1. 1
Spiral Quasar Census
Veekash Patel
Abstract
Much study has been done on the black hole mass function. The black hole mass function is an
equation that can accurately predict the mass of a black hole based on various measurable properties of
the body. There has however been little study done on finding the mass of supermassive black holes at
the center of spiral galaxies compared to the amount of study done on elliptical galaxies. Even less work
has been done concerning the mass of quasars. I have compiled a list of spiral galaxies with quasars in
the center, and have graphed them into a series of histograms with bins based on virial mass estimates.
Virial mass estimators are a technique used by astronomers to estimate the mass of a quasar based on
the gas that moves around the body.
Introduction
Most galaxies in the known universe have a supermassive black hole at the center of them. It is
theorized that these supermassive black holes date back to the period of galaxy formation, not long after
recombination. The first stars started to form at about the same time. These stars became very large due
to their accretion of all the matter in each of their vicinities. The first black holes in the universe started
to form about 1 billion years after the big bang brought the universe into existence. These black holes
became the seeds that grew the galaxies that are known today.
There are two types of black holes if separated by mass. Stellar mass black holes can be as large
as 10-30 times the size of the sun. These black holes formed recently as a result of a stellar supernova.
The second type is the supermassive black hole which can be found at the center of galaxies.
Supermassive black holes are millions or even billions of times the size of the sun. Accretion is the
process of gas and dust being absorbed by a larger body in this case a black hole. The mass of a black
hole and the rate at which the body accretes are related. Generally, black holes with larger masses have

2. 2
the ability to accrete at higher rates than ones with smaller masses. The rate at which a black hole
accretes is also dependent upon having a source of matter. Some black holes have stopped accreting
because they have fed upon all the matter they can reach.
Active Galactic Nuclei (AGN for short) are supermassive black holes that are currently accreting.
The process of accretion creates an accretion disk around the outside of the black hole. The accretion
disk emits a glow that can be seen across the electromagnetic spectrum. Many galaxies have a quiet
center which does not accrete. Some are Seyfert galaxies which give off a moderate amount of light
which show emission and absorption lines. These lines can show some of the elements that are found in
the galaxy seen. About 10% of AGN give off a narrow jet of charged particles and a magnetic field from
both sides. These quasi-stellar radio sources or quasars are AGNs that give off 10 to 1000 times the
brightness of Seyfert galaxies and produce a radio signal. It is thought that there were more quasars in
the universe a long time ago since most of the quasars that are seen are very far away. Blazars are a type
of AGN that gives off high amounts of energy and radio signal like a quasar. In addition, blazars have one
of their sides pointed towards the earth. This allows astronomers on earth to see the widest range of the
spectrum that a quasar can emit.
Astronomers cannot directly measure the mass of a black hole. Instead, astronomers calculate
the black hole’s mass by observing objects around it. In the case of supermassive black holes,
astronomers often use a spectrograph to find the mass. The quasar gives off light which can be shown on
a spectrograph. Astronomers measure the absorption and emission lines to find out the speed of the gas
that is moving around the black hole. The gas is assumed to be a certain radius away from the black hole.
The mass of the black hole is then calculated by relating the amount of gravitational force needed to
keep the cloud of gas moving at the speed and distance it does when measured. Different clouds of gas
are used to estimate the mass of black holes. Some popular black hole mass estimator emission lines are

