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arXiv:astro­ph/0207156
v2
14
Jul
2002
Draft version July 16, 2002
Preprint typeset using L A T E X style emulateapj v. 16/07/00
NE2001. I. A NEW MODEL FOR THE GALACTIC DISTRIBUTION
OF FREE ELECTRONS AND ITS FLUCTUATIONS
J. M. Cordes
Astronomy Department and NAIC, Cornell University, Ithaca, NY 14853
cordes@spacenet.tn.cornell.edu
T. Joseph W. Lazio
Naval Research Lab, Code 7213, Washington, D.C. 20375-5351
Joseph.Lazio@nrl.navy.mil
Draft version July 16, 2002
ABSTRACT
We present a new model for the Galactic distribution of free electrons. It (a) describes the distribution
of the free electrons responsible for pulsar dispersion measures and thus can be used for estimating the
distances to pulsars; (b) describes large-scale variations in the strength of uctuations in electron density
that underly interstellar scattering; (c) can be used to interpret interstellar scattering and scintillation
observations of Galactic objects and of extragalactic objects, such as intrinsically compact AGNs and
Gamma-ray burst afterglows; and (d) serves as a preliminary, smooth spatial model of the warm ionized
component of the interstellar gas. This work builds upon and supercedes the Taylor & Cordes (1993)
model by exploiting new observations and methods, including (1) a near doubling in the number of lines
of sight with dispersion measure or scattering measurements; (2) a substantial increase in the number and
quality of independent distance measurements or constraints; (3) improved constraints on the strength
and distribution of scattering in the Galactic center; (4) improved constraints on the (Galactocentric)
radial distribution of free electrons; (5) redenition of the Galaxy's spiral arms, including the in uence
of a local arm; (6) modeling of the local interstellar medium, including the local hot bubble identied in
X-ray and Na I absorption measurements; and (7) an improved likelihood analysis for constraining the
model parameters. For lines of sight directed out of the Galactic plane, the new model yields substantially
larger values for pulsar dispersion measures, expect for directions dominated by the local hot bubble.
Unlike the TC93 model, the new model provides suôcient electrons to account for the dispersion measures
of the vast majority of known, Galactic pulsars. The new model is described and exemplied using plots
of astronomically useful quantities on Galactic-coordinate grids. Software available on the Internet is
also described. Future observations and analysis techniques that will improve the Galactic model are
outlined.
Subject headings: distance measurements, interstellar medium, electron density, pulsars
1. introduction
Radio wave propagation measurements provide unique
information about the magetoionic component of the
interstellar medium (ISM). Pulsars are important probes
because they emit short duration radio pulses that are
modied by intervening plasma and also because they
are highly spatially coherent, allowing scattering processes
to signicantly perturb their radiation. Other compact
sources, both Galactic and extragalactic, also serve as
probes of the plasma.
In this rst of a series of papers, we present a new
model for the free electron density of the Galaxy. It is
called \NE2001" because it incorporates data obtained
or published through the end of 2001. A short history
of such models prior to 1993 is given in Taylor &
Cordes (1993, hereafter TC93). Our work builds upon and
supercedes the TC93 model by exploiting new dispersion
and scattering measurements and also by employing new
techniques for modeling. Following Cordes et al. (1991)
and TC93, we model uctuations in electron density as
well as the local mean density.
Since TC93 was written, signicant developments
have taken place that increase the sample of relevant
measurements and indicate shortcomings of the model.
Most importantly, independent distance measurements are
available on about 50% more objects. Some of these
are precise parallax measurements obtained through pulse
timing or interferometric techniques. Others result from
H I absorption measurements combined with a kinematic
rotation model for the Galaxy. Still others arise from
the association of pulsars with supernova remnants and
globular clusters. Distance estimates combined with
dispersion measures quantify the line-of-sight average
electron density. The new distance constraints indicate,
in a minority of cases, that some of the distances derived
from the TC93 model using pulsar dispersion measures
are in error by factor of two or more. However, we point
out that some of the parallax measurements also dier
from previous ones by signicant amounts. Additional
information is provided by the distribution of dispersion
measures for the entirety of available pulsar samples.
The number of such measurements is about double of
that available in 1993. Constraints on the square of the
electron density arise from scattering measurements such
as angular broadening, pulse broadening and diractive
1

2
scintillation measurements. The number of scattering
measurements has almost doubled since 1993.
The TC93 model is awed in several respects, some of
which were apparent even at the time of its development.
First, it provides insuôcient column density at high
Galactic latitudes so that only lower bounds on pulsar
distances can be derived from it. Second, in some
directions, particularly in the fourth quadrant along
tangents to the Carina-Sagittarius and Crux-Scutum
spiral arms, the model provides either too many electrons
for some objects (Johnston et al. 2001) or too few for
others (as discussed below), indicating that the spiral
arms need redenition. Third, in the direction of the
Gum Nebula and Vela supernova remnant, the TC93
model provides too little scattering to account for the
pulse broadening of some pulsars (Mitra & Ramachandran
2001). Fourth, interstellar scintillations of nearby pulsars
have scintillation bandwidths (which measure the column
density of electron density uctuations) that are not well
modeled (Bhat & Gupta 2002). Fifth, similar to the rst
deciency, the calibration between scattering of Galactic
and extragalactic sources needs revision in order to
ascertain the column density of scattering material toward
cosmological sources as compared to that of Galactic
objects outside of but near the apparent boundary of free
electrons.
Our knowledge of the ISM has increased signicantly
from a host of other investigations across the
electromagnetic spectrum. The local ISM, in particular,
is now much better modeled and we incorporate that
information into our model for the free electron density.
The local ISM has been probed using continuum X-ray
measurements and absorption of Na I toward nearby stars.
Other models for the mean electron density have been
presented since TC93. These include the recent work
of Gomez, Benjamin & Cox (2001; hereafter GBC01),
who presented a two-component, axisymmetric model,
not dissimilar in form to that used by Cordes et al.
(1991). The two components have sech 2 (r=R)sech 2 (z=H)
variations with dierent radial and z scales. GBC01 do not
attempt to model electron density uctuations relevant
to scattering and their model is based solely on the 109
objects available to them that have independent distance
estimates. As we demonstrate, though their model is
adequate for nearby pulsars, it grossly underpredicts
the dispersion measures of many distant pulsars at low
Galactic latitudes and some at high latitudes. Their
work underscores the need, demonstrated before by others
(Ghosh & Rao 1992; TC93), for spiral-arm structure in
the free-electron distribution.
Our model uses signicantly larger data samples than
were available for TC93 and makes use of all available
data, including independent distance constraints on pulsar
distances, dispersion and scattering data on pulsars,
and scattering of other Galactic as well as extragalactic
sources. We also incorporate published, multiwavelength
data that allows modeling of the local ISM and of the spiral
arms of the Galaxy.
In this rst paper we present the model and its usage.
In a second paper (Cordes & Lazio 2002b; hereinafter
Paper II) we describe the likelihood analysis and
modeling, alternative model possibilities, and discussions
of particular lines of sight. Future papers will apply
the model to various astronomical and astrophysical
applications. The plan of this paper is as follows. In
x2 we describe the observable quantities that we use to
constrain the NE2001 model parameters. In x3 we describe
the various components of the NE2001 model. In x4
we demonstrate the model's ability to account for the
distances and scattering of pulsars and discuss brie y
astronommical applications of the model. Extensive
discussion of applications of NE2001 is deferred to a later
paper.
In x5 we summarize the results and outline future
prospects for improving the model. These will rest largely
on usage of the Parkes Multibeam Pulsar sample (e.g.
Manchester et al.2001), improved parallax measurements
using very long baseline interferometry, and incorporation
of additional multiwavelength observations into the model
denition and tting. Appendix A describes our model for
the local interstellar medium. Appendix B describes how
to obtain the model as a set of Fortran subroutines and its
implementation in tools available through the World Wide
Web.
2. observables
In constructing the new model, we have used a variety
of measurements, largely at radio wavelengths, but also
including the results of optical and X-ray observations that
probe various aspects of the local ISM. In this section we
summarize the measurements used, dening line-of-sight
integrated quantities in some detail because we provide
expressions and software for estimating them using our
model.
Radio data consist of measurements along particular
lines of sight of propagation eects that are sensitive to
the electron density and its uctuations. In addition,
there are independent distance estimates or constraints
based on a variety of techniques (H I absorption,
interferometric or timing parallaxes, and associations
with globular clusters or supernova remnants). The
wave-propagation data include: (a) dispersion measures
(DMs) of pulsars obtained through measurements of
dierential arrival times; (b) temporal broadening of
pulses from pulsars with large DM caused by multipath
scattering from electron density variations, ôn e ; (c)
scintillation bandwidth measurements of low-DM pulsars;
(d) angular broadening of Galactic and extragalactic
sources caused by scattering from ôn e ; and (e) emission
measures.
In Table 1 we summarize the data sets by specifying the
numbers of each kind of measurement. Figure 1 shows the
relative number of measurments for pulsars.

