# Evidence for microlensing by primordial black holes in quasar broad emission
lines

M. R. S. Hawkins 1
1Institute for Astronomy (IfA), University of Edinburgh, Royal Observatory,
Blackford Hill, Edinburgh EH9 3HJ, UK
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

With the detection of black hole mergers by the LIGO gravitational wave
telescope, there has been increasing interest in the possibility that dark
matter may be in the form of solar mass primordial black holes. One of the
predictions implicit in this idea is that compact clouds in the broad emission
line regions of high redshift quasars will be microlensed, leading to changes
in line structure and the appearance of new emission features. In this paper
the effect of microlensing on the broad emission line region is reviewed by
reference to gravitationally lensed quasar systems where microlensing of the
emission lines can be unambiguously identified. It is then shown that although
changes in Seyfert galaxy line profiles occur on timescales of a few years,
they are too nearby for a significant chance that they could be microlensed,
and are plausibly attributed to intrinsic changes in line structure. In
contrast, in a sample of 53 high redshift quasars, 9 quasars show large
changes in line profile at a rate consistent with microlensing. These changes
occur on a timescale an order of magnitude too short for changes associated
with the dynamics of the emission line region. The main conclusion of the
paper is that the observed changes in quasar emission line profiles are
consistent with microlensing by a population of solar mass compact bodies
making up the dark matter, although other explanations like intrinsic
variability are possible. Such bodies are most plausibly identified as
primordial black holes.

###### keywords:

quasars: emission lines – gravitational lensing: micro – dark matter

††pubyear: 2022††pagerange: Evidence for microlensing by primordial black
holes in quasar broad emission lines–References

##  1 Introduction

The recent detection of black hole mergers by the LIGO gravitational wave
observatory has in the first instance been attributed to the merging of
massive stellar black hole remnants (Abbott et al., 2016). However, it has
also been seen as adding considerable weight to the idea that dark matter is
in the form of primordial black holes (Bird et al., 2016). The idea was that
the detections would form part of a high mass tail to an expected broad mass
function peaking at around a solar mass. From a theoretical perspective, a
mechanism for the formation of primordial black holes in the early Universe
was discussed by Carr & Hawking (1974), with the additional suggestion
(Chapline, 1975) that such objects might make up the dark matter. Constraints
appearing to rule out this idea on the basis that it implied excessive, unseen
variations in quasar brightness due to microlensing by the black holes acting
as lenses (Schneider, 1993) were shown to be insecure by Zackrisson & Bergvall
(2003), on the basis that an unrealistically small source size had been
assumed for the quasar accretion disc.

The first claim that primordial black holes had actually been detected
(Hawkins, 1993) made the case that the observed brightness variations in
samples of quasars could only be explained by the effects of microlensing by a
large population of compact bodies, most plausibly primordial black holes.
These bodies would have to make up a large fraction of the dark matter. In the
ensuing years, a number of varied observations suggested that optical
variability in quasars was at least partly the result of microlensing by a
population of stellar mass compact bodies. These results were summarised by
Hawkins (2011) as a case for primordial black holes as dark matter.

The idea that dark matter is in the form of compact bodies has a long and
controversial history. An early review by Trimble (1987) largely focussed on a
variety of elementary particles as dark matter candidates, although she did
include a number of compact objects including cosmic strings, quark nuggets
and primordial black holes as alternative possibilities. It seems fair to say
that the consensus view at that time was that dark matter was in the form of
elementary particles, which would soon be detected by one of a number of
ongoing experiments. In the event, particle dark matter has not so far been
detected, and as detection limits approach the neutrino floor, the prospects
for such detections are not good. There have nonetheless been a number of
attempts to detect or put limits on any population of compact bodies which
might contribute to or account for the dark matter. Perhaps the most
significant of these was the large scale survey by the MACHO collaboration
(Alcock et al., 2000) to detect microlensing events in the light of Magellanic
Cloud stars by compact bodies along the line of sight in the Galactic halo.
The results of this project were controversial, as although the number of
events detected exceeded any known stellar population, it was less than that
expected for a halo entirely composed of compact bodies.

Since the publication of the results of the MACHO collaboration (Alcock et
al., 2000), there have been a number of attempts to constrain any population
of compact bodies making up the dark matter. In the first instance the
microlensing observations were repeated by two other groups, the EROS and OGLE
collaborations (Tisserand et al., 2007; Wyrzykowski et al., 2011). The results
of these two surveys were in significant ways inconsistent with those of the
MACHO collaboration (Hawkins, 2015), which led to a variety of new approaches
to constraining dark matter in the form of compact bodies, and in particular
primordial black holes (Carr et al., 2010, 2017). The constraints included so-
called pixel-lensing in M31, brightness changes in Type Ia supernovae due to
microlensing, the disruption of wide binary star systems by compact bodies,
the depletion of stars in the centre of dwarf galaxies due to mass
segretation, excess X-ray luminosity in the Galactic centre due to interaction
of compact bodies with the inter-stellar medium and distortions in the Cosmic
Microwave Background due to accretion onto primordial black holes in the early
Universe. However, all these constraints are based on assumptions which have
been vigorously challenged in the literature (Byrnes et al., 2018).