3. 3
the lines belonging to Hα, Hβ, MgII, and CIV (Shen 2013). It is important to note how the measuring
instruments are calibrated for the light coming from local stars and galaxies.
Redshift and blueshift are a result of the galaxy moving away or towards our galaxy. This is often
symbolized as the letter z. If z is positive, then the galaxy has redshift and that galaxy is moving away
from us. Most galaxies are moving away from us which causes the wavelength of light to increase thus
exhibiting redshift. If z is negative, then the galaxy is moving towards us. If a galaxy is moving towards
the earth, then the wavelength of light is being decreased which gives the body blueshift.
Spiral galaxies are a striking feature. It is the most obvious and common feature found in galaxies
(Davis et all, 2015). The quasars chosen from SDSS-7 are all spiral galaxies for this study. There is
evidence that correlates the pitch angle of the spiral arms of a galaxy, the amount and distribution of
atomic hydrogen in the disk, and central bulge mass of that galaxy. The ability of astronomers to
correctly find the mass of a galaxy is paramount to research such as this.
Data & Analysis
The sample used in this study is taken from Sloan Digital Sky Survey Data Release 7 quasar
catalog (henceforth known as SDSS-7) (3). Each galaxy that was chosen is a spiral galaxy with a quasar at
its center. There are 220 galaxies in this sample in all. There are three sets of measurements used in this
study. Calibrations belonging to certain data sets are noted using the names of the astronomers and year
the measurement was taken. For example, the calibration taken from Vestergaard & Peterson from 2006
is noted as VP06. Another important calibration used in the sample is McLure & Dunlop from 2004
(henceforth known as MD04).
The first set is composed of 219 spiral quasars whose masses were measured using the McLure
& Dunlop 2004 black hole mass calibrations. In some cases a particular line may be unavailable on the
spectrum or the spectrum is too faint for an accurate measurement (Shen et all., 2011).One galaxy from

4. 4
SDSS-7 did not have a mass measurement so it was excluded from this set. This set measured the Hβ
emission line.
The second set of measurements is from Vestergaard & Peterson 2006 black hole mass
calibrations. This set also includes 219 spiral quasar galaxies. One galaxy was excluded because it was
unable to be measured for this calibration. This set of quasars also measured the Hβ emission line(Shen
et all., 2011).
The third set of measurements is the adopted fiducial virial masses of SDSS-7 (Shen et all., 2011).
This set of data comes from multiple methods of measuring and different calibrations in order to create
the most accurate data set possible. This set was able all 220 mass estimation. This used the Hβ and CIV
emission lines from the VP06 calibration for all z < 0.7. For 0.7 ≤ z < 1.9, MgII emission lines were
measured. This calibration is known as S10 which is a combination of VP06 and MD04. For estimates
where z ≥ 1.9, CIV emission lines were measured using the VP06 calibration. All the quasars used in the
data were redshifts of 0.1 < z < 0.602.
The data was analyzed using Microsoft excel. Excel was used to compile all of the data into a
single spreadsheet. Using the software’s sorting functions, the chosen spiral quasars were picked out of
the 105,783 quasars that were studied on SDSS-7 (Shen et all., 2011). Excel’s graphing function was then
used to create histograms out of the sets of measurements. A best fit line was calculated using excel’s
line of best fit function to better show the distribution of quasars by mass.
All of the masses shown in the data are virial masses. Virial masses are a type of mass estimator
which relates the movement of gas to the gravitational force exerted on the gas by some object (Shen et
all, 2011). The movement of gas is related to the gravitational force via the velocity at which the gas is
moving and the luminosity given off by the quasar. The virial mass can be estimated by:

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 1144
2log
10
loglog
kms
FWHM
+
ergs
Lλ
b+a=
M
M λ
o
virBH,
(1)

5. 5
Equation (1) is equation (2) from Shen et all. MBH,vir is the virial black hole mass in solar masses. FWHM
represents the Full Width Half Maximum of the gaussian curve created by the emission line. The FWHM
has been imposed a limit of 1200km*s-1
. The wavelength (λ) is dependent upon the chosen measured
emission line. The luminosity (Lλ) is dependent upon both the wavelength of light being measured and
the brightness of the light. The light from the quasar can be contaminated by local AGN or by the host
galaxy. Luminosity is given in erg*s-1
. The coefficients a and b are calibrated for each time data was
gathered. The different possible values of a and b for the different calibrations are as follows:
(a, b) = (0.672, 0.61) MD04;Hβ (2)
(a, b) = (0.910, 0.5) VP06;Hβ (3)
(a, b) = (0.660, 0.53) VP06;CIV (4)
(a, b) = (0.740, 0.62) S10;MgII (5)
The parameters for each of these calibrations come from Shen et all. It is important to know that these
calibrations are often created in relation to each other or earlier calibrations. The parameters of (5) were
calculated by using the parameters from (3) because FWHM of both emission lines were measured in a
similar fashion.
Results
The following figures are the results of graphing the virial masses of the spiral quasars from
SDSS-7. There are tables showing how many quasars are in each bin in Appendix A for each histogram.

