HI velocity dispersion in NGC 1058

TL;DR

This study uses high-resolution VLA observations to analyze the HI velocity dispersion across NGC 1058, revealing a complex interstellar medium with dispersions not directly linked to star formation or spiral arms.

Contribution

First detailed analysis of HI profile shapes across an entire external galaxy disk using high-resolution VLA data.

Findings

HI velocity dispersions range from 4 to 15 km/sec.

Dispersions are not correlated with star formation or spiral arms.

Velocity dispersions decrease with radius but show significant local variations.

Abstract

We present excellent resolution and high sensitivity Very Large Array (VLA) observations of the 21cm HI line emission from the face-on galaxy NGC 1058, providing the first reliable study of the HI profile shapes throughout the entire disk of an external galaxy. Our observations show an intriguing picture of the interstellar medium; throughout this galaxy velocity-- dispersions range between 4 to 15 km/sec but are not correlated with star formation, stars or the gaseous spiral arms. The velocity dispersions decrease with radius, but this global trend has a large scatter as there are several isolated, resolved regions of high dispersion. The decline of star light with radius is much steeper than that of the velocity dispersions or that of the energy in the gas motions.

Figures

Tables

Table 1. Table 1: General Properties

	NGC 1058
R.A.(B1950)	02 40 23.2
Dec (B1950)	+37 07 48.0
Morphological type	Sc
Vsys [km/sec]	518
LB [L⊙]	$1.5\times {10}^9$
MHI[M⊙]	$2.3\times {10}^9$
SFR [M⊙ yr-1]aaSFR stands for Star Formation Rate, it was calculated from H$\alpha$ fluxes by Ferguson, Gallagher & Wyse (1998)	$3.5\times {10}^{-2}$
D${}_{25}{}^{}\times$d25 [arcmin]bbNASA/IPAC extragalactic database (NED)	$3.0\times 2.8$
Distance[Mpc]ccFerguson, Gallager, & Wyse (1998)	10
Physical equivalent of 1″	48.5 pc
Inclinationddvan der Kruit & Shostak (1984)	4–11∘
Environmentee Lewis (1975)	member of the NGC 1023 Group

Equations

$$f(v)=\frac{1}{\sigma \sqrt{2\pi }}exp\left[-\left(\frac{1}{2{{\sigma }_{\mathrm{v}}}^2}\right){(v-v_0)}^2\right]$$

$$v_z(x,y)=v_z(r_d,\theta )cos(i)+v_{circ}(r_d)sin(i)cos(\theta )+v_{red}$$

Full text

galaxies: kinematics and dynamics — individual:NGC 1058; galaxies:ISM

1 Introduction

Observations of H I velocities perpendicular to the disk ($v_{z}$) are necessary for studies of both the interstellar medium (ISM) (McKee & Ostriker 1977, Kulkarni & Heiles 1988, Braun 1992, 1997) and disk dynamics (Oort 1932; Rupen 1987; Lockman & Gehman 1991; Merriefield 1993; Malhotra 1994, 1995; Olling 1995) because they set a direct upper limit on the thermal and kinetic temperature of the gas. Hence the H I velocities perpendicular to the disk are an important dynamical tracer and as such can be used to constrain, both the gas mass distribution in the plane and its vertical structure (i.e., density as a function of height-$z$ above the plane)(van der Kruit & Shostak 1982,1984, Lockman & Gehman 1991, Malhotra 1995).

The behavior of the velocity dispersions as a function of galactic radius is important for determinations of the shape of dark matter halos. To date even the most sophisticated methods (e.g. Olling 1995, 1996) assume either a constant or an azimuthally symmetric velocity dispersion. Our measurements can therefore be used with studies of edge-on systems to determine radial variations in the mass to light (M/L) ratio.

Processes associated with star formation,such as stellar winds and multiple supernova explosions are thought to put energy into the ISM in the form of mechanical energy, starlight (which leads to photoelectric emission from dust grains), and cosmic rays. The velocity dispersion in the $z$ direction is intimately connected to the forces holding the gas against gravitational instabilities and hence to star-formation in the disk (e.g. Mac Low & Klessen 2004, Li, Mac Low & Klessen 2005). Measuring the degree of correlation between the locations of star-forming regions and those of high dispersion is a good method to investigate the relation between star-related energy sources and H I bulk motions.