A more direct approach to the question of whether the dark matter in galaxy
halos can be in the form of compact bodies is based on analysing photometric
variations in the multiple images of gravitationally lensed quasars
(Mediavilla et al., 2009; Pooley et al., 2012). The idea is that although
intrinsic variations in the quasar will be observed in all the quasar images,
subject to time delays approropriate to the light travel time to the
individual images, it is also the case that the images vary independently of
each other. This is widely interpreted to be due to microlensing by a
population of stellar mass compact bodies, where the light from each quasar
image traverses a different amplification pattern on its trajectory to the
observer. The mass estimate is derived from the characteristic timescale of
the events, and the question of interest is whether the lenses are stars in
the lensing galaxy, or compact bodies making up the dark matter halo.

The conventional approach to determining the stellar fraction of the lensing
galaxy halo has been to use a maximum likelihood estimate of the ratio of mass
in compact bodies to that in smoothly distributed particles, based on the
observed microlensing amplifications. This procedure has tended to give low
values for the ratio of compact to smoothly distributed matter, consistent
with the stellar population of the lensing galaxy acting as the lenses
(Mediavilla et al., 2009; Pooley et al., 2012). However, this result does not
agree with direct measurements of the stellar population in the vicinity of
the quasar images from the distribution of starlight in a sample of wide
separation systems where the quasar images lie well clear of the stellar
population, and yet are strongly microlensed (Hawkins, 2020a, b). The problem
seems to be that the maximum likelihood estimates are based on large samples
of mostly compact lens systems, where the quasar images are buried deep within
the stellar distribution of the lensing galaxy and the disc stars form a large
optical depth to microlensing. In this case there is no reason to doubt that
the observed microlensing can be produced by the stellar population. This is
clear from the work of Pooley et al. (2012), where in a subsample of wide
separation lensed quasars the observed variations are not consistent with
microlensing by the relatively sparse stellar population.

A direct measurement of star light in wide separation lensed quasar systems
where the images lie well clear of the stellar population of the lensing
galaxies (Hawkins, 2020a) has shown that stars in the galaxy halos are far too
sparse to account for the observed microlensing amplifications. The most
convincing evidence comes from the cluster lens SDSS J1004+4112 (Hawkins,
2020b) where strong microlensing is observed in the light curves of the quasar
images some 60 kpc from the cluster centre. As the optical depth to
microlensing $\tau_{*}$ by the stellar population has already dropped to
negligible levels 25 kpc from the cluster centre, it seems clear that the
microlenses must be part of some other population of compact bodies. In
addition, for quasars in the general field it has been shown that the observed
variations in quasar brightness cannot be accounted for by intrinsic changes
in luminosity (Hawkins, 2022). The additional contribution of the microlensing
amplification predicted for a population of solar mass compact bodies making
up the dark matter is required to provide a good match to the data. There are
a number of constraints on the identification of a population of compact
bodies making up the dark matter (Hawkins, 2020a). For a start they must be
non-baryonic, as well as sufficiently compact to act as lenses, and the
timescale of microlensing events implies that the mass of the lenses must peak
at around a solar mass. These constraints appear to rule out all known
candidates for the compact bodies apart from primordial black holes (Hawkins,
2020a). In addition, there is a strong theoretical framework for the creation
of primordial black holes in the early Universe (Byrnes et al., 2018), with a
mass function peaking at around a solar mass.

For a quasar accretion disc to be microlensed, it must be more compact than
the Einstein ring associated with the lensing objects. For most cosmological
situations this implies a lens of around a solar mass for a typical quasar
accretion disc. The question of whether the broad emission lines are
microlensed is less clear, and depends on the structure of the broad emission
line region (BLR). At the time of early work on microlensing (Schneider &
Wambsganss, 1990) it was generally believed that the BLR was large, of the
order of a light year, and an order of magnitude larger than a typical
Einstein ring for a solar mass lens. On this basis, Schneider & Wambsganss
(1990) concluded that the flux from the BLR would not be significantly
affected by microlensing unless the internal structure of the BLR was non-
uniform. The idea that the BLR might not be uniform, but confined by magnetic
stresses (Rees, 1987) was developed by Bottorf & Ferland (2001) to argue that
the clouds within the BLR are not isolated individual entities embedded within
a confining medium, but transient knots of higher density within an overall
turbulent BLR. This idea was developed by Lewis & Ibata (2006) who showed that
although the integrated microlensing effect of a fractal structure would
result in an overall constant light curve, significant magnification of
substructures could alter the emission line profiles in the BLR.

