Integrated Radio Continuum Spectra of Galaxies
aa r X i v : . [ a s t r o - ph . GA ] A ug Draft version September 10, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
INTEGRATED RADIO CONTINUUM SPECTRA OF GALAXIES
Joshua Marvil National Radio Astronomy Observatory , Socorro, NM 87801 andNew Mexico Tech, Socorro, NM 87801 Frazer Owen
National Radio Astronomy Observatory, Socorro, NM 87801 andJean Eilek
National Radio Astronomy Observatory, Socorro, NM 87801 andNew Mexico Tech, Socorro, NM 87801
Draft version September 10, 2018
ABSTRACTWe investigate the spectral shape of the total continuum radiation, between 74 MHz and 5 GHz (400to 6 cm in wavelength), for a large sample of bright galaxies. We take advantage of the overlappingsurvey coverage of the VLA Low-Frequency Sky Survey, the Westerbork Northern Sky Survey, theNRAO VLA Sky Survey, and the Green Bank 6 cm survey to achieve significantly better resolution,sensitivity, and sample size compared to prior efforts of this nature. For our sample of 250 brightgalaxies we measure a mean spectral index, α , of -0.69 between 1.4 and 4.85 GHz, -0.55 between 325MHz and 1.4 GHz, and -0.45 between 74 and 325 MHz, which amounts to a detection of curvaturein the mean spectrum. The magnitude of this curvature is approximately ∆ α = − . ± Subject headings: radio continuum: galaxies — galaxies: statistics INTRODUCTION
Early radio continuum observations of bright galaxiesestablished an approximately power-law relation betweenflux S and frequency ν , typically parameterized by thespectral index α , defined here as the positive power-lawexponent: S ( ν ) ∝ ν α . The spectral index is an impor-tant observational quantity since it can be interpretedas a measure of a source’s physical properties and pro-cesses. The spectra below ∼
50 GHz from star forminggalaxies are typically modeled as the sum of synchrotronemission, with non-thermal spectral index α NT ∼ -0.8,and thermal bremsstrahlung, with thermal spectral in-dex α T ∼ -0.1 ( e.g. , Condon 1992); an illustration of present address: CSIRO Astronomy and Space Sci-ence, PO Box 76, Epping, NSW 1710, Australia; email:[email protected] The National Radio Astronomy Observatory is a facilityof the National Science Foundation operated under cooperativeagreement by Associated Universities, Inc. this model is provided in Figure 1. Prior surveys of spi-ral galaxies have reported narrow distributions of spec-tral indices: Sramek (1975) found α = -0.85 between 1.4and 5 GHz, Klein & Emerson (1981) found α = -0.71 be-tween 408 MHz and 10.7 GHz with a dispersion of 0.08dex, and using a larger sample, Gioia et al. (1982) found α = -0.74 with a dispersion of 0.12 dex over the samefrequency range.These sharply peaked empirical distributions of spec-tral indices are often interpreted as measures of the con-stancy of both the non-thermal spectral index and thethermal fraction among sampled galaxies. These stud-ies typically find that the spectra are well describedby power laws over observed frequency ranges spanningone or two orders of magnitude, a conclusion most evi-dent from the “average” spectrum shown by Gioia et al.(1982). These results have led to the following commongeneralizations regarding the population of normal galax-ies: (1) the total radio spectral index is ∼ -0.7, (2) the Marvil et al. (cid:0) log ( Frequency / 1 GHz ) l o g F l u x [ a r b i t r a r y un i t s ] VLSSr WENSS NVSS GB6 (cid:1) low (cid:2) mid (cid:3) high
Fig. 1.—
Illustration of a generic radio spectrum with ba-sic power-law model components: steep spectrum synchrotron(dashed) with spectral index α NT = − .
8, flat-spectrum free-free(dash-dot) with spectral index α T = − .
1, and sum (shaded). Thelocations of the radio survey data are indicated with filled circles.Spectral indices α low , α mid , and α high are calculated from the totalradio spectrum between adjacent frequency intervals. synchrotron spectral index is ∼ -0.8, and (3) synchrotronemission dominates over thermal emission at frequenciesbelow 10 GHz, with the thermal fraction dropping to lessthan 10% at frequencies . e.g. ,Figure 1, the total spectrum flattens with increasing fre-quency as the thermal component becomes the domi-nant emission mechanism. Niklas et al. (1997) use thiscurvature to fit for the thermal fraction at 1 GHz andfind 8% ±
1% for a sample of 74 Shapley-Ames galax-ies. However, a similar study by Duric et al. (1988)of 41 spiral galaxies reports a much larger variation inthermal fraction. This spectral decomposition methodis difficult, since the power-law models often used maynot be good approximations of the emission components.One such case against a power-law model is presentedby Williams & Bower (2010), who favor a curved syn-chrotron spectrum to model the data. Additionally, thesynchrotron spectral index may be significantly steeperin some sources (Niklas et al. 1997) than the mean valuetypical of the galaxy population.Other departures from the simple model are evident atlow radio frequencies ( ν . e.g. ,Slee 1972; Israel & Mahoney 1990; Pohl et al. 1991a),but the physical interpretation remains uncertain. Sev-eral plausible scenarios have been proposed includingthermal absorption of a power-law synchrotron compo-nent or intrinsic curvature in the synchrotron spectrum.For some ordinary galaxies, the case for thermal ab-sorption appears to require unlikely physical parameters(Pohl et al. 1991b; Hummel 1991) but plausible mod-els have been presented for more extreme systems ( e.g. ,Anantharamaiah et al. 2000; Lacki 2013). Models of the synchrotron spectrum are often basedon a population of relativistic electrons with a power-lawdistribution of energy γ : q ( γ ) = q γ − s . Several energy-dependent processes can alter the shape of this parti-cle distribution and thereby alter the shape of the syn-chrotron spectrum. These processes include ionizationand electronic excitation (Gould 1975), inverse Compton,synchrotron radiation, and relativistic bremsstrahlung,although the latter is only weakly dependent on theparticle’s energy. The combined effect of these energy-dependent losses is that the initial power-law energy dis-tribution (and resulting synchrotron spectrum) developsconcave curvature, i.e. , steeper at the higher energies(higher frequencies) and flatter at lower energies (lowerfrequencies).A family of more elaborate models can be developedby considering the time evolution of the the synchrotron-emitting cosmic ray electron (CRE) population, oftenby invoking a ‘single box’ with uniform particle andenergy density, or a ‘dynamical halo’ model consist-ing of a 2-d galactic disk with perpendicular wind (seePohl & Schlickeiser 1990, and references therein). Forinjection which is constant in time, these losses causebreaks of ∆ s = 1 . α = 0 . α = 1 .
