Experience WorldWide Telescope, free, at worldwidetelescope.org

Alyssa A. Goodman

Harvard-Smithsonian Center for Astrophysics @AAGIE

Seeing

Stars form

the Milky Way

in

Relative Strengths

Pattern RecognitionCreativity

Calculations

Communication

Cognition

*“Language” includes words & math

DataLanguage*

Pictures

WorldWide  Telescope

gluemultidimensional data exploration

AuAuthorea

“Linking

Visualization &

Understanding

in Astronomy”

data, CLUMPFIND typically finds features on a limited range of scales,above but close to the physical resolution of the data, and its results canbe overly dependent on input parameters. By tuning CLUMPFIND’stwo free parameters, the same molecular-line data set8 can be used toshow either that the frequency distribution of clump mass is the sameas the initial mass function of stars or that it follows the much shal-lower mass function associated with large-scale molecular clouds(Supplementary Fig. 1).

Four years before the advent of CLUMPFIND, ‘structure trees’9

were proposed as a way to characterize clouds’ hierarchical structure

using 2D maps of column density. With this early 2D work as inspira-tion, we have developed a structure-identification algorithm thatabstracts the hierarchical structure of a 3D (p–p–v) data cube intoan easily visualized representation called a ‘dendrogram’10. Althoughwell developed in other data-intensive fields11,12, it is curious that theapplication of tree methodologies so far in astrophysics has been rare,and almost exclusively within the area of galaxy evolution, where‘merger trees’ are being used with increasing frequency13.

Figure 3 and its legend explain the construction of dendrogramsschematically. The dendrogram quantifies how and where local max-ima of emission merge with each other, and its implementation isexplained in Supplementary Methods. Critically, the dendrogram isdetermined almost entirely by the data itself, and it has negligiblesensitivity to algorithm parameters. To make graphical presentationpossible on paper and 2D screens, we ‘flatten’ the dendrograms of 3Ddata (see Fig. 3 and its legend), by sorting their ‘branches’ to notcross, which eliminates dimensional information on the x axis whilepreserving all information about connectivity and hierarchy.Numbered ‘billiard ball’ labels in the figures let the reader matchfeatures between a 2D map (Fig. 1), an interactive 3D map (Fig. 2aonline) and a sorted dendrogram (Fig. 2c).

A dendrogram of a spectral-line data cube allows for the estimationof key physical properties associated with volumes bounded by iso-surfaces, such as radius (R), velocity dispersion (sv) and luminosity(L). The volumes can have any shape, and in other work14 we focus onthe significance of the especially elongated features seen in L1448(Fig. 2a). The luminosity is an approximate proxy for mass, suchthat Mlum 5 X13COL13CO, where X13CO 5 8.0 3 1020 cm2 K21 km21 s(ref. 15; see Supplementary Methods and Supplementary Fig. 2).The derived values for size, mass and velocity dispersion can then beused to estimate the role of self-gravity at each point in the hierarchy,via calculation of an ‘observed’ virial parameter, aobs 5 5sv

2R/GMlum.In principle, extended portions of the tree (Fig. 2, yellow highlighting)where aobs , 2 (where gravitational energy is comparable to or largerthan kinetic energy) correspond to regions of p–p–v space where self-gravity is significant. As aobs only represents the ratio of kinetic energyto gravitational energy at one point in time, and does not explicitlycapture external over-pressure and/or magnetic fields16, its measuredvalue should only be used as a guide to the longevity (boundedness) ofany particular feature.