Figure 1: Emission lines from Keck spectra of the wide separation
gravitational lense system SDSS J1004+4112. The left hand panel shows the Si
iv $\lambda 1400$ line for the A image (blue), and the B image (red). The
dashed vertical line shows the systemic wavelength. The right hand panel shows
similar data for the C iv $\lambda 1549$ line.

One of the first gravitational lens systems to be analysed for microlensing
effects is the quadruply imaged Q2237+0305, also known as the Einstein Cross.
A relative change in the brightness of two of the images was definitively
observed by Irwin et al. (1989), and was in fact the first detection of a
microlensing event. Q2237+0305 has continued to be a valuable laboratory for
exploring the effects of microlensing of the continuum source associated with
the accretion disc, and was an obvious choice for early investigations into
the possible microlensing of the BLR. The first such study (Wayth et al.,
2005) was largely focussed on measuring the ratio of the size of the C iii]/Mg
ii regions. In the process they convincingly showed that the broad lines were
being microlensed. They noted that the flux ratios for the two BLRs were
consistent with each other, but not with that for the continuum. From this
they concluded that the two emission regions were of the same size, and
located along the same line of sight.

Since this early work there have been extensive efforts to look for the
effects of microlensing on broad line regions in gravitationally lensed quasar
systems (Sluse et al., 2012; Guerras et al., 2013; Fian et al., 2021). From
these studies it is clear that in most of these systems the broad line region
is being microlensed. This conclusion is primarily based on the observation
that after allowing for time delays beween the images, the structure of the
emission lines is significantly different. This is interpreted as a
consequence of the differing amplification patterns due to a population of
stellar mass lenses traversed by light rays from each image to the observer.
The question of the nature of the lenses is not addressed in these papers, but
the implication seems to be that they must be stars in the lensing galaxy, as
advocated in earlier work on microlensing of the continuum light from the
quasar accretion disc (Mediavilla et al., 2009; Pooley et al., 2012). This
orthodoxy has recently been challenged (Hawkins, 2020a, b), where it is shown
that in wide separation lens systems the stellar population of the lensing
galaxy in the vicinity of the quasar images is far to sparse to be responsible
for the observed microlensing.

The idea behind the present paper is as follows. If the dark matter is indeed
made up of stellar mass primordial black holes, then these compact bodies
should microlens the broad emission lines of a substantial fraction of quasar
spectra. This microlensing effect would result in a change in the structure of
the emission lines over a period of a few years, by analogy with changes
observed in the images of gravitationally lensed quasars. If no such changes
are seen then this would be inconsistent with the view that the dark matter is
largely composed of compact bodies. If changes in emission line structure are
observed, then although these observations would be consistent with a compact
body component of the dark matter, there remains the question of whether they
can be attributed to intrinsic changes in the velocity structure of the broad
line region.

##  2 Microlensing of the quasar broad line region

The question of the extent to which the quasar BLR can be microlensed is an
interesting one. Firstly, the mass of the lensing bodies is of particular
importance as the maximum source size which can be significantly microlensed
is a function of the Einstein radius of the lens. For this investigation a
lens mass of $1M_{\odot}$ is adopted, in line with the detections of solar
mass bodies in the Galactic halo by the MACHO collaboration (Alcock et al.,
2000). This implies an Einstein radius $R_{E}$ of the order of $10^{17}$cm, or
40 lt-day for a typical lensed quasar system. Early measures of the size of
the BLR in quasars suggested an upper limit of around 1 lt-yr, but it soon
became clear from a large sample of quasars monitored for several years (Kaspi
et al., 2000) that typical rest frame time lags were around 100 days. This is
close enough to the size of $R_{E}$ to expect measurable microlensing effects
as the lenses cross the line of sight to the BLR.

In order to detect microlensing in the BLR, a strategy similar to that used
for microlensing of the accretion disc has been employed. The idea here is to
monitor the spectra of individual images in gravitationally lensed quasar
systems, and after allowing for differences in light travel time to compare
the strength and shape of the broad emission lines. As all images are of the
same quasar, corrected to the same epoch, any differences are taken to be the
result of microlensing (Richards et al., 2004; Wayth et al., 2005). In the
event that the BLR is smaller than the Einstein radius of the lens, the effect
of microlensing will be to amplify the flux of an emission line, with little
distortion of the overall shape. However, if the BLR is a complex structure of
transient knots within an overall turbulent cloud region (Lewis & Ibata,
2006), then provided the knots are of comparable size or smaller than the
Einstein disc of the lenses, individual hot spots of random radial velocity
will be microlensed to produce additional broad emission lines with discrepant
redshifts.