0. Additionally, energy-dependent CRE re-acceleration (Pohl et al. 1991b) and energy-dependentdiffusion combined with advective escape can present ob-servable spectral curvature.However, quantitative conclusions drawn from thesemodels remain questionable since they do not considerthe high degree of inhomogeneity in real galaxies ( e.g. ,Lisenfeld et al. 1998; Tabatabaei et al. 2013). Specifi-cally, spatial variations in physical quantities such as den-sity, magnetic field, cosmic ray injection, and interstel-lar radiation will result in spatial variations in the radiospectrum. Since the integrated spectrum is the sum overthese different regions, the spectral features predicted bysimple models will be smeared out over a larger frequencyrange and it becomes difficult to relate characteristics ofthe integrated spectrum to a single set of physical quan-tities. Due to these uncertainties, it is advantageous toexplore additional relationships to better understand thenature of radio sources in galaxies. Some trends havealready been identified in previous studies, such as a re-lation between spectral index and galaxy morphologicaltype (Condon et al. 1991; Sramek 1975, wherein earlytypes have slightly flatter spectra), between spectral in-dex and optical color (Deeg et al. 1993, wherein reddergalaxies are slightly flatter), and spectral index versusoptical axial ratio (Israel & Mahoney 1990), althoughthe latter two results have not been well established.It is the goal of this paper to better establish the shapeof the integrated radio continuum spectrum below 5 GHzntegrated Radio Continuum Spectra of Galaxies 3and to test for relationships between source properties.In order to achieve a substantially larger sample of galax-ies than previous efforts, and to better guard against se-lection effects and background source confusion, we havedesigned a new study to investigate the nature of low-frequency radio spectra using a suite of high-resolutionsurvey data. We describe the properties of these sur-veys and the sample selection strategy in Section 2. Sur-vey measurement techniques and derivation of additionalsource properties are detailed in Section 3. The measuredspectral indices and their relationships with source prop-erties and ancillary data are presented in Section 4 anddiscussed in Section 5. SURVEY PROPERTIES AND SAMPLE SELECTION
We selected four northern-hemisphere large-area ra-dio surveys as the basis for the spectral data: the VLALow-Frequency Sky Survey Redux (VLSSr; Lane et al.(2012)), the Westerbork Northern Sky Survey (WENSS;Rengelink et al. (1997)), the NRAO VLA Sky Survey(NVSS; Condon et al. (1998)), and the Green Bank 6cm Survey (GB6; Gregory et al. (1996)). Table 1 sum-marizes key properties of these surveys and Figure 1demonstrates how they sample the radio spectrum, from74 MHz to 4.85 GHz, in roughly equal intervals. TheVLSSr, a re-reduction of the original VLSS survey data(Cohen et al. 2007) incorporating enhanced data pro-cessing and imaging algorithms, provides a critical im-provement in sensitivity necessary to detect many of thesources in our sample.We restrict this project to an annulus in declination,+35 ≤ δ ≤ +75, which is covered by all surveys and forwhich the WENSS declination-dependent resolution ele-ment is not very distorted. All entries in the 3rd Catalogof Bright Galaxies (RC3; de Vaucouleurs et al. (1991))inside this declination range, with optical magnitude (B-band, 400-500 nm) B T <
14 and optical major axis < ′ are compiled, resulting in a sample size of 787. Notethat this restriction on optical size is important to en-sure accurate measurements of the total flux from theradio surveys.Image cutouts (15 ′ × ′ ) are obtained at the locationof each optical position for each of the VLSSr, WENSS,and NVSS surveys and all radio data are scaled to theflux-density standard of Baars et al. (1977). Each sourceis first investigated using the NVSS survey images, forwhich the point source sensitivity and resolution are su-perior to the other surveys. Since background confu-sion is known to be a serious concern (the NVSS cata-log source density is 50 per square degree brighter than2 mJy) we adopt a radio-optical coherence length of30 ′′ to reject background sources with 99% confidence(Condon et al. 1998). Additionally, we want to avoidbackground objects which could create confusion for thelower resolution surveys, so we reject sources having mul-tiple radio components within 2 ′ of the optical position.A total of 197 galaxies are rejected on the basis of coher-ence length or multiple components.We also restrict our sample to include only radiosources for which the NVSS-WENSS 2-point spectral in-dex can be well determined. Based on simulated mea-surements with a standard α = − . α pt ≤ . ≥ σ (NVSS sources ≥ σ ). Furthermore, by setting a demanding NVSS fluxthreshold, we can expect to detect these sources in theWENSS survey even if they have atypical spectra. Hadwe set a lower flux threshold, flat spectrum sources wouldhave been too faint to be detected in WENSS, leadingto a preference for steeper spectrum sources in the fi-nal sample. A total of 321 galaxies are rejected for nothaving radio counterparts bright enough for our spectralinvestigation. A small number of additional galaxies arerejected due to issues obtaining one or more of the sur-vey cutouts, or because the cutouts are severely contam-inated by artifacts from a bright nearby source. Afterthese selections, 250 galaxies remain in our final sample. DATA
Survey Measurements
Since many galaxies in our sample have optical sizeslarger than the survey resolution element, a 2-d Gaus-sian fit at the full survey resolution may not provide thebest estimate of the total flux (Owen & Morrison 2008).Accordingly, the NVSS and WENSS survey cutouts areconvolved with Gaussian beams 2, 3, and 4 times largerthan the native survey resolution to produce lower res-olution images. The radio source is fit using the
AIPS task
JMFIT for each scale; if the source size is resolvedand the integrated flux is at least 10% larger than thepeak flux then the integrated flux is recorded, otherwisethe peak flux is used. The final flux is taken from thescale which produces the greatest signal-to-noise ratiowhile maintaining coincidence with the optical position.This method produces values which are on average 5.4%greater than those listed in the NVSS catalog and 4.5%greater than values in the WENSS catalog.The VLSSr peak flux is measured from the full resolu-tion survey cutout at the position of the optical sourceand corrected for beam resolution using the measuredNVSS size. The source-free RMS in the VLSSr cutout isused to determine the uncertainty in the VLSSr flux. TheGB6 fluxes and errors are compiled from the publishedcatalog using entries within 1 ′ of the optical positions.Sources having no GB6 association are assigned 5 σ upperlimits using the GB6 declination-dependent sensitivity.Using these methods, we record NVSS fluxes for250 sources, WENSS fluxes for 233 sources, VLSSrfluxes (greater than 3 σ ) for 89 sources, and GB6 fluxes(greater than 5 σ ) for 85 sources. The upper limits arealso recorded and used in further statistical analysis.The survey measurements are listed in their entirety inTable 2. The nine columns of Table 2 give the followinginformation: Column 1.