3
Fig. 1.| Venn diagram showing the number of DM
measurements, independent distance measurements (D), pulse
broadening measurements ( d ; also includes scintillation bandwidth
measurements,
 d , because the two quantities are reciprocally
related; c.f. Eq. 9-10) and the overlap of distance and
pulse-broadening measurements. In addition to pulsar data, there
are 118 angular broadening measurements on non-pulsar Galactic
sources and on 97 extragalactic sources. These numbers include
upper limits. See Table 1 for additional information.
2.1. DM, EM, and Distance Measurements
The data used include 1143 dispersion measures,
DM 
Z D
0
ds n e ; (1)
(Taylor, Manchester, & Lyne 1993; Princeton pulsar
catalog; 1 Parkes Multibeam survey 2 ).
We characterize distance constraints (e.g., from H I
absorption measurements) with an interval [DL ; DU ],
where the lower and upper distance limits, DL ; DU , are
assumed to be hard limits, with uniform probability within
the interval. A compilation with references is given on a
web site. 3 The best distance constraints are from parallax
measurements using pulse timing techniques (e.g. van
Straten et al. 2001) and very-long-baseline interferometry
(Chatterjee et al. 2001; Brisken et al.2002).
The emission measure EM is the integral of the squared
electron density,
EM =
Z D
0
ds n 2
e ; (2)
and thus provides information about uctuations in
electron density and their spatial distribution.
2.2. Radio Wave Scattering Measurements
We use three kinds of measurements: the angular
broadening (\seeing") diameter  d ; the pulse broadening
time,  d , that measures the temporal smearing associated
with the multipath propagation; and the scintillation
bandwidth,
 d , the frequency range over which
diractive scintillations are correlated. All three
observables are sensitive to the detailed distribution along
the line of sight of the scattering strength, owing to
standard geometrical leveraging eects encountered in
optics. Details are summarized below and discussed
thoroughly in Cordes & Rickett (1998, hereafter CR98;
see also Deshpande & Ramachadran 1998).
Angular broadening is characterized as the full-width at
half-maximum (FWHM) of the scattering contribution to
the measured brightness distribution.
The pulse broadening time  d is determined by
deconvolving intrinsic and measured pulse shapes. The
broadening times are roughly the e 1 time of the
pulse broadening function, which is roughly a one-sided
exponential (e.g., Cordes & Rickett 1998; Lambert &
Rickett 1999).
The scintillation bandwidth (
 d ) is estimated as
the half-width at half maximum of the autocorrelation
function of intensity along the frequency-lag axis (Cordes
1986; Johnston, Nicastro, & Koribalski 1998; Bhat, Rao,
& Gupta 1999). The \uncertainty" relation between  d
and
 d may be written as 2
 d  d = C 1 , where C 1
is a constant that depends on the wavenumber spectrum
and on the large-scale distribution of scattering material
along the line of sight (CR98). We use C 1 = 1:16, the
value appropriate for a uniform medium and having a
Kolmogorov wavenumber spectrum.
2.2.1. Density Spectrum and Scattering Measure
We assume that ôn e / n e but with a proportionality
constant that varies between dierent components of the
Galactic plasma. Also, we adopt a power-law wavenumber
spectrum for ôn e ,
P ôn e (q) = C 2
n q  ;
2
` 0
 q  2
` 1
; (3)
` 1 and ` 0 are the inner and outer scales of the uctuations
in ôn e and C 2
n is the spectral coeôcient (the \level of
turbulence"). We take  = 11=3, the \Kolmogorov"
spectrum because it is appropriate for many lines of sight
(e.g. Lee & Jokipii 1976; Armstrong, Rickett & Spangler
1995). We point out that there are numerous caveats on
this choice of , both empirical and theoretical, which we
discuss in Paper II. 4 The scattering measure is the path
integral of C 2
n :
SM 
Z D
0
ds C 2
n : (4)
Dierent observables correspond to dierent LOS
weightings for C 2
n , yielding dierent eective values for
1
http://pulsar.princeton.edu/pulsar/catalog.shtml
2
http://www.atnf.csiro.au/research/pulsar/pmsurv/
3
http://www.astro.cornell.edu/shami/psrvlb/parallax.html
4
Brie y, some observable quantities scale with frequency or distance dierently than what is expected for a simple Kolmogorov model. Estimates
of SM based on measured quantities may accordingly be in error. However, these errors are no more than a factor of a few and can be compared
with line-of-sight variations of several orders of magnitude in SM that we aim to model.

4
the scattering measure. Following Cordes et al. 1991
and TC93, we dene expressions for the eective SM if
a uniform medium is assumed:
(1) For measurements of angular diameters of
extragalactic sources,
SM ;x = SM: (5)
(2) For angular diameters of Galactic sources,
SM ;g = 3
Z D
0
ds (1 s=D) 2 C 2
n ; (6)
where the integration is from observer to source.
(3) For pulse broadening and scintillation
measurements,
SM  = 6
Z D
0
ds (s=D)(1 s=D)C 2
n : (7)
With these expressions, the true SM for a statistically
uniform medium would be estimated correctly. For
nonuniform media, the results are only approximations to
the true SM.
Under the same assumption of a uniform medium, we
calculate observables in terms of these weighted SMs using
(with  in GHz and SM in units dened above):
 d =  11=5 
8
> <
> :
128 mas SM 3=5
;x Extragalactic Sources
71 mas SM 3=5
;g Galactic Sources:
(8)
The pulse broadening time and scintillation bandwidth are
given by
 d = 1:10 ms SM 6=5
  22=5 D (9)

 d = 168 Hz SM 6=5
  22=5 (C 1 =1:16)D 1 : (10)
The coeôcient in Eq. 10 is the same as Eq. 48 of Cordes
& Lazio (1991) if, as assumed there, C 1 = 1:53, the value
appropriate for a medium with a square-law structure
function. However, C 1 = 1:16 applies for a Kolmogorov
medium that is statistically homogeneous and which we
consider to be a better default model than a medium with
square-law structure function.
Following Cordes et al. (1991) and TC93, we relate C 2
n
to the local mean electron density inside ionized clouds n e
and calculate line of sight integrals taking into account the
volume lling factor  of those clouds and cloud-to-cloud
variations of the internal density. We use n e = n e to
denote the local spatially-averaged density. We relate SM
to DM using
d DM= n e ds; (11)
d SM = CSM F n 2
e ds ; (12)
where F is a uctuation parameter,
F =  2  1 ` 2=3
0 ; (13)
that depends on the fractional variance inside clouds,
 2 = h(ôn e ) 2 i=n e
2 , the normalized second moment of
cloud-to-cloud uctuations in n e ,  = hn e
2 i=hn e i 2 , and
the outer scale ` 0 expressed in parsec units. We dene the
constant, CSM = [3(2) 1=3 ] 1 Cu , where the scale factor
Cu = 10:2 m 20=3 cm 6 yields SM in the (unfortunately)
conventional units of kpc m 20=3 for n e in cm 3 , ds in
kpc, and ` 0 in AU.
The emission measure may be expressed as
dEM = [3(2) 1=3 ]` 2=3
0  2 (1 +  2 ) dSM
= 544:6 pc cm 6 ` 2=3
0  2 (1 +  2 ) dSM: (14)
For completeness, we provide expressions for the
free-free optical depth, the related intensity of H
emission, and the transition frequency between weak
and strong scattering. These quantities are evaluated
using subroutines provided in the software described in
Appendix B. The free-free optical depth is   = 5:47 
10 8  2 T 3=2
4 g(; T ) EM ( in GHz, T 4 = temperature
in units of 10 4 K, and g = Gaunt factor  1) (Rybicki &
Lightman 1979, p. 162). Relating EM to SM, we nd that
the implied free-free optical depth is
  = 10 4:53  2 T 3=2
4  2 ` 2=3
0  2 (1 +  2 )SM: (15)
The intensity of H emission (in Rayleighs) in terms of
SM (Haner, Reynolds, & Tufte 1998, Eq. 1) is
I H = 198RT 0:9
4  2 (1 +  2 )` 2=3
0 SM: (16)
The expression for the transition frequency between
weak and strong scattering (Rickett 1990) used in the
software discussed in Appendix B is
 trans = 318 GHz  10=17 SM 6=17 D 5=17
e ; (17)
where D e is now an eective distance to the scattering
medium and the factor   1 allows scaling of one's
preferred denition for the Fresnel scale (e.g.  = (2) 1=2
is commonly used, decreasing the coeôcient by a factor
0.58). For spherical waves embedded in a medium with
constant C 2
n , the coeôcient is multiplied by a factor
( 1) 2=(+2) and becomes 225 GHz. Thus, for nearby
pulsars with log SM  4 and D  0:1 kpc,  trans  5
GHz.
3. galactic model for electron density
3.1. Basic Structure
As in TC93, we use a right-handed coordinate system
x = (x; y; z) with its origin at the Galactic center, x axis
directed parallel to l = 90 ô , and y axis pointed toward
l = 180 ô . The Galactocentric distance projected onto the
plane is r = (x 2 + y 2 ) 1=2 .
The electron density is the sum of two axisymmetric
components and a spiral arm component, combined with
terms that describe specic regions in the Galaxy. Table 2
gives the details of the functional forms, which we describe
brie y here.
We have distinguished terms that represent the local
ISM (n lism ), the large scale distribution (n gal ), the
Galactic center (nGC ), and individual clumps (n clumps )
and voids (n voids ). The large scale distribution, n gal ,
consists of two axisymmetric components, a thick (1) and
thin (2) disk, and spiral arms. The weight factor w lism =
0; 1 switches o or on the local ISM component and
switches on or o the smooth, large scale components of
the model (and also the Galactic-center component, nGC ).
Superposed with the large-scale and local-ISM components
are \clumps" of excess electron density that we infer from
the database of measurements as outliers from the smooth
model. They most likely correspond to individual H II