The effect of microlensing on the shape of quasar emission lines in multiply
lensed quasar systems is well illustrated by Keck
spectra111https://nexsci.caltech.edu/archives/koa of the wide separation
quadruple lens SDSS J1004+4112 (Richards et al., 2004). Fig. 1 shows plots of
the Si iv $\lambda 1400$ and C iv $\lambda 1549$ broad emission lines for the
A and B images of SDSS J1004+4112, and in both emission lines the broad blue
wing seen in the spectrum of image A is replaced by a somewhat narrower red
wing for the B image. Changes such as this are commonly found in spectrospic
surveys of gravitationally lensed quasars (Sluse et al., 2012; Guerras et al.,
2013; Fian et al., 2021), and in more detailed studies of individual systems
(Eigenbrod et al., 2008; Braibant et al., 2014). As a result of these studies,
a few general points can be made about microlensing of the BLR. As mentioned
above, if the entire emission region is sufficiently compact, that is smaller
than the Einstein disc of the lenses, then microlensing will be seen as an
increase in broad line flux, but with little or no associated distortion of
the line profile. However, for a larger and more complex structure of the BLR,
individual knots with non-systemic radial velocities can act as lenses to
create composite time-varying line profiles. The change in shape of the Si iv
and C iv emission lines illustrated in Fig. 1 for SDSS J1004+4112 would appear
to be an example of this.

These observations raise the question of the timescale of structural changes
in the BLR. In their analysis of broad line microlensing in SDSS J1004+4112
Richards et al. (2004), as well as noting differences in line profile between
images A and B, also find that for image A the profile of the C iv line
changes by a large amount over a period of 6 months. This very short timescale
should be compared with the dynamical or cloud crossing timescale (Peterson,
1993) for the BLR in quasars, given by

$\tau_{\rm{dyn}}=\frac{r}{V_{\rm{FWHM}}}\approx{50}\;\rm{years}$ (1)

where $r$ is the radius of the BLR as measured in reverberation mapping
experiments, and is typically about a year for quasars (Lira et al., 2018),
and $V_{\rm{FWHM}}$ is the Doppler width of the broad line with a typical
value of 6000 km sec-1. Given that by comparing the spectra of different
images it is established that the BLR is being microlensed, it seems
reasonable to conclude that the very short timescale event in image A is also
the result of microlensing. This would be in line with results from monitoring
of the accretion disc of SDSS J1004+4112 for microlensing variations, where
image C was observed to increase in brightness by 0.7 magnitudes in 200 days
(Hawkins, 2020b). The implication here is that the accretion disc and BLR are
being microlensed by the same population of compact stellar mass bodies.

##  3 Intrinsic variability of quasar broad emission line profiles

Figure 2: Emission line profiles for the H$\beta$ line in the Seyfert galaxy
NGC 5548 from International AGN Watch data showing variations on a timescale
of $\sim 5$ years.

It has for some time been well-established that changes in continuum flux from
the accretion disc of low luminosity Active Galactic Nuclei (AGN) or Seyfert
galaxies can produce variations in the strength of quasar broad emission lines
(Peterson et al., 2002). In this case, the changes in emission line strength
typically follow the continuum flux changes by a few days, representing the
light travel time from the accretion disc to the broad line clouds. This
reverberation effect has also been observed by Kaspi et al. (2000) in
relatively low luminosity quasars from the PG sample of nearby quasars
(Schmidt & Green, 1983). More recently, reverberation mapping has been
extended to samples of luminous quasars (Kaspi et al., 2007; Lira et al.,
2018), and some interesting trends have emerged. It is clear that as AGN
become more luminous, the associated BLR becomes more fragmented, and the
response of the emission lines to changes in continuum flux becomes more
patchy.

Although most changes in emission lines can be explained by a simple increase
in brightness in response to changes in continuum flux from the accretion
disc, changes in the line profiles of Seyfert galaxies are also observed on
timescales of around 5 years (Wanders & Peterson, 1996), consistent with the
dynamical timescale for Seyfert galaxies,
$\tau_{\rm{dyn}}\approx{3-5}\;\rm{years}$ (Peterson, 2001). These changes in
line profile are well illustrated in Figure 39 from Peterson (2001), and in
Fig. 2 the superpositon of two H$\beta$ line profiles from AGN
Watch222http://www.astronomy.ohio-state.edu/ agnwatch data illustrates changes
over the course of $\sim 5$ years. However, an important point to make is that
there is no evidence for significant changes in the shape or profile of the
emission lines in response to variations in the luminosity of the accretion
disc. This is consistent with results from Peterson et al. (1999), who
conclude on the basis of an 8 year survey that broad line profile changes are
not reverberation effects, but are due to mass motions within the BLR on the
dynamical timescale.