6. 6
7
7.2
7.4
7.6
7.8
8
8.2
8.4
8.6
8.8
9
9.2
9.4
0
5
10
15
20
25
30
H β MD 0 4 S a m p le
L og B H Ma s s (Mo)
Fre que nc y
Figure 1. Histogram of virial mass estimate from SDSS-7 using MD04 calibration for emission line Hβ
Masses shown are the log base 10 of the mass in solar masses. The tallest bar is 8.1 so most
quasars have a mass near 108.1
Mo. The graphing function from excel created a clear Gaussian curve from
the provided data with a peak near 8.3. For the Hβ emission line, a wavelength of 5100Å and calibrations
for a and b from (2) were input into equation (1) to find the virial mass. There are 219 quasars accounted
for on this histogram.
7
7.2
7.4
7.6
7.8
8
8.2
8.4
8.6
8.8
9
9.2
9.4
0
5
10
15
20
25
30
H β V P 0 6 S a m p le
L og B H Ma s s (Mo)
Fre que nc y
Figure 2. Histogram of virial mass estimates from SDSS-7 using VP06 calibration for emission line Hβ

7. 7
Of the quasars measured with the VP06 calibration for Hβ, bin 8.3 holds the highest amount of
them. Excel has fitted a gaussian curve to the histogram. The curve peaks between 8.3 and 8.4. 5100Å is
still used for the wavelength, but the calibrations from (3) are used in these virial mass estimates. There
are 219 quasars accounted for in this histogram.
7
7.2
7.4
7.6
7.8
8
8.2
8.4
8.6
8.8
9
9.2
9.4
0
5
10
15
20
25
30
L og B H S a m p le
L og B H Ma s s (Mo)
Fre que nc y
Figure 3. Histogram of virial mass estimates from SDSS-7 using the logBH data
This graph was created using the fiducial mass data set. All 220 quasars were used to create this
graph. The largest amount of quasars is in bin 8.3. The gaussian curve fitted by excel peaks between bins
8.3 and 8.4. The calibrations for these quasars changed depending on the redshift of the quasars. If z <
0.7, then the parameters from (3) are used in equation (1), but if 0.7 ≤ z < 1.9, then calibration (5) is used
(Shen et all., 2011). There are no quasars with redshifts greater than 1.9 in this sample. The wavelength
of Hβ is 5100Å, and for MgII, it is 3000Å. There does seem to be a single outlier in bin 7 for this set of
data.
There are issues with using virial mass estimators to find the mass of black holes. According to
Steinhardt, virial mass estimators may have systematic affine biases. Affine biases translate, shift,
stretch, or contract the distribution of quasars in the Log M – Log L plane. This affine bias is consistently
present in virial mass estimators because the velocity found from the broad line region may not be as