Uppsala General Catalog (UGC) number(Nilson 1973).
Columns 2, 3.
NVSS flux and uncertainty in mJy,measured from the survey cutout images using the
AIPS task
JMFIT , selected from multiple resolutions.
Columns 4, 5.
NVSS fitted size in arcseconds andposition angle in degrees, nominal full-width at halfmax, from
JMFIT . Columns 6, 7
WENSS flux and uncertainty in mJy,measured from the survey cutout images using the
AIPS task
JMFIT , selected from multiple resolutions.
Columns 8, 9.
VLSSr flux and error in mJy,measured from the survey cutout images. Flux values Marvil et al.
TABLE 1Survey Properties.
Survey Frequency Coverage Resolution LAS a SensitivityName (MHz) ( ◦ ) ( ′′ ) ( ′ ) (mJy beam − )VLSSr 74 δ > -30 75 ×
75 13.3 54 b WENSS 325 δ > +28.5 54 × δ
60 3.6NVSS 1400 δ > -40 45 ×
45 15 0.45GB6 4850 +75 > δ > ×
204 10 3.8 ca The largest angular scale to which the survey is sensitive. b The median source-free RMS measured from the survey cutouts used in this project. c The average over the declination-dependent sensitivity curve appearing inGregory et al. (1996) for the declination range +35 ≤ δ ≤ +75. are determined by taking the image value at the locationof the optical source center and correcting for the ratioof peak to integrated flux based on the measured NVSSsize. Flux uncertainties are the source-free RMS of thecutout image multiplied by the same size correctionfactor that was used for the flux. Additional Source Properties
We compile a suite of additional data for each sourcebased on available optical, infrared and radio informa-tion, which will be tested for relationships with radiospectral properties in Sections 4.3 and 4.4. The opticalmorphology is assessed using the numerical Hubble stageT, a progression from early to late types, as recorded inthe RC3 catalog. Values for the position, optical majoraxis (D25), optical axial ratio, B-band magnitude, B-Vand U-B colors, and systemic velocity are also taken fromthe RC3 catalog.Infrared fluxes at 60 and 100 µ m are extracted fromthe following IRAS databases, in order of preference: The Bright Galaxy Sample (Soifer et al. 1989),
LargeOptical Galaxies (Rice et al. 1988),
Small-Scale Struc-ture Catalog (Helou & Walker 1988),
Faint Source Cat-alog (Moshir et al. 1992), and the
Point Source Cata-log (Beichman et al. 1988). Only IRAS sources within2 ′ of the optical positions are considered. The 60 and100 µ m fluxes are combined into a single quantity, F IR ,which estimates the flux between 42.5 and 122.5 µ m(Helou et al. 1985), F IR = 1 . × − (cid:0) . S µ m + S µ m (cid:1) W m − (1)where S µ m and S µ m are the 60 and 100 µ m fluxesin Jy.We adopt the relation between star formation rate(SFR) and radio free-free luminosity, L th , given inMurphy et al. (2011) SF R M ⊙ yr − = 4 . × − (cid:18) L th ergs s − Hz − (cid:19) × (cid:18) T e K (cid:19) − . (cid:18) ν GHz (cid:19) . (2)and the relation between SFR and IR luminosity, L IR ,from Kennicutt (1998) SF R M ⊙ yr − = 4 . × − (cid:18) L IR ergs s − (cid:19) (3) By equating Equation 2 and Equation 3 we derive an ex-pression for the optically-thin thermal radio flux, IR S th , IR S th ( ν ) = 1 . × (cid:18) F IR
W m − (cid:19) × (cid:18) T e K (cid:19) . (cid:18) ν GHz (cid:19) − . Jy (4)for which we have assumed L IR (8 − µ m) =1 . L FIR (42 . − . µ m) as in Yun et al. (2001). Weintroduce the superscript ‘IR’ to remind the reader thatthis quantity is derived from the far-IR flux using sim-ple assumptions. We adopt an electron temperature of10 K and tabulate the thermal radio flux at 1.4 GHz, IR S th , . = IR S th (1 . f th , as the ratio ofthermal radio flux to total radio flux, f th ( ν ) = S th ( ν ) /S ( ν ) (5)We tabulate the thermal fraction at 1.4 GHz, IR f th , . ,using IR S th , . as the thermal radio flux and our mea-surement of the NVSS flux as the total radio flux at 1.4GHz, IR f th , . = IR S th , . /S NVSS (6)The radio-FIR ratio q is calculated from the IRASdata and our NVSS survey measurements followingHelou et al. (1985), q = log (cid:18) F IR . × W m − (cid:19) − log (cid:18) S . W m − Hz − (cid:19) (7)Since the expressions for IR f th , . and q both containthe ratio of F IR to the total radio flux, IR f th , . can beexpressed as a function of q , IR f th , . = 1 . × ( q − . (8)Based on this relation sources with small values of q ,which would classically be described as having a radio ex-cess, could alternatively be interpreted as having a lowthermal fraction. Note that values of q more extremethan 3.29 would be difficult to interpret in this manner,since their thermal fractions would exceed unity. How-ever, not only does our study not contain any sourcesntegrated Radio Continuum Spectra of Galaxies 5 TABLE 2Survey Measurements.
NVSS Quantities WENSS Quantities VLSSr Quantities GB6 QuantitiesGalaxy Name Flux Error θ M × θ m P. A. Flux Error Flux Error Flux Error(UGC ′′ × ′′ ) ( ◦ ) (mJy) (mJy) (mJy) (mJy) (mJy) (mJy)(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)444 10.0 1.1 37 ×
26 81 24 2 < · · · < · · ·
480 38.4 1.6 40 ×
38 125 109 4 311 61 < · · ·
528 142 4 48 ×
45 79 262 10 444 63 58 6625 19.6 1.2 45 ×
31 134 42 5 287 75 < · · ·
758 20.6 0.9 26 ×
17 72 52 4 189 50 < · · · ×
10 42 64 4 < · · · < · · · ×
13 22 45 4 < · · · < · · · ×
32 104 31 6 < · · · < · · · ×
11 85 263 10 840 62 32 41355 18.5 0.9 23 ×
21 39 37 4 < · · · < · · · Note . — Table 2 is published in its entirety in the electronic edition of the
Astronomical Journal . A portion is shown herefor guidance regarding its form and content. with q this extreme, but neither does the study ofYun et al. (2001) which includes more than 1800 sources.The infrared fluxes and derived quantities are listed inTable 3. The seven columns of Table 3 give the followinginformation: Column 1.
UGC number.