Following on from the success of the International AGN Watch programme
(Peterson et al., 2002) which focused on the Seyfert galaxy NGC 5548,
attention turned to investigating reverberation in more luminous AGN where the
BLR is expected to be larger. This challenge was addressed by Kaspi et al.
(2000) with a programme to monitor a well-defined sample of 28 Palomar-Green
(PG) nearby AGN (Schmidt & Green, 1983) to look for reverberation effects in
the broad emission lines. The very large number of spectra which make up this
survey are available on line333http://wise-obs.tau.ac.il/$\sim$shai/PG/.
Although it is true, as pointed out by Kaspi et al. (2000), that there were
changes in emission line profiles over the course of the 10 years of their
survey, examination of the spectra has shown that this only applies to the low
luminosity subset of their sample. For quasars with $M_{B}<-23$ and
reverberation timescales of around 200 days, the changes in emission line
shape are very small compared with those observed in Seyfert galaxies, as
shown in Fig. 2. This difference between changes in emission line structure
for high and low luminosity AGN is illustrated in Fig. 3, which shows the
largest observed variation in emission line shape for quasars over the 10 year
monitoring period of PG quasars by Kaspi et al. (2000). It may be seen from
Fig. 3 that the only difference between the two profiles is a small
enhancement of flux in the blue wing of the H$\beta$ line, very different from
the large changes in shape illustrated in Fig. 2. This result is not
surprising, as the dynamical timescale for quasars or luminous AGN from Eq. 1
is of the order of 50 years, far longer than the 10 years of the PG
spectroscopic monitoring programme (Kaspi et al., 2000).

Figure 3: Emission line profiles for the H$\beta$ line of the low redshift
quasar PG1351+640 from the spectroscopic monitoring programme undertaken by
Kaspi et al. (2000).

##  4 Microlensing in high redshift quasar spectra

Figure 4: Emission line profiles for the H$\alpha$ line from SDSS archive
spectra of the the quasar SDSS J0396+5331.

An interesting development in the study of emission line changes in quasar
spectra came from a search for evidence for binary supermassive black holes in
quasars (Liu et al., 2014). The investigation took the form of a search for
quasars with bulk velocity offsets in the broad Balmer lines with respect to
the systemic redshift of the host galaxy. This resulted in the compilation of
a catalogue of 399 quasars from the Sloan Digital Sky Survey (SDSS) with
offset broad H$\beta$ lines, and a mean redshift $z=0.43$, around twice the
mean redshift of the PG quasars. Second epoch spectra of 50 of the candidates
showed that for the most part any changes in the spectra were limited to
additional velocity offset, with little change in the structure of the
emission line profiles. However, the authors flagged the case of SDSS
J0936+5331 (illustrated in Fig. 4) which shows a strong additional red feature
which disappeared on a timescale of 10 years. This short timescale suggests
that some other process unrelated to the dynamic timescale may be involved,
and provides a useful comparison with the PG quasars with a mean redshift
$z=0.20$.

The possibility that the rapid changes in quasar emission line profiles are
associated with the presence of a binary supermassive black hole (BBH) is
addressed by Liu et al. (2014), who argue that most BBHs will not exhibit
double-peaked broad lines due to limitations in parameter space. By
implication, this rules out profile changes similar to those illustrated in
Fig. 4 for SDSS J0936+5331. On this basis, Liu et al. (2014) rejected quasars
with double peaked broad emission lines from their sample of BBH candidates,
which leaves open the question of what physical processes are involved.

Further interest in changes in quasar emission lines was focussed on the
emergence or disappearance of broad emission lines in so-called ‘changing
look’ (CLQ) quasars (MacLeod et al., 2016). Subsequent surveys for CLQs were
based on finding quasars for which large changes were observed in the broad
H$\beta$ line flux (MacLeod et al., 2019; Green et al., 2022). Between these
two surveys some 30 new CLQs were discovered satisfying the adopted search
criteria, which meant that the recorded changes in the H$\beta$ line were
confined to total flux and not variations in line width or profile. The first
attempt to find CLQs at high redshift $(z>2)$ focussed on changes in the C iv
$\lambda 1549$ emission line flux (Ross et al., 2020), resulting in the
discovery of three quasars with large changes to the C iv flux. Ross et al.
(2020) also found the C iv profile to be approximately constant, with the line
flux responding to changes in continuum luminosity.

Figure 5: Emission line profiles for the C iii] line from SDSS archive spectra
of quasars in the redshift range $1.5<z<3.0$, chosen for showing small changes
in structure on a timescale of 10 years in the quasar rest frame.

Figure 6: Emission line profiles for the C iii] line from SDSS archive spectra
of quasars in the redshift range $1.5<z<3.0$, showing changes in structure on
a timescale of 10 years in the quasar rest frame.

