The refractive index is the fundamental property controlling aerosol optical properties. Secondary organic aerosol (SOA) real refractive indices (mr) were derived from polar nephelometer measurements using parallel and perpendicular polarized 670 nm light, using a genetic algorithm method with Mie-Lorenz scattering theory and measured particle size distributions. The absolute error associated with the mr retrieval is ±0.03, and the instrument has sufficient sensitivity to achieve reliable retrievals for particles larger than about 200 nm. SOA generated by oxidizing α-pinene, β-pinene, and toluene with ozone and NOx/sunlight are explored. Retrieved refractive indices for the SOA vary between 1.38 and 1.61, depending on several factors. For α- and β-pinene ozonolysis, SOA mr ranges from 1.4 to 1.5 and, within the resolution of our method and bounds of our experiments, is not affected by the addition of an OH scavenger, and is only slightly dependent on the aerosol mass concentration. For photochemically generated SOA, mr generally increases as experiments progress, ranging from about 1.4 to 1.53 for α-pinene, 1.38 to 1.53 for β-pinene, and 1.4 to 1.6 for toluene. The pinene SOA mr appear to decrease somewhat toward the end of the experiments. Aspects of the data suggest aerosol mass concentration, oxidation chemistry, temperature, and aerosol aging may all influence the refractive index. There is more work to be done before recommendations can be made for atmospheric applications, but our calculations of the resulting asymmetry parameter indicate that a single value for SOA refractive index will not be sufficient to accurately model radiative transfer.
 Aerosol optical properties, which depend on the size distribution of the particles, their chemical composition, mixing state, shape, and wavelength, are crucial to determining the amount of radiation scattered and absorbed (i.e., the aerosol direct effect). Refractive indices are also necessary to determine the factors relevant to radiative transfer, such as single scatter albedo, asymmetry factor and specific absorption using Mie-Lorenz theory. Additionally, reliable phase function and polarization information is essential for the interpretation of satellite and aircraft measurements to infer aerosol optical depth, size and single scatter albedo [Mishchenko et al., 2007].
 Organic compounds make up a substantial fraction of atmospheric aerosols, accounting for 20−90% of aerosol mass in the lower troposphere, of which about 70% is secondary [Hallquist et al., 2009]. The α- and β-pinene and toluene, the subjects of this study, contribute a substantial fraction of SOA in many local areas, as well as globally, although the precise contribution of each species is debated [Hallquist et al., 2009; Pye and Seinfeld, 2010].
 The radiative properties of these ubiquitous SOA particles are poorly understood [Kanakidou et al., 2005]. Their contribution to the global radiation balance depends on their production and loss rates, their interactions with other radiatively important atmospheric constituents, (via the ‘indirect and semidirect’ effects), and on their direct interactions with solar insolation and upwelling terrestrial infrared radiation. The experiments in this paper explore SOA parameters key to the direct effect, at the wavelength of 670 nm. SOA absorb very little or not at all at around 670 nm [Schnaiter et al. 2005; Kanakidou et al., 2005]; hence only the scattering properties of these SOA have an effect on radiative transfer. Scattering from particles is described by the scattering phase function, which is parameterized in radiative transfer models using the cosine weighted integral of the particle scattering intensities, known as the asymmetry parameter. Changes to the asymmetry parameter resulting from changes to the refractive index within the range of values measured here for SOA are discussed in section 4.5 of the paper.
 A tiny handful of experimental investigations have begun to derive refractive indices from secondary organic aerosols themselves. Schnaiter et al.  estimated the α-pinene-O3 SOA refractive index of 1.5 by fitting Mie-Lorenz calculations to scattering and absorption measurements at 3 wavelengths. Using an earlier version of our polar nephelometer, our group [Barkey et al., 2007] retrieved a refractive index of 1.42 for SOA formed by α-pinene reacting in the presence of NOx. Lang-Yona et al.  very recently reported retrievals of refractive indices of SOA generated from a mixture of biogenics (mostly terpenes) released directly from plants, using cavity ring down. The biogenic hydrocarbons were oxidized in a chamber using O3 and OH at very low NOx levels, and the resulting SOA had an mr of 1.53 ± (0.06–0.08). The reported and estimated values span a reasonably wide range, but the values generally agree within the (reasonably large) measurement uncertainties, so it is unclear how much refractive indices vary between different SOA, or which value(s) are most representative.