The face-on spiral galaxy NGC 1058 (e.g. Eskridge et al. 2002) is ideal for studies of H I $v_{z}$ dispersions. Its low inclination (4°–11°) (Lewis 1987, van der Kruit & Shostak 1984) means that the gradient in rotational velocity is small across the beam and therefore it does not significantly corrupt measurements of velocities perpendicular to the disk.

Single dish studies of NGC 1058 (Allen & Shostak 1979, Lewis 1975, Lewis 1984) lack the resolution to trace the dispersion across the disk but through modeling of the rotational component these authors estimate it to range between 7 and 9 km/sec. In a series of papers (1982-1984) van der Kruit & Shostak analyze H I emission profiles in a number of face-on galaxies and determine that the velocity dispersions in NGC 1058 range only between 7 to 8 km/sec at all radii with very little variation. Dickey, Hanson, & Helou (1990) find the that velocity dispersion in NGC 1058 decreases with optical surface brightness but that in the extended gas disk, beyond the Holmberg radius the velocity dispersion is 5.7 km/sec everywhere, that is no variations with spiral phase or H I surface density are found.

All previous determinations of the H I velocity dispersion in NGC 1058 have been hindered by low spatial (e.g., Lewis 1984) and/or spectral (e.g., van der Kruit & Shostak 1984) resolution as well as by relatively poor sensitivity, requiring smoothing over large sections of the galactic disk, or missing up to 40$\%$ of the total flux (Dickey, Hanson, & Helou 1990). These trade-offs have led to significantly different conclusions about the H I velocity dispersion. Our sensitive observations at high spatial and velocity resolution as well as recovery of the entire single dish flux, allowed us to accurately measure the profile widths even in the outskirts of the H I disk, to resolve the arm from the interarm regions, and to analyze in detail the H I profile shapes, not just their breadths throughout the H I disk.

2 Observations and Data Reductions

The 21cm line of neutral hydrogen in NGC 1058 was observed with the VLA in the C and CS111The CS (shortened C) configuration moves two antennas from intermediate stations in the standard C configuration to the center of the array. The resulting short spacings significantly increase the sensitivity of the array to extended structure, while maintaining the same spatial resolution (Rupen 1997). configurations. The C configuration data was taken on 14 and 15 June 1993 for a total time on-source of 12.23 hours. The D configuration observation were performed on 7 and 8 November 1993 for a total time on source of 2.67 hours, and CS configuration data was collected on January 3, 1995 for a total time on-source of 5.42 hours. Rupen (1997,1998) gives a detailed account of the UV coverage in each of the configurations, compares the merits of each configuration, and discusses the benefits of combining them.

Both the C and CS configurations have a maximum baseline of 3.6 km, while the D configuration has a maximum baseline 1 km). The minimum baseline, which determines the size of the most extended feature which can be observed by the VLA, is 35 m. All observations were taken in dual polarization mode and Hanning smoothing was applied on-line; resulting in 127 independent spectral channels with a velocity width of 2.58 km/sec. We followed the normal AIPS calibration procedures and used the same flux (3C48) and phase (0234+285) calibrators throughout. The continuum emission was approximated as a linear fit to visibilities in 20 line-free channels on each side of the signal, and this fit was then subtracted from the uv-data in all the channels. Rupen (1999), gives a detailed description of the bandpass calibration and continuum subtraction.

The data cube presented here was deconvolved using the CLEAN algorithm as implemented by AIPS task IMAGR.222A description of IMAGR can be found in the AIPS cookbook available online at $http://www.aoc.nrao.edu/aips/cook.html$., iterated until the residuals were nearly zero and the flux density in the CLEAN model was stable. The cube was tapered to a resolution of $30\arcsec\times 29\arcsec$, or $1.3\,\times\,1.3$ kpc at a distance of 10 Mpc (Ferguson et al. 1998). Rupen (1997), presents a detailed comparison of several cleaning algorithms and motivates the use of the CLEAN algorithm for this data. A more general discussion of CLEAN as implemented in AIPS is given in chapter 5, of the AIPS cookbook as well as in Cornwell, Braun, & Briggs 1999. A more specific examination of deconvolution algorithms as applied on our NGC 1058 data is presented in Rupen (1997,1999).