5
regions or portions of ionized shells surrounding supershell
regions. Finally, we also include \voids" that generally are
regions of lower than ambient density which are mutually
exclusive of all components (except clumps) rather than
superposing with them. Voids override all components
other than clumps and are required to account for the
distances of some pulsars.
Associated with each component in the model is a
separate value of the uctuation parameter, F . Details
about the functions used are given in Table 2 and
summarized in sections below. As in TC93, we use
sech 2 (jzj=H) for the z dependences of most components
to produce a \rounder" variation at z = 0 than an
exponential dependence / exp(jzj=H). Both the
exponential and sech 2 functions integrate to the same
asymptotic value (H) and have nearly equal 1=e locations.
Table 3 gives parameter values for the large scale
parameters and compares them, where appropriate, with
those of the TC93 model. The best-tting parameters were
found by an iterative likelihood analysis that is similar to
that used in TC93 but with a number of improvements in
the details of the tting (Paper II).
Fig. 2.| Electron density corresponding to the best t model
plotted as a grayscale with logarithmic levels on a 3030 kpc
x-y plane at z=0 and centered on the Galactic center. The most
prominent large-scale features are the spiral arms, a thick, tenuous
disk, a molecular ring component. A Galactic center component
appears as a small dot. The small-scale, lighter features represent
the local ISM and underdense regions required for by some lines
of sight with independent distance measurements. The small dark
region embedded in one of the underdense, ellipsoidal regions is the
Gum Nebula and Vela supernova remnant.
Fig. 3.| Top: Electron density plotted against Galactocentric
radius in the direction from the Galactic center through the Sun
for the various large-scale components. Bottom : Electron density
plotted against jzj. For the inner Galaxy (thin disk) component,
the prole is for r = 3:5 kpc, the peak of the annular component.
For the thick disk component, the cut is at r = R . The spiral arm
cut is at (x; y) = 0; 10:6 kpc.
3.1.1. Outer, Thick Disk Component
The outer, thick disk component is responsible for the
DMs of globular cluster pulsars and the low-frequency
diameters of high-latitude extragalactic sources (e.g., as
inferred from interplanetary scintillation measurements).
In TC93 this component was determined to have a scale
height of roughly 1 kpc with a Galactocentric radial scale
length of roughly 20 kpc. However, the data available for
TC93 did not allow a rm constraint on the Galactocentric
scale length; scale lengths as large as 50 kpc were also
allowed by the data. Through measurements of scattering
of extragalactic sources toward the Galactic anticenter,
Lazio & Cordes (1998a,b) inferred a scale length  20
kpc and a functional form that truncates at this scale.
Alternatives are discussed in Paper II.
3.1.2. Inner, Thin Disk Component
An inner Galaxy component (n 2 ) consisted of a
Gaussian annulus in TC93. Data available to TC93 could
not distinguish a lled Gaussian form in Galactocentric
radius from an annular form, but the latter was chosen
for consistency with the molecular ring seen in CO (e.g.,
(Dame et al. 1987)). We adopt the same form in our
model; in Paper II we discuss alternatives to the annular
form.
3.1.3. Spiral Arms
Is spiral arm structure required by pulsar dispersion
measures and distance constraints? TC93 argue that it
is by referring to the asymmetry of the distribution of
DM vs. Galactic longitude (c.f. their Figure 2). The same
asymmetry appears in the larger sample now available
(Paper II). A direct demonstration can be made by
calculating the DM decit for individual pulsars for various
electron-density models, dened as the dierence between

6
the model DM integrated to innite distance and the
pulsar DM:
DM = DM DM1(model). In Figure 4
we show
DM plotted against Galactic coordinates for
the axisymmetric model of GBC01. There is a large
number of DM decits, both along the Carina-Sagittarius
arm (`  65 ô  10 ô ) and extending (at low latitudes)
continuously to ` = +60 ô . This broad longitude range
encompasses all of the spiral arms interior to the solar
circle and the molecular ring. GBC01 identify the need
for spiral structure in similar directions by comparing
predicted and actual DMs for the much smaller data set
they considered. The large number of decits we identify
with their model (183 out of 1143 objects) is a much
stronger signal for spiral structure. Spiral arm structure
appears to be mandatory in any electron density model
that aspires to realism.
The TC93 model, though containing spiral structure,
also has insuôcient DM (Figure 5) along the
Carina-Sagittarius arm and at high latitudes. The
low latitude decits are removed in the new model
by redening and retting the spiral arms while the
high latitude decits are removed by retting the outer,
thick-disk component and the spiral arm scale heights.
Fig. 4.| Plot of DM decit,
DM = DM DM1(GBC01)
against Galactic coordinates, where DM1(GBC01) is the maximum
DM obtained by integrating the axisymmetric model of Gomez,
Benjamin & Cox (2001; GBC01) to innite distance. Longitudes
0 ô - 180 ô are on the left. Only positive residuals are shown, yielding
183 objects out of the 1143 pulsars in the combined Princeton and
(public) Parkes Multibeam samples. The lled circles (going from
smallest to biggest) represent
DM < 50, 50 <
DM  200, and
200 <
DM  400 pc cm 3 . The open circles are for
DM >
400 pc cm 3 . Ellipses designate pulsars in the Large and Small
Magellanic Clouds and the Vela supernova remnant region. The
rectangular region designates objects aected by the Gum Nebula.
The GBC01 model is clearly decient in a number of directions,
including the cluster of objects near (`; b) = 65 ô  10 ô ; 0 ô , which
indicates insuôcient column density along the Carina-Sagittarius
spiral arm. A large number of objects have
DM > 0 from
longitudes 65 ô to +60 ô , indicating the need for spiral structure
in their model like that in TC93 and in the present model.
Fig. 5.| Plot of DM decit,
DM = DM DM1(TC93)
against Galactic coordinates, where DM1(TC93) is the maximum
DM obtained by integrating the TC93 model to innite distance.
The format is the same as in Figure 4. The TC93 model is clearly
decient in a number of directions, 136 out of 1143 pulsars having
values of DM too large to be accounted for, including the cluster
of objects near (`; b) = 65 ô  10 ô ; 0 ô , which indicates insuôcient
column density along the Carina-Sagittarius spiral arm. The new
model corrects these deciencies.
The spiral arm centroids in the new model are dened
as logarithmic spirals with perturbed locations similar to
those used in TC93. Centroid parameters are similar to
those of Wainscoat et al. (1992). The spiral structure is
similar to that proposed by Ghosh & Rao (1992) and also
described by Vallee (1995, 2002). We have maintained
usage of a Sun-Galactic Center distance of 8.5 kpc, the
IAU recommended value, although recent work favors a
smaller distance,  7:1  0:4 kpc (e.g., Reid 1993; Olling
& Merreeld 1998) 5 . Details are given in Paper II. The
new model includes a local (Orion-Cygnus) spiral arm.
Also, each arm has an individual centroid electron density,
width, scale height and F parameter. Figure 6 shows the
locations of spiral arms as dened in TC93 and as modied
by us.
We emphasize that the spiral arm components in our
model, like those in TC93, are modeled as overdense
regions. Astrophysically, however, the enhanced star
formation in spiral arms will produce underdensities as
well as overdensities, as has been demonstrated by the
identication of supershells. Though we have adopted
spiral arms as overdense regions, to account for DM
and SM we have had to introduce ellipsoidal underdense
perturbations (\voids") in particular directions (x3.6).
5
In the next version of the model, we will explore usage of a smaller Sun-GC distance.