 A few studies of ambient aerosols with SOA as a major component are available. Dick et al.  measured the refractive indices of aerosols near Smokey Mountain National Park and found real refractive indices of 1.49 for dry and 1.42 for wet aerosol, with little dependence on size between 0.2 and 0.5 μm. They modeled their observed angular scattering data (between 40° and 140°) using volumetric fractions of the different constituents measured on filters, and known or estimated refractive indices for the components. The best fit was obtained when the refractive index of the OC component was adjusted to 1.46. By inverting optical counter data, Hock et al.  measured rural aerosol with a ratio of highly oxidized aerosol to hydrocarbon-like organic aerosol of 4:1 and found 1.40−1.45. Moffet et al.  estimated optical properties of ambient aerosols from size-dependent scattering as a function of chemical composition using an aerosol time-of-flight mass spectrometer. Most of their results are for mixed aerosols, however they did report a value for mr of 1.53 ± 0.04 for a class of spherical particles from Mexico City classified as high-mass organic carbon.
 Polar nephelometers (PN) have been used to make angular scattering measurements with the goal of deriving various physical parameters of aerosol particles, including the complex refractive index. Several theoretical studies [Shaw, 1979; Verhaege et al., 2008] have shown it is possible to determine both the real refractive index and some monomodal size distribution parameters from PN measurements, if the particles are spherical and homogeneous. Experimentally, Jones et al.  used a 15-channel polar nephelometer with an 840 nm laser to determine the refractive index and size distribution of polystyrene latex (PSL) spheres. Zhao  estimated a retrieval error of a few percent in the real component and up to 50% in the imaginary for their goniometer type PN. Lienert et al.  determined aerosol size distributions using a 532 nm goniometer PN using the genetic algorithm (GA) method, Mie-Lorenz scattering and an assumed refractive index. We have demonstrated real refractive index, size distribution mean and standard deviation retrievals from angular scattering measurements of aerosols with a polar nephelometer designed at UCLA [Barkey et al., 2007]. The retrievals reported here use a GA method and assume size distributions are lognormal and monomodal.
 In this paper we study SOA particles generated from α- and β-pinene and toluene using several different oxidation chemistries, in an effort to probe the importance of oxidation chemistry and other factors on SOA refractive indices. For dark ozone reactions of unsaturated hydrocarbons, reactions can be initiated either solely by O3 or by O3 together with OH. For VOC/NOx photochemistry, at “high” VOC/NOx ratios, organic peroxy radicals (RO2) react with RO2 or HO2 to produce lower volatility products than the RO2 + NO reactions that dominate under “low” VOC/NOx conditions [Ng et al., 2007; Presto et al., 2005]. These chemistries are used here to generate SOA in an outdoor chamber. Angular scattering, including polarization, was measured with a second-generation polar nephelometer. Refractive indices of the aerosols are retrieved from the resulting angular scattering data. The resolution of the refractive indices is sufficiently high that, for the first time, the importance of SOA generation chemistry, mass concentration, aging and parent hydrocarbon on aerosol refractive index can be probed.
2. Experimental Methods
 Experiments were performed in a 24 m3 Teflon chamber constructed on the roof of the Math Sciences Building at UCLA. The chamber is described in detail by Chung et al. . Air is supplied to the chamber by two 33 gallon oil-free portable air compressors (Craftsman) after passing through a series of packed bed scrubbers filled with Purafil Triple Blend (Purafil Inc.), activated charcoal, and HEPA capsule filters (Gelman). The scrubbed air has < 50 particles cm−3, and NOx (Thermo Electron model 14B/E), O3 (Dasibi 1001-RS), and organics (GC, HP 5890-II) levels below the 1 ppb detection limits. Between experiments, a vent is opened and the chamber is flushed with clean air for 10 h in full sun in preparation for the next experiment. The α- and β-pinene (Fluka, 98.5%) and toluene (Aldrich, 99.8%) were used as received.
Tables 1 and 2 show initial conditions and summary statistics for 28 experiments. For photo-oxidation experiments, the chamber, covered with a black tarpaulin (supported on a frame above the chamber), was half filled with purified air. At this point, gas-phase reagents such as NO (Scott Specialty Gasses) and propene (Aldrich, as a photochemical initiator for toluene) were added. Finally, the SOA precursor hydrocarbon liquid was evaporated into the air stream filling the chamber. The chamber contents were allowed to mix for about 40 min. Once the gas chromatograph returned two measurements within 2% of one another, the tarps were removed and photochemistry initiated. The overall oxidation times for each species were 2.5 h, 4 h and 4–6 h for α- and β-pinene and toluene, respectively.
Table 1. Initial Conditions, Temperatures, Relative Humidities, and Results of the Photo-oxidation Experiments
Initial and final temperature and relative humidity.
Final aerosol number concentration and size mode. These values have not been adjusted for wall losses.
Mass concentration in the chamber was determined from the SMPS measured size distribution in the chamber over the period for which meaningful polar nephelometer (PN) measurements were made. Particle density was assumed as 1.2 g/cm3 for α- and β-pinene and 1.24 g/cm3 for toluene.
Mass concentration when [NO] went below the 1 ppb detection limit of the NOx instrument. [NO] did not reach this level on 14 August and 9 October.
Calculated from peak measured aerosol mass corrected for wall losses and the corresponding quantity of reacted hydrocarbon. Because of the uncertainties in the measurement from GC (±3%) and measurement of SMPS (±10%), yields are uncertain to ±10%.
Table 2. Initial Conditions, Temperatures, Relative Humidities, and Results of the Ozonolysis Experiments
Because hydrocarbons react immediately with O3, hydrocarbon initial concentrations are estimated based on injected liquid and are accurate to within ±20%.
Final aerosol number concentration and size mode. These values have not been adjusted for wall losses.
Mass was determined from the SMPS measured size distribution in the chamber over the period for which meaningful PN measurements were made. Particle density was assumed as 1.2 g/cm3 for α- and β-pinene and 1.24 g/cm3 for toluene. Measured particle number concentrations were corrected.
Calculated from peak measured aerosol mass corrected for wall losses and the corresponding quantity of reacted hydrocarbon. Because of the uncertainty in the initial concentrations (±20%), measurement of GC (±3%) and measurement of SMPS (±10%) yields are uncertain to ±25%.
Cyclohexane was added in 50-fold excess compared to the hydrocarbon to suppress OH formation.
 For ozone experiments, ozone was generated by flowing pure oxygen (0.5 L/min) through a mercury lamp O3 generator (Jelight, model 600) into a covered chamber as it was being filled. For selected experiments, an OH scavenger (cyclohexane) was injected. When ozone and/or scavenger were well mixed, the hydrocarbon of interest was injected and the chamber mixed manually to minimize inhomogeneities.
 Aerosols were characterized with the polar nephelometer (described below), an integrating nephelometer (Ecotech M9003), a scanning mobility particle sizer (SMPS, TSI model 3080), and by gravimetric mass (±1 μg, Sartorius). The integrating nephelometer measures scattering at 700 nm as well as relative humidity and temperature with 1 min time resolution. The SMPS measures the 19–948 nm particle size distributions every 3 min. Filter samples for gravimetric analysis were collected on preweighed 47 mm Teflon filters (Pallflex) for 5−10 min at 30 LPM toward the end of the experiments.
3. Polar Nephelometer and Calibration
 The polar nephelometer used in this study is an upgraded version of the instrument described by Barkey et al. . Every 16 s it measures light intensities scattered into 21 discrete angles by a stream of aerosols intersecting the beam of a 350 milliwatt 670 nm diode laser. A 1/2 wave plate appropriate for the 670 nm wavelength rotates the polarization plane of the incident light to be parallel or perpendicular to the measurement scattering plane. The 1 LPM aerosol sample flow is confined to the center of the scattering plane by a 10 LPM sheath flow. Upgrades include a machined aluminum casing that provides a hermetic seal for the scattering volume. The instrument dynamic range has been increased about a decade from improvements to the photodiode detector/amplifier circuits. Finally, detector aperture diameters are now inversely proportional to the expected intensity levels to reduce the large range in detector signals that results from uniform aperture sizes.
 PSL microspheres (Duke Scientific) with well-characterized size distributions and a manufacturer specified mr of 1.5854 at 670 nm are used to calibrate the PN. The PSL particles were aerosolized in a Collison spray nebulizer (BGI Inc.) and then directed through sufficient desiccant tubes to dry them completely. Shown in auxiliary material Figure S1a is a plot of the light scattered by 800 nm in diameter PSL spheres as measured by the uncalibrated PN along with Mie-Lorenz determined expectations. Calibration constants, ki, are developed from these measurements via
where μ and σ are the manufacturers specified geometric mean and standard deviation, respectively, Pp,thy(θi, mr, μ, σ) is the theoretically determined relative intensity for a discrete sensing angle (θi) and Vp,meas(θi) is the measured detector voltage signal at θi. The subscript ‘p’ is either ‘l’ for incident light polarized parallel to the scattering plane and ‘r’ for perpendicular polarization. The theoretical results are adjusted to the PN instrument geometric intensity response characteristics as described by Barkey et al. , and are fitted to the measurement using the method of least squares. Calibration constants are derived from relatively isotropic scattering measurements, i.e., the parallel incident light results of the 800 nm PSL particles shown in Figure S1a, rather than the highly variable scattering pattern for the perpendicular incident light for the same particle. The signal responses at angles with low intensities, such as the dips near 60° and 100° (Figure S1a), are more susceptible to noise and multiple internal reflections within the scattering volume.
 The constants, ki, are multiplicative corrections for the measured voltages and should be the same for any calibration particle size. Any differences in ki developed using different size PSL particles are due to instrument noise or differences in the amount of unwanted signal from stray reflections. Shown in Figure S1b are the calibration constants that range from about 0.5 to 1.8, developed using measurements of the 800 nm PSL particles (Figure S1a) as well as for those developed using PSL particles with a mean diameter of 596 nm. Error bars based on the standard deviation of calibration constants developed from 40 to 50 separate PN measurements of the PSL particles average 2–3% and range from 0.7 to 5%. These error bars are less than the average difference (3.4%) between the calibration constants for the 596 and 800 nm PSL particles, which have a maximum difference of 9% at 18°. The larger difference at 18° is caused by laser beam directional drift. However, the values are still low, due to efforts to redirect unwanted scattering signals into light absorbers positioned above and below the scattering plane. Importantly, differences below 15% produce mr retrieval uncertainties below ±0.03, as discussed below (section 4.3). PSL particles smaller than about 500 nm are not used for calibration as they have a tendency to clump into dimers which cannot be modeled with the single particle Mie-Lorenz solution.
4. Results and Discussion
4.1. Reaction Profile of a Photo-oxidation Experiment
Figures 1 and 2 show chamber results from a typical photo-oxidation experiment (21 October). Figure 1a shows NO, NOx, O3, α-pinene and wall-loss corrected aerosol mass concentration. The experiment had initial concentrations of 500 ppb α-pinene and 260 ppb NO. SOA began to nucleate 33 min after the chamber was initially exposed to sunlight, and quickly grew to several hundred nanometers. Figure 1b shows the evolution of particle numbers, mean diameter, and integrated scattering (βsca). The particles continued to grow throughout, however particle number concentrations dropped slowly due to coagulation and wall loss after 1310 local time (LT). Viable retrievals from the PN signal were first obtained when the particles had grown to about 200 nm at 1312 LT (Figure 1c). The βsca continues to increase as particle numbers drop until 1405 LT, after which it declines slowly. At this point, the increases in scattering associated with growing particles is overtaken by the decreases due to decreasing numbers (Figure 1c).
 Selected phase functions for the growing particles are shown in Figure 2a, including the first measurement at 1258 LT to the final measurement at 1455 LT. As expected, as particle sizes increase, scattering intensities increase. Typically, particle growth is rapid initially, and then slows considerably, thus after about 1320 LT there is little change in the angular scattering properties. There is more electronic noise in the earlier scans, which are at the lower limits of the instrument sensitivity. Initially the intensity minimum is at about 90°. Because larger particles scatter light predominantly in the forward direction, the minimum is reduced and moves toward 130° as time progresses.
4.2. Aerosol Formation Yields
Tables 1 and 2 show aerosol yields (aerosol mass/HC reacted, both in μg/m3), calculated from SMPS volumes. SOA are accepted to be reasonably spherical, as verified by Barkey et al. . Reports of α- and β-pinene SOA densities are in the range 1.19−1.65 g/cm3 [Malloy et al., 2009; Saathoff et al., 2009; Shilling et al., 2009], and 1.24−1.48 g/cm3 has been reported for toluene [Ng et al., 2007]. At small mass concentrations, SOA densities appear to decrease as the SOA mass concentration increases and/or as the particles grow [e.g., Malloy et al., 2009; Shilling et al., 2009]. Because of the polar nephelometer detection limits, most of our experiments were performed with significantly higher initial hydrocarbon concentrations, and as a result higher SOA mass concentrations than those for which density measurements have been made, we used density values at the low end of the literature reports. SOA mass was calculated based on size distributions measured by the SMPS assuming spherical particles with a density of 1.2 g/cm3 for α- and β-pinene and 1.24 g/cm3 for toluene. Measured particle number concentrations were corrected for size-dependent wall loss, using coefficients determined from separate wall loss experiments. The wall loss rates ranged from 0.0012 to 0.0081 min−1. Gravimetric mass measurements were used to check the SMPS masses, and averaged 87 ± 12% of SMPS mass measurements. The gravimetric filter samples are expected to underestimate particle mass due to evaporation of semivolatiles from collected particles [e.g., Chung et al., 2008].
 Aerosol yields and chemical composition are controlled by the parent hydrocarbon, oxidation chemistry, temperature and aerosol mass concentration [Hallquist et al., 2009, and references therein]. Our yield data bear out the expected trends; where we have pairs or sets of similar experiments, yields appear to be higher at lower temperatures, higher initial HC/NOx ratios, and higher aerosol mass in the chamber. Because of significantly higher initial hydrocarbon concentrations and resulting high aerosol mass concentrations, yields at or above the upper end of literature values [Griffin et al., 1999; Ng et al., 2007; Saathoff et al., 2009] are expected for our experiments (Tables 1 and 2). The only SOA for which a direct comparison is available is α-pinene ozonolysis; Saathoff et al.  report yields of ∼30% for experiments carried out at similar temperature and aerosol masses of 100–200 μg/m3. Our yields for aerosol masses between 450–1000 μg/m3 are in good agreement at 32–50%, but very high aerosol masses appear to lead to qualitatively higher yields (55 and 97%, Table 2).
4.3. Determination of the Refractive Index
 A detailed description of the genetic algorithm real refractive index retrieval scheme is provided by Barkey et al.  thus here we provide a brief description of the method and focus on changes applied in this study. The GA is a directed search, or optimization method that mimics the way the best organisms are selected for their environment. For PN retrievals, a population of possible solutions consisting of real refractive indices and size distribution parameters is randomly selected from within predefined search limits. The population is examined numerically to see which member best describes the measured scattering, Pl,meas(θj) via a fitness value defined by
where Pp,thy(θj, mr, μ, σ) is the theoretically determined intensity for each discrete sensing angle (θj) as described in equation (1) [Lienert et al., 2003]. The fitness values for the two light polarization orientations are combined via F = Fr + Fl, where l indicates polarization parallel to the scattering plane and r indicates the perpendicular orientation.
 The limits to the refractive index search space were set at 1.1 to 1.7. The search space for the lognormal distribution parameters are set at ±30% of the SMPS measured mean and standard deviation. The accuracy of the size distributions returned by the SMPS (with a scan time of 180s) is ±10%, [Russell et al., 1995; Tokonami and Knutson, 2000]. However, the search space for the SMPS measured mean and standard deviation is set to ±30% because of differences in the measured size distribution and the lognormal distribution assumed in the GA retrieval scheme, and to provide sufficient search space for the inherent error in SMPS distribution during the rapid growth phase (below). The difference between the measured distribution profile (PDFmeas(x)) and the assumed lognormal profile (PDFcalc(x, μ, σ)) is defined by
and are normalized such that
where x is the particle diameter. The profiles of measured distributions with Δdist < 0.07 do not seem distorted at first glance, while Δdist values > 0.2 can have distinct dual mode features. Barkey et al.  show theoretically and experimentally that the retrieved mr is accurate to within ±0.014 of the expected mr when Δdist is less than 0.585. The average Δdist for the aerosols seen in these experiments is about 0.2, with a range of 0.04 to 0.4. Although increasing the size distribution search space always produces better fitness values, the GA retrieved mean is usually higher than the measured value and the GA determined standard deviation is lower than measured. The mean falls within ±10% in 77% of cases. This is expected as the scattering from a nonlognormal distribution is not the same as that from a lognormal distribution as discussed by Barkey et al. .
Figure 2b shows the PN measurement from 1316 LT (i.e., Pp,meas(θj) of equation (2)), and the GA determined best fit Mie-Lorenz theoretical expectation, (or Pp,thy(θj, mr, μ, σ) of equations (1) and (2)). Six separate GA searches were performed, each with an aggressive population of 300. Each search ran for three generations and had a mutation factor of 0.9. A population size of 50 is usually sufficient, however, the larger population ensures that the solution converges and that the highly complex solution space [Hodgson, 2000] is thoroughly searched. The retrieved mr of each of these six searches varied less than 1% from the average GA-determined refractive index of 1.48. The small difference between each search indicates that the solution has converged to a single result and that the selected search spaces are reasonable; that is, the spaces are not so large as to include two or more possible results. The average fitness value retrieved was 0.965. GA mr retrievals of the scattering from ammonium sulfate and water drops and various sizes of PSL spheres with this instrument has shown that the GA mr is accurate to ±0.03 for detector noise levels of over 15% as long as the particles are spherical and homogeneous [Barkey et al., 2007]. At the start of the experiment, the signal-to-noise ratio is low (∼1 to 3) due to low particle concentrations and small particle sizes and produces the obviously noisy scattering patterns at 1258 and 1304 LT in Figure 2a. GA retrieved parameters from these scans have fitness values below 0.8, and are not reliable. Normally, once the scattering coefficient has increased to about 500 Mm−1, at which time the particles have grown to over 200 nm, the fitness values increase to above 0.94.
 The PN measurement frequency (16 s) is higher than that of the SMPS (3 min). At later times the SMPS mean and standard deviation do not change significantly during the 3 min SMPS sampling time. However, during the initial particle growth period (such as 1300 – 1320 LT, Figure 1b), there is a systematic error in the SMPS measurement as the particle mean size changes significantly (∼12 nm/min) during the 3 min scanning interval. The resulting inconsistencies are generally acceptable within the framework of the GA retrieval. This is first because the phase function itself is only slightly affected by the shifting size distribution as the mean size changes only by about 3 nm during the 16 s time period of the PN measurement, a small change compared to the particle size of 200 nm. Further, any difference between the actual size distribution at the measurement time and that produced from the SMPS measurement is encompassed by the large (±30%) GA size parameter search space. GA searches converged on the size parameters and mr for all retrievals in rapid growth regions, indicating solution viability.
4.4. SOA Refractive Indices
Figures 3–5 show refractive indices retrieved as a function of particle mass concentration (in the chamber, not corrected for wall losses) from angular scattering data for groups of SOA generated in the chamber. All but four of the retrieved mr had fitness values of at least 0.94; the remaining 4 were between 0.92 and 0.94. Particle chemical composition is expected to depend on the parent hydrocarbon, its oxidation chemistry, the particle mass concentration, the temperature, and on longer time scales, in-particle reactions and heterogeneous aging.