Self-gravitatingleaves

CLUMPFIND segmentation

vz

x (RA)

y (d

ec.)

vz

x (RA)

y (d

ec.)

c

d

8

6

4

2

0

8

6

4

2

0

T mb

(K)

T mb

(K)

Self-gravitatingstructures

All structure

a b

Click to rotate

Figure 2 | Comparison of the ‘dendrogram’ and ‘CLUMPFIND’ feature-identification algorithms as applied to 13CO emission from the L1448region of Perseus. a, 3D visualization of the surfaces indicated by colours inthe dendrogram shown in c. Purple illustrates the smallest scale self-gravitating structures in the region corresponding to the leaves of thedendrogram; pink shows the smallest surfaces that contain distinct self-gravitating leaves within them; and green corresponds to the surface in thedata cube containing all the significant emission. Dendrogram branchescorresponding to self-gravitating objects have been highlighted in yellowover the range of Tmb (main-beam temperature) test-level values for whichthe virial parameter is less than 2. The x–y locations of the four ‘self-gravitating’ leaves labelled with billiard balls are the same as those shown inFig. 1. The 3D visualizations show position–position–velocity (p–p–v) space.RA, right ascension; dec., declination. For comparison with the ability ofdendrograms (c) to track hierarchical structure, d shows a pseudo-dendrogram of the CLUMPFIND segmentation (b), with the same fourlabels used in Fig. 1 and in a. As ‘clumps’ are not allowed to belong to largerstructures, each pseudo-branch in d is simply a series of lines connecting themaximum emission value in each clump to the threshold value. A very largenumber of clumps appears in b because of the sensitivity of CLUMPFIND tonoise and small-scale structure in the data. In the online PDF version, the 3Dcubes (a and b) can be rotated to any orientation, and surfaces can be turnedon and off (interaction requires Adobe Acrobat version 7.0.8 or higher). Inthe printed version, the front face of each 3D cube (the ‘home’ view in theinteractive online version) corresponds exactly to the patch of sky shown inFig. 1, and velocity with respect to the Local Standard of Rest increases fromfront (20.5 km s21) to back (8 km s21).

Inte

nsity

leve

l

Local max

Local max

Local max

Merge

Merge

Leaf

Leaf

Leaf

Bra

nch

Trun

k

Test level

Figure 3 | Schematic illustration of the dendrogram process. Shown is theconstruction of a dendrogram from a hypothetical one-dimensionalemission profile (black). The dendrogram (blue) can be constructed by‘dropping’ a test constant emission level (purple) from above in tiny steps(exaggerated in size here, light lines) until all the local maxima and mergersare found, and connected as shown. The intersection of a test level with theemission is a set of points (for example the light purple dots) in onedimension, a planar curve in two dimensions, and an isosurface in threedimensions. The dendrogram of 3D data shown in Fig. 2c is the directanalogue of the tree shown here, only constructed from ‘isosurface’ ratherthan ‘point’ intersections. It has been sorted and flattened for representationon a flat page, as fully representing dendrograms for 3D data cubes wouldrequire four dimensions.

LETTERS NATURE | Vol 457 | 1 January 2009

64 Macmillan Publishers Limited. All rights reserved©2009

WorldWide  Telescope

gluemultidimensional data exploration

AuAuthorea

data, CLUMPFIND typically finds features on a limited range of scales,above but close to the physical resolution of the data, and its results canbe overly dependent on input parameters. By tuning CLUMPFIND’stwo free parameters, the same molecular-line data set8 can be used toshow either that the frequency distribution of clump mass is the sameas the initial mass function of stars or that it follows the much shal-lower mass function associated with large-scale molecular clouds(Supplementary Fig. 1).

Four years before the advent of CLUMPFIND, ‘structure trees’9

were proposed as a way to characterize clouds’ hierarchical structure

using 2D maps of column density. With this early 2D work as inspira-tion, we have developed a structure-identification algorithm thatabstracts the hierarchical structure of a 3D (p–p–v) data cube intoan easily visualized representation called a ‘dendrogram’10. Althoughwell developed in other data-intensive fields11,12, it is curious that theapplication of tree methodologies so far in astrophysics has been rare,and almost exclusively within the area of galaxy evolution, where‘merger trees’ are being used with increasing frequency13.

Figure 3 and its legend explain the construction of dendrogramsschematically. The dendrogram quantifies how and where local max-ima of emission merge with each other, and its implementation isexplained in Supplementary Methods. Critically, the dendrogram isdetermined almost entirely by the data itself, and it has negligiblesensitivity to algorithm parameters. To make graphical presentationpossible on paper and 2D screens, we ‘flatten’ the dendrograms of 3Ddata (see Fig. 3 and its legend), by sorting their ‘branches’ to notcross, which eliminates dimensional information on the x axis whilepreserving all information about connectivity and hierarchy.Numbered ‘billiard ball’ labels in the figures let the reader matchfeatures between a 2D map (Fig. 1), an interactive 3D map (Fig. 2aonline) and a sorted dendrogram (Fig. 2c).