The RMS noise level in the line channels of the cube was 0.5 and mJy/beam, corresponding to a column density of $1.6\times 10^{18}$ cm*-2* per channel. The H I integrated line profile agrees with those obtained in single dish studies (Allen $\&$ Shostak 1979) after both the single dish and the VLA data are corrected for primary beam response.

Figure 1 presents the frames of the 30″ data cube. Each image (traditionally called a channel map) in this figure represents the 21 cm line emission at a certain velocity, the abscisa and ordinate axis are the RA and Dec coordinates. The lack of artifacts in these images (such as a negative bowl around the galaxy) also suggests that the images have been correctly deconvolved.

3 Results and Analysis

The general properties of NGC 1058 are presented in Table 1. Figure 2 shows intensity weighted mean velocity contours atop the H I intensity map and presents the H I spiral structure of NGC 1058. Figure 2 also illustrates the superb sensitivity and resolution of these studies, which allowed us to measure the H I emission at distances of approximatively 10 kpc from the center of the disk and to differentiate between the arms and the inter-arms. We characterize the widths of the H I profiles by the relative dispersions $\sigma_{\rm{v}}$ of the best Gaussian fit 333 The FWHM is often use to characterize the H I line widths. This tradition is based upon the fact that H I profiles are modeled by one or multiple Gaussians, where the flux as a function of velocity $v$ is given by

$f(v)={1\over{\sigma\sqrt{2\pi}}}exp\left[-\left(1\over{2{\sigma_{\mathrm{v}}}^{2}}\right){(v-v_{0})}^{2}\right]$

and $v_{0}$ is the velocity at associated with the peak flux.; the fits were done using a least squares minimization algorithm.

Figures  3 and  4, show the observed profiles for a few pixels throughout NGC 1058 from the 45″ and the 30″ data sets respectively. The single Gaussians which best approximate the shapes of these profiles, as well as their residuals are also shown. Note, that each of the profiles is representative of the remainder of the spectra, it is not a *best find * or the result of averaging over large areas of the disk or velocity space.

While the residual patterns suggest that a single Gaussian is not a good functional description of the H I profiles in NGC 1058, the FWHM and $\sigma_{v}$ derived from the single Gaussian fits track well the intrinsic width of the H I spectrum. This proportionality allows us to describe the widths of the profile in terms of the results of our least squares fitting. The general characteristics of the velocity dispersion will be discussed in terms of the 45″and 30″ cubes.

4 General Characteristics of the Velocity Dispersion

Figure 5 presents the distribution of velocity dispersions across the disk of NGC 1058. Unlike previous observers of NGC 1058, we find a wide range of dispersions from $~{}4$ to 14 km sec*-1* in addition to a few extremely narrow profiles with $\sigma_{v}~{}\sim~{}3.5$  km sec*-1*. These narraow profiles are found in regions of relatively low column density at radii greater than $300\arcsec$ or 13 kpc. There are three regions of high dispersion which stand out in Figure 5: one in the center (labeled C and $\sim 4.5$ kpc across) and two others symmetric about the center in the North-West (N $\sim 3$ kpc) and South-East (S $\sim~{}3\times 5$ kpc) of the center. We find no obvious correlation between high H I velocity dispersion and stars or star formation tracers such as $H_{\alpha}$ (Figure 10), radio contiuum, SNe except in the central region C. The most probable explanation for the observed highest dispersions outside the central region (i.e. in N and S) are small scale ($\leq 0.7$ kpc) bulk motions (see section 7 below). In the southern, part the disk could be warping (van der Kruit & Shostak 1984, Shen & Sellwood 2006) leading to the observed broad profiles. Figure 6 shows that H I profiles from N and S are also assymmetric. However, a similar explanation for region N would suggest rather impressive small-scale structure in the warp as it would requiere the inclination to change $\sim$ 3 degrees over a region smaller than 0.7 kpc in diameter, if we assume from Tully Fisher an intrinsic rotation velocity of 150 km s*-1* . A more exciting alternative explanation for the bulk motions observed in N is that they are caused by the infall of gas left over from galaxy formation. However, this is somewhat difficult to reconcile with the relatively low column density in these regions.