The selection criteria adopted by Ross et al. (2020) for their sample of high
redshift CLQs appear to leave open the question of the extent to which changes
in emission line profiles occur in the spectra of quasars with $z>2$. To
address this issue, the SDSS Time Domain Spectroscopic Survey (TDSS)444
https://www.sdss4.org/dr17/spectro/extragalactic-observing-programs/tdss/
provides a very good basis for selecting a sample of quasars for the
investigation of changes in emission line profiles. TDSS comprises a number of
sub-samples focusing on different categories of variable objects, and of
particular relevance for the study of quasar emission line variability is the
sample associated with the bitmask TDSS_FES_HYPQSO of variable QSOs chosen for
repeated observation. In order to identify profile changes in high redshift
quasars, a subsample of the HYPQSO sample was selected with redshift
$1.5<z<3.0$, and the further requirement that there were at least two spectra
included in the HYPQSO sample for each quasar. This resulted in a final set of
53 quasars for further study. Spectra of these candidates were then plotted
out and examined for obvious changes in emission line structure. The idea was
not to compile a complete sample, but to establish whether profile changes do
occur in high redshift quasars. As expected, most of the quasar emission lines
showed little or no significant changes in emission profile. As a general rule
the C iii] line lies in the part of the SDSS spectra with the best signal-to-
noise for the redshift range $1.5<z<3.0$, and Fig. 5 illustrates three typical
examples showing little or no change of structure in the C iii] line. However,
detailed examination of the spectra and superposition of emission lines from
different epochs revealed 9 quasar spectra, illustrated in Fig. 6, with
unmistakeable changes in the C iii] emission line profile. These make up
around 20% of the sample and show changes on a timescale of 10 years. The
changes typically take the form of a broad emission line feature emerging in
the blue wing of the C iii] line. Although it is possible that in some cases
such changes could be produced by misalignment of the object in the aperture,
where several observations are available new line structures typically persist
between two epochs separated by a short timescale.

The most natural explanation for the observed changes in line structure is
that they are intrinsic to the broad line region, resulting from knots in a
turbulent BLR emitting at non-systemic velocities in an analagous way to that
observed in Seyfert galaxies (Wanders & Peterson, 1996), and illustrated in
Fig. 2 above. Rapid changes in broad line shape are only very rarely observed
in low redshift quasars (Liu et al., 2014), and the dynamical timescale given
in Eq. 1 for luminous quasars would seem to make such changes unlikely. This
appears to leave room for a mechanism for variation external to the BLR for
high redshift quasars where rapid broad line changes are observed, and on the
basis of the discussion in Section 2 above, microlensing of the BLR by a
population of stellar mass compact bodies would appear to be a possibility. It
is also worth pointing out that the microlensing of other blended lines may be
responsible for the change in shape of C iii]. In particular, Al iii lies
close to the appearance of new features in Fig. 6, and microlensing of this
line may well contribute to the overall change in the structure of the C iii]
line.This of course does not mean that the broad emission lines are being
microlensed, but that if the conclusions of Hawkins (2020a, b, 2022) are
correct, then the expected microlensing of quasar broad emission lines is
plausibly observed.

Rapid changes in emission line shape due to microlensing are well illustrated
by considering the differences in emission line profile due to microlensing in
the cluster lens SDSS J1004+4112, illustrated in Fig. 1. The difference in
light travel time between the two images is very short, image B leading image
A by 41 days (Fohlmeister et al., 2008), which implies that the observed
change in emission line structure cannot be intrinsic to the emission line
region. After a careful study of various possibilities Richards et al. (2004)
conclude that the observed variations in emission line profile must be
attributed to microlensing of part of the broad line region of the quasar,
resolving structure in the source plane on a scale of $\sim\\!10^{16}$ cm.

As mentioned above, an important indication that high redshift quasars may be
microlensed is the contrast between line profile changes in low and high
redshift quasar samples. Although the quasar sample of Liu et al. (2014)
provides a useful low redshift sample for comparison, a more direct control
sample was obtained from the low redshift HYPQSO quasars. In the parent sample
there were 10 members with redshift $z<0.4$, corresponding to a probability of
microlensingg of around 1%. Here the H$\beta$ line is prominent in the high
S/N part of the SDSS spectra, and the 10 quasars in this subsample were
examined in a similar way to the high redshift objects, but in this case there
was no evidence for significant changes in emission line structure for any of
the quasars. This is consistent with the results of Liu et al. (2014) for
changes in the H$\beta$ line for a sample of 50 low redshift quasars.

Despite the dynamical timescale given by Peterson (1993) in Eq. 1 of around 50
years for intrinsic changes to broad emission line structure in quasars, there
are some caveats with the argument that this completely excludes short term
intrinsic variability of emission line structure. For example, a high
ionization emission line blended with C iii] can be globally magnified by
intrinsic variability, implying that changes in the broad emission lines of
quasars can take place over relatively short timescales and induce an apparent
change in the shape of the C iii] line (Shen et al., 2023). A related
possibility is that regions with different velocities can respond with
different time lags to intrinsic variability causing differences in the shape
of emission line profiles observed at different epochs (Grier et al., 2013; De
Rosa et al., 2018).

Richards et al. (2004) appeared to accept the widely held view at the time
that the compact bodies acting as microlenses were stars in the lensing
cluster. Given the apparent absence of starlight at such a great distance (60
kpc) from the cluster centre of SDSS J1004+4112, this somewhat implausible
hypothesis was examined in detail by Hawkins (2020b). The result of this
study, as dicussed above, showed that from measurements of starlight in the
vicinity of the quasar images, the optical depth to microlensing from stars
was far too small to explain the observed differential changes in brightness
of the quasar images. The main conclusion was that to account for the observed
microlensing, the lenses must make up at least a large part of the dark
matter. This conclusion was reinforced by a more general study of quasar
variability on a cosmological scale (Hawkins, 2022), where it was concuded
that to account for the distribution of quasar lightcurve amplitudes it was
necessary to include the microlensing effects of a cosmologically distributed
population of stellar mass compact bodies. These results suggest that such a
population of compact bodies might also be responsible for microlensing the
broad line regions of quasars in the general field, and thus produce the
observed rapid changes in broad line profile.