A dendrogram of a spectral-line data cube allows for the estimationof key physical properties associated with volumes bounded by iso-surfaces, such as radius (R), velocity dispersion (sv) and luminosity(L). The volumes can have any shape, and in other work14 we focus onthe significance of the especially elongated features seen in L1448(Fig. 2a). The luminosity is an approximate proxy for mass, suchthat Mlum 5 X13COL13CO, where X13CO 5 8.0 3 1020 cm2 K21 km21 s(ref. 15; see Supplementary Methods and Supplementary Fig. 2).The derived values for size, mass and velocity dispersion can then beused to estimate the role of self-gravity at each point in the hierarchy,via calculation of an ‘observed’ virial parameter, aobs 5 5sv

2R/GMlum.In principle, extended portions of the tree (Fig. 2, yellow highlighting)where aobs , 2 (where gravitational energy is comparable to or largerthan kinetic energy) correspond to regions of p–p–v space where self-gravity is significant. As aobs only represents the ratio of kinetic energyto gravitational energy at one point in time, and does not explicitlycapture external over-pressure and/or magnetic fields16, its measuredvalue should only be used as a guide to the longevity (boundedness) ofany particular feature.

Self-gravitatingleaves

CLUMPFIND segmentation

vz

x (RA)

y (d

ec.)

vz

x (RA)

y (d

ec.)

c

d

8

6

4

2

0

8

6

4

2

0

T mb

(K)

T mb

(K)

Self-gravitatingstructures

All structure

a b

Click to rotate

Figure 2 | Comparison of the ‘dendrogram’ and ‘CLUMPFIND’ feature-identification algorithms as applied to 13CO emission from the L1448region of Perseus. a, 3D visualization of the surfaces indicated by colours inthe dendrogram shown in c. Purple illustrates the smallest scale self-gravitating structures in the region corresponding to the leaves of thedendrogram; pink shows the smallest surfaces that contain distinct self-gravitating leaves within them; and green corresponds to the surface in thedata cube containing all the significant emission. Dendrogram branchescorresponding to self-gravitating objects have been highlighted in yellowover the range of Tmb (main-beam temperature) test-level values for whichthe virial parameter is less than 2. The x–y locations of the four ‘self-gravitating’ leaves labelled with billiard balls are the same as those shown inFig. 1. The 3D visualizations show position–position–velocity (p–p–v) space.RA, right ascension; dec., declination. For comparison with the ability ofdendrograms (c) to track hierarchical structure, d shows a pseudo-dendrogram of the CLUMPFIND segmentation (b), with the same fourlabels used in Fig. 1 and in a. As ‘clumps’ are not allowed to belong to largerstructures, each pseudo-branch in d is simply a series of lines connecting themaximum emission value in each clump to the threshold value. A very largenumber of clumps appears in b because of the sensitivity of CLUMPFIND tonoise and small-scale structure in the data. In the online PDF version, the 3Dcubes (a and b) can be rotated to any orientation, and surfaces can be turnedon and off (interaction requires Adobe Acrobat version 7.0.8 or higher). Inthe printed version, the front face of each 3D cube (the ‘home’ view in theinteractive online version) corresponds exactly to the patch of sky shown inFig. 1, and velocity with respect to the Local Standard of Rest increases fromfront (20.5 km s21) to back (8 km s21).