Two global trends are evident from the derived dispersions: a radial fall-off, shown in Figure 7, and a predominance of the broadest profiles in the inter-arm regions of the galaxy (Figure 9). Ferguson et al. (1998) used deep $H\alpha$ observations to reveal the presence of H II regions in the central 6 kpc of NGC 1058. There are several knots of high dispersion (12 to 13.5 km/sec) in region C, with most of the profiles measuring between 7.5 and 11 km/sec. However, none of the star formation sites outside the central $\sim$2 kpc discovered in that study seem to affect the width of the profiles. Also, regions N and S are located in the inter-arm regions and are not associated with sufficiently strong star formation to be detected in the Ferguson et al. (1998) study. Therefore we find that the dispersions do not correlate with star formation as shown from the overlay of Feruson et al (1998)’s H$\alpha$ map atop contours of velocity dispersion Figure 10.

Figure 8 shows the kinetic energy in the gas associated with motions perpendicular to the disk. Because only a qualitative behaviour was of interest here, the kinetic energy in vertical motions at a certain pixel location was roughly approximated as the product of total intensity times the square of the velocity dispersion. Approximated as such, the kinetic energy in vertical motions does not follow the decline in star light which drops with radius as $\sim\rm{exp}^{-{{r}\over{30\arcsec}}}$. Figure 9 shows that, the broadest profiles seem to be found in relatively low column density areas between the spiral arms (as traced by H I). As such we do not find a correlation between the velocity dispersion of stars in the disk or the H I column density.

The dissimilarity between stars, star-formation, H I intensity, and the kinetic energy in the gas implies that processes other than those directly associated with stars put energy into the ISM. Sellwood $\&$ Balbus (1999) suggested that magnetic fields with strengths of a few micro-gauss in these extended disks allow energy to be extracted from galactic differential rotation through MHD-driven turbulence. While that mechanism predicted a uniform dispersion outside of the optical disk, in an attempt to explain lower quality data on NGC 1058, a similar mechanism has the potential of explaining the level and behaviour of the velocity dispersions as a function of radius (Sellwood, private communication). The Sellwood & Balbus (1999) paper generated significant work on numerical models that predict the occurance of the magnetorotational instability in galactic disks (e.g. Dziourkevitch, Elstner, & Rudiger 2004, Pionteck & Ostriker 2004).

5 Profile Shapes

Any model that would explain how energy is put into the ISM must account for the shape of the profiles in NGC 1058. A single Gaussian least-squares fitting routine was run on the 30″ and 45″ data sets. In both cases, we found that while the signal to noise for most profiles was excellent the chisq per degree of freedom was larger than a few, the residuals also suggested that the wings were broader than those of a Gaussian.

To understand whether how the H I line shapes varied throughout the galaxy, the profiles were normalized by flux, aligned so that their peaks were at the same central velocity. These were plotted in units of FWHM (2.354$\sigma_{v}$), using the parameters from the single Gaussian fits to control the scaling. This was done to reveal only the difference in the line shapes and not other differences such as the width of peak intensity. While stacking up the 45″ profiles it became clear that almost all profiles appeared to have the same shape. Figure 13 suggests that despite it being non-Gaussian, the shapes of the line profiles are identical throughout most of the galaxy when scaled by $\sigma_{v}$ and their peak flux and aligned so that their peaks occur at the same velocity.

For the 45″ data, median shapes from profiles within different width and peak intensity ranges were compared and found to be identical within the error-bars. The method used to derive such median line shapes is fairly straightforward. After the pixel selection (by FWHM, location in the galaxy, etc.) the profiles corresponding to every pixel were normalized in intensity dividing by the peak flux. A grid of 63 channels for the 45″  data and 108 for the 30″   data was set up to replace the velocity axis from units of km/sec to units of FWHM. For example suppose that the velocity corresponding to the peak of a certain profile (in the 45″ cube) is $V_{cen}$ km s*-1* and that its FWHM is $FW$ km s*-1*. Only the channels between $V_{cen}\,-\,3\times FW$ and $V_{cen}\,+\,3\times FW$ were used in deriving the median shape. The normalized fluxes corresponding to these channels were then resampled onto a grid where each bin (i.e.; channel) is 6 $FW$ divided by the number of channels. Each bin therefore contains a certain number distribution of normalized fluxes; these fluxes were then sorted and the middle value is taken as the median.