##  5 Discussion

Figure 7: Light curve for the quasar SDSS J0151+0100 in the g-band (blue
filled circles) and the r-band (red open circles). Data for the years 1998 to
2007 are from the SDSS stripe 82 archive, and for 2010 to 2013 from the Pan-
STARRS1 data archive. The green arrows mark the epochs of the two spectra
shown in Fig. 7

The idea behind this paper has been to review evidence that quasar broad
emission lines are being microlensed. For this to occur, there must be a
substantial optical depth to microlensing $\tau$ of lenses along the line of
sight to the quasar. For quasars in multiply lensed systems there remains the
possibility that the population of lenses is associated with the dark matter
in the lensing galaxy or cluster halo, but for isolated quasars in the general
field where the lenses are assumed to make up the dark matter, the expectation
of microlensing events will depend on the redshift of the quasar.

It has been demonstrated above that low luminosity AGN or Seyfert galaxies at
low redshift show changes in emission line profile on a timescale of a few
years. This is compatible with the dynamical timescale of 3-5 years for such
small broad line regions, and there is no need to invoke microlensing which
would be very unlikely at such low redshift with a corresponding low value of
$\tau$. On the other hand, the low redshift sample of quasars show no
significant changes in emission line profiles. These quasars are certainly too
nearby for there to be any significant chance of microlensing, and the
dynamical timescale for the large associated BLR means that any intrinsic
changes to the emission line profiles would occur on a timescale of
$\sim\\!50$ years, far longer than the length of the monitoring programme
(Kaspi et al., 2000). There are however some caveats to this broad picture. A
high ionization line such as Al iii blended with the C iii] line can
reverberate differently to changes in continuum flux, which can occur on short
timescales. The resulting changes in the flux ratio from the two lines
centered on different wavelenghts can thus plausibly result in significant
changes in broad line structure over a relatively short timescale. Another
possibility is that regions with different velocities can respond with
different time lags to changes in the continuum source. This can then result
in apparent changes in the structure of the broad line region when observed at
different epochs.

A new approach to changes in quasar broad lines was proposed by Liu et al.
(2014), with the focus on measuring bulk offsets in line velocity relative to
the systemic redshift of the quasar. The idea was to look for evidence of
binary supermassive black holes in quasars, but their data have turned out to
be very useful for studying changes in quasar emission line profiles. In the
sample of 50 candidates selected by Liu et al. (2014), only the quasar SDSS
J0936+5331 showed unmistakeable evidence for changes in the H$\beta$ line
profile, with a marginal additional candidate SDSS J1345+1144. Given that the
target emission line was H$\beta$, the typical redshift of the sample members
was inevitably small, with a median value $z\approx 0.4$ corresponding to an
optical depth to microlensing $\tau=0.01$ in a standard $\Lambda$CDM Universe
(Fukugita et al., 1992). This implies a probability of microlensing for an
average sample member of $\sim 1\%$, which is not inconsistent with the
microlensing of just one sample member. However, the important thing to note
is that there is no evidence for widespread changes in emission line profile
in such a low redshift sample. This is consistent with the long dynamical
timescale expected in quasars for changes in the structure of the broad line
region, as well as the small probability of microlensing in such a low
redshift sample.

The question of emission line profile changes in high redshift $(z>2)$ quasars
was first addressed by Ross et al. (2020). Their candidates were selected from
the SDSS archives on the basis of optical variability and the availability of
a second spectrum. Subsequent visual inspection revealed 3 quasars showing
interesting emission line behaviour, and follow-up spectroscopy confirmed the
changing nature of the emission lines, with particular focus on the Ly
$\alpha$, C iv and Mg ii lines. The main changes observed in the emission
lines were line emergence and collapse, but no evidence was reported for
significant changes in the shapes of the line profiles. The authors further
conclude that the main driver for emission line variability is the broad-band
continuum itself, but declare themselves ‘agnostic’ as to the underlying
physical processes.

An outstanding question remaining after the investigation by Ross et al.
(2020) is whether structural changes in broad emission line profiles can occur
in high redshift quasar spectra on timescales of a few years, as occasionally
observed in low redshift quasar samples (Liu et al., 2014). To answer this
question, the HYPQSO sample of quasars earmarked for repeated observations has
provided a useful start. Given the rarity of changes in emission line profiles
for low redshift quasars (Liu et al., 2014), where emission line changes are
largely confined to increase or decrease in line flux with no associated
change in the shape of the line profile, it was surprising to find that
profile changes in the HYPQSO sample with $1.5<z<3.0$ were readily identified,
as illustrated in Fig. 6. The implied dependence of changes in line profile on
redshift rather than BLR size suggests that some external mechanism may be
involved. Given that compact bodies are well known to microlens broad emission
lines in multiply imaged quasar systems (Richards et al., 2004; Sluse et al.,
2012; Fian et al., 2021), microlensing of the broad emission lines may provide
a solution to the observed changes in emission line structure in luminous
quasars.