Inte

nsity

leve

l

Local max

Local max

Local max

Merge

Merge

Leaf

Leaf

Leaf

Bra

nch

Trun

k

Test level

Figure 3 | Schematic illustration of the dendrogram process. Shown is theconstruction of a dendrogram from a hypothetical one-dimensionalemission profile (black). The dendrogram (blue) can be constructed by‘dropping’ a test constant emission level (purple) from above in tiny steps(exaggerated in size here, light lines) until all the local maxima and mergersare found, and connected as shown. The intersection of a test level with theemission is a set of points (for example the light purple dots) in onedimension, a planar curve in two dimensions, and an isosurface in threedimensions. The dendrogram of 3D data shown in Fig. 2c is the directanalogue of the tree shown here, only constructed from ‘isosurface’ ratherthan ‘point’ intersections. It has been sorted and flattened for representationon a flat page, as fully representing dendrograms for 3D data cubes wouldrequire four dimensions.

LETTERS NATURE | Vol 457 | 1 January 2009

64 Macmillan Publishers Limited. All rights reserved©2009

Alyssa A. Goodman

Harvard-Smithsonian Center for Astrophysics @AAGIE

Seeing

Stars form

the Milky Way

in

“Galactic Plane”

“Galactic Plane”

the Milky Way

Seeing

Stars form

the Milky Way

in

Stellar MassN

umbe

r of S

tars

of e

ach

Mas

s

Galaxy

Star Cluster

Molecular Cloud Complex Star-Forming “Globule” Circumstellar Disk Extrasolar System

?

Alves, Lombardi & Lada 2007

Stars formhow

Image Credit: Jonathan Foster & Jaime Pineda CfA/COMPLETE Deep Megacam Mosaic of West End of Perseus

Radiation

“Turbulence”(Random Kinetic Energy)

Magnetic Fields Gravity

Outflows & Winds

Chemical & Phase Transformations

Thermal Pressure

~1 pc

A complicated Recipe

A complicated Recipe

prep time: without galaxy formation, ~1 Million years (If you want to form your own Galaxy first, allow at least 10 billion years extra.)

STARS

ingredients: gas, dust, photons, and a touch of dark matter

equipment: gravity, magnetic fields, thermodynamics, chemical reactions

instructions: mix all above ingredients, using equipment “as needed”, stir well, using turbulence generated by stellar winds, Galactic shear, and more. Beware of shocks.

Simulations of Bate 2009

Primitive Cooking, with “Simple" recipes

Simulation Synthetic Data

Nature

Observing System

Synthetic Observing System

Radiative Transfer

(+Chemistry) Code(s)

Observed Data

Taste Tests

EnabledIndirectly

Sample Taste Test

Frac

tion

of E

mis

sion

in

Self-

Gra

vita

ting

Stru

ctur

es

Scale (pc)

The “Taste-Testing” Process

Taste Test

“synthetic observation”“depletion, opacity”

For today’s purposes:We devise and use high-dimensional statistics to compare the real and simulated Universe.

Results: Simulations are getting better, but none is fully realistic yet. Goal is to guide input Physics.

Seeing

Stars form

the Milky Way

in

What we “see”

Dust

“Stars”

Gas

Spectral Line Observations

Wide DataWhat we “see”

How we “see”

in 3D

Spectral Line Observations

1.5

1.0

0.5

0.0

-0.5

Inten

sity

400350300250200150100

"Velocity"

Observed Spectrum

Telescope +Spectrometer

All thanks to Doppler

Velocity from Spectroscopy

Spectral-line Mapping

We wish we could measure…

y

x

z

vz

vx

vy

y

-x-vz

But we can measure…

vz only from “spectral-line

maps”

This is called “p-p-v” or “position-

position-velocity” space.

Seeing in P-p-V Space

Spectral Line Observations

Mountain Range No loss ofinformation

Loss of1 dimension

1D: Columns = “Spectra”, “SEDs” or “Time Series”2D: Faces or Slices = “Images”3D: Volumes = “3D Renderings”, “2D Movies”4D: Time Series of Volumes = “3D Movies”

1D2D3D4D

Data-Dimensions-Display

mm peak (Enoch et al. 2006)

sub-mm peak (Hatchellet al. 2005, Kirk et al. 2006)

13CO (Ridge et al. 2006)

mid-IR IRAC composite from c2d data (Foster, Laakso, Ridge, et al.)