Median profiles were also derived and compared from various areas throughout the disk and the line shapes appeared similar everyhwere except in N and S, where the profiles where more asymmetric as previously discussed. For brevity we present just two of these tests in Figure 14. The same median comparison tests were done on the 30″ data. At the 30″ resolution median profiles derived for certain ranges of peak flux and from various areas throughout the galaxy were also identical. However, the median profiles derived for various ranges of FWHM appeared to vary in the shape of their wings, perhaps because of the lower signal to noise in this data set, and to the smaller number of broad ($\sigma_{v}\geq 10km~{}s^{-1}$) than that of narrow lines.

Throughout our analysis we assumed that the noise characteristic in each profile is random and that the rms noise is the same regardless of the strengh of the signal. This assumption need not be true as deconvolution algorithms seem to produce noise that is proportional in a non-linear fashion with signal (Rupen 97). However different noise for different flux levels will hardly lead to a universal, non-Gaussian line shape. A double Gaussian (a narrow and a broad component) as shown in Figure 15 is a good fit to the median profile derived from the 45″ data.

6 Kinetic Energy Distribution

The uniformity of the profile shape in NGC 1058 suggests that on scales of 2.5 kpc, the neutral gas is being stirred into the same distribution of energy per unit mass and that this distribution is different than that for other galaxies (e.g. the Milky Way). Figure 16 shows the normalized kinetic energy (KE) distribution for the Milky Way and for NGC 1058. This comparison is only qualitative. The term “normalized” in the case of the Milky Way refers to the fact that the KE distribution was obtained from a model (i.e. double Gaussian fit) of the H I emission at the North Galactic Pole; this model was presented in Kulkarni & Fich (1985), hereafter KF85, and it only includes “normal” emission, i.e. it does not include emission from the H I falling into the disk. These authors corrected for the infalling emission by assuming that the huge bump on one side of the profile represented infalling gas. To remove the bump they reflected the profile about the velocity corresponding to the peak flux and obtained the profile shown in Figure 16. The units of the KF plot are Kelvin2 km2 s*-2*. The units for the NGC 1058 are arbitrary, and the term “normalized” in this case means that instead of flux or temperature, we use flux divided by peak flux, and bin numbers instead of velocities. To compare those qualitatively we aligned the KF profile with the NGC 1058 median profile from the entire 45″ data set. The aligning was done by fitting a single Gaussian to the KF85 profile and to the NGC 1058 median profile. We require and that the limits of the KF85 and the NGC 1058 profiles span an equal number of FWHM.

The striking feature in the Galactic energy distribution, also noted by Kulkarni & Fich (1985) is the almost constant kinetic energy for about 50 km/sec. In contrast, NGC 1058’s KE curve is more centrally peaked. Presumably the KE distribution is set both by the galactic potential as well as explosive ISM events (such as SNe, star formation, and infalling gas). It is not perfectly clear how these factors have shaped the energy distribution as a function of velocity of either the Milky Way or NGC 1058. function of velocity.

7 Beam Smearing and Bulk Motions

An accurate study of the profile shapes throughout the galaxy require us to understand the effect of beam smearing on our measurements. Consider a round spiral disk with gas moving in circular orbits at a velocity $v_{circ}$; attaching polar coordinates to this disk ($r_{d},\theta$) and letting the angle between the normal to the plane of the galaxy and line-of sight be referred to as the inclination angle ($i$) the observed radial velocity on a set of sky-coordinates ($x,y$) will be

[TABLE]

where $v_{red}$ is the velocity of the galaxy for which with respect to the observer. Obviouosly a smaller $i$ is (a more face-on) makes it easier to measure the true $v_{z}$ distribution. A gradient in the $v_{circ}(r_{d})sin(i)cos(\theta)$ across the resolution element (beam) will increase the width of the profile and confuse the measurements of the velocities perpendicular to the disk. This problem is known as beam smearing.

Two tests were performed using our highest resolution (15″) data to quantify the effect of beam smearing on our measurements of $\sigma_{v}$. First, we determined the maximum in-plane velocity difference within a beam which would contribute to the width of the line profile at a certain position in the galaxy (i.e. at a pixel). This was done by finding the maximum difference (hereafter $\rm{M_{diff}}$) between the central velocity $\rm{v_{cen}}$ (i.e. the velocity associated with the peak flux as derived from the single Gaussian fit to the 15″ data) of the H I pixel and the central velocities of all the pixels within a square with 32″ sides centered on that pixel. Figure 11 shows the map of these maximum difference. This method is based on the assumption that differences in $\rm{v_{cen}}$ are due to gas motions in the plane of the galaxy. This test shows that $\sigma_{v}$ is correlated with $\rm{M_{diff}}$. The correlation between $\sigma_{v}$ and $\rm{M_{diff}}$ suggests the exitence of bulk motions on scales smaller and equal to those probed by our highest resolution data 15″ (0.7 kpc).