Columns 2, 3.
The 60 and 100 µ m IRAS fluxes usedin this study. Column 4.
The total Far-IR emission between 42.5and 122.5 µ m, calculated with Equation 1. Column 5.
The thermal flux in mJy calculated withEquation 4.
Column 6.
The thermal fraction at 1.4 GHz, calcu-lated with Equation 6.
Column 7.
The radio-FIR ratio q , calculated withEquation 7.Additional quantities are tabulated for the radio mor-phology and luminosity. We characterize the nature ofthe radio source by its compactness, defined as the ra-tio of the fitted NVSS major axis to the optical majoraxis, and by the radio surface brightness, using the ra-tio of the NVSS flux to the NVSS solid angle defined bythe fitted source size. The Hubble flow distance is calcu-lated from the RC3 velocity (galactic standard of rest) byadopting a value of H ◦ = 70 km s − Mpc − . Radio andinfrared luminosities are estimated in the standard fash-ion, L = 4 πD S , for distance D and flux S . Hubble flowdistances less than 20 Mpc and any derived luminositiesare not considered in further analysis due to their largeuncertainty.A selection of source properties are listed in Table4. The eight columns of Table 4 give the followinginformation: Column 1.
UGC number.
Column 2.
Alternate source name.
Column 3.
Optical position from RC3
Column 4.
Optical axial ratio (minor to major)derived from RC3.
Column 5.
Numerical Hubble type from RC3, fromearly to late morphologies. Ellipticals are in the range -6to -4, lenticulars -3 to -1, spirals (from Sa to Sd) 0 to 8,Magellanic spirals and irregulars 9 and 10, respectively,compact irregulars, 11, non-Magellanic irregulars 90,and peculiars 99.
Column 6.
Log of the surface brightness, calculatedas the NVSS flux divided by the NVSS solid angle(major axis diameter by minor axis diameter), in unitsof mJy per square arcminute.
Column 7.
Radio compactness parameter, the ratioof NVSS major axis (Gaussian full-width at half max)to RC3 optical major axis (D25).
Column 8.
The Hubble flow distance in Mpc. RESULTS
Spectral Properties of the Sample
The goal of this section is to present our spectral mea-surements and to describe the average spectrum of theentire sample. We calculate the spectral index betweenadjacent frequency pairs, when sources are detected inboth surveys, or constrain the spectral index in the casethat the source is only detected in one survey in the pair.Spectral index limits are calculated between the detec-tion and the value of the flux upper limit; no value isproduced when the source is not detected in either sur-vey in the pair. Due to dissimilar survey sensitivities,many sources detected in the WENSS survey are not de-tected in the VLSSr, leading to lower limits on the low-frequency spectral index, and many sources detected inthe NVSS survey are not detected in GB6, leading toupper limits on the high-frequency spectral index.We label these spectral indices α low , α mid and α high torepresent their relationship to our frequency samplingas illustrated in Figure 1, and provide these spectralmeasurements in Table 5. The nine columns of Table 5give the following information: Column 1.
UGC number.
Columns 2, 3.
Spectral index α low and uncertaintymeasured between the VLSSr and WENSS data. Limitsare given when only one flux is detected, calculatedas the slope between the detection and the flux upperlimit. No value is given when there are non-detectionsat both bands. Column 4, 5.
Spectral index α mid and uncertaintymeasured between the WENSS and NVSS data. Non-detections are treated as in columns 2 and 3. Column 6, 7.
Spectral index α high and uncertaintymeasured between the NVSS and GB6 data. Non-detections are treated as in columns 2 and 3. Marvil et al. TABLE 3Far-IR Data and Derived Quantities.
Galaxy Name S µ m S µ m F IR IR S th , . f th , . R-FIR q (UGC − W m − ) (mJy) (%)(1) (2) (3) (4) (5) (6) (7)444 0.8 2.2 5.4 0.7 7 2.16480 1.4 3.6 9.0 1.1 3 1.79528 25 44 137 17 12 2.41625 2.4 6.6 16 2.0 10 2.34758 2.0 5.2 13 1.7 8 2.241111 2.0 3.5 11 1.4 4 1.961220 1.9 4.6 12 1.5 8 2.221347 1.5 3.8 9.7 1.2 10 2.301348 0.2 0.9 1.9 0.2 < Note . — Table 3 is published in its entirety in the electronic edition of the
AstronomicalJournal . A portion is shown here for guidance regarding its form and content.
TABLE 4Additional Source Properties.
Galaxy Name Alt. Name Position (J2000) Axial Ratio Type log Σ compact D (Mpc)(1) (2) (3) (4) (5) (6) (7) (8)444 · · ·
00 42 04.7 36 48 15 0.69 · · · · · · · · ·
625 IC 65 01 00 55.8 47 40 51 0.30 4 1.7 0.19 40758 NGC 425 01 13 02.5 38 46 07 0.93 · · · · · · · · ·
01 52 45.8 36 37 07 0.87 5 1.5 0.57 811348 NGC 708 01 52 46.4 36 09 06 0.83 -5 2.7 0.24 711355 · · ·
01 53 36.5 43 57 58 0.87 3 2.1 0.28 91
Note . — Table 4 is published in its entirety in the electronic edition of the
Astronomical Journal . A portionis shown here for guidance regarding its form and content.
TABLE 5Spectral Properties.
UGC α low ∆ α low α mid ∆ α mid α high ∆ α high R low ∆ R low (1) (2) (3) (4) (5) (6) (7) (8) (9)444 > -1.28 · · · -0.60 0.09 < · · · -0.3 0.1480 -0.71 0.14 -0.71 0.04 < -0.58 · · · < -0.06 · · · < -0.08 · · · > -0.67 · · · -0.48 0.04 < -0.43 · · · > -0.92 · · · -0.57 0.06 < -0.03 · · · > -1.29 · · · -0.60 0.15 < · · · > -1.27 · · · -0.47 0.08 < -0.01 · · · Note . — Table 5 is published in its entirety in the electronic edition of the
Astro-nomical Journal . A portion is shown here for guidance regarding its form and content.
Column 8, 9.
