The Black Hole Mass – Pitch Angle Relation Toward a Supermassive Black Hole Mass Function 21/10/20137th Korean Astrophysics1 Julia Kennefick University of Arkansas Fayetteville Department of Physics Arkansas Center for Space and Planetary Science

The Arkansas Galaxy Evolution Survey (AGES) Principles Dan Kennefick Julia Kennefick Claud Lacy Marc Seigar (UALR) Postdocs Joel Berrier (Rutgers) Patrick Treuthardt (Adler Planetarium) UAF Graduate Students R. Scott Barrows (Ph.D.) Ben Davis Doug Shields J. Adam Hughes Amanda Schilling Jazmin Berlanga- Medina Kim Zoldak Jon Bessler Michael Fusco 21/10/20137th Korean Astrophysics2

Outline Classification of Galaxies The Black Hole Mass – Pitch Angle Relation Measuring Pitch Angle A Local Black Hole Mass Function of Late Type Galaxies Why does this work? – A little theory Current and Future Work 21/10/20137th Korean Astrophysics3

“Early Types” “Late Types” 21/10/201347th Korean Astrophysics

Which came first, the black hole or the galaxy? Current questions center on structure and galaxy formation and evolution Do black holes “seed” galaxies, or do they form as the galaxy collapses? Need to determine what galaxies are like now, and what they were like in the past, including their central masses Build a “black hole mass function” – number of black holes as a function of mass and time 21/10/20137th Korean Astrophysics5

Why Spirals? Most correlations involve the bulge of the galaxy, but bulge features can be difficult to measure in spirals. Therefore, less work done on spirals to date. Lots of galaxies are spirals – 70% in the field Cleaner histories – fewer mergers Represent the lower mass end of the BHMF – relic AGN Local BHMF can be used to constrain AGN accretion rates 21/10/20137th Korean Astrophysics6 Photo T. Davis

Are Pitch Angle and Central Mass Related? Hints from work by Seigar et al. that they might be D. Kennefick suggests we look at M vs. P for a sample of local galaxies Seigar measures P for a sample of 28 galaxies with measured or estimated central black hole masses (13 direct, 11 from sigma, 4 limits) 21/10/20137th Korean Astrophysics7 Early version from Seigar et al. 2008

Spiral Arm Pitch Angle Most disk galaxies are found to have a logarithmic spiral structure This results in a constant pitch angle, P, over the extent of the spiral arms 21/10/20137th Korean Astrophysics8

How do you measure P? 2DFFT code from Saraiva Schroeder et al. (1994) Based on FOURN routine in Numerical Recipes Decomposes observed distributions into a superposition of logarithmic spirals of different P’s and number of arms, m. p is equivalent to frequency and then pitch angle, P or ϕ, is like a wavelength. 21/10/20137th Korean Astrophysics9 Davis et al. 2012, ApJS, 199, 33 NGC 5054

How do you measure P? 21/10/20137th Korean Astrophysics10 Deproject Star subtract

How do you measure P? Where do you start? 21/10/20137th Korean Astrophysics11

How do you measure P? Compute P over all possible inner radii out to some maximum radius and then average over the stable region. The quoted error will be (largely) the variation of the pitch angle over the stable region, although currently we are bump those up a bit for objects with short stable regions. 21/10/20137th Korean Astrophysics12

How do you measure P? NGC 5054, m=3 harmonic mode dominates Red contours show a inverse FFT of spiral arms with P=-40°.60 from pixels (20”-118”), over about 75% of the galaxy 21/10/20137th Korean Astrophysics13 NGC 5054

How do you measure P? 21/10/20137th Korean Astrophysics14 “Raw” Galaxy: P=-24°.5 ± 12°.8 Symmetrical component: P=-25°.6 ± 3°.7 NGC 5054

How do you measure P? Sometimes you need to select a different outer radius. P = 19°.1 ± 4°.8 vs. P=16°.3 ± 3°.2 21/10/20137th Korean Astrophysics15 M51

How do you measure P? Sometimes things work out just fine… P = -19°.4 ± 3°.2 21/10/20137th Korean Astrophysics16 NGC 7083

New Results for M-P relation Updated methodology for measuring P More masses available All masses are “directly” measured χ 2 = 4.68 with a scatter of 0.38 dex. Pearson Rank Correlation Coefficient test gives -0.81, a strong anti-correlation with a 99.7% significance, a 3-σ result. 21/10/20137th Korean Astrophysics17 star and gas dynamics (10) reverberation mapping (12) masers (12) Berrier et al., 2013, ApJ

How does it compare to M-σ? 21/10/20137th Korean Astrophysics18 σ’s from Ferrarese (2002) masses from M-σ Scatter of spiral galaxies about the M-σ relation is ~0.56 dex (Gultekin et al. 2009)

Local Black Hole Mass Function 21/10/20137th Korean Astrophysics19 Sample selected from Carnegie-Irvine Galaxy Survey 0f 605 galaxies (Ho et al. 2011) Volume limited to z= (D L = 25.4 Mpc) and M B = spiral galaxies within V C = 3.37 x 10 4 (Mpc/h ) 3 and t L ≤ (Myr/h )

Multi-armed Galaxies While two armed galaxies are the most common type, three armed galaxies are also found fairly frequently. Galaxies with four or more arms often represent flocculents where the number of arms present can be hard to determine by eye. 21/10/20137th Korean Astrophysics20

Pitch Angle and Mass Distributions 21/10/20137th Korean Astrophysics21 Mass peaks around 10 7 for late types, compared to 10 8 for ellipticals Each galaxy modeled as a normalized Gaussian, with the error as the standard deviation. Errors in mass also include uncertainties in M-P relation, giving a smoother curve

Local Black Hole Mass Function 21/10/20137th Korean Astrophysics22 Davis et al., accepted to ApJ BHMF generated from pitch angle distribution. Errors determined using a Monte Carlo sampling of the 128 measured galaxies, with pitch angles randomly generated from the data with a Gaussian distribution within 5σ of each measured value. The M-P relation was also allowed to vary within its uncertainties.

Other BHMF’s 21/10/20137th Korean Astrophysics23 Late types Marconi uses many steps… Vika uses more distant galaxy sample, perhaps missing dimmer galaxies We can include brighter galaxies as well…

What about non-locally? Looking at evolution in pitch angle as a function of time. Using GOODS fields imaging Simulations Numerical modeling Selection efficiencies Signal filtering 21/10/20137th Korean Astrophysics24 z = (3.4 Gyr) P = ± 4.4 z = (4.3 Gyr) P = 33.5 ± 5.8 z = (4.9 Gyr) P = ± 3.7 z = (5.7 Gyr) P = ± 13.1 Shields et al., in prep.

Spiral AGN in GOODS Found 3 AGN with spiral structure and existing spectra with Mg II line Preliminary results are consistent with local M-P relation Need a larger sample 21/10/20137th Korean Astrophysics25

The GOODS Sample 21/10/20137th Korean Astrophysics26 Masses determined from existing spectroscopy of GOODs galaxies, using the broad Mg II line and appropriate scaling relations. z = 1.2 is 8.5 Gyr light travel time

Type -1 Project Design SDSS DR7 quasar catalog – 105,783 sources (at least one broad emission line) Requiring extended structure and z < 1.0 – 4124 sources Examine image cutouts – 221 sources (z < 0.64 – 5.9 Gyr) Prefer 20 pixel radius in the galaxy images to measure P Imaging: SDSS imaging for z < 0.15, KPNO pODI at WIYN for 0.1 < z < 0.3 (3 nights in Nov.) HST for z > 0.25 (2.9 Gyr) 21/10/20137th Korean Astrophysics27

Type-1 Imaging Goals 221 spiral type-1 AGN from SDSS DR7 quasar catalog HST and KPNO proposals for higher resolution imaging 21/10/2013 7th Korean Astrophysics 28 Four objects with existing HST imaging Find that we can measure P in SDSS imaging data out to at least z = 0.15

KPNO in November 21/10/20137th Korean Astrophysics29 The Milky Way would extend 6.6 arcsec on the sky at z = 0.3 Pixels are 12 μm square Giving a pixel scale 0.11 arcsec/pixel ~30 pixels over which to measure P

Why should this work? One of the first qualitative observations of galaxies – the Hubble Sequence: galaxies with tighter arms have bigger bulges. That black hole mass depends on the mass of the central galactic bulge is now well established. Spiral density wave theory – standing waves pitch angle (i) – wavelength disk mass density (σ) – density of medium central mass (M) – tension To be continued… 21/10/20137th Korean Astrophysics30 Shu (1984) in the case of Saturn (bulge dominated).

Conclusions Discovered a possible correlation between central black hole mass and pitch angle in disk galaxies Developed a robust methodology for measuring P Confirmed the M-P relation in a sample of galaxies with direct measurements of their central black hole masses. M-P relation has the lowest scatter of any method currently used to estimate the mass of SMBH’s residing in spiral galaxies. Computed a local black hole mass function for late-type galaxies Developing a sample of more distant galaxies to explore evolution of the M-P relation for use at earlier times. Physical basis for relation – standing waves 21/10/20137th Korean Astrophysics31

Future Work Needed Need to address image quality – signal filtering Need to address selection effects to estimate completeness Surface brightness Redshift Inclination angle Pitch Angle Need a larger sample pODI at WIYN in November for higher-res imaging data Explore HST archive Type-2 AGN (sigma proxy) 21/10/20137th Korean Astrophysics32