Figure 3 shows results for SOA for α-pinene ozonolysis performed with the same initial hydrocarbon concentration, with and without an OH scavenger. Because the yield of OH radicals from the α-pinene reaction with ozone is about 70% [Paulson et al., 1998], in the absence of scavenger, nearly half of the α-pinene molecules react with OH rather than ozone. Within the resolution of our method however the retrieved refractive indices are not distinguishable from one another (Figure 3), indicating the differences in SOA chemical composition for these two oxidation chemistries are not sufficient to affect the optical properties. In contrast, SOA particles that are generated at lower temperatures (12 February, ∼14°C instead of 26°C, Table 2) appear to have significantly lower refractive indices (1.4 to 1.44). A handful of recent papers suggest α-pinene aerosol chemical composition changes with temperature [e.g.,Warren et al., 2009; Y. Wang et al., Hydrogen peroxide generation from α- and β-pinene and toluene secondary organic aerosols, submitted to Atmospheric Environment, 2010]. The retrieved refractive index of the 26 ± 4°C experiments (all experiments shown in Figure 3 except 12 February) increases slightly as the particle mass concentration increases from about 200 to about 1100 μg/m3 from about 1.45 to 1.5.
Figure 4 compares retrieved refractive indices for SOA formed by ozonolysis (without scavenger) of α-pinene (Figure 4a) and β-pinene (Figure 4b) at several initial concentrations. The β-pinene required significantly higher precursor concentrations to produce similar mass concentration of SOA formed by ozonolysis of α-pinene. The refractive indices of both types of SOA increase slowly as the aerosol mass concentration increases over a wide range (60–4000+ μg/m3), from about 1.4 to 1.5 for α-pinene and 1.43 to 1.48 for β-pinene. We note that the mass concentrations, which can affect particle chemical composition by shifting partitioning, are generally well above ambient levels, and thus lower values seem to be implied for ambient aerosol mass concentrations.
4.4.2. Photochemically Generated SOA
Figure 5 shows mr for photochemically generated aerosol from α- and β-pinene and toluene. In each case, the photochemically derived SOA cover a wider range of mr values than ozonolysis. As the experiments progress, several factors may influence particle chemical composition and refractive index; the aerosol mass concentration, the relative contribution of RO2 radical reactions with NO versus HO2 or RO2, the temperature and other factors such as water uptake and heterogeneous and in-particle reactions. The photochemical experiments were performed in a relatively narrow range of relative humidities (11–22%) in a region in which water uptake, or phase, is not expected to be changing rapidly [e.g., Mikhailov et al., 2009]. Temperatures span a moderate range (medians vary by 4°–9°C depending on hydrocarbon, Table 1) and do not appear to explain the observed variability.
 The α- and β-pinene SOA refractive indices (Figures 5a and 5b) increase from about 1.38 to a maximum of about 1.52, with somewhat different mass concentration dependences, and for both pinenes they drop off somewhat at the highest mass concentrations. For α-pinene, there is some spread at lower mass concentrations, the source of which is not clear. We note that the higher refractive indices at mass concentrations between 0 and 1000 are associated with experiments in which NO dropped below our 1 ppb detection limit at an early point relative to the first viable mr retrieval (Table 1, yield column). Some time after this point, RO2 and HO2 radicals may build up to sufficient levels to successfully compete with NO to be the predominant reaction partner for RO2. This may hint at a higher mr for the condensed products of RO2 reacting with RO2/HO2 compared to NO. The β-pinene data are all in good agreement with one another (within the resolution of our method) and do not provide as much support for the notion that mr increases as NO becomes depleted and the oxidation chemistry shifts through the experiment. The data do suggest that increasing aerosol mass causes species with higher mr to condense, although clearly other mechanisms may be at play, such as a changing product spectrum as the experiment progresses. The apparent decrease of mr at the highest mass concentrations (and also at the end of the experiments) might be due to changes in particle composition brought about by heterogeneous [e.g., George et al., 2007] or in-particle reactions (Wang et al., submitted manuscript, 2010) (i.e., aging) or shifts in the composition of the condensing material. Ng et al.'s  suggestion that parent hydrocarbons with one double bond such as α- and β-pinene generate SOA from the first oxidation step, thus SOA precursors do not change appreciably as the hydrocarbon is consumed, leaves open the possibility that aging plays a role.