Optical image (Barnard 1927)

Seeing Wide Data in “3D”

13CO (Ridge et al. 2006)Seeing Wide Data in “3D”

“Keith” “Perseus”

Astronomical Medicine

“z” is depth into head “z” is line-of-sight velocity

“AstroMed” collaborators include Douglas Alan, Chris Beaumont, Michelle Borkin, Jonathan Foster, Michael Halle, Nick Holliman, Jens Kauffmann, Jaime Pineda, Tudor Platon, Erik Rosolowsky, and more

AstronomicalMedicine@

3D Viz made with VolView

Perseus

Galaxy

Star Cluster

Molecular Cloud Complex Star-Forming “Globule”

Stellar Mass

Num

ber o

f Sta

rs o

f eac

h M

ass

Circumstellar Disk Extrasolar System

?

Alves, Lombardi & Lada 2007

Galaxy

Star Cluster

Molecular Cloud Complex Star-Forming “Globule”

Galaxy

Star Cluster

Molecular Cloud Complex Star-Forming “Globule”

Galaxy

Star Cluster

Molecular Cloud Complex

Star-Forming “Globule”

Nessie B5

CoherenT Cores

Islands of Calm in turbulent Seas(?)

The 30-year story: Myers & Benson 1983, Goodman et al. 1998, Pineda et al. 2010, 2011, 2014

R.A.

Dec.

vLSR

many thanks to Jaime Pineda & Jens Kauffmann for this figureCOMPLETE data: 13CO from Ridge et al. 2006; NH3 from Pineda et al. 2010

weak 13COstrong 13CO

weak NH3 strong NH3

Position-Velocity structure of the B5 region in Perseus

weak 13CO

strong 13CO

weak NH3strong NH3

STRONG Evidence for ”Velocity Coherence” in Dense Cores

GBT NH3 observations of the B5 core (Pineda et al. 2010)

greyscale shows NH3 velocity dispersion, arrows show gradient in dispersion

non-thermal line width constant in core, then jumps abruptly to turbulent values

NH3 .Benson & Myers 1989

R.A.

Dec.

vLSR

many thanks to Jaime Pineda & Jens Kauffmann for this figureCOMPLETE data: 13CO from Ridge et al. 2006; NH3 from Pineda et al. 2010

weak 13COstrong 13CO

weak NH3 strong NH3

Position-Velocity structure of the B5 region in Perseus

But then...

Pineda et al. 2011

we found sub-structure

gold contour shows

“coherent” core

but maybe it’s different?

isothermal, hydrostatic filaments, not turbulent ones?

Pineda et al. 2011

But what if filaments continuE across “core” boundaries?!

blue =VLA ammonia (high-density gas); green=GBT ammonia (lower-res high-density gas); red=Herschel 250 micron continuum (dust)

Goodman, Chen, Offner & Pineda 2014 in prep.

B5-ish Simulation (no Magnetic field)

Offner (priv. comm.) 2014

Pineda, Offner, Parker, Arce, Goodman, Caselli, Fuller, Bourke & Corder 2014, submitted to Nature (do not reproduce without permission)

shhh...We now also know that b5 is forming a bound cluster

[B5 image removed to comply with Nature “embargo” rules.]

Galaxy

Star Cluster

Molecular Cloud Complex

Star-Forming “Globule”

Nessie B5

Galaxy

Star Cluster

Molecular Cloud Complex

Star-Forming “Globule”

Nessie

Once upon a time (2012), in an enchanted castle (in Bavaria)

...at a conference about “The Early Phases of Star Foration”

Andi Burkert asked a question:

Is Nessie “parallel to the Galactic Plane”?

No one knew.

The Milky Way “Galactic Plane”

“Is Nessie Parallel to the Galactic Plane?”

Yes but why not at Zero of Latitude (b=0)?

Where are we, really?“IAU Milky Way”, est. 1959

True Milky Way, modern

Sun is ~75 light years

“above” theIAU Milky Way

Plane

Galactic Center is

~20 light yearsoffset from the

IAU Milky Way Center

+ =The Galactic Plane is not quite

where you’d think it is when you look at the sky

[Blaauw et al. 1959]

Galactic Longitude (l)

Gal

actic

Lat

itude

(b)

no tilt of plane

with tilt

Galactic Longitude (l)

Gal

actic

Lat

itude

(b)

no tilt of plane

with tilt

In the plane! And at distance of spiral arm!

Galactic Longitude (l)

Gal

actic

Lat

itude

(b)

no tilt of plane

with tilt

Galactic Longitude (l)

Gal

actic

Lat

itude

(b)

no tilt of plane

with tilt...eerily precisely...How do we know

the velocities?

A full 3D skeleton?

(flipped) image of IC342 from Jarrett et al. 2012; WISE Enhanced Resolution Galaxy Atlas simulations courtesy Clare Dobbs

state of the art simulation 2013

100 pc

Smith et al. 2014, using AREPO

New!

2014 Simulation

+20 pc

-20 pc

100 pc

Smith et al. 2014, using AREPO

New!

2014 Simulation

+20 pc

-20 pc

AuAuthorea

3D

2D

Data Abstraction

Statistics

0

25

50

75

100

Linked Views of High-dimensional Data

figure, by M. Borkin, reproduced from Goodman 2012, “Principles of High-Dimensional Data Visualization in Astronomy”

John Tukey

gluemultidimensional data exploration

Nessie in Glue gluemultidimensional data exploration

Video courtesy of Chris Beaumont, Lead Glue Architect

gluemultidimensional data exploration

WorldWide  Telescope

WorldWide  Telescope

Communication

Cognition

*“Language” includes words & math

DataLanguage*

Pictures

Paper of the Future

https://www.authorea.com/users/23/articles/8762/_show_article

WorldWide  Telescope

gluemultidimensional data explorationAu

Authorea

data, CLUMPFIND typically finds features on a limited range of scales,above but close to the physical resolution of the data, and its results canbe overly dependent on input parameters. By tuning CLUMPFIND’stwo free parameters, the same molecular-line data set8 can be used toshow either that the frequency distribution of clump mass is the sameas the initial mass function of stars or that it follows the much shal-lower mass function associated with large-scale molecular clouds(Supplementary Fig. 1).

Four years before the advent of CLUMPFIND, ‘structure trees’9

were proposed as a way to characterize clouds’ hierarchical structure

using 2D maps of column density. With this early 2D work as inspira-tion, we have developed a structure-identification algorithm thatabstracts the hierarchical structure of a 3D (p–p–v) data cube intoan easily visualized representation called a ‘dendrogram’10. Althoughwell developed in other data-intensive fields11,12, it is curious that theapplication of tree methodologies so far in astrophysics has been rare,and almost exclusively within the area of galaxy evolution, where‘merger trees’ are being used with increasing frequency13.

Figure 3 and its legend explain the construction of dendrogramsschematically. The dendrogram quantifies how and where local max-ima of emission merge with each other, and its implementation isexplained in Supplementary Methods. Critically, the dendrogram isdetermined almost entirely by the data itself, and it has negligiblesensitivity to algorithm parameters. To make graphical presentationpossible on paper and 2D screens, we ‘flatten’ the dendrograms of 3Ddata (see Fig. 3 and its legend), by sorting their ‘branches’ to notcross, which eliminates dimensional information on the x axis whilepreserving all information about connectivity and hierarchy.Numbered ‘billiard ball’ labels in the figures let the reader matchfeatures between a 2D map (Fig. 1), an interactive 3D map (Fig. 2aonline) and a sorted dendrogram (Fig. 2c).

A dendrogram of a spectral-line data cube allows for the estimationof key physical properties associated with volumes bounded by iso-surfaces, such as radius (R), velocity dispersion (sv) and luminosity(L). The volumes can have any shape, and in other work14 we focus onthe significance of the especially elongated features seen in L1448(Fig. 2a). The luminosity is an approximate proxy for mass, suchthat Mlum 5 X13COL13CO, where X13CO 5 8.0 3 1020 cm2 K21 km21 s(ref. 15; see Supplementary Methods and Supplementary Fig. 2).The derived values for size, mass and velocity dispersion can then beused to estimate the role of self-gravity at each point in the hierarchy,via calculation of an ‘observed’ virial parameter, aobs 5 5sv

2R/GMlum.In principle, extended portions of the tree (Fig. 2, yellow highlighting)where aobs , 2 (where gravitational energy is comparable to or largerthan kinetic energy) correspond to regions of p–p–v space where self-gravity is significant. As aobs only represents the ratio of kinetic energyto gravitational energy at one point in time, and does not explicitlycapture external over-pressure and/or magnetic fields16, its measuredvalue should only be used as a guide to the longevity (boundedness) ofany particular feature.

Self-gravitatingleaves

CLUMPFIND segmentation

vz

x (RA)

y (d

ec.)

vz

x (RA)

y (d

ec.)

c

d

8

6

4

2

0

8

6

4

2

0

T mb

(K)

T mb

(K)

Self-gravitatingstructures

All structure

a b

Click to rotate

Figure 2 | Comparison of the ‘dendrogram’ and ‘CLUMPFIND’ feature-identification algorithms as applied to 13CO emission from the L1448region of Perseus. a, 3D visualization of the surfaces indicated by colours inthe dendrogram shown in c. Purple illustrates the smallest scale self-gravitating structures in the region corresponding to the leaves of thedendrogram; pink shows the smallest surfaces that contain distinct self-gravitating leaves within them; and green corresponds to the surface in thedata cube containing all the significant emission. Dendrogram branchescorresponding to self-gravitating objects have been highlighted in yellowover the range of Tmb (main-beam temperature) test-level values for whichthe virial parameter is less than 2. The x–y locations of the four ‘self-gravitating’ leaves labelled with billiard balls are the same as those shown inFig. 1. The 3D visualizations show position–position–velocity (p–p–v) space.RA, right ascension; dec., declination. For comparison with the ability ofdendrograms (c) to track hierarchical structure, d shows a pseudo-dendrogram of the CLUMPFIND segmentation (b), with the same fourlabels used in Fig. 1 and in a. As ‘clumps’ are not allowed to belong to largerstructures, each pseudo-branch in d is simply a series of lines connecting themaximum emission value in each clump to the threshold value. A very largenumber of clumps appears in b because of the sensitivity of CLUMPFIND tonoise and small-scale structure in the data. In the online PDF version, the 3Dcubes (a and b) can be rotated to any orientation, and surfaces can be turnedon and off (interaction requires Adobe Acrobat version 7.0.8 or higher). Inthe printed version, the front face of each 3D cube (the ‘home’ view in theinteractive online version) corresponds exactly to the patch of sky shown inFig. 1, and velocity with respect to the Local Standard of Rest increases fromfront (20.5 km s21) to back (8 km s21).

Inte

nsity

leve

l

Local max

Local max

Local max

Merge

Merge

Leaf

Leaf

Leaf

Bra

nch

Trun

k

Test level

Figure 3 | Schematic illustration of the dendrogram process. Shown is theconstruction of a dendrogram from a hypothetical one-dimensionalemission profile (black). The dendrogram (blue) can be constructed by‘dropping’ a test constant emission level (purple) from above in tiny steps(exaggerated in size here, light lines) until all the local maxima and mergersare found, and connected as shown. The intersection of a test level with theemission is a set of points (for example the light purple dots) in onedimension, a planar curve in two dimensions, and an isosurface in threedimensions. The dendrogram of 3D data shown in Fig. 2c is the directanalogue of the tree shown here, only constructed from ‘isosurface’ ratherthan ‘point’ intersections. It has been sorted and flattened for representationon a flat page, as fully representing dendrograms for 3D data cubes wouldrequire four dimensions.

LETTERS NATURE | Vol 457 | 1 January 2009

64 Macmillan Publishers Limited. All rights reserved©2009

Alyssa A. Goodman

Harvard-Smithsonian Center for Astrophysics @AAGIE

Seeing

Stars form

the Milky Way

in

A Rotating (Spiral) Galaxy Observed from its Outskirts...

velocity along line of sight

distance

velocity along line of sight

distance

back