7
Perseus
Outer
Fig. 6.| Solid lines: spiral model of the Galaxy used in TC93,
dened according to work by Georgelin & Georgelin (1976), modied
as in TC93. Dashed lines: a four-arm logarithmic spiral model
combinedwith a local (to the Sun) arm using parameters from Table
1 of Wainscoat et al. (1992), but modied so that the arms match
some of the features of the arms dened in TC93. The names of the
spiral arms, as in the astronomical literature, are given. A + sign
marks the Galactic center and the Sun is denoted by .
3.2. Local ISM (LISM)
We model the local ISM in accord with DM and SM
measurements of nearby pulsars combined with parallax
measurements and guided by H observations that provide
estimates of EM. Observations and analysis by Heiles
(1998), Toscano et al. (1999 and references therein),
Snowden et al. (1998), Ma  iz-Apell  iz (2001) and others
(see Appendix A) suggest the presence of four regions
of low density near the Sun: (1) a local hot bubble
(LHB) centered on the Sun's location; (2) the Loop I
component (North Polar Spur) that is long known because
of its prominence in nonthermal continuum maps; (3)
a local superbubble (LSB) in the third quadrant; and
(4) a low density region (LDR) in the rst quadrant.
Additional features have been identied by Heiles (1998)
but the available lines of sight to pulsars appear to not
require their inclusion in our model. Bhat et al. (1999)
explicitly tted for parameters of the LHB using pulsar
measurements and a model having a low-density structure
surrounded by a shell of material that produces excess
scattering. Some of the parallax distances used by Toscano
et al. (1999) have been revised, in some cases substantially,
implying lower densities in the third quadrant than they
inferred.
Appendix A describes the mathematical models used
for the four regions. Table 4 lists the parameters of the
local ISM model and their values based on the tting we
describe in Paper II.
­0.5 0 0.5
8
8.5
9
9.5
X (kpc)
Fig. 7.| Projection onto the Galactic (X-Y) plane of the
four local interstellar medium components, LHB, LSB, LDR and
Loop I along with the clumps dening the Gum Nebula and
the Vela supernova remnant. The LSB and LDR are the large
ellipsoids, the LHB is the annular hatched region, and the LHB
is the small ellipsoid containing the Sun (). Filled circles show
the DM-predicted locations using NE2001 of those pulsars having
parallax measurements. The lines plotted through each point (not
all are visible) represent the allowed distance ranges from the
parallax measurements. The three unlabeled points closest to the
Sun are pulsars B1237+25, J0437 4715, and B1133+16 in order of
increasing projected distance from the Sun.
3.3. Galactic Center (GC) Component
A new component is the region in the Galactic center
that is responsible for scattering of Sgr A  and OH masers
(van Langevelde et al. 1992; Rogers et al. 1994; Frail
et al. 1994). Typical diameters, scaled to 1 GHz, are
approximately 1 00 , roughly 10 times greater than that
predicted by TC93, even with the general enhancement
of scattering toward the inner Galaxy in that model.
The model of the region is based on work by Lazio &
Cordes (1998c,d) who used angular sizes of extragalactic
sources viewed through Galactic center to localize and
model the region.
We use a slightly altered version of the axisymmetric
model of Lazio & Cordes (1998d). We use a scale height
HGC  0:026 kpc and slightly smaller radial scale, RGC 
0:145 kpc. In addition we have oset the center of the
distribution by (x GC ; z GC ; z GC ) = ( 0:01; 0; 0:02) kpc.
The oset ellipsoid exponential is truncated to zero for
arguments smaller than 1. A value FGC  6  10 4
produces SM values needed to account for the scattering
diameters of Sgr A  and the OH masers.
3.4. Gum Nebula and Vela Supernova Remnant
In TC93 a large region was included which perturbed the
dispersion measures of pulsars viewed through the Gum
Nebula but did not in uence the scattering. Since the
writing of TC93, investigations of the Vela pulsar and
other pulsars indicate that scattering is large within a
region of at least 16 degrees diameter centered roughly on
the direction of the Vela pulsar (Mitra & Ramachandran

8
2001). We have modeled the Gum/Vela region based
on the scattering measurements and also on the fact
that enhanced, local mean electron density is required to
account for the dispersion measures and/or distances of
ve objects.
We model the direction toward the Gum Nebula with an
overlapping pair of spherical regions describing the Gum
Nebula itself and another for the immediate vicinity of
the Vela pulsar. These are included in the list of \clumps"
that enhance the electron density and F (see below).
3.5. Regions of Intense Scattering (\Clumps")
In addition to regions that perturb the scattering
of the Vela pulsar and other pulsars near it and the
Galactic center, other regions of intense scattering must
exist to account for the large angular diameters and/or
pulse broadening seen toward a number of Galactic
and extragalactic sources. We dene \clumps" as
regions of enhanced n e or F or both and identify
them by iterating with preliminary ts to the smooth
components of the electron-density model (e.g., the
thin and thick disk components and the spiral arms).
Clumps are eectively manifestations of the Galaxy's
mesoscale structure not modeled adequately by the
assumed large-scale components.
We model clumps with thickness
s  D, and we
use parameters n e c ; F c and d c (electron density inside the
clump, uctuation parameter, and distance from Earth).
The implied increments in DM and SM are
DM c = n e c
s
SM c = CSM F c n 2
e c

s = 10 5:55 DM 2
c F c =
s kpc ; (18)
where the last equality holds for DM and SM in standard
units. Equation 18 implies that relatively modest
contributions to DM can produce large changes in SM if
the clump is small and uctuation parameter large. For
example, DM c = 10 pc cm 3 , F c = 1 and
s = 0:02 kpc
yield SM c = 0:014 kpc m 20=3 . For a pulsar 1 kpc away,
the clump would perturb DM and the resultant distance
estimate by perhaps 30% while SM would increase by
about a factor of 100. Thus pulsars which have anomalous
scattering relative to the smooth model can, in many
cases, be well modeled with only small perturbations to
the DM predictions of the model. This also means that
the model is expected to be much better for distance and
DM estimation than for scattering predictions.
Table 5 lists clumps needed to account for the scattering
toward specic AGNs that have enhanced scattering; most
are in the Cygnus region. Table 6 lists clumps needed to
account for the scattering of non-pulsar Galactic sources;
all are OH masers except for the Galactic continuum
source Cyg X-3. For these non-pulsar sources, only the
scattering is measured and so the clump perturbation,
SM c , is the most robustly determined clump parameter.
We adopt reasonable | but non-unique | values for the
clump distance, radius, and uctuation parameter which
imply a value for the clump's DM c , which we also tabulate.
For pulsar lines of sight, on the other hand, the clump's
contributions to both DM and SM are constrained if a
scattering measurement exists. Included in Table 7 are
those clumps that have DM c > 20 pc cm 3 or SM c > 1
kpc m 20=3 . Operationally, the model includes additional,
weaker clumps that bring the scattering and distances into
accord with observations. The software implementation of
the model (see below) includes these weaker clumps as well
as those listed in Tables 5{7.
In most cases our tting procedure does not provide
unambiguous distance estimates for the clumps. The
distances listed in Tables 5{7 are \plausible" distance
estimates for clumps, locating them, for instance, in or
near spiral arms or in specic HII complexes that contain
molecular masers.
3.6. Regions of Low Density (\Voids")
We found that some pulsar distance constraints could
not be satised using the previously dened structures
without recourse to placement of a low-density region
along the line of sight. We call these regions \voids"
although they simply represent, typically, regions with
lower-than-ambient density. By necessity, they take
precedence over all other components (except clumps),
which we eect by usage of a void weight parameter,
w voids = 0; 1, that operates similarly to w lism . The
mathematical form is given in Table 2. We use elliptical
gaussian functions with semi-major and semi-minor axes
a; b; c and a rotation angle  z about the z axis. Table 8 lists
the properties of all voids used in the current realization
of the model.
4. model performance
The quality of the model can be evaluated on the basis
of how well it estimates the distances and scattering of
pulsars with appropriate measurements.
Figure 7 shows nearby pulsars with parallax distance
ranges plotted as lines projected onto the Galactic plane.
Extrapolations of these lines intersect the Sun's location.
The lled circles indicate the distance estimated with
NE2001. As can be seen, distance estimates for most of the
nearby pulsars are acceptable. A uniform medium or one
with only large-scale structure (i.e. one without the Gum
Nebula, Vela supernova remnant, and LISM components)
would do much more poorly.
Figure 8 shows a projection onto the Galactic plane
of distance ranges and model estimates for those pulsars
having independent distance constraints and Galactic
latitudes, jbj < 5 ô . Only six objects have model distances
that fall outside the distance range. As commented upon
in Paper II two objects have questionable lower distance
bounds from H I absorption. The other four lines of
sight are toward pulsars in low-latitude globular clusters
toward the Galactic center. Also shown in the gure along
the perimeter (as lled circles) are objects for which the
TC93 model could provide only a lower distance bound.
These occur in the directions along the Carina-Sagittarius
spiral arm, through the Gum Nebula, and toward the inner
Galaxy near `  20 ô . The new model accounts for the
DMs of these objects by having larger electron densities
along the relevant lines of sight.
Figure 9 shows the DM-calculated distance plotted
against independent distance constraints, [DL ; DU ]. Model
estimates are bracketed by [DL ; DU ] in the large majority
of cases (90 of 120 total, though not all are plotted and
some of the 30 non-bracketed cases are multiple pulsars
in the same globular cluster). For most cluster pulsars,

9
the distance is underestimated because the cluster is well
beyond the electron layer of the Galaxy.
Figure 10 quanties the model's ability to account
for the scattering of known objects as a histogram of
the quantity r scatt = (predicted scattering)/(measured
scattering). The large peak centered on r scatt = 1 indicates
that most lines of sight are well modeled, though some
outliers remain. The outliers are largely globular cluster
pulsars whose distances are poorly estimated by the model
and a few objects whose lines of sight are dominated by the
local ISM. It should be emphasized that many of the small
scale features in the present model were introduced to yield
a good prediction of the scattering, so the histogram is
largely a manifestation of our modeling approach. The
predictive aspect of the model will be tested when it is
applied to objects on which new scattering measurements
are obtained.
Fig. 8.| Distances calculated from model NE2001 projected onto
the Galactic plane for objects with jbj < 5 ô . In the interior of the
box, plotted lines indicate independent distance ranges, [D L ; DU ],
open circles denote \good" ts (i.e. model distances ^
D that are
within the empirical range) while the six lled circles designate
pulsars where the model distance underestimates the minimum
empirical distance. Two of these objects (B1930+22, ` = 57:4 ô ,
b = 1:6 ô ; J1602 5100, ` = 29:3 ô , b = 1:3 ô ) have uncertain
lower distance bounds from HI absorption while the other four are
globular cluster pulsars at low latitudes toward the Galactic center
(0 ô . ` . 40 ô ). On the perimeter of the box, lled circles denote
pulsars with jbj  5 ô for which the TC93 model fails to yield distance
estimates because their dispersion measures exceed those of the
model: DM > DM1(TC93). These points are at or near tangents
to the spiral arms in the fourth quadrant ( 83 ô  `  67 ô ) and
along the line of sight through the Gum Nebula. The new model
corrects these defects and has DM(NE2001) > DM for all objects
except those in the Magellanic clouds.
Fig. 9.| Distances calculated from the model plotted against
independent empirical ranges, [D L ; DU ], shown as horizontal lines.
A lled circle is plotted at (D L +DU )=2) when the range is relatively
small, DU =D L < 2. For globular cluster pulsars, an open circle is
plotted.
Fig. 10.| Histogram of the scattering prediction ratio, r scatt ,
dened as r scatt = predicted / actual value of scattering observable
for angular and pulse broadening and r scatt = actual / predicted
for scintillation bandwidths. Thus r scatt > 1 (r scatt < 1) means
scattering is overpredicted (underpredicted).
4.1. Asymptotic Values for DM
Figure 11 shows asymptotic values for DM in our model,
DM1 , plotted against Galactic longitude. In the inner
Galaxy, the asymptotic values exceed the highest known
DM (1209 pc cm 3 ) by a substantial factor. The lack
of pulsars with such large values of DM is consistent
with various selection eects, as we discuss in Paper II.
For instance, the channel bandwidths used in the Parkes
survey imply dispersion smearing of order 15 ms for DM =
2000 pc cm 3 , comparable to the pulse width of many
pulsars. More importantly, the pulse broadening from
scattering will exceed 1 s for many objects. Combined

10
with inverse square law eects, one would not expect to
nd pulsars with much larger values of DM to be present
in the existing surveys.
Fig. 11.| Plot of DM1 (`; b), the maximum DM obtained
by integrating the NE2001 model. Heavy solid line: b = 0 ô .
Light solid line: b = 5 ô . Dotted line: b = +5 ô (oset by -20
pc cm 3 in the vertical direction for clarity). Plotted points are
pulsars with jbj < 5 ô . Filled circles: pulsars from the Princeton
catalog. Open circles: pulsars from the public Parkes Multibeam
catalog. Labelled features include tangents to the spiral arms and
maxima associated with the ring component, the Gum Nebula and
Vela supernova remnant, and the H II complex NGC 6334. The
gaps near ` = +15 ô and 20 ô and DM . 200 pc cm 3 are real,
appearing in both samples, and signify either the real absence of
pulsars in the corresponding volume or the presence of large electron
densities in these directions fairly close to the solar system. The
absence of pulsars above  1200 pc cm 3 is due to selection against
such objects by pulse broadening from dispersion smearing and
scattering.
4.2. Distance Errors to be Expected
An ionized feature not included in our model will
perturb the dispersion measure toward an individual
object by an amount
DM. From the denition of DM,
it follows that the consequent distance error, if small, will
be

D =
DM
n e (x(D)) : (19)
Thus, for given
DM, the distance error is larger for a
pulsar in a region of small electron density compared to
one in a dense region. (Of course, the perturbation can
be large enough to render a very large distance error not
describable by Eq. 19.) A particularly important case is
for an object that is more than one scale height above the
Galactic disk. Using a simple plane-parallel model as an
example, the distance error is

D =
DM
n e0 (1 DM=DM1 ) ; (20)
where DM1 = n e0 H= sin jbj is the maximum DM of the
model with midplane density n e0 and scale height H
toward a direction at Galactic latitude b. For objects with
DM near the asymptotic value, distance errors are much
larger than for objects within one scale height of the plane.
This is true for both positive and negative perturbations
from density enhancements and voids, respectively. For
large positive perturbations of DM the measured DM can
exceed DM1 (or its analog in our multicomponent model).
In this case, the model can yield only a lower bound on
the distance.
For NE2001, we have explicitly constructed the model
so that nearly all known pulsars have DM < DM1 . This
feature may introduce bias in the model because there very
well could be pulsars at large distances with DMs that are
small because an unmodeled void is present along the line
of sight. We estimate that the number of lines of sight for
which this would be true is a small fraction of the total
pulsar sample.
In Figure 12 we show the distance errors that ensue
when we perturb DM by amounts corresponding to H II
regions of dierent kinds. For reference, we expect
perturbations in DM with the following amplitudes (e.g.
Prentice & ter Haar 1969; Bronfman et al. 2000):
1. Stromgren sphere around an O5 star:
DM  75
pc cm 3 .
2. Stromgren sphere around an O9/B1 star:

DM  3 to 10 pc cm 3 .
3. OB association:
DM  100 to 200 pc cm 3 .
4. Ultra-compact H II region:
DM  300 to 500 pc
cm 3 . Through a simulation of pulsar and UCHII
regions born in spiral arms and the molecular ring,
we nd that one expects only about one pulsar out
of the observed population to intersect an UCHII
region.
Fig. 12.| Plot of fractional distance error,
D=D, against
Galactic longitude where
D = ^
D D. The curves are calculated
for perturbations to DM of 
DM which increase or decrease the
model distance, ^
D, from the actual distance. Thickest line: D = 5
kpc and
DM = 30 pc cm 3 . Medium line: D = 2 kpc and

DM = 10 pc cm 3 . Thinnest line: D = 1 kpc and
DM = 5 pc
cm 3 .
4.3. Applications
To illustrate model predictions we show the model DM
for lines of sight in the Galactic plane (b = 0) in Figure 13.

11
Figure 14 shows DM plotted against Galactic coordinates
in an Aito project when integrating the electron density
to innite distance. A similar pair of plots for SM is shown
in Figures 15 and 16.
Fig. 13.| Contours of DM plotted on the Galactic plane.
Contours are at 20, 30, 50, 70, 100, 200, 300, 500, 700, 1000, 1500,
2000, 3000 and 4000 pc cm 3 , with the lowest contour nearest the
Sun (), assumed to be 8.5 kpc from the Galactic center (+ symbol
at plot center).
Fig. 14.| Contours of DM integrated to innite distance
and plotted against Galactic latitude and longitude on an Aito
projection with the Galactic center in the middle and negative
longitudes to the right. Contours are at 4000=2 n pc cm 3 for
n = 0; 1; : : : ; 7, with the lowest contour at the Galactic poles.
Fig. 15.| Contours of log SM plotted on
the Galactic plane. Contours are at log SM =
5; 4; 3; 3; 2; 1; 0; 0:50:67;0:83;1; 2; 3; 4; 5; and 6 kpc
m 20=3 , chosen to bring out salient features. The lowest contour is
near the Sun (). SM is in uenced much more than DM by small
scale features in the model.
Fig. 16.| Contours of log SM integrated to innite distance
and plotted against Galactic latitude and longitude on an Aito
projection with the Galactic center in the middle and negative
longitudes to the right. Contours are at 4 n=2 kpc m 20=3 for
n = 0; 1; : : : ; 16, with the lowest contour at the North Galactic pole.
5. summary & conclusions
We have presented a new model, NE2001, for the
Galactic distribution of free electrons and the uctuations
within it. As observational constraints we make use of
pulsar dispersion measures and distances and radio-wave
scattering measurements available at the end of 2001
(hence its name), and we are guided by multi-wavelength
observations of the Galaxy, particularly of the local
interstellar medium.
Building on the Taylor-Cordes model (TC93), we
model the free electron distribution as composed of three
large-scale components, a thick disk, thin disk, and spiral
arms. Since the publication of the TC93 model, though,
the number of available data have expanded greatly (e.g.,
the number of pulsar DMs available is now approximately
double the number available to TC93). With this larger
data set, it is clear that \smooth," large-scale components
are insuôcient to produce a realistic description of the
electron density distribution. We must take into account
the distribution of electrons in the local ISM, and we
require \clumps" and \voids" of electrons, mesoscale

12
structures distributed throughout the Galaxy on a large
number of lines of sight in order to produce reasonable
agreement with the observations.
Tables 2{4 summarize the model and the best-tting
parameters of the large-scale and local ISM components.
Tables 5{8 lists the lines of sight requiring clumps or
voids and the relevant parameter for each clump or void.
Figure 2 shows the model electron density in the Galactic
plane.
We used an iterative likelihood method to nd the
best-tting model parameters. Our focus here has been on
the exposition of the model. In a companion paper (Cordes
& Lazio 2002b) we describe details of the tting procedure
and discuss those lines of sight that require a clump or void
or are otherwise problematic. We also discuss possible
alternative tting approaches and models.
Our model, NE2001, improves upon the TC93 model.
First, the distance estimates obtained from the model
agree with available distance constraints for nearly
all pulsars with such constraints. Second, none
of the parameters of the large-scale components are
indeterminate (e.g., as was the case with the thick disk
for TC93). The cost of these improvements has been an
increase in the complexity of the model, particularly with
respect to the number and location of clumps and voids.
We believe, however, that this additional complexity is
justied both by the quantity of data and because it is
astrophysically reasonable. A small number of pulsars
or extragalactic sources has been known for some time
to have anomalously large DMs or scattering properties
or both due to intervening H II regions or supernova
remnants.
While we consider NE2001 to be an improvement over
TC93, we forsee a number of probable developments
that will allow future generations of electron density
models. We group these improvements into increases in
the quantity of data and improvements in the modeling
technique. Perhaps most important will be an increase in
the number of pulsar parallaxes, both from pulse timing
methods applied to millisecond pulsars and from large
programs using very long baseline interferometry (VLBI).
Also, using pulsar luminosities to estimate distances
should become feasible once beaming of pulsar radiation
becomes better understood and despite the fact that the
luminosity function for radio emission from pulsars is
very broad. DM-independent distances provide crucial
calibration information for NE2001 or any successors, and
we regard it as likely that the number of pulsars with
DM-independent distances will double in the next few
years. We have made use of only the positions and DMs
of pulsars discovered in the Parkes multibeam sample.
Eorts are underway to measure the scattering along the
lines of sight to many of these pulsars, which could increase
the number of lines of sight with measured SMs by roughly
50% or more. The advent of the Green Bank Telescope and
the refurbished Arecibo telescope suggest the possibility of
conducting a northern hemisphere equivalent of the Parkes
multibeam sample, which could increase the number of
pulsars by at least another 50%.
Possible improvements in modeling include the adoption
of a more realistic location for the Sun. NE2001 places
the Sun in the Galactic plane at a Galactocentric distance
of 8.5 kpc, though a smaller distance from the Galactic
center ( 7:1 kpc) and a modest oset from the plane
( 20 pc) seem warranted. Although we have provided
a formalism for comparing DM and SM to EM, we have
made little use of it. Future work to include observational
constraints on EM, e.g., from H surveys, has the potential
of producing a better model for the local ISM.
Finally, Figure 11 suggests that the large-scale structure
of the Galaxy could be determined ab inito, provided
that a suôcient number of lines of sight exist. Rather
than imposing a large-scale structure as done both here
and previously, the presence and location of large-scale
components, particularly the spiral arms, could be
determined directly from the population of pulsars. Future
pulsar surveys may yield the number of lines of sight
required to employ this approach.
We thank Z. Arzoumanian, R. Bhat, F. Camilo, S.
Chatterjee, D. Cherno, M. Goss, Y. Gupta, S. Johnston,
F. J. Lockman, R. N. Manchester, and B. Rickett for
useful discussions. Our research is supported by NSF
grant AST 9819931 and by the National Astronomy
and Ionosphere Center, which operates the Arecibo
Observatory under cooperative agreement with the NSF.
Basic research in radio astronomy at the NRL is supported
by the Oôce of Naval Research.
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J. S., Kulkarni, S. R., & Anderson, S. B. 1999, ApJ, 523, L171
Vallee, J. P. 1995, ApJ, 454, 119
Vallee, J. P. 2002, ApJ, 566, 261
van Langevelde, H. J., Frail, D. A., Cordes, J. M., & Diamond, P. J.
1992, ApJ, 396, 686
van Straten, W., Bailes, M., Britton, M., Kulkarni, S. R., Anderson,
S. B., Manchester, R. N., & Sarkissian, J. 2001, Nature, 412, 158
Vergely, J.-L., Freire F. R., Siebert, A., & Valette, B. 2001, A&A,
366, 1016
Wainscoat, R. J., Cohen, M., Volk, K., Walker, H. J., and Schwartz,
D. E. 1992, ApJS, 83, 111
Table 1
Data Summary
Number of Measurements
Work D a
DM  d
 d  d;Gal  d;xgal
TC93 74 553 120 74 38 42
This paper 112 1143 162 110 118 97
a The number of distances is the number of distinct lines of
sight. A globular cluster with multiple pulsars is counted as
only one line of sight.

14
Table 2
NE2001 Model Components
ne(x) = (1 wvoids )f(1 wlism) [n gal (x) + nGC(x)] +wlismnlism (x)g + wvoidsnvoids (x) + nclumps(x)
Component Functional Form Parameters No. Parameters Comments
Smooth Components n gal (x) = [n 1 G 1 (r; z) + n 2 G 2 (r; z) + naGa (x)]
Thick Disk n 1 G 1 (r; z) = n 1 g 1 (r)h(z=H 1 ) n 1 ; H 1 ; A 1 ; F 1 4
Thin Disk n 2 G 2 (r; z) = n 2 g 2 (r)h(z=H 2 ) n 2 ; H 2 ; A 2 ; F 2 4
Spiral Arms naGa (x) f j na ; h j Ha ; w j wa ; F j 20
j = 1; : : : ; 5
Galactic Center (n GC ) nGC0 e [ôr 2
? =R 2
GC +(z z GC ) 2 =H 2
GC ] nGC0 ; RGC ; hGC 3
ôr 2
? = (x xGC ) 2 + (y y GC ) 2
Local ISM (n lism ) n lism (x), F lism (x), w lism (x) See Table 4 36 Excludes Gum, Vela
See below & Appendix A
Clumps (n clumps )
N clumps X
j=1
ncj e jx x c j j 2 =r c
2
j t cj (x) N clumps 6N clumps + 1 Includes Gum, Vela
ncj ; xcj ; rcj ; Fcj (6/clump)
Voids (n voids )
N voids
X
j=1
nvj gv (x; vj )tvj (x) N voids 8N voids + 1
nvj ; xvj ; vj ; Fvj (8/void)
Functions:
h(x) = sech 2 (x)
U(x) = unit step function
g 1 (r) = [cos(r=2A 1 )= cos(R=2A 1 )]U(r A 1 )
g 2 (r) = exp( (r Aa ) 2 =A 2
a )U(r)
Ga (x) =
P
j f j ga j (r; s j (x)=w j wa )h(z=h j ha ) s j (x) tabulated
ga j (x) = e (s j (x)=w j wa ) 2
sech 2 (r Aa )=2U(r Aa )
n lism (x) = (1 w lhb )f(1 w loopI )[(1 w lsb )n ldr (x) + w lsb n lsb (x)] + w loopI n loopI (x)g + w lhb n lhb (x)]
F lism (x) = (1 w lhb )f(1 w loopI )[(1 w lsb )F ldr (x) + w lsb F lsb (x)] + w loopI F loopI (x)g + w lhb F lhb (x)]
w lism (x) = max[w ldr (x); w lhb (x); w lsb (x); w loopI (x)] = (0; 1) LISM weight function
t cj (x) = [1 ecj U(jx xcj j rcj )]; ecj = (0; 1) truncation function
gv (x; vj ) = elliptical gaussian = exp( Q(x xcj ), vj = (a j ; b j ; c j ; y j ; z j )
t vj (x) = [1 evj U(Q 1)]; evj = (0; 1) truncation function
Q = (x xcj ) y V 1 (x xcj ), V = rotation matrix ellipsoidal quadratic form
w voids = (0; 1) weight function for voids
Weight functions:
w voids ; w lism ; w ldr ; w lhb ; w lsb ; w loopI switch components on and o.
Truncation functions:
t cj , t vj truncate component at 1/e point if ecj , evj = 1.

15
Table 3
Parameters of Large Scale Components of TC93 and NE2001
Parameter TC93 Values NE2001 Values a
n 1 h 1 (cm 3 kpc). . . 0:0165  0:0006 0.033
h 1 (kpc) . . . . . . . . . . 0:88  0:06 0.95
A 1 (kpc) . . . . . . . . . . & 20 17
F 1 . . . . . . . . . . . . . . . . 0:36 +0:30
0:10 0.20
n 2 (cm 3 ) . . . . . . . . 0:10  0:03 0.090
h 2 (kpc) . . . . . . . . . . 0:15  0:05 0.14
A 2 (kpc) . . . . . . . . . . 3:7  0:3 3.7
F 2 . . . . . . . . . . . . . . . . 43 +30
13 110
naf j (cm 3 ) . . . . . . 0:084  0:008 0.030 (0:50; 1:2; 1:3;1:0; 0:25)
hah j (kpc) . . . . . . . . 0:3  0:1 0.25 (1:0; 0:8;1:3; 1:5; 1:0)
waw j (kpc) . . . . . . . 0:3 0.6 (1; 1:5;1; 0:8;1)
Aa (kpc) . . . . . . . . . . 8:5 11.0
FaF j . . . . . . . . . . . . . . 6 +5
2 10 (1:1; 0:3; 0:4; 1:5;0:3)
nG (cm 3 ) . . . . . . . . 0.25



FG . . . . . . . . . . . . . . . . 0.0



nGC (cm 3 ) . . . . . . .


10.0
FGC . . . . . . . . . . . . . .


5  10 4
Table 4
Local ISM Components
Component Location Size & Shape Density
x y z a b c  a
ne F
(kpc) (kpc) (kpc) (kpc) (kpc) (kpc) (deg) (cm 3 )
LDR 1.36 8.06 0.0 1.5 0.75 0.5 24:8 0.012 0.1
LHB 0.01 8.45 0.17 0.085 0.1 0.33 15 0.005 0.01
LSB 0:75 9.0 0:05 1.05 0.425 0.325 139 0.016 0.01
Loop I (NPS) Location Size Density
x y z r
r ne
ne F vol F shell
(kpc) (kpc) (kpc) (kpc) (kpc) (cm 3 ) (cm 3 )
0:045 8.4 0.07 0.14 0.03 0.0125 0.010 0.20 0.01
a For LSB and LDR,  is the angle of the major axis of the ellipsoid with respect to the the x axis (` = 90 ô ),
increasing counterclockwise looking down on the Galactic plane. For the LHB,  is measured from the z axis and
describes the slant of the axis of the cylinder in the y-z plane. Loop I has a hemispherical shape with internal
volume and shell component that contributes only for z  0.

16
Table 5
Clump Parameters for Lines of Sight to Extragalactic Sources
LOS ` b dc log SMc DMc rc
(deg) (deg) (kpc) (kpc m 20=3 ) (pc cm 3 ) (kpc)
B1741 312 2:14 1:00 8:50 1:40 89 0:01
1905 + 079 41:91 0:09 8:00 1:55 106 0:01
2008 + 33D 71:16 0:09 2:35 0:35 27 0:01
2021 + 317 71:40 3:10 2:35 0:91 6 0:01
2023 + 336 73:10 2:40 2:35 0:20 14 0:01
2014 + 358 74:04 0:36 2:35 0:09 16 0:01
2020 + 351 74:14 1:01 2:35 0:68 39 0:01
2005 + 372 74:18 2:61 2:35 0:56 34 0:01
2048 + 313 74:60 8:04 2:35 0:09 16 0:01
2013 + 370 74:90 1:20 2:20 0:45 11 0:01
2012 + 383 75:78 2:19 2:35 0:05 17 0:01
2005 + 403 76:80 4:30 2:35 0:00 18 0:01
2050 + 364 78:90 5:10 2:35 1:40 4 0:02
0241 + 622 135:70 2:40 2:20 0:09 16 0:01
Table 6
Clump Parameters for Galactic, Non-Pulsar Lines of Sight
LOS ` b dc log SMc DMc rc
(deg) (deg) (kpc) (kpc m 20=3 ) (pc cm 3 ) (kpc)
MonR2 146:30 12:60 0:41 0:96 6 0:01
NGC6334N a 8:80 0:65 1:67 3:61 142 0:01
OH353:298 6:70 1:54 8:40 6:35 886 0:05
OH355 4:23 1:75 8:40 6:46 886 0:05
OH357:849 2:15 9:74 8:40 5:75 886 0:05
OH359:140 0:86 1:14 8:40 7:00 886 0:05
OH359:540 0:44 1:29 8:40 4:79 886 0:05
OH000:125 + 5:111 0:12 5:11 8:40 4:60 886 0:05
OH000:892 + 1:342 0:89 1:34 8:40 4:95 886 0:05
OH20:1 0:1 20:07 0:09 4:00 3:56 177 0:01
OH35:2 1:7 35:20 1:73 2:80 0:30 35 0:01
OH40:6 0:2 40:62 0:14 2:20 3:75 53 0:00
W49N 43:16 0:01 8:50 1:69 124 0:02
OH43:80 0:13 43:78 0:14 2:60 2:16 213 0:02
CygX 3 79:85 0:70 2:35 1:69 124 0:02
W75S 81:80 0:64 2:40 1:69 124 0:02
CepA 109:87 2:10 0:60 0:16 21 0:02
NGC7538 111:54 0:77 3:40 0:00 18 0:02
W3OH 133:95 1:06 2:20 3:80 354 0:02
a The clump toward NGC6334N also aects the strongly scattered extragalactic source,
NGC6334B (see Paper II).

17
Table 7
Clumps for Pulsar Lines of Sight with DMc > 20 pc cm 3 or log SMc > 0
LOS ` b dc DMc log SMc rc
(deg) (deg) (kpc) (pc cm 3 ) (kpc m 20=3 ) (kpc)
0611 + 22 171:21 2:40 0:65 23:2


0:01
GumI 100:00 1:00 0:50 110:5


0:14
GumII 97:20 2:70 0:50 28:4 0:59 0:03
VelaIras 96:75 9:00 0:25 269:4 1:54 0:04
J1019 5749 76:20 0:68 4:21 709:0 2:60 0:01
J1022 5813 75:70 0:83 4:21 354:5 2:60 0:01
J1031 6117 73:12 2:88 3:00 35:4 0:70 0:02
J1056 6258 69:71 2:97 2:20 177:2 0:13 0:02
1112 60 68:56 0:32 6:13 9:9 0:19 0:01
J1119 6127 67:85 0:54 2:30 35:4 0:70 0:02
J1128 6219 66:51 0:97 2:30 35:4 0:60 0:02
1131 62 65:79 1:30 6:51 10:8 0:27 0:01
J1201 6306 62:69 0:79 2:00 78:0 0:02 0:02
J1216 6223 61:08 0:20 2:10 106:3 0:25 0:02
J1305 6256 55:50 0:12 8:00 354:5 2:60 0:01
J1324 6146 53:10 0:85 8:00 354:5 2:60 0:01
1334 61 51:63 0:30 6:50 13:5 0:46 0:01
1338 62 51:27 0:04 7:21 12:6 0:40 0:01
1430 6623 47:35 5:40 0:90 33:1


0:01
1508 57 39:23 0:11 3:00 88:6


0:01
1419 3920 39:07 20:45 0:30 26:1


0:01
1627 47 23:52 0:62 3:43 33:9 1:26 0:01
1630 44 21:27 1:98 3:38 10:8 0:27 0:01
1641 45 20:81 0:20 3:40 53:2 0:25 0:02
1643 43 18:89 0:97 3:34 10:8 0:27 0:01
1703 40 14:28 0:20 1:45 15:2 0:57 0:01
1718 36 9:07 0:00 1:50 72:0


0:01
1727 33 5:87 0:09 1:48 21:4 0:86 0:01
1736 31 2:90 0:22 3:31 17:0 0:66 0:01
1746 30 0:54 1:24 2:00 77:3


0:01
1807 2715 3:84 3:26 1:50 70:2


0:01
1758 23 6:81 0:08 6:63 17:9 0:71 0:01
1815 14 16:41 0:61 4:83 11:7 0:34 0:01
1820 14 17:25 0:18 3:50 301:3


0:01
1824 10 21:29 0:80 1:92 15:2 0:57 0:01
1836 1008 22:26 1:42 2:00 47:1


0:01
1830 08 23:39 0:06 4:40 141:8


0:01
1832 06 25:09 0:55 2:06 36:5 1:32 0:01
1839 04 28:35 0:17 2:23 15:8 0:60 0:01
1849 + 00 33:30 0:10 7:40 354:5 3:60 0:02
1821 + 05 34:99 8:86 0:44 22:5


0:01
1900 + 01 35:73 1:96 2:80 141:8 0:11 0:04
1859 + 07 40:57 1:06 3:50 35:4 0:70 0:02
1907 + 10 44:83 0:99 0:60 34:6


0:01
1914 + 13 47:58 0:45 4:00 88:8


0:01
2044 + 46 85:43 2:11 2:00 177:2 2:00 0:01
2036 + 53 90:37 7:31 2:00 88:6 1:40 0:01

18
Table 8
Void Parameters
LOS ` b dv nev Fv av bv cv vz
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
GumIedge 81:50 0:60 0:50 0:500 1:00 0:02 0:02 0:04 9:00
J1224 6407 60:02 1:42 1:90 0:002 0:10 0:50 0:05 0:10 30:00
J1453 6413 44:27 4:43 1:50 0:005 0:10 0:25 0:10 0:10 46:00
J1600 5044 29:31 1:63 1:50 0:001 0:10 1:00 0:10 0:10 61:00
J1600 5044 29:31 1:63 3:60 0:001 0:10 0:50 0:20 0:20 61:00
J1559 4438 25:46 6:37 1:30 0:020 0:00 0:90 0:07 0:07 64:54
J1709 4428 16:90 2:68 1:50 0:010 0:10 0:40 0:10 0:10 73:00
1757 24 5:31 0:02 3:00 0:035 10:00 1:20 0:03 0:10 95:31
1759 2205 7:47 0:81 2:00 0:055 1:30 1:20 0:02 0:10 97:47
1821 24 7:80 5:58 1:50 0:005 0:10 0:40 0:20 0:20 0:00
1534 + 12 19:85 48:34 0:35 0:004 0:00 0:20 0:20 0:30 70:15
Interarm2 3 31:00 0:00 4:20 0:010 0:10 0:80 0:45 0:20 25:00
1859 + 03 37:21 0:64 6:00 0:100 1:00 0:90 0:02 0:04 127:21
Interarm3 4 45:00 0:00 2:00 0:024 0:10 0:80 0:30 0:20 25:00
1915 + 13 48:26 0:62 3:00 0:024 20:00 0:20 0:20 0:20 41:74
2334 + 61 114:28 0:23 2:50 0:005 0:10 0:50 0:10 0:10 24:00
0138 + 59 129:15 2:10 1:50 0:017 0:10 0:70 0:10 0:10 39:00
The columns are (1) line of sight name; (2)-(3) Galactic coordinates in degrees; (4) void
distance (kpc); (5) void electron density (cm 3 ); (6) void uctuation parameter; (7)-(9)
ellipsoidal semi-axes (kpc); (10) rotation angle (degrees) of semi-major axis about the z axis,
referenced to the x axis.