Finding $\rm{M_{diff}}$ across NGC 1058’s disk gives an upper limit to the broadening of the H I profiles. To better understand the effect of beam smearing on our observations we constructed a simple model of how H I in NGC 1058 would appear if it was an infinitely cold disk; we then convolved this model with a 30″ beam and ran our Gaussian least squares fitting routine on the resulting H I profiles. The widths of these final model profiles were significantly smaller than those measured in NGC 1058 (Figure 12) suggesting that beam smearing does not have a significant impact on our observations.

8 Summary and Conclusions

Excellent resolution and high sensitivity H I observations of NGC 1058 show an intriguing picture of the interstellar medium throughout this galaxy: the velocity dispersion ranges from 4 to 14 km/sec but is not correlated with star formation or the spiral arms, which is another major ISM regulator. Global trends such as a radial fall-off must be explained in the context of significant local effects; most notable among these are isolated, resolved regions of high velocity dispersions as well as significant scatter in the dispersion at a given radius. In summary unlike some previous studies, we find that the dispersion is not constant and it does not simply decline with radius. we also find that there is no tight correlation between the width of the profiles and the spiral arms.

The most probable source for the highest dispersions observed outside the central regions are small scale ($\leq$0.7 kpc) bulk motions. The energy sources supporting such motions are not entirely clear. The disk is warped in the southern part (van der Kruit & Shostak 1984, Shen & Sellwood 2006), leading to the observed broad profiles: however, a similar explanation for region N would suggest a rather impressive small-scale structure in the warp, as it would require the inclination to change by $\sim$ 3 degrees over a size smaller than 0.7 kpc.

There is no obvious correlation with stars or star formation tracers such as H$\alpha$, radio continuum, SNe except in region C; nor is it clear what role, if any, is played by spiral arms in driving the observed small scale bulk motions. Some of the measured velocity dispersions are higher than the 10 km $s^{-1}$ canonical sound speed in the ISM, but since we cannot easily measure directly the pressure and 3-dimensional density structure of the gas, we cannot determine the exact sound speed to know if we are indeed seeing supersonic motions.

The shapes of the H I profiles in NGC 1058 are non-Gaussian and hence cannot be explained as emission from single temperature gas. Therefore, it is not clear whether these narrow profiles are evidence of a lower thermal balance point between heating and cooling mechanisms in NGC 1058’s outskirts as compared to the rest of the galaxy.

A double Gaussian description of the H I profile is far from a complete surprise. The surprise is the constancy between the broad and narrow components throughout NGC 1058’s H I disk. In previous studies (e.g. Mebold 1972, Young & Lo 1996) it was found that some of the H I profiles were well described by double Gaussians, and these associated the narrow Gaussians with the CNM and the broad with the WNM. Young & Lo (1996) found that the narrow component existed only in regions of high H I column density, next to areas with active star formation. It is unlikely that the universal profile in NGC 1058 can be explained as a combination of cold and warm medium for the narrow and broad component respectively, because it seems difficult to have the same ratio of warm to cold gas in regions associated with stars and star fromation and at radii three times the optical $R_{25}$. Also, high resolution observations in other galaxies (Braun 1998) showed that the CNM dissappears at the edges of the optical disk.

Further quests on the observational front such as (at what resolution will this universality break down, is this spatial scale particular to NGC 1058, can we see the same shape and/or its universality in other systems), as well as theoretical efforts to model mechanisms of injecting energy into the ISM, and determine how that energy dissipates throughout a fractal ISM are necessary to understand the full significance of the universal profile in our 45″ data cube.

A.P. would like to thank Jacqueline van Gorkom for invaluable help in designing the experiment, as well as during during the analysis process and in editing this document. A.P. would also like to thank Liese van Zee, Mordecai Mac-Low and Jennifer Donovan for their helpfull suggestions and discussions. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc..