INTO THE VOID: MASS FUNCTION OF

SUPERMASSIVE BLACK HOLES IN THE LOCAL UNIVERSE

A thesis talk by Farhanul Hasan ’18 Advisers: Alison Crocker (S),

Johnny Powell (F)

I. DISCOVERY1916: Black holes

predicted by GR

1971: First discovery of a black hole (Cygnus X-1)

1943: Seyfert Galaxies

1950s: Radio sources

II. MONSTERS IN GALACTIC NUCLEI

1960s+: Redshifted Quasars

Active Galactic Nuclei (AGN): Emit trillion (1012) suns’ energy in light weeks

Gas moving very fast near center of M87, M31, M32 - cores not as bright

Conclusion: SUPERMASSIVE BLACK HOLES (SMBH) in galactic nuclei!

III. SOLTAN’S ARGUMENT (1982)

Observed quasar count per volume:

n(S,z)

Likely to find “Dead quasar” within few Mpc of us

⇢ = u✏c2 > 105M� Mpc�3

u = 4⇡c

R(1 + z) n(S, z) S dz dS

IV. WHERE WE ARE NOWCurrent picture of SMBH growth:

“Active”“Quiescent”

V. THE DATA: SLOAN DIGITAL SKY SURVEY (SDSS)Obtained data for ~364000 gals. in z<0.1

“Complete” at r <17.77 mags

Apache Point Observatory Source: New Mexico State

University

Mr = r �h5 log

⇣DL(z)10pc

⌘i

VI. BLACK HOLE MASS FUNCTION (BHMF)

BHMF = number density of SMBHs of given mass per dex

Shankar (2009)

Constraints on growth, regardless of formation

models

Demographics of SMBH population

Can test theory of accretion

VI. MEASURING BLACK HOLE MASSES (MBH)

Spectroscopy of gas, stars, matter, inside the sphere of influence

Infer mass from Newtonian gravity:

Machetto et. al. (1997)

GMBH = v2cr

VIII. STELLAR VELOCITY DISPERSION (𝛔)

Dispersion about mean velocity of stars in galaxy

Measured by doppler shift of absorption lines

Impacted by potential well of entire galaxy

X. SURPRISE! MBH AND 𝛔 CORRELATE

van den Bosch (2016)

➙ Do SMBHs and their host galaxies co-evolve?

M-sigma relation:log

⇣MBH

M�

⌘= (8.32± 0.04)

+ (5.35± 0.23) log�

�200 km s�1

�

XI. YOU COMPLETE MEComplete sample: Ensures sample isn’t biased

XII. COMPLETENESS FOR ALL (REDSHIFTS)

�lim(z) = 1.57 + 10.47z � 37.7z2Repeat for many redshift limits

50 120 190 260 330

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20

Magnitude-limited sample

�-complete sample

�25 �23 �21 �19 �17

Ratio

(norm

alized

to

maxim

um

)

� [km s�1] �� [km s�1] Mr

XIII. FINISH LINE: THE MASS FUNCTION

�j(MBH)� logMBH =P

Nbin

i

1Vmax,i

Convert 𝛔 to MBH for each galaxy

Bin in masses of logMBH = 0.2:

Accounts for Malmquist Bias

Credits: Jason Lisle

XIII. FINISH LINE: THE MASS FUNCTION

6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5log MBH [M�]

�7

�6

�5

�4

�3

�2

log

�(M

BH

)[M

pc�

3dex

�1]

Schechter-like fit to BHMF

Derived BHMF

�(MBH) = �?

⇣MBH

M?

⌘↵+1exp

1�

⇣MBH

M?

⌘��

XIV. PAST WORKS

XV. IN A COSMIC CONTEXT⇢BH =

Z log(MBH/M�)=9.6

log(MBH/M�)=6�(MBH)MBH d logMBH

Assuming SMBH forms mostly thru accretion of baryons,

Percent of baryons locked up in SMBHs = ⌦BH

⌦baryon

' (0.0049± 0.001)%

⇢quasars > 105M� Mpc�3⇢BH =

�2.71+0.55

�0.43

�⇥ 105 M� Mpc�3

ACKNOWLEDGEMENTSJohnny for appreciating my work and

pushing me forward

Alison for being very calm and very supportive throughout a very tough

semester

Joel for help with the integrals

Matyas, Amanda, and Ali for feedback on fine tuning the talk

REFERENCESA. Sołtan. (1982). Mon. Not. R. Astron. Soc. 200: 115–122.

F. Macchetto et al. (1997). Astrophys. J. 489: 579–600.

R. Van den Bosch. (2016). Astrophys. J. 831: 134-158.

J. Sohn, et. al. (2017). Astrophys. J. 845: 73.

R. Shankar. (2009). Astrophys. J. 690: 20–41.

P. Schechter. (1976). Astrophys. J. 203: 297–306.

M. Vika. (2009). Mon. Not. R. Astron. Soc. 400: 1451–1460.

R. Shankar. (2004). Mon. Not. R. Astron. Soc. 354: 1020–1030.

APP. MAXIMUM VOLUMEVmax,i =

4⇡3

⌦survey

⌦sky

⇥DC(zmax,i)3 �DC(zmin,i)3

⇤

• zmin,i = 0.03

• zmax,i = max. redshift for object i based on �-completeness

APP. VELOCITY DISPERSION FUNCTION (VDF)

�j(�)� log � =PNbin

i1

Vmax,i

APP. FROM THE VDF TO THE BHMF

�(MBH) = 1p2⇡✏2

Z�(�) exp

� [MBH � (a+ b�)]2

2✏2

�

Convolve �(�) with MBH � � relation,assuming gaussian distribution of MBH