19
APPENDIX
a. lism model form
The local ISM is modeled with four components that augment the large scale Galactic features. These are the local
hot bubble (LHB) in which the Sun sits, a low-density region (LDR) primarily in the rst quadrant of the Galaxy, a
local superbubble (LSB) region in the third quadrant, and the \Loop I" feature that includes the North Polar Spur (e.g,
Berkhuijsen, Haslam, & Salter 1971; Spoelstra 1972)
We model the LDR and LSB as ellipsoids with one axis perpendicular to the plane of the Galaxy and the other making
an angle  with the x direction (i.e. ` = 90 ô ). The semi-major axes are denoted a; b; c and the ellipsoid center is given
by x; y; z. The internal density n e and uctuation parameter F are also individual attributes for each region. Parameter
values are given in Table 4.
For the LHB we use the work of Bhat et al.(1999), Sfeir et al.(1999), Vergely et al.(2001) and Ma  iz-Apellaniz (2001)
as a guide for dening its structure. Using contours of Na I absorption given by Sfeir et al.(1999), which delineate the
absence of absorbing gas, and the electron density implied by X-ray observations (Snowden et al.1998), n e  0:005 cm 3 ,
we dene the LHB as follows. The LHB is a slanted, ellipsoidal cylinder with cross section in the x y plane described
by the parameters a and b. The cylinder has total length 2c in the z direction and a mean z given by z. For z  0, the
cylinder has constant cross section at constant z. For z < 0, a declines linearly, reaching zero at z = z c. the b parameter
is constant for all z within the cylinder. Finally, the cylinder axis is slanted in the y-z plane with angle tan  = dy=dz.
The internal density and uctuation parameter are also parameters for the LHB. Parameter values are given in Table 4.
The Loop I component is modeled only for z  0 as a hemisphere of radius r surrounded by a shell of thickness
r.
The hemispherical volume and shell have dierent internal densities and F values. Parameter values given in Table 4 are
guided by those given by Heiles (1998) but result from tting for the best values of the parameters.
All four LISM regions have internal electron densities that are less than those in the large-scale Galactic structures.
Therefore, to ensure that densities are mutually exclusive (not additive) between dierent components, we combine
components by assigning weight factors w lhb ; w lsb , w ldr and w loopI to each region and, together, use them to dene
an overall LISM weight, w lism . The weights are either 0 or 1. They are dened with the following hierarchy:
LHB:LoopI:LSB:LDR:ISM, meaning that the LHB overrides all other components (LISM and large scale), Loop I overrides
the LSB, the LSB overrides the LDR, and any LISM component overrides the large scale components. For the LDR and
LSB, the weight is unity inside the e 1 contour of each ellipsoid while for the LHB, the weight is unity anywhere inside
the cylinder. For Loop I, the weight is unity anywhere inside the hemispherical sphere or shell.
b. fortran code
Our model is implemented in Fortran routines similar in functionality to those presented in TC93, but that represent
a complete revision according to the new features presented in the main text. A master program NE2001 evaluates
the model by returning the integrated measures (DM, SM, etc.) and/or distance given an input direction and
DM or distance. Integrations are performed in the the subroutine dmdsm, which evaluates the model by making
calls to subroutine density 2001. Copies of all code and necessary input les are available over the Internet at
http://www.astro.cornell.edu/cordes/NE2001 and http://rsd-www.nrl.navy.mil/7213/lazio/ne model/. The
code is packaged as a tar le, NE2001.tar, that includes a makele for compiling the code in a Unix/Linux environment.
The functionality of the code is as follows: The call to dmdsm is of the form
call dmdsm(l,b,ndir,dm,dist,limit,sm,smtau,smtheta,smiso) .
Here the input data include Galactic longitude and latitude, l and b (in radians), and a ag ndir indicating whether
distance is to be calculated from dispersion measure (ndir 0), or vice-versa (ndir< 0). In either case, dm and dist
have units of pc cm 3 and kpc, respectively. A ag limit is set if ndir 0 and the model distance is a lower limit; this
will occur, for example, if a large dm is specied at high Galactic latitude. The subroutine also returns four estimates of
scattering measure, all having units kpc m 20=3 . The rst, sm, conforms to the denition in Eq. (4) with uniform weighting
along the line of sight. The next two estimates, smtau and smtheta, correspond to line-of-sight weightings appropriate for
temporal and angular broadening of Galactic sources, respectively. Temporal broadening emphasizes scattering material
midway between source and observer, while angular broadening favors material closest to the observer; see Eqs. (A14,
B2) of Cordes, Weisberg, & Boriako (1985). The last estimate, smiso, uses the weighting appropriate for calculating the
isoplanatic angle of scattering.
Integrations in dmdsm involve evaluations of the model at a given Galactic location (x; y; z) through a call to subroutine
density 2001, where x,y,z are Galactocentric Cartesian coordinates, measured in kiloparsecs, with the axes parallel to
(l; b) = (90 ô ; 0 ô ), (180 ô ; 0 ô ), and (0 ô ; 90 ô );
call density_2001(x,y,z,
. ne1,ne2,nea,negc,nelism,necN,nevN,
. F1, F2, Fa, Fgc, Flism, FcN, FvN,
. whicharm, wlism, wldr, wlhb, wlsb, wloopI,
. hitclump, hitvoid, wvoid).
The routine returns values for the electron density in seven components (ne1,


, nevN), the corresponding F parameters
(F1,


, FvN), followed by a series of integer-valued ags. The meanings of these ags are as follows:

20
1. whicharm = 0,


, 5 indicates which spiral arm contributes to the density, with numbering as in the text and
where a zero value denotes an interarm region.
2. wlism, wldr, wlhb, wlsb and wloopI take on values of 0 or 1 as described in Appendix A.
3. hitclump denotes whether a clump has been intersected in the integration; if so, then hitclump denotes the
clump number in the table of clumps; if not, hitclump = 0.
4. hitvoid works in the same fashion for voids; additionally, wvoid = 0,1 is used in evaluating the total density
and indicates if a void has been hit (wvoid = 1).
The calling program, NE2001, is executed using command-line arguments that specify the Galactic longitude and
latitude, an input DM or distance value, and a ag (ndir) that species whether a distance is calculated from DM (ndir
 0) or a DM calculated from an input distance (ndir < 0):
Usage: NE2001 l b DM/D ndir
l (deg)
b (deg)
DM/D (pc cm^{-3} or kpc)
ndir = 1 (DM->D) 2 (D->DM)
Program NE2001 uses output from dmdsm to calculate scattering and scintillation quantities by making suitable calls
to a series of functions. Input distances, scattering measures, frequencies and velocities are in standard units (kpc, kpc
m 20=3 , GHz, and km s 1 ):
1. tauiss(d,sm,nu): calculates the pulse broadening time,  d (ms). See Eq. 9.
2. scintbw(d,sm,nu): calculates the scintillation bandwidth,
 d (MHz). See Eq. 10.
3. scintime(sm,nu,vperp): calculates the scintillation time,
t ISS (sec) (Cordes & Lazio 1991; Cordes & Rickett
1998).
4. specbroad(sm,nu,vperp): calculates the spectral broadening,
 b (Hz), that is proportional to the reciprocal of
the scintillation time (Cordes & Lazio 1991).
5. theta xgal(sm,nu): calculates the angular broadening,  d (mas), appropriate for the scattering geometry for an
extragalactic source. See Eq. 8.
6. theta gal(sm,nu): calculates the angular broadening,  d (mas), of a Galactic source. See Eq. 8.
7. em(sm): calculates the emission measure, EM (pc cm 6 ), associated with the scattering measure; note that the
value calculated assumes a particular outer scale for a Kolmogorov wavenumber spectrum and represents a lower
bound on EM (see Eq. 14).
8. theta iso(smiso,nu): calculates the isoplanatic angle,  iso (mas), the region on the sky over which scintillations
are correlated.
9. transition frequency(sm,smtau,smtheta,dintegrate): calculates the frequency of transition,  trans (GHz),
between the weak and strong scattering regimes (Eq. 17).
Sample output for ` = 45 ô ; b = 5 ô , and DM = 50 pc cm 3 is:
#NE2001 input: 4 parameters
45.0000 l (deg) GalacticLongitude
5.0000 b (deg) GalacticLatitude
50.0000 DM/D (pc-cm^{-3}_or_kpc) Input_DM_or_Distance
1 ndir 1:DM->D;2:D->DM Which?(DM_or_D)
#NE2001 output: 14 values
2.6365 DIST (kpc) ModelDistance
50.0000 DM (pc-cm^{-3}) DispersionMeasure
4.3578 DMz (pc-cm^{-3}) DM_Zcomponent
0.3528E-03 SM (kpc-m^{-20/3}) ScatteringMeasure
0.2367E-03 SMtau (kpc-m^{-20/3}) SM_PulseBroadening
0.7719E-04 SMtheta (kpc-m^{-20/3}) SM_GalAngularBroadening
0.1307E-02 SMiso (kpc-m^{-20/3}) SM_IsoplanaticAngle
0.1921E+00 EM (pc-cm^{-6}) EmissionMeasure_from_SM
0.1293E-03 TAU (ms) PulseBroadening @1GHz
0.1428E+01 SBW (MHz) ScintBW @1GHz
0.4943E+03 SCINTIME (s) ScintTime @1GHz @100 km/s
0.2420E+00 THETA_G (mas) AngBroadeningGal @1GHz
0.1086E+01 THETA_X (mas) AngBroadeningXgal @1GHz
14.02 NU_T (GHz) TransitionFrequency
The Fortran program can be run using a perl script (also included in the tar le) which allows selection of an individual
eld for output:

21
run_NE2001.pl
Usage:
run_NE2001 l b DM/D ndir field
deg deg pc-cm^{-3} 1,-1 D etc
or kpc
Possible Fields (case insensitive):
Dist, DM, SM, EM, TAU, SBW, SCINTIME, THETA_G, THETA_X, NU_T, ALL