 The shape of the mr curve for toluene SOA (Figure 5c) is markedly different than that of the pinenes, and the range of values is larger (1.4–1.61). We note that the 10 August experiment is different in many respects from the other experiments. The only obvious difference is that this experiment had a lower initial hydrocarbon concentration, although it is unclear how this might influence results. In this data set, we see little support for the notion that mass concentration is a controlling variable. The data cluster in two distinct groups: high and low initial HC/NOx ratio (Figure 5c). In general, the toluene SOA begin at low mr values and then begin to increase dramatically at some point as the particles grow. As the mass concentration at which the mr begins to increase covers a wide range, the phenomenon is more consistent with mr dependence on shifting chemical composition as the experiments progress.
 There are three previous laboratory measurements of SOA to which we can compare our results. In our earlier study, we reported 1.42 ± 0.02 for photochemically generated α-pinene SOA. The experiments on which this was based were similar to the 15 July and 23 September experiments described here, which have final mr in the 1.45–1.5 range (Figure 5), in reasonable agreement within uncertainties. The current value is more reliable however; in earlier work, there was a mismatch between SMPS time stamps and clock time, and distribution distortion was not accounted for in the analysis. Schnaiter et al.  derived a refractive index of 1.5 for α-pinene ozonolysis based on scattering and extinction measurements at 450, 550 and 700 nm, for particles of unspecified size and mass concentration. Lang-Yona et al.  report values of 1.53 ± (0.06–0.08) for mixed biogenic SOA oxidized with O3, OH and low NOx. The Lang-Yona et al.  and possibly the Schnaiter et al.  values are expected to be slightly higher than ours (by up to 0.02) because the measurements were made at different wavelengths. The values are in general agreement with our results.
4.5. Effect of the Refractive Index on Radiative Transfer
 The value of the real refractive index affects the bulk radiative properties of aerosols. For instance, the asymmetry parameter 〈g〉, a key parameter in radiative transfer calculations, is defined as
where the integration is over the scattering angle, θ. The azimuthal component of the solid angle (Ω) integration is constant when random particle orientation is assumed [van de Hulst, 1957]. The nondimensional scattering phase function P(Ω) describes the average light intensity scattering properties of the particle distribution and is normalized via
Here 〈g〉 describes the relative amount of light scattered by the particles into the forward or reverse hemispheres; 〈g〉 = 1 for full forward scattering, −1 for scattering into the reverse hemisphere and 0 for isotropic scattering. Generally, 〈g〉 decreases as mr increases for distributions associated with aerosols. Using the Mie-Lorenz scattering theory, wavelength = 670 nm and mr = 1.4, 〈g〉 = 0.744 for a lognormal distribution with E(x) = 200 nm and a standard deviation of 200. Changing the mr to 1.5 produces 〈g〉 = 0.677. This change can produce an increase in the radiative forcing by at least 12% for nonabsorbing particles [Marshall et al., 1995].
 This work is the first study to investigate SOA refractive indices with sufficient resolution to begin to assess variability of SOA mr with precursor hydrocarbon, oxidation chemistry, aerosol mass concentration and possibly other factors such as temperature and aerosol aging. Aerosol mr for SOA studied here varies from about 1.38 to 1.61, a range likely to have a significant impact on radiative transfer calculations. Because of the polar nephelometer constraints, the experiments were performed at higher aerosol masses than generally observed in the atmosphere, which limits their direct applicability to radiative transfer calculations. Ongoing updates to the polar nephelometer will lower detection limits to a range more relevant to atmospheric conditions. More work is also needed to determine how mr for SOA changes with hydrocarbon precursor, oxidation chemistry, mass concentration, temperature and other factors.
 This work was supported by the Department of Energy's Atmospheric Science Program (Office of Science, BER, grant DE-FG02-05ER64011:A004). Assistance with experiments from Ying Wang is gratefully acknowledged. Helpful comments of several anonymous reviewers greatly improved the paper.