8. 8
accurate as originally thought. The concern is the velocity of the gas cannot be fully defined by the
FWHM of the broad line region. A solution for this type of systematic bias is applying a compressive
correction. By compressing the distribution of quasars by a calculated amount then this systematic error
could be reduced. Another systematic affine bias that could reduce the accuracy of virial mass estimates
is the disagreement between Hβ and MgII emission lines. There is consistent discrepancy between these
two emission lines, which could be the result of difficulties in separating the MgII line from nearby Fe
emission lines. This sort of bias would require an expansive correction. The argument for this type of
correction comes from the weak correlation of the spectral slope and the Eddington ratio in MgII based
masses compared to the strong correlation found when using Hβ based masses (Risaliti et all, 2009). The
argument is also made that CIV emission lines are an unreliable source for quasar mass estimates
because the correlation is even weaker than in MgII emission lines.
Discussion
Most studies of the black hole mass function have focused on elliptical galaxies. Relatively little
has been done until recently about the mass function of black holes in spiral galaxies. Different methods
are used for the two kinds of galaxies and it has been found that they have quite different black hole
mass functions (spirals have smaller black holes on average). Yet, in studying quasars, up to now no
distinction has been made between quasars in spirals and those in elliptical ones. This is the first attempt
to actually examine the black hole mass function of active spirals and the results are in broad agreement
with those found for nearby quiescent spirals given in Davis et al 2014.

9. 9
Figure 4. Markov Chain Monte Carlo sampling of late-type black hole mass function (rough black line)
with the best fit model probability distribution function (solid red line) surrounded by an error region
(gray shading). This figure comes from Davis et al 2014.
Figure 4 shows a distribution of black holes calculated according to the black hole mass function. The
rough black line shows agreement with the figures 1,2, and 3. The sampling in figure 4 was based was
not only based on quasar type galaxies. It was based on the local supermassive black holes of spiral
galaxies; this is why the late-type of the black hole mass function is used. This could account for the
concentration of black holes being more towards a mass of M≈107
Mo. The black hole mass function used
in Davis et al 2014 is based on calculating the mass of supermassive black holes by measuring the pitch
angle between the arms of a spiral galaxy.
There are a few conditions that the black hole mass function must satisfy. According to Small and
Blandford 1992, the conservation equation must be satisfied
〈 〉 ( , ) (6)

10. 10
where N is the number density of black of black holes being changed over time (t). S(M,t) is the source
function. This is assumed to be 0 so that no black holes are created, destroyed, or merged. 〈 〉( , )
refers to the mean accretion rate for holes of mass M.
The author would like to thank Amanda Schilling for helping compile the list of spiral quasars
used in this paper. I acknowledge the use of Sloan Digital Sky Survey’s quasar catalog and property
catalog. The plots that were generated for this paper were made in Microsoft Excel. The author would
also like to thank Dr. Daniel Kennefick for all the direction and advice he has given that went to the
writing of this paper.
Appendix A
The following tables show the amount of spiral quasars that are in each bin for figures 1,2, and 3.
Table 1.
Bin sizes and the amount of quasars in each bin for Hβ MD04 Sample
Bin Frequency
7 0
7.1 0
7.2 1
7.3 1
7.4 4
7.5 3
7.6 6
7.7 7
7.8 8
7.9 8
8 15
8.1 24
8.2 20
8.3 17
8.4 14
8.5 18
8.6 11
8.7 22
8.8 13
8.9 14
9 6
9.1 3
9.2 3

11. 11
9.3 1
9.4 0
More 0
Table 2
Bin sizes and the amount of quasars in each bin for Hβ VP06 Sample
Bin Frequency
7 0
7.1 0
7.2 0
7.3 4
7.4 4
7.5 4
7.6 7
7.7 6
7.8 12
7.9 9
8 9
8.1 12
8.2 14
8.3 24
8.4 16
8.5 14
8.6 14
8.7 21
8.8 8
8.9 11
9 13
9.1 9
9.2 2
9.3 3
9.4 3
More 0
Table 3
Bin sizes and the amount of quasars in each bin for Hβ VP06 Sample
Bin Frequency
7 1
7.1 0
7.2 0
7.3 4
7.4 4
7.5 4

12. 12
7.6 7
7.7 6
7.8 12
7.9 9
8 9
8.1 12
8.2 14
8.3 24
8.4 16
8.5 14
8.6 14
8.7 21
8.8 8
8.9 11
9 13
9.1 9
9.2 2
9.3 3
9.4 3
More 0
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