Center for Astro, Particle, and Planetary Physics

Using 143 early-and late-type galaxies (ETGs and LTGs) with directly-measured super-massive black hole masses (M BH ), we build upon our previous discoveries that: (i) LTGs, most of which have been alleged to contain a pseudobulge, follow the relation M BH ∝ M 2.16±0.32 * ,sph ; and (ii) the ETG relation M BH ∝ M 1.27±0.07 * ,sph is an artifact of ETGs with/without disks following parallel M BH ∝ M 1.9±0.2 * ,sph relations which are offset by an order of magnitude in the M BH -direction. Here we searched for substructure in the M BH -(central velocity dispersion, σ) diagram using our recently published, multicomponent, galaxy decompositions; investigating divisions based on the presence of a depleted stellar core (major dry-merger), a disk (minor wet/dry-merger, gas accretion), or a bar (evolved unstable disk). The Sérsic and core-Sérsic galaxies define two distinct relations: M BH ∝ σ 5.86±0.33 and M BH ∝ σ 8.54±1.07 , with ∆ rms|BH = 0.51 and 0.47 dex, respectively. We also report on the consistency with the slopes and bends in the galaxy luminosity (L)-σ relation due to Sérsic and core-Sérsic ETGs, and LTGs which all have Sérsic light-profiles. The bend in the M BH -σ diagram (superficially) reappears upon separating galaxies with/without a disk, while we find no significant offset between barred and non-barred galaxies, nor between galaxies with/without active galactic nuclei. We also address selection biases purported to affect the scaling relations for dynamically-measured M BH samples. These new, type-dependent, M BH -σ relations more precisely estimate M BH in other galaxies, and hold implications for galaxy/black hole co-evolution theories, simulations, feedback, the pursuit of a black hole fundamental plane, and calibration of virial f -factors for reverberation-mapping.

The density-wave theory of spiral structure proposes that star formation occurs in or near a spiral-shaped region of higher density that rotates rigidly within the galactic disk at a fixed pattern speed. In most interpretations of this theory, newborn stars move downstream of this position as they come into view, forming a downstream spiral which is tighter, with a smaller pitch angle than that of the density wave itself. Rival theories, including theories which see spiral arms as essentially transient structures, may demand that pitch angle should not depend on wavelength. We measure the pitch angle of a large sample of galaxies at several wavelengths associated with star formation or very young stars (8.0 μm, H-α line and 151 nm in the far-UV) and show that they all have the same pitch angle, which is larger than the pitch angle measured for the same galaxies at optical and near-infrared wavelengths. Our measurements in the B band and at 3.6 μm have unambiguously tighter spirals than the starforming wavelengths. In addition we have measured in the u band, which seems to fall midway between these two extremes. Thus, our results are consistent with a region of enhanced stellar light situated downstream of a starforming region.

We have conducted an image analysis of the (current) full sample of 44 spiral galaxies with directly measured supermassive black hole (SMBH) masses, M BH , to determine each galaxy's logarithmic spiral arm pitch angle, φ. For predicting black hole masses, we have derived the relation: log(M BH /M ) = (7.01 ± 0.07) − (0.171 ± 0.017) [|φ| − 15 • ]. The total root mean square scatter associated with this relation is 0.43 dex in the log M BH direction, with an intrinsic scatter of 0.33 ± 0.08 dex. The M BH -φ relation is therefore at least as accurate at predicting SMBH masses in spiral galaxies as the other known relations. By definition, the existence of an M BH -φ relation demands that the SMBH mass must correlate with the galaxy discs in some manner. Moreover, with the majority of our sample (37 of 44) classified in the literature as having a pseudobulge morphology, we additionally reveal that the SMBH mass correlates with the largescale spiral pattern and thus the discs of galaxies hosting pseudobulges. Furthermore, given that the M BH -φ relation is capable of estimating black hole masses in bulgeless spiral galaxies, it therefore has great promise for predicting which galaxies may harbour intermediate-mass black holes (IMBHs, M BH < 10 5 M ). Extrapolating from the current relation, we predict that galaxies with |φ| ≥ 26. • 7 should possess IMBHs.

Aims. This work is the first stage of a campaign to search for intermediate-mass black holes (IMBHs) in low-luminosity active Galactic nuclei (LLAGN) and dwarf galaxies. An additional and equally important aim of this pilot study is to investigate the consistency between the predictions of several popular black hole scaling relations and the fundamental plane (FP) of black-hole activity (FP-BH). Methods. We used well established X-ray and radio luminosity relations in accreting black holes, along with the latest scaling relations between the mass of the central black hole (M BH ) and the properties of its host spheroid, to predict M BH in seven LLAGN, that were previously reported to be in the IMBH regime. Namely, we used the recently re-evaluated M BH − M sph (M sph : spheroid absolute magnitude at 3.6 µm) scaling relation for spiral galaxies, the M BH − n sph (n sph : major axis Sérsic index of the spheroid component) relation, the M BH − PA (PA: spiral pitch angle) relation, and a recently re-calibrated version of the FP-BH for weakly accreting BHs, to independently estimate M BH in all seven galaxies. Results. We find that all LLAGN in our list have low-mass central black holes with log M BH /M ⊙ ≈6.5 on average, but that they are, most likely, not IMBHs. All four methods used predicted consistent BH masses in the 1σ range. Furthermore, we report that, in contrast to previous classification, galaxy NGC 4470 is bulge-less, and we also cast doubts on the AGN classification of NGC 3507. Conclusions. We find that our latest, state-of-the-art techniques for bulge magnitude & Sérsic index computations and the most recent updates of the M BH − L sph , M BH − n sph , and M BH − PA relations and the FP-BH produce consistent results in the low-mass regime. We thus establish a multiple-method approach for predicting BH masses in the regime where their spheres of gravitational influence cannot be spatially resolved. Our approach mitigates against outliers from any one relation and provides a more robust average prediction. We will use our new method to revisit more IMBH candidates in LLAGN.

We present a determination of the supermassive black hole (SMBH) mass function for early-and latetype galaxies in the nearby universe (z < 0.0057), established from a volume-limited sample consisting of a statistically complete collection of the brightest spiral galaxies in the southern hemisphere. The sample is defined by limiting luminosity (redshift-independent) distance, D L = 25.4 Mpc, and a limiting absolute B-band magnitude, M B = −19.12. These limits define a sample of 140 spiral, 30 elliptical (E), and 38 lenticular (S0) galaxies. We established the Sérsic index distribution for earlytype (E/S0) galaxies in our sample. established the pitch angle distribution for their sample, which is identical to our late-type (spiral) galaxy sample. We then used the pitch angle and the Sérsic index distributions in order to estimate the SMBH mass function for our volume-limited sample. The observational simplicity of our approach relies on the empirical relation between the mass of the central SMBH and the Sérsic index ) for an early-type galaxy or the logarithmic spiral arm pitch angle ) for a spiral galaxy. Our SMBH mass function agrees well at the high-mass end with previous values in the literature. At the low-mass end, while inconsistencies exist in previous works that still need to be resolved, our work is more in line with expectations based on modeling of black hole evolution.

The density-wave theory of galactic spiral-arm structure makes a striking prediction that the pitch angle of spiral arms should vary with the wavelength of the galaxy's image. The reason is that stars are born in the density wave but move out of it as they age. They move ahead of the density wave inside the co-rotation radius, and fall behind outside of it, resulting in a tighter pitch angle at wavelengths that image stars (optical and near infrared) than those that are associated with star formation (far infrared and ultraviolet). In this study we combined large sample size with wide range of wavelengths, from the ultraviolet to the infrared to investigate this issue. For each galaxy we used an optical wavelength image (B-band: 445 nm) and images from the Spitzer Space Telescope at two infrared wavelengths (infrared: 3.6 and 8.0 µm) and we measured the pitch angle with the 2DFFT and Spirality codes . We find that the B-band and 3.6 µm images have smaller pitch angles than the infrared 8.0 µm image in all cases, in agreement with the prediction of density-wave theory. We also used images in the ultraviolet from Galaxy Evolution Explorer, whose pitch angles agreed with the measurements made at 8 µm. Because stars imaged at those wavelengths have not had time during their short lives to move out of the star-forming region.

We present the MATLAB code Spirality, a novel method for measuring spiral arm pitch angles by fitting galaxy images to spiral templates of known pitch. Computation time is typically on the order of 2 minutes per galaxy, assuming at least 8 GB of working memory. We tested the code using 117 synthetic spiral images with known pitches, varying both the spiral properties and the input parameters. The code yielded correct results for all synthetic spirals with galaxy-like properties. We also compared the code's results to two-dimensional Fast Fourier Transform (2DFFT) measurements for the sample of nearby galaxies defined by DMS PPak. Spirality's error bars overlapped 2DFFT's error bars for 26 of the 30 galaxies. The two methods' agreement correlates strongly with galaxy radius in pixels and also with i-band magnitude, but not with redshift, a result that is consistent with at least some galaxies' spiral structure being fully formed by z=1.2, beyond which there are few galaxies in our sample. The Spirality code package also includes GenSpiral, which produces FITS images of synthetic spirals, and SpiralArmCount, which uses a one-dimensional Fast Fourier Transform to count the spiral arms of a galaxy after its pitch is determined. The code package is freely available at

Spiral structure is the most distinctive feature of disk galaxies and yet debate persists about which theory of spiral structure is correct. Many versions of the density wave theory demand that the pitch angle be uniquely determined by the distribution of mass in the bulge and disk of the galaxy. We present evidence that the tangent of the pitch angle of logarithmic spiral arms in disk galaxies correlates strongly with the density of neutral atomic hydrogen in the disk and with the central stellar bulge mass of the galaxy. These three quantities, when plotted against each other, form a planar relationship that we argue should be fundamental to our understanding of spiral structure in disk galaxies. We further argue that any successful theory of spiral structure must be able to explain this relationship.

We investigate the use of spiral arm pitch angles as a probe of disk galaxy mass profiles. We confirm our previous result that spiral arm pitch angles (P) are well correlated with the rate of shear (S) in disk galaxy rotation curves. We use this correlation to argue that imaging data alone can provide a powerful probe of galactic mass distributions out to large look-back times. We then use a sample of 13 galaxies, with Spitzer 3.6-µm imaging data and observed Hα rotation curves, to demonstrate how an inferred shear rate coupled with a bulge-disk decomposition model and a Tully-Fisher-derived velocity normalization can be used to place constraints on a galaxy's baryon fraction and dark matter halo profile. Finally we show that there appears to be a trend (albeit a weak correlation) between spiral arm pitch angle and halo concentration. We discuss implications for the suggested link between supermassive black hole (SMBH) mass and dark halo concentration, using pitch angle as a proxy for SMBH mass.

We present our determination of the nuclear supermassive black hole mass (SMBH) function for spiral galaxies in the local universe, established from a volume-limited sample consisting of a statistically complete collection of the brightest spiral galaxies in the southern (δ < 0 • ) hemisphere. Our SMBH mass function agrees well at the high-mass end with previous values given in the literature. At the low-mass end, inconsistencies exist in previous works that still need to be resolved, but our work is more in line with expectations based on modeling of black hole evolution. This low-mass end of the spectrum is critical to our understanding of the mass function and evolution of black holes since the epoch of maximum quasar activity. A limiting luminosity (redshift-independent) distance, D L = 25.4 Mpc (z = 0.00572) and a limiting absolute B-band magnitude, M B = −19.12 define the sample. These limits define a sample of 140 spiral galaxies, with 128 measurable pitch angles to establish the pitch angle distribution for this sample. This pitch angle distribution function may be useful in the study of the morphology of late-type galaxies. We then use an established relationship between the logarithmic spiral arm pitch angle and the mass of the central SMBH in a host galaxy in order to estimate the mass of the 128 respective SMBHs in this volume-limited sample. This result effectively gives us the distribution of mass for SMBHs residing in spiral galaxies over a lookback time, t L ≤ 82.1 h −1 67.77 Myr and contained within a comoving volume, V C = 3.37 × 10 4 h −3 67.77 Mpc 3 . We estimate that the density of SMBHs residing in spiral galaxies in the local universe is ρ = 5.54 +6.55 −2.73 × 10 4 h 3 67.77 M ⊙ Mpc −3 . Thus, our derived cosmological SMBH mass density for spiral galaxies is Ω BH = 4.35 +5.14 −2.15 × 10 −7 h 67.77 . Assuming that black holes grow via baryonic accretion, we predict that 0.020 +0.023 −0.010 h 3 67.77 of the universal baryonic inventory (Ω BH /ω b ) is confined within nuclear SMBHs at the center of spiral galaxies.

A logarithmic spiral is a prominent feature appearing in a majority of observed galaxies. This feature has long been associated with the traditional Hubble classification scheme, but historical quotes of pitch angle of spiral galaxies have been almost exclusively qualitative. We have developed a methodology, utilizing two-dimensional fast Fourier transformations of images of spiral galaxies, in order to isolate and measure the pitch angles of their spiral arms. Our technique provides a quantitative way to measure this morphological feature. This will allow comparison of spiral galaxy pitch angle to other galactic parameters and test spiral arm genesis theories. In this work, we detail our image processing and analysis of spiral galaxy images and discuss the robustness of our analysis techniques.

Using the latest sample of 48 spiral galaxies having a directly measured supermassive black hole mass, M_BH, we determine how the maximum disk rotational velocity, v_max (and the implied dark matter halo mass, M_DM), correlates with the (i) M_BH, (ii) central velocity dispersion, σ_0, and (iii) spiral-arm pitch angle, ϕ. We find that M_BH∝ v_max^10.62±1.37∝ M_DM^4.35±0.66, significantly steeper than previously reported, and with a root mean square scatter (0.58 dex) similar to that about the M_BH-σ_0 relation for spiral galaxies - in stark disagreement with claims that M_BH does not correlate with disks. Moreover, this M_BH-v_max relation is consistent with the unification of the Tully-Fisher relation (involving the total stellar mass, M_*,tot) and the steep M_BH∝ M_*,tot^3.05±0.53 relation observed in spiral galaxies. We also find that σ_0∝ v_max^1.55±0.25∝ M_DM^0.63±0.11, consistent with past studies connecting stellar bulges (with σ_0≳100 km s^-1), dark matter halos, and a noncon...

We present our determination of the nuclear supermassive black hole mass (SMBH) function for spiral galaxies in the local universe, established from a volume-limited sample consisting of a statistically complete collection of the brightest spiral galaxies in the southern (δ < 0 • ) hemisphere. Our SMBH mass function agrees well at the high-mass end with previous values given in the literature. At the low-mass end, inconsistencies exist in previous works that still need to be resolved, but our work is more in line with expectations based on modeling of black hole evolution. This low-mass end of the spectrum is critical to our understanding of the mass function and evolution of black holes since the epoch of maximum quasar activity. A limiting luminosity (redshift-independent) distance, D L = 25.4 Mpc (z = 0.00572) and a limiting absolute B-band magnitude, M B = -19.12 define the sample. These limits define a sample of 140 spiral galaxies, with 128 measurable pitch angles to establish the pitch angle distribution for this sample. This pitch angle distribution function may be useful in the study of the morphology of late-type galaxies. We then use an established relationship between the logarithmic spiral arm pitch angle and the mass of the central SMBH in a host galaxy in order to estimate the mass of the 128 respective SMBHs in this volume-limited sample. This result effectively gives us the distribution of mass for SMBHs residing in spiral galaxies over a lookback time, t L ≤ 82.1 h -1 67.77 Myr and contained within a comoving volume, V C = 3.37 × 10 4 h -3 67.77 Mpc 3 . We estimate that the density of SMBHs residing in spiral galaxies in the local universe is ρ = 5.54 +6.55 -2.73 × 10 4 h 3 67.77 M ⊙ Mpc -3 . Thus, our derived cosmological SMBH mass density for spiral galaxies is Ω BH = 4.35 +5.14 -2.15 × 10 -7 h 67.77 . Assuming that black holes grow via baryonic accretion, we predict that 0.020 +0.023 -0.010 h 3 67.77 of the universal baryonic inventory (Ω BH /ω b ) is confined within nuclear SMBHs at the center of spiral galaxies.

Spiral structure is the most distinctive feature of disk galaxies and yet debate persists about which theory of spiral structure is correct. Many versions of the density wave theory demand that the pitch angle be uniquely determined by the distribution of mass in the bulge and disk of the galaxy. We present evidence that the tangent of the pitch angle of logarithmic spiral arms in disk galaxies correlates strongly with the density of neutral atomic hydrogen in the disk and with the central stellar bulge mass of the galaxy. These three quantities, when plotted against each other, form a planar relationship that we argue should be fundamental to our understanding of spiral structure in disk galaxies. We further argue that any successful theory of spiral structure must be able to explain this relationship.

We have conducted an image analysis of the (current) full sample of 44 spiral galaxies with directly measured supermassive black hole (SMBH) masses, M BH , to determine each galaxy's logarithmic spiral arm pitch angle, φ. For predicting black hole masses, we have derived the relation: log(M BH /M) = (7.01 ± 0.07) − (0.171 ± 0.017) [|φ| − 15 • ]. The total root mean square scatter associated with this relation is 0.43 dex in the log M BH direction, with an intrinsic scatter of 0.33 ± 0.08 dex. The M BH-φ relation is therefore at least as accurate at predicting SMBH masses in spiral galaxies as the other known relations. By definition, the existence of an M BH-φ relation demands that the SMBH mass must correlate with the galaxy discs in some manner. Moreover, with the majority of our sample (37 of 44) classified in the literature as having a pseudobulge morphology, we additionally reveal that the SMBH mass correlates with the largescale spiral pattern and thus the discs of galaxies hosting pseudobulges. Furthermore, given that the M BH-φ relation is capable of estimating black hole masses in bulgeless spiral galaxies, it therefore has great promise for predicting which galaxies may harbour intermediate-mass black holes (IMBHs, M BH < 10 5 M). Extrapolating from the current relation, we predict that galaxies with |φ| ≥ 26. • 7 should possess IMBHs.

Black hole mass (M BH) scaling relations are typically derived using the properties of a galaxy's bulge and samples dominated by (high-mass) early-type galaxies. Studying late-type galaxies should provide greater insight into the mutual growth of black holes and galaxies in more gas-rich environments. We have used 40 spiral galaxies to establish how M BH scales with both the total stellar mass (M * ,tot) and the disk's stellar mass, having measured the spheroid (bulge) stellar mass (M * ,sph) and presented the M BH-M * ,sph relation in Paper I. The relation involving M * ,tot may be beneficial for estimating M BH either from pipeline data or at higher redshift, conditions that are not ideal for the accurate isolation of the bulge. A symmetric Bayesian analysis finds log (M BH /M) = 3.05 +0.57 −0.49 log M * ,tot /[υ(6.37 × 10 10 M)] + (7.25 +0.13 −0.14). The scatter from the regression of M BH on M * ,tot is 0.66 dex; compare 0.56 dex for M BH on M * ,sph and 0.57 dex for M BH on σ *. The slope is > 2 times that obtained using core-Sérsic early-type galaxies, echoing a similar result involving M * ,sph , and supporting a varied growth mechanism among different morphological types. This steeper relation has consequences for galaxy/black hole formation theories, simulations, and predicting black hole masses. We caution that (i) an M BH-M * ,tot relation built from a mixture of early-and late-type galaxies will find an arbitrary slope of approximately 1-3, with no physical meaning beyond one's sample selection, and (ii) evolutionary studies of the M BH-M * ,tot relation need to be mindful of the galaxy types included at each epoch. We additionally update the M * ,tot-(face-on spiral arm pitch angle) relation.

Recent X-ray observations by Jiang et al. have identified an active galactic nucleus (AGN) in the bulgeless spiral galaxy NGC 3319, located just $14.3\pm 1.1$ Mpc away, and suggest the presence of an intermediate-mass black hole (IMBH; $10^2\leq M_\bullet/\textrm{M}_{\odot}\leq 10^5$ ) if the Eddington ratios are as high as 3 to $3\times10^{-3}$ . In an effort to refine the black hole mass for this (currently) rare class of object, we have explored multiple black hole mass scaling relations, such as those involving the (not previously used) velocity dispersion, logarithmic spiral arm pitch angle, total galaxy stellar mass, nuclear star cluster mass, rotational velocity, and colour of NGC 3319, to obtain 10 mass estimates, of differing accuracy. We have calculated a mass of $3.14_{-2.20}^{+7.02}\times10^4\,\textrm{M}_\odot$ , with a confidence of 84% that it is $\leq $ $10^5\,\textrm{M}_\odot$ , based on the combined probability density function from seven of these individual estimat...