The ratio and uncertainty between theVLSSr and WENSS flux measurements. Negative valuesare due to the VLSSr flux measurement technique. Novalue is given when the WENSS flux is not detected.After calculating the spectral index, our next goal isto characterize the distributions of α low , α mid and α high .When dealing with flux upper limits, we employ the Non-detects and Data Analysis ( NADA ) package from the [R]computer language. Specifically, the Akritas-Theil-Sen (ATS) nonparametric line is used to determine the pop-ulation mean, which considers both detections and cen-sored data using survival analysis techniques; the uncer-tainty in the population mean is estimated by nonpara-metric bootstrap.The most precise measure of the spectral index is be-tween the 325 and 1400 MHz data (WENNS - NVSS,referred to herein as α mid ). A value of α mid is availablefor each of the 250 sources and has a typical uncertaintyof ± α mid of -0.55 andntegrated Radio Continuum Spectra of Galaxies 7 (cid:4) (cid:5) (cid:6) (cid:7) spectral index (cid:8) mid g a l a x i e s p e r b i n Fig. 2.—
The distribution of spectral index α mid , calculated be-tween the WENSS and NVSS survey data, is shown for the sampleof 250 sources (shaded). These data have mean value -0.55 andstandard error 0.01, calculated after outlier rejection. The uncer-tainties in the flux measurements are used to simulate the spec-tral index distribution which we would expect to observe if everysource’s intrinsic spectral index were equal to that of the samplemean. The dispersion in α mid is substantially broader than can beexplained by measurement uncertainty alone (solid line), indicat-ing that much of the observed variability is intrinsic to the sourcepopulation. dispersion between 0.10 and 0.20 depending on the de-gree of outlier rejection, resulting in a standard error inthe mean of approximately 0.01. A simulation incorpo-rating the measured flux uncertainties is used to estimatethe effect of measurement error on the dispersion in α mid .By scaling each source to have the same spectral indexas the mean of α mid and resampling α mid using a para-metric uncertainty model, we construct the distributionwe would expect to observe if each source had the samespectral index (see the solid curve in Figure 2). Since thedispersion in this simulated distribution is approximately0.05, we find that much of the observed dispersion in α mid is due to intrinsic variability within the population andcan not be attributed to measurement error.The spectral index between the lowest frequency datain our study, α low , is calculated using flux measurementsat 74 and 325 MHz (VLSSr - WENSS). We choose tocensor the VLSSr flux measurements below 3 σ for thepurposes of calculating the spectral index and insteaduse the 3 σ value to determine a lower limit to α low . Wefind a mean α low for the sample of − . ± .
05, incorpo-rating both the detections and limits with survival anal-ysis (see Figure 3). The dispersion, considering only thedetections, is 0.37. The low frequency flux ratio R low ,defined as the ratio of VLSSr to WENSS flux, is also cal-culated for each source. The advantage of R low is thatit has been tabulated along with an uncertainty for eachsource instead of being censored in the manner of α low .Between 1400 and 4850 MHz (NVSS - GB6) we cal-culate α high , the spectral index between the highest fre-quency pair. The GB6 5 σ declination-dependent upperlimits are used to produce corresponding upper limitsin α high when catalog fluxes are unavailable. A samplemean of − . ± .
04 (see Figure 4) is determined usingsurvival analysis, and the dispersion of the detections is0.30. (cid:9) (cid:10) (cid:11) (cid:12) spectral index (cid:13) low g a l a x i e s p e r b i n Fig. 3.—
The distribution of spectral index α low , taken betweenthe VLSSr and WENSS survey data, is shown for the sample of 250sources. Measurements (shaded) are computed from detections atboth frequencies; 3 σ lower limits (hashed) are derived from VLSSrnon-detections. The sample mean (dashed line) is determined tobe − . ± .
05, incorporating both the detections and limits usingsurvival analysis. The arrow overlaid on the hashed bins empha-sizes the direction of the spectral index limits and therefore theinfluence these bins have on the sample mean. (cid:14) (cid:15) (cid:16) (cid:17) spectral index (cid:18) high g a l a x i e s p e r b i n Fig. 4.—
The distribution of spectral index α high , between theNVSS and GB6 survey data, for the sample of 250 sources. Mea-surements (shaded) are computed from detections at both frequen-cies; 5 σ upper limits (hashed) are based on NVSS detections forwhich no corresponding GB6 catalog association was identified.The sample mean, − . ± .
04, is fit with survival analysis tech-niques to incorporate the detections and limits. The arrow overlaidon the hashed bins emphasizes the direction of the spectral indexlimits and therefore the influence these bins have on the samplemean.
The differences between mean values of α low , α mid , and α high are tested for significance against the t-distribution,where the variance and effective degrees of freedom areestimated following procedures for samples with unequalvariances. The change from α low to α mid is suggestivebut not highly significant, at a level of 95%, whereasthe differences between α mid and α high and between α low and α high are both deemed significant at a level greaterthan 99.9%. Taken as a whole these results demonstratethat, across the entire frequency range of this study, the Marvil et al. (cid:19) (cid:20) (cid:21) log ( Frequency / 1 GHz) l o g F l u x [ a r b i t r a r y un i t s ] VLSSr WENSS NVSS GB6 (cid:22) low (cid:23) mid (cid:24) high =-0.45 =-0.55 =-0.69
Fig. 5.—
Illustration summarizing the results of our spectralmeasurements for the galaxy sample. The scaled mean flux for eachradio survey (filled circles) is fit with a function having spectralindex α = -0.7 at 10 GHz and curvature ∆ α = -0.2 per logarithmicfrequency decade (shaded). R-FIR q g a l a x i e s p e r b i n thermal fraction [%] Fig. 6.—
The distribution of the radio to far-IR ratio q , calculatedwith Equation 7, for a sample of 221 galaxies for which IRAS datawas available. The mean value from Yun et al. (2001), q = 2 .
34, isindicated by the dashed line. Also labeled is the thermal fractionat 1.4 GHz, IR f th , . , calculated with Equation 6. The medianvalue of q for our sample is 2.27, which corresponds to a thermalfraction of 9%. We attribute the displacement of these values of q from those in Yun et al. (2001) to differences in sample selection:our sample is limited by radio flux and optical magnitude, andtheirs is 60 µ m flux limited. average spectrum of galaxies in our sample can not bewell described by a single power law; this amounts to adetection of curvature among the general population inour sample. The average spectrum can be approximatedby a generic function with logarithmic curvature β = − .
1, where S ( ν ) ∝ ν α + β log ν . For this function, thespectral index changes by a value ∆ α = 2 β for eachlogarithmic decade in frequency. A summary of theseresults is illustrated in Figure 5, which shows a spectrumderived from the mean spectral indices. Calculations of the Thermal Fraction
In this section, two independent methods are used tocalculate the thermal fraction, f th , . , defined as the ratio thermal fraction from decomposition [%] t h e r m a l f r a c t i o n f r o m R - F I R q [ % ] Fig. 7.—
This scatter plot is used to test for a correlation be-tween the thermal fraction determined from two independent meth-ods.