The idea that quasar emission lines are being microlensed raises some
immediate questions. Firstly, what is the origin of the lenses? This can be
answered on the basis of the original motivation for this paper, which arose
from evidence (Hawkins, 2020a, b, 2022) that microlensing observations implied
at least a major component of dark matter to be in the form of stellar mass
compact bodies, most plausibly primordial black holes. One of the consequences
of this would be the microlensing of the BLR in quasars of sufficiently high
redshift, thus providing an explanation for the observed changes in emission
line profiles. To put this on a firmer statistical basis the probability of
microlensing can be estimated from the optical depth to microlensing $\tau$.
Using the equations of Fukugita et al. (1992), the value of $\tau$ for a
quasar with $z=2$ in a $\Lambda$CDM Universe is $\tau\approx 0.2$, implying a
probability of around 20% that the quasar will be significantly microlensed.
This is interestingly close to, and certainly consistent with, the proportion
of quasars found to show changes in emission line structure for the TDSS
subsample described in Section 4. In fact the probability is somewhat higher
than this, as for values of $\tau\gtrsim 0.1$, the amplification patterns of
the individual lenses will start to combine in a non-linear way to form a
pattern of high-amplification caustics (Kofman et al., 1997). However, at a
redshift $z\sim 2$ this effect will be small.

By a fortunate circumstance, one of the high redshift quasars described in
Section 4 and illustrated in Fig. 6, where changes in emission line profile
were detected, was also included in the SDSS Legacy photometric monitoring
programme in Stripe 82555https://faculty.washington.edu/ivezic/macleod/qso-
dr7/Southern.html, providing the opportunity to look for any unusual features
in the light curve which might be connected with changes in emission line
profile. The SDSS lightcurve for SDSS J0151+0100 is plotted in Fig. 7,
together with additional measures from the Pan-STARRS1 data archive
666https://catalogs.mast.stsci.edu/panstarrs/(Flewelling et al., 2020). The
light curve shows achromatic variation with amplitude of a magnitude over a
timescale of around 10 years. There is no indication of short term
fluctuations in brightness which might be associated with changes in emission
line strength.

##  6 Conclusions

This paper has set out to investigate whether changes in the structure of
quasar broad emission lines are consistent with the expected microlensing by a
population of stellar mass primordial black holes making up a large fraction
of dark matter. Evidence for such a population has been published recently
(Hawkins, 2020a, b, 2022), which raises the possibility that these compact
bodies may also be detected by microlensing the broad emission line clouds
associated with quasars. Microlensing effects are expected to change the shape
of the broad line profile, typically resulting in the appearance of new
emission features offset from the systemic velocity of the quasar. Although
such changes can happen as a result of random motions of the clouds in the
broad emission line region, they would be expected to occur over very long
dynamical timescales of the order of 50 years or more, as opposed to
microlensing timescales of around 5 years. A further discriminant comes from
the redshift of the quasar. Low redshift quasars are very unlikely to be
microlensed due to the predicted small optical depth to microlensing of the
lenses, but for redshift $z>2$ the probability of microlensing rises to around
20%.

The main results of the paper are as follows:

  1. 1.

The paper starts by characterising the changes in quasar emission line
structure due to microlensing, based on spectroscopy from the literature of
quasar spectra from gravitational lens systems where microlensing is known to
occur.

  2. 2.

Changes in emission line structure in low redshift Seyfert galaxies are
illustrated, and attributed to cloud motions in the BLR. These changes occur
on short timescales of the order of 5 years, corresponding to the dynamical
timescale of the BLR.

  3. 3.

Luminous low redshift quasars show no changes in emission line structure. This
is attributed to the much larger size of the BLR, with a dynamical timescale
of the order of 50 years.

  4. 4.

Luminous quasars at high redshift $(z>2)$ exhibit different behaviour, with
around 20% showing strong changes in emission line structure on a timescale of
5 years. This is consistent with the expected microlensing from a population
of solar mass compact objects comprising at least a large fraction of the dark
matter, although intrinsic variability is an alternative explanation. The most
plausible candidates for the compact bodies are primordial black holes.

## Acknowledgements

This research has made use of the Keck Observatory Archive (KOA), which is
operated by the W.M.Keck Observatory and the NASA Exoplanet Science Institute
(NExScI), under contract with the National Aeronautics and Space
Administration.

## Data Availability

The data upon which this paper is based are all publicly available and are
referenced in the text, with footnotes to indicate online archives where
appropriate.

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