith ◽

Alan Uomoto ◽

Jeffrey R. Pier ◽

...

Keyword(s):

Vertical Distribution ◽

Stellar Population ◽

Milky Way ◽

Population Studies ◽

The Vertical Distribution

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Mass Distribution and Gravitational Potential of the Milky Way

Open Astronomy ◽

10.1515/astro-2017-0002 ◽

2017 ◽

Vol 26 (1) ◽

pp. 1-6

Author(s):

Slobodan Ninković

Keyword(s):

Exact Solution ◽

Poisson Equation ◽

Mass Distribution ◽

Milky Way ◽

Dark Halo ◽

New Formalism ◽

The Poisson Equation ◽

Cumulative Mass ◽

First Time ◽

Special Case

AbstractModels of mass distribution in the Milky Way are discussed where those yielding the potential analytically are preferred. It is noted that there are three main contributors to the Milky Way potential: bulge, disc and dark halo. In the case of the disc the Miyamoto-Nagai formula, as simple enough, has shown as a very good solution, but it has not been able to satisfy all requirements. Therefore, improvements, such as adding new terms or combining several Miyamoto-Nagai terms, have been attempted. Unlike the disc, in studying the bulge and dark halo the flattening is usually neglected, which offers the possibility of obtaining an exact solution of the Poisson equation. It is emphasized that the Hernquist formula, used very often for the bulge potential, is a special case of another formula and the properties of that formula are analysed. In the case of the dark halo, the slopes of its cumulative mass for the inner and outer parts are explained through a new formalism presented here for the first time.

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ISM turbulence driven by the magnetorotational instability

Proceedings of the International Astronomical Union ◽

10.1017/s1743921307001238 ◽

2006 ◽

Vol 2 (S237) ◽

pp. 65-69

Author(s):

Robert A. Piontek ◽

Eve C. Ostriker

Keyword(s):

Star Formation ◽

Vertical Distribution ◽

Thermodynamic Model ◽

Milky Way ◽

Ambient Medium ◽

Low Density ◽

Magnetorotational Instability ◽

Multi Phase ◽

The Vertical Distribution ◽

Ism Magnetic Fields

AbstractWe have performed numerical simulations which were designed to further our understanding of the turbulent interstellar medium (ISM). Our simulations include a multi-phase thermodynamic model of the ISM, magnetic fields, and sheared rotation, allowing us to study the effects of the magnetorotational instability (MRI) in an environment containing high density cold clouds embedded in a warm, low density, ambient medium. These models have shown that the MRI is indeed a significant source of turbulence, particularly at low mean densities typical of the outer regions of the Milky Way, where star formation rates are low, but high levels of turbulence persist. Here, we summarize past findings, as well as our most recent models which include vertical stratification, allowing us to self-consistently model the vertical distribution of material in the disk.

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Vertical distribution of HMXBs in NGC 55: Constraining their centre of mass velocity

Proceedings of the International Astronomical Union ◽

10.1017/s1743921319001236 ◽

2018 ◽

Vol 14 (S346) ◽

pp. 358-361

Author(s):

Babis Politakis ◽

Andreas Zezas ◽

Jeff J. Andrews ◽

Stephen J. Williams

Keyword(s):

Vertical Distribution ◽

Mass Velocity ◽

Milky Way ◽

Compact Object ◽

High Mass ◽

Centre Of Mass ◽

X Ray ◽

Star Forming ◽

X Ray Binaries ◽

The Vertical Distribution

AbstractWe analyse the vertical distribution of High Mass X-ray Binaries (HMXBs) in NGC 55, the nearest edge-on galaxy to the Milky Way. Our analysis reveals significant spatial offsets of HMXBs from the star forming regions, greater than those observed in the SMC and the LMC but similar with the Milky Way. The spatial offsets can be explained by a momentum kick the X-ray binaries receive during the formation of the compact object. The difference between the scale height of the vertical distribution of HMXBs and the vertical distribution of star-forming activity is 0.48±0.04 kpc. The centre-of-mass velocity of the distribution of HMXBs in NGC 55 is moving at a velocity of 52.4±11.4 km s−1, greater than the corresponding velocity of HMXBs in the SMC and LMC, but consistent with velocities of Milky Way HMXBs.

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Vertical stellar density distribution in a non-isothermal galactic disc

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa2924 ◽

2020 ◽

Vol 499 (2) ◽

pp. 2523-2533

Author(s):

Suchira Sarkar ◽

Chanda J Jog

Keyword(s):

Density Distribution ◽

Theoretical Estimate ◽

Solar Radius ◽

Dark Matter Halo ◽

Galactic Disc ◽

Limit Value ◽

The Galaxy ◽

Vertical Density ◽

External Galaxies ◽

Isothermal Case

ABSTRACT The vertical density distribution of stars in a galactic disc is traditionally obtained by assuming an isothermal vertical velocity dispersion of stars. Recent observations from SDSS, LAMOST, RAVE, Gaia etc. show that this dispersion increases with height from the mid-plane. Here, we study the dynamical effect of such non-isothermal dispersion on the self-consistent vertical density distribution for the thin disc stars in the Galaxy, obtained by solving together the Poisson equation and the equation of hydrostatic equilibrium. We find that in the non-isothermal case the mid-plane density is lower and the scale height is higher than the corresponding values for the isothermal distribution, due to higher vertical pressure, hence the distribution is vertically more extended. The change is $\sim \! 35 {{\ \rm per\ cent}}$ at the solar radius for a stars-alone disc for the typical observed linear gradient of +6.7 km s−1 kpc−1 and becomes even higher with increasing radii and increasing gradients explored. The distribution shows a wing at high z, in agreement with observations, and is fitted well by a double $\operatorname{sech}^{2}$, which could be mis-interpreted as the existence of a second, thicker disc, specially in external galaxies. We also consider a more realistic disc consisting of gravitationally coupled stars and gas in the field of dark matter halo. The results show the same trend but the effect of non-isothermal dispersion is reduced due to the opposite, constraining effect of the gas and halo gravity. Further, the non-isothermal dispersion lowers the theoretical estimate of the total mid-plane density i.e. Oort limit value, by 16 per cent.

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