IAC-22-B4

# Observing M Dwarfs UV and optical flares from a CubeSat and their
implications for exoplanets habitability

Julien Poyatos1∗ , Octavi Fors1 , José Maria Gómez Cama2

(1Departament de Física Quàntica i Astrofísica, Institut de Ciències del
Cosmos (ICCUB), Universitat de Barcelona, IEEC-UB, Martí i Franquès 1, E-08028
Barcelona, Spain
2Departament d’Enginyeria Electrònica i Biomèdica, Institut de Ciències del
Cosmos (ICCUB), Universitat de Barcelona, IEEC-UB, Martí i Franquès 1, E-08028
Barcelona, Spain
∗Corresponding author
)

## Abstract

M dwarfs show the highest rocky planet occurrence among all spectral types, in
some instances within the Habitable Zone. Because some of them are very active
stars, they are often subject to frequent and powerful flaring, which can be a
double-edged sword in regard of exoplanet habitability. On one hand, the
increased flux during flare events can trigger the chemical reactions that are
necessary to build the basis of prebiotic chemistry. On the other hand,
sufficiently strong flares may erode exoplanets’ atmospheres and reduce their
UV protection. Recent observations of flares have shown that the flaring flux
can be $\times$100 times stronger in UV than in the optical. UV is also
preferable to constrain more accurately both the prebiotic abiogenesis and the
atmospheric erosion. For these reasons, we are developing a CubeSat payload
concept to complement current flare surveys operating in the optical. This
CubeSat will observe a high number of flaring M dwarfs, following an all-sky
scanning law coverage, both in the UV and the optical to better understand the
different effective temperatures as wavelengths and flaring status go. This
will complement the bright optical flares data acquired from the current
ground-based, high-cadence, wide FoV surveys. Another scientific planned goal
is to conduct few-minute after-the-flare follow-up optical ground-based time-
resolved spectroscopy, that will be triggered by the detection of UV flares in
space on board of the proposed CubeSat. Finally, the study of M dwarfs stellar
activity in the UV band will provide useful data for larger forthcoming
missions that will survey exoplanets, such as PLATO, ARIEL, HabEx and LUVOIR.

Keywords: M dwarf, flares, CubeSat, exoplanets, habitability, UV

##  1 Introduction

###  1.1 Stellar flares and exoplanet habitability

M dwarfs make up to $\sim$75% of the stellar population and frequently host
terrestrial planets in their habitable zones (Henry et al., 2006; Covey et
al., 2008). Their small radii and low temperatures enable the detection and
atmospheric characterization of these planets, making M dwarfs excellent
targets in the search of habitable exoplanets (Kaltenegger and Traub, 2009).
However, these stars are known to be very active (with stars later than M4
being fully convective), making them prone to frequently emit large stellar
flares throughout their lifetimes (Kowalski et al., 2010). Powerful flares are
also often associated with Coronal Mass Ejections (CMEs), streams of charged
particles ejected into space. Flares and CMEs can play an important role in
planetary evolution and habitability, mainly through atmospheric erosion, and
act as stressors for surface life (Tarter et al., 2007). The span of the HZ
around M dwarfs is much smaller than that around earlier-type stars. In
consequence, exoplanets orbiting in the HZ of M dwarfs are more affected by
flares and CMEs. In the most extreme scenario, intense flaring activity could
render the surface of an exoplanet uninhabitable, leaving only a chance for
life to develop in an ocean or underground (Tilley et al., 2019; Estrela and
Valio, 2018). More optimistically, flares may catalyse biosignatures, or serve
as a source for otherwise scarce visible-light photosynthesis on planets
orbiting M dwarfs. Indeed, recent work suggests that sufficient UV radiation
might trigger the synthesis of prebiotic chemistry, turning inorganic matter
on a planet’s surface (mineral dust, meteoritic dust, etc) into the bases of
life (sugars, nucleobases, carboxylic acids, amino acids, etc) (Ranjan et al.,
2017; Rimmer et al., 2018). The typical effective temperatures of M dwarfs
makes them unlikely to produce sufficient UV radiation for this purpose, in
this case the required amount of UV radiation can only come from flares (Chen
et al., 2021). In sum, there seems to exist a ”sweet spot” where M dwarfs
could be flaring just enough to provide enough UV radiation for the trigger of
prebiotic chemistry, but not too much to induce atmospheric erosion and
surface sterilization. It is therefore essential to gather information on the
frequency and energy of host star’s flares to better characterise the
habitability of their surrounding planets.

###  1.2 CubeSats for astrophysics

CubeSats are a type of small satellites (i.e. less than 100kg) composed of one
or several standardised units of 10x10x10cm. This format allows them to use
off-the-shelf components, drastically lowering the cost and construction time
of satellite missions (Poghosyan and Golkar, 2017). These are getting more and
more popular in the recent years, allowing individuals, startups of
universities to lead their own missions. Space agencies are also adopting
CubeSats through their New Space strategies.