Ordinate : the thermal fraction calculated with the IRAS andNVSS fluxes, IR f th , . , as in Figure 6. Abscissa : the thermal frac-tion calculated from spectral decomposition, R f th , . , from Equa-tion 9. The dashed line indicates a 1:1 correlation, which wouldbe expected if both methods produced accurate estimates of thethermal fraction; however, no such relationship is observed. of the free-free emission to the total radio continuum at1.4 GHz, and the results are compared. The first method,discussed in Section 3.2, uses the IRAS and NVSS fluxesto produce the values of IR f th , . which appear in Table 3.The value of IR f th , . can also be expressed as a functionof the radio far-IR ratio q as specified by Equation 8. Thedistribution of these values of q , and the correspondingvalues of IR f th , . are displayed in Figure 6.The second method of calculating the thermal frac-tion is based on the model of power-law emission com-ponents, i.e. , synchrotron and free-free having spectralindices − . − .
1, respectively, as illustrated withFigure 1. The functional form of this model can be writ-ten as in Equation 9, S ( ν ) ∝ f th (cid:18) νν (cid:19) − . + (1 − f th ) (cid:18) νν (cid:19) − . (9)where f th is the thermal fraction at a chosen referencefrequency ν . By evaluating this model at ν = 325 MHzand ν = 1 . R f th , . as a function of α mid : R f th , . = ( ν /ν ) α mid − ( ν /ν ) − . ( ν /ν ) − . − ( ν /ν ) − . (10)where the superscript ‘R’ denotes that this value is de-rived solely from radio observations plus simple assump-tions. Equation 10 represents a process which is often re-ferred to as spectral decomposition. Some applications ofspectral decomposition, having available a larger numberof frequency measurements across a wider bandwidth,have allowed the synchrotron spectral index to be a freeparameter; here, we avoid this additional complexity inorder to prevent a degenerate parameter space. Notethat our model does not satisfactorily explain observedspectral indices flatter than -0.1 or steeper than -0.8, andas such we assign such observations thermal fractions of100% and 0%, respectively.ntegrated Radio Continuum Spectra of Galaxies 9 (cid:25) Numerical Hubble Type R - F I R q E L Sa Sb Sc Sd I
Fig. 8.—
A plot of the radio-farIR ratio q , as defined in Equa-tion 7, versus the numerical Hubble type. The crosses indicatethe mean and standard deviation for bins containing E, L, Sa, Sb,Sc, and Sd/I types. The dashed line indicates the value q = 2 . q values which are less than 1.64 belong toa radio-excess population commonly associated with AGN. Theearly-type galaxies in our sample have, on average, lower values of q than later morphological types. In Figure 7, the distribution of IR f th , . (from Equa-tion 6) is compared to the distribution of R f th , . (cal-culated with Equation 10). We find no correlation be-tween the thermal fractions estimated from these inde-pendent methods. Moreover, the values of IR f th , . arenarrowly distributed with a median of 9% and disper-sion 3%, and agree well with the expected values fromprior studies, while the values of R f th , . are, on aver-age, much larger and have much greater variation (mean51% and dispersion 26%). The values produced by spec-tral decomposition are unsatisfying for several reasons,most notably the large mean and dispersion, and fail-ure to properly account for spectral indices outside theinterval − . − .
1. This suggests that the spectral de-composition model given by Equation 9 is an inadequatedescription of the spectra below 1 GHz.
Relationships with Hubble Type
We investigate relations between the tabulated sourceproperties ( i.e. , spectral measurements, FIR-derivedquantities and additional data) and the numerical Hub-ble type. The data are binned by morphological typesE, L, Sa, Sb, Sc, and Sd/I and the bin means and stan-dard errors are used to determine the significance levelof correlation. After reviewing a large number of pos-sible correlations, we present in this section the resultsdeemed most relevant to this study.First, we discuss the observed relation between q andnumerical Hubble type, shown in Figure 8. Taken as awhole, the early-type (E and L) galaxies in our samplehave significantly smaller values of q than spiral types Sathrough Sd. While the late types in our sample typicallyhave values of q consistent with the expected value forordinary star-forming galaxies, many early types in oursample have ‘radio-excess’ values of q which can be anindicator of AGN activity (Yun et al. 2001).We identify a relationship between the numerical Hub-ble type and our radio compactness parameter, the ra- (cid:26) Numerical Hubble Type c o m p a c t n e ss E L Sa Sb Sc Sd I
Fig. 9.—
The radio-optical compactness parameter, defined asthe ratio of the radio major axis to the optical major axis, versusthe numerical Hubble type. The crosses indicate the mean andstandard deviation for bins containing E, L, Sa, Sb, Sc, and Sd/Itypes. (cid:27)
Numerical Hubble Type (cid:28) (cid:29) (cid:30) s p e c t r a l i n d e x (cid:31) m i d E L Sa Sb Sc Sd I
Fig. 10.—
This scatter plot is used to explore the relationshipbetween spectral index α mid and morphological type, using the nu-merical Hubble type. The crosses indicate the mean and standarddeviation for bins containing E, L, Sa, Sb, Sc, and Sd/I types.No appreciable differences are identified in the spectral index ofdifferent morphological types. tio of the radio to optical major axis diameter (see Fig-ure 9). On average, the early-type galaxies in this sam-ple harbor radio sources which are smaller with respectto the optical host as compared with later morphologicaltypes. There also exists substantial variation in compact-ness within the sub-population of spiral types Sa to Sd,where the later tends to be more extended than the for-mer. One possible explanation is that the star formationin late types is more distributed throughout the opticaldisk but is more nucleated in early types; alternatively,the radio emission from early types may be due in partto a low-luminosity AGN. A relationship between com-pactness and radio surface brightness is also identified,although this may be due in part to selection effects fromusing a flux threshold.We test for a relationship between α mid and Hubbletype, but do not identify a significant trend in our data0 Marvil et al.(see Figure 10). This is an unexpected result consid-ering that some prior studies have detected such a re-lation ( e.g. , Condon et al. 1991; Deeg et al. 1993), al-though they typically used data at higher frequencies tocalculate the spectral index. Additionally, the distribu-tions of q and the compactness parameter (see Figures8 and 9) suggest that the radio sources in early typesmay have different properties or be driven by differentprocesses. However, it appears from our results thatthe magnitude of the spectral index across the frequencyrange used for α mid (325 - 1400 MHz) is not sensitive tothese differences. Relationships with Additional Data
Relationships between spectral measurements ( i.e. , α mid and R low ) and various additional source propertiesare investigated in order to better understand the phys-ical processes which shape the radio spectrum. Trans-formations are applied to the data and outliers are re-jected, when necessary, to better meet the requirementsof normality before testing for correlations. For contin-uous variables, the significance of the relation is judgedusing Pearson’s correlation coefficient.Significant trends are detected between the steepnessof the spectral slope (using either α mid and R low ) andthe source luminosity (using either NVSS or IRAS). Ineach case the steeper spectra are correlated with sourceshaving higher luminosity. One such example is shown inFigure 11, the case of α mid versus the log of NVSS lu-minosity, in which we have only considered sources withHubble flow distances greater than 20 Mpc and luminosi-ties less than log L = 23 .
