Dark Matter in GalaxiesENCYCLOPEDIA OF ASTRONOMY AND ASTROPHYSICSDark Matter in GalaxiesDark matter in spiral galaxiesSPIRAL GALAXIES are flat rotating systems. The stars andgas in the disk are moving in nearly circular orbits, withthe gravitational field of the galaxy providing the inwardacceleration required for the circular motion. The rotationof these galaxies is usually not like a solid body: theangular velocity of the rotation typically decreases withradius. To a fair approximation, assuming Newtoniangravity, the rotational velocity V(r) at radius r is relatedto the total mass M(r) within radius r by the equationV2(r) = GM(r)/r, where G is the gravitational constant.The radial variation of the rotational velocity (therotation curve) is most readily measured from the gasin the disks. The emission lines of ionized gas in theinner regions are measured with optical spectrographs.With radio synthesis telescopes, rotation curves can bemeasured from the neutral hydrogen (H I) which emitsa narrow spectral line at 1420 MHz (21 cm wavelength).The interest in measuring rotation curves of spiral galaxiesis that they give a direct measure of the radial distributionof the total gravitating mass.Until the early 1970s, most of the rotation data forspirals came from optical observations which did notextend beyond the luminous inner regions. At that time,the optical rotation curves seemed consistent with thedistribution of luminous matter. With the constructionofRADIO TELESCOPES like the Westerbork Radio SynthesisTelescope in The Netherlands, it became possible tomeasure the distribution and rotation of the H I in spiralgalaxies. It was soon discovered that the H I in manyspirals extended far beyond the starlight, and that theH I rotation curves in such galaxies often showed nearlyconstant rotational velocity out to the radial limits of thedata.This was unexpected, because a flat rotation curvemeans that the total mass of the spiral within some radiusr increases linearly with r, while the total luminosityapproaches a finite asymptotic limit as r increases. It soonbecame clear that a large amount of invisible gravitatingmass (more than 90% of the total mass in some examples)is needed to explain these flat rotation curves.The problem is illustrated in figure 1. The rotationcurve comes from H I observations of a well studiedspiral, NGC 3198. The curve labelled disk is the rotationcurve that would be expected if the surface mass densityin this galaxy were proportional to the light distributionshown in the upper panel. In this analysis, the constantof proportionality (the ratio of mass to light) was made aslarge as possible, with the criterion that the total expectedrotation curve should not exceed the observed rotationcurve. The gas in the galaxy also contributes to theexpected rotation curve, as shown by the curve labelledgas (see alsoGAS IN GALAXIES). The contributions to theexpected rotation curve from stars and gas must be addedin quadrature to derive the total expected rotation curve.From the curves in this figure, there is no way that the starsFigure 1. The upper panel shows the R-band radial surfacebrightness distribution of the spiral galaxy NGC 3198. Thelower panel shows itsHIrotation curve (points). The curvelabelled disk shows the expected rotation curve if the surfacedensity distribution followed the surface brightness distributionin the upper panel. The curve labelled gas is the contribution tothe rotation curve from the observed gas. Together, the gas andthe disk cannot reproduce the observed flat rotation curve atlarge radius. An extra gravitating component, the dark halo, isneeded. The curve labelled halo is the rotation curve of theadopted dark halo model: the three labelled rotation curves,when added in quadrature, produce the total rotation curve thatpasses through the observed points. (From Begeman K 1987 PhDThesis University of Groningen.)and gas together can produce the flat observed rotationcurve. An additional massive and extended distributionof dark matter is needed. The rotation contribution for asimple dark halo model is shown in the figure: the modelis chosen so that the dark halo plus disk plus gas togethergive the rotation curve that passes through most of theobserved points in the figure. At the radial limit of the data,the dark halo is providing most of the total gravitationalfield.The halo model in figure 1 is a minimum halo, in thesense that the contribution of the disk to the rotation curvewas made as large as possible. If a lower mass-to-light(M/L) ratio had been adopted for the disk, then a morecentrally concentrated halo would be needed to make upthe larger discrepancy between the observed and expectedrotation curves. It is difficult to measure the M/L ratiofor disks independently of the rotation curve itself, andthere is still a lot of controversy about the correctness ofthe maximum disk approach as shown in figure 1.The situation shown in figure 1 is typical of almostCopyright © Nature Publishing Group 2001Brunel Road, Houndmills, Basingstoke, Hampshire, RG21 6XS, UK Registered No. 785998and Institute of Physics Publishing 2001Dirac House, Temple Back, Bristol, BS1 6BE, UK1Dark Matter in GalaxiesENCYCLOPEDIA OF ASTRONOMY AND A STROPHYSICSall DISK GALAXIES that have extended H I distributions,including the smallDWARF IRREGULAR GALAXIES that are alsoin rotational equilibrium. In almost every example, amassive dark halo that dominates the enclosed mass M(r)at large r is needed to explain the observed rotation curves.The nature of this dark matter remains unknown (seeDARKMATTER: ITS NATURE), and is one of the great problems ofmodern astrophysics.For decompositions as shown in the figure, the darkhalo is often modelled for simplicity as a spherical systemwith a radial volume density distribution of the formρ(r) = ρ(0)/(1+r2/a2), where a is a scale length and ρ(0)the central density. This particular distribution is chosenbecause it generates a flat rotation curve at large radius.The spherical shape is simply an assumption. It turnsout to be very difficult to measure the shapes of darkhalos. The thin neutral hydrogen layer in edge-on spiralsis observed to flare beyond the edge of the stellar disk,where the vertical restoring force of the disk is reduced.The extent of this flaring can be used to estimate theflattening of the dark halo (a flat halo would lead to lessflaring). Another idea is to study thePOLAR RING GALAXIES,inwhich material is rotating in two