In this context, we are studying a CubeSat concept to implement in a future
mission, in order to observe M dwarfs flares in the UV and the optical. This
$\geq$6U CubeSat will gather light curves and images of flaring M dwarfs in
both bands split in several filters to compare the difference in flux ratios.
These data products will allow to complement our understanding on stellar
physics for future missions (such as PLATO, ARIEL, HabEx and LUVOIR), and to
provide new inputs in the Star-Planet Interaction models. The CubeSat will
also be used to detect flares as early as possible in UV, then trigger alerts
to ground-based observatories to observe few-mins after-the-flare time-
resolved follow-up spectroscopy. In general, UV flares reach their peak faster
than optical flares. We could, in the best case, use the detection of UV
flares as a trigger for optical flares spectroscopy, which would give precious
data on the flare physics scenario (mainly the evolution of the continuum of
Hα and optical lines associated with CMEs) (Fuhrmeister et al., 2022; Wu et
al., 2022). Finally, it will be able to detect Quasi-Periodic Pulsations
(QPPs) (Fleming et al., 2022; Doyle et al., 2022). These flares happening at
an almost fixed period are interpreted as a modulation of the flare’s
chromospheric thermal emission through periodic triggering of reconnection by
external magnetohydrodynamic oscillations in the corona (Doyle et al., 2022;
Fleming et al., 2022). Observations of multiple flares per active stars will
allow to test this interpretation.

We report in this paper the first calculations on the expected number of
detectable flares per day by our CubeSat concept, for different target types.
This work will be organised as follow: In Section 2, we present the catalog,
equations and component characteristics we used for the calculations. In
Section 3, we provide the calculation results for different types of M dwarfs,
according to their mass and distance. In Section 4, we discuss possible
consequences on the CubeSat mission primary and secondary science goals and
possible future mission prospects. We conclude in Section 5.

##  2 Materials and methods

###  2.1 The TOI catalog

TESS (Transiting Exoplanet Survey Satellite) is searching the entire sky since
2018 for transiting exoplanets (Ricker et al., 2014). Since then, more than
5000 TESS Objects of Interest (TOIs), have been identified. These includes
both new planet candidates found by TESS and previously-known planets
recovered by TESS observations. Howard (2022) explored the light curves of the
2250 non-retired TOIs from the Sectors 1 & 2 and extrapolated the flare rates
through flare injection and recovery for their 2096 host stars.

Flare emission from stars is described by a power law in which higher energy
flares are emitted less frequently than lower energy flares. Flare Frequency
Distribution (FFDs) are computed for each TOI host star given the cumulative
rate at which flares of energy $E$ or larger are observed per day and the
total observing time. FFDs are fit in a log-log space in the usual way:

$\log\nu=(1-\alpha)\log E+\beta$ (1)

where $\nu$ is the number of flares with an energy greater than or equal to
$E$ erg per day, $1-\alpha$ describes the frequency at which flares of various
energies occur, and $\beta$ determines the overall rate of flaring. This
catalog places upper limits on the flare rate of host stars. Injection and
recovery tests of flares are performed for non-flaring stars which enables to
place upper limits on their flare rates when combined with the total
observation time.

We cross-match M dwarfs from the TOI catalog with the TIC catalog to obtain
their distance and radius. Following the method in Howard (2022), we separate
the stars in different groups according to their mass and distance in order to
facilitate comparisons. The different groups are sorted as in Table 1. Winters
et al. (2021) determines 15 pc as the demarcation distance between nearby and
distant M-dwarfs. We extrapolate an equivalent demarcation distance for larger
mass groups such that the apparent magnitude of stars in each group is
approximately comparable to M dwarfs observed from 15 pc. For this work, we
only consider in Section 2.3 flares from M dwarfs (corresponding to the groups
1-4 in Table 1). However, our CubeSat concept could easily detect K dwarf
flares as well (corresponding to groups 5-8 in Table 1). We plot in Figure 1
the distribution of the targets from Groups 1-4 on a mass and distance
diagram.

Group number | Spectral type | Mass [$M_{\odot}$] | Distance [pc] | Number of targets
---|---|---|---|---
1 | Late M | 0.1 - 0.3 | 0 - 15 | 10
2 | Early M | 0.3 - 0.6 | 0 - 15 | 5
3 | Late M | 0.1 - 0.3 | 15 - 36 | 53
4 | Early M | 0.3 - 0.6 | 15 - 36 | 210
5 | Late K | 0.6 - 0.75 | 0 - 36 | 20
6 | Early K | 0.75 - 0.9 | 0 - 36 | 13
7 | Late K | 0.6 - 0.75 | 36 - 