6, for L in [W Hz − ]. The equa-tion of the regression line determined from these data is α mid = 2 . − .
13 log L .One particular relation which has been discussed inprevious studies is between the low frequency spectralindex and optical axial ratio (as a proxy for galaxy in-clination), motivated by observation as well as geomet-ric models of thermal absorption. We test our data forrelationships between the optical inclination, as derivedfrom the optical axial ratio, and spectral properties α mid and R low . In pursuit of a better parameter to gauge theamount of expected thermal absorption, we quantify theprojected path length through the galaxy disk by usingour knowledge of the optical size, inclination, Hubbleflow distance, and assuming disk scale height equal to10% of the diameter. We also test both the full galaxysample as well as a subset containing only Hubble typesSa to Sc, since this subset is expected to better conformto our disk model. We find no significant relationshipsfor any of these combinations; one example, α mid versusinclination angle, is provided with Figure 12.A final test of considerable interest is α mid versus IR f th , . (See Figure 13) From the simple model of power-law thermal and non-thermal emission, e.g. , Figure 1, aflatter spectral index is expected to correlate with in-creasing thermal fraction, but no such relationship is de-tected. This indicates that the simple model of optically-thin power-law components does not provide an adequatedescription of the spectral index α mid ; this issue is dis-cussed in greater detail in Section 5.After reviewing a large number of possible correlationsbetween spectral properties (Table 5) and the tabulatedsource properties (Tables 3 and 4) and rejecting those log ( NVSS Luminosity / W Hz ) ! " s p e c t r a l i n d e x $ m i d Fig. 11.—
The values of α mid plotted as a function of NVSSluminosity. The crosses mark the mean and standard deviation ofbins containing an equal number of sources. A significant trend isidentified whereby the higher luminosity sources in our sample areassociated with steeper spectral index. optical inclination [ % ] & ’ ( s p e c t r a l i n d e x ) m i d Fig. 12.—
The values of α mid plotted as a function of opticalinclination angle and crosses marking the mean and standard de-viation of bins containing equal numbers of sources. We do notsee this relation in our data after testing α mid , R low and projectedlinear size versus inclination angle, where the linear size was calcu-lated using the optical size, inclination and Hubble flow distance. which could be attributed to selection effects, only therelation between spectral index and luminosity is foundto be significant. A number of supplemental tests are alsoconducted using optical colors B-V and U-B, the ratio ofthe 60 and 100 µ m fluxes, the radio axial ratio and thedifference between radio and optical position angles, butno significant trends are identified. DISCUSSION AND CONCLUSIONS
For most galaxies in our sample, the fractional sensi-tivity for our set of flux measurements is not adequate todistinguish the standard power-law model from alterna-tives based on goodness-of-fit statistics. For this reason,we focus not on fitting the individual galaxy spectra butinstead on descriptive population statistics. This sectiondiscusses our interpretation of (1) the mean values of thespectral index and generalized curvature, (2) the disper-ntegrated Radio Continuum Spectra of Galaxies 11 * thermal fraction [%] + , - . / s p e c t r a l i n d e x m i d Fig. 13.—
This scatter plot is used to test for a correlationbetween the thermal fraction, as determined from the IRAS andNVSS fluxes (Equation 8), and spectral index α mid , with crossesshowing the mean and standard deviation for bins containing equalnumbers of sources. No significant relationship is detected betweenthese quantities. sion in the distribution of α mid , and (3) relationships be-tween spectral characteristics of the radio emission andadditional source properties.From the distributions of α low , α mid , and α high , we findthat there is low frequency curvature present in the radiospectra of galaxies. Comparing our result to the averagespectra of the Gioia et al. (1982) sample, we find that weagree asymptotically at the high frequency part of thespectrum but diverge at lower frequencies. One possibleexplanation is that the Gioia et al. (1982) sample suf-fers from selection effects— approximately 40% of theiroriginal volume limited sample was discarded because ofnon-detections at the lowest frequency. Other studiessuch as the one by Israel & Mahoney (1990), which ex-tends down to 57.5 MHz, found that spectral curvaturein the form of low frequency flattening is not uncommonin spiral galaxies. Therefore we conclude that low fre-quency galaxy spectra are, on average, better modeledby a function having logarithmic curvature than by asingle power law. We find that ∆ α = − . >
10 GHz ( e.g. ,Tarchi et al. 2000; McDonald et al. 2002), these are pref-erentially found in dense starburst galaxies and do notcover a large fraction of the source. On the other hand,the hot ISM has a large covering factor but can not pro-duce the required emission measures given typical sizesand densities. Therefore, we conclude that thermal ab-sorption of power-law synchrotron emission can not be the primary mechanism which produces the observedcurvature.We also want to discuss some of the physical mech-anisms which could be responsible for a curved syn-chrotron spectrum. Here, we adopt a model where cos-mic rays are injected into the system with a power-lawenergy distribution via shock acceleration, where the in-jection index s ∼ α ∼ − . e.g. , Green1984). One description of the spectral curvature de-tected in the average spectrum (see 5) is that we areobserving a gradual transition from the injection indexto a steeper spectrum at higher frequencies. This spec-tral behavior is typically associated with radiative losses( i.e. , synchrotron and inverse Compton), for which theloss rate is proportional to the CRE energy. However,strong radiative cooling (an essential component in manyR-FIR models) alone would produce a power-law spec-trum with a much steeper spectral index α ∼ − .
0. Here,we propose two scenarios under which radiative coolingcould produce the observed curvature. For one, the ra-diative cooling could transition from weak, at the lowerfrequencies, and become stronger at the higher observedfrequencies. In this scenario, electrons radiating belowabout 1 GHz would need to be younger than their radia-tive lifetime. Alternatively, the curvature could be pro-duced by the combination of strong radiative losses andanother loss mechanism such as ionization or relativisticbremsstrahlung. In this second scenario, the energy lossrates of these processes would need to be comparable forelectrons radiating near 1 GHz.Some studies have used the integrated spectrum to es-timate physical parameters such as the density and mag-netic field. For example, Yoast-Hull et al. (2013) com-pares the results of several models applied to the spec-trum of M82. However, the variability of these resultsemphasizes that the estimated parameters depend uponthe details of the models and their incorporated assump-tions. An additional consideration which is often ne-glected when analyzing the total radio spectrum is theeffect of inhomogeneous sources. It is known that thephysical conditions within galaxies ( e.g. , SFR, density,temperature, magnetic field, interstellar radiation field)vary as a function of position, and consequently, CRE in-jection, radiation and CRE energy loss mechanisms alsovary accordingly. If different regions within the sourceproduce distinctly different spectra, then the uniform‘single box’ models may not be adequate to interpretthe net spectrum of these regions ( e.g. , as discussed byLisenfeld & V¨olk 2000). A number of observations havedemonstrated the high degree of inhomogeneity in starforming systems, including spatial variations of the radiospectrum ( e.g. , Seaquist & Odegard 1991; Reuter et al.1992; Lisenfeld et al. 1996; Tabatabaei et al. 2013). Ad-ditionally, a new study of the resolved radio continuum oftwo nearby galaxies (Marvil et al. 2013, in preparation)demonstrates the importance of inhomogeneities in shap-ing the integrated spectrum. For these reasons, we electnot to pursue this type of quantitive interpretation of thespectral results.The origin of the observed dispersion in α mid is an-other point of considerable interest. On one hand, the2 Marvil et al.dispersion is small enough that it would appear that thephysical conditions among the majority of galaxies in oursample are remarkably similar. Yet on the other hand,this distribution is broad enough that we can not explainit solely by measurement uncertainty alone, indicatingthat some galaxies have intrinsically steeper or flatterspectra than the average.One possible model which can address the intrinsic dis-persion in α mid involves a thermal fraction which varieswithin the sample, such that low f th , . sources havespectra which resemble the underlying non-thermal spec-trum ( α NT . − .
7) and high f th , . sources have spectrawhich approach a purely free-free spectrum ( α ≥ − . α mid wouldfurther support this explanation. However, we do notdetect correlations between IR f th , . and α mid or R low aswould be predicted by such a model. Additionally, thelarge thermal fractions needed to explain the typical α mid values near -0.55, based on the decomposition model ofEquation 10, are much higher than those found in similarstudies.Several other factors may contribute to the dispersionin α mid . We considered the effect of the relation be-tween spectral index and radio luminosity, but this onlyaccounts for a small fraction of the α mid dispersion. De-spite testing a large number of potential correlations, wewere unable to identify any additional relationships withwhich to illuminate the nature of this dispersion. Thesource’s star formation history may also play an impor-tant role in determining the spectral index; variations ofthe constant-injection model of synchrotron spectral ag-ing predict that post-starburst galaxies will have signifi-cantly steeper spectra while sources whose star formationrate is increasing with time will have flatter spectra. Al-though we tested for and found no relationships between α mid and optical colors U-B and B-V, a more accuratemeasure of star formation history may be necessary toreveal such a relationship if it exists. Galaxy mass isanother source property which we were unable to testfor, and may affect the spectral index as discussed byKlein et al. (1991).There are a small number of outliers in the α mid dis-tribution (see Figure 2) which we have tried to betterunderstand. Here, we discuss 16 outliers identified ashaving values of α mid outside the interval (-1,0). Wefind that their uncertainties are not significantly largerthan the average uncertainties in the sample, and as such,their differences from the sample mean are highly signif-icant. We also find that these outliers are much morelikely to lack IRAS identifications (38%) when comparedto the rest of the distribution (9%). For the outlierswhich have IRAS detections, their mean value of q is1.97, which, compared with the distribution of q fromYun et al. (2001), is about 3 σ away from the mean value(on the radio-loud side). Since these outliers are, on av-erage, radio loud, it is plausible that those lacking IRASidentifications are also radio-loud ( i.e. . too faint to beincluded in the IRAS catalog). There is also the issue ofNVSS source identifications, for which we accepted ap-proximately 1% background radio sources not associatedwith the optical galaxy; this would lead to ∼ i.e. , V´eron-Cetty & V´eron 2010;Best & Heckman 2012) and examination of very high res-olution radio continuum images. Moreover, we find thatover 60% of 22 outliers in the q distribution can also beassociated with AGN using these same techniques.From the tested correlations with Hubble type, we findseveral distinguishing characteristics within our sample:the radio sources in early types appear to be more com-pact, have higher surface brightness and have excess ra-dio emission as compared to infrared emission. Never-theless, the mean spectral index of radio sources in ourearly types appears to be the same as the mean spec-tral index of radio sources in spiral types. Therefore, itwould appear that the magnitude of the spectral indexcan not be used to probe the physical nature of the radiosource unless the spectral index takes on extreme valuesindicative of purely thermal or non-thermal processes.One of the primary goals at the outset of this investiga-tion was to measure relationships between source prop-erties and spectral characteristics in order to better un-derstand how the radio continuum spectrum is relatedto a source’s physical conditions and star formation his-tory. However, this analysis was limited by the sensitiv-ity of current large-area radio survey data, which is notadequate to accurately measure spectral curvature forindividual objects in our sample. New large-area radiosurveys with enhanced frequency coverage and sensitiv-ity are highly desirable to improve the detection statisticsand extend the range over which the spectrum can be an-alyzed. Additionally, improving the spatial resolution ofthe spectral data may provide an important probe of thesource’s physical nature. Furthermore, it may be neces-sary to expand the set of source properties ( e.g. , gravi-tational potential, ISM density, magnetic field strength,wind velocity) to identify stronger correlations.JM was supported by a NRAO Grote Reber DoctoralFellowship. The VLSSr, NVSS and GB6 surveys wereconducted using instruments of the National Radio As-tronomy Observatory. The National Radio AstronomyObservatory is a facility of the National Science Foun-dation operated under cooperative agreement by Asso-ciated Universities, Inc. Special thanks to Joe Lazio,Namir Kassim, Wendy Peters and Bill Cotton for sta-tus updates and early access to the VLSSr survey data.The WENSS project was a collaboration between theNetherlands Foundation for Research in Astronomy andthe Leiden Observatory. We have made use of the WSRTon the Web Archive ( ). TheWesterbork Synthesis Radio Telescope is operated bythe Netherlands Institute for Radio Astronomy AS-TRON, with support of NWO. This research hasmade use of the NASA/IPAC Extragalactic Database(NED) which is operated by the Jet Propulsion Lab-oratory, California Institute of Technology, under con-tract with the National Aeronautics and Space Ad-ministration. The VizieR (Ochsenbein et al. 2000)archive server was used extensively for catalog queries( http://cdsarc.u-strasbg.fr/vizier/ ).ntegrated Radio Continuum Spectra of Galaxies 13).ntegrated Radio Continuum Spectra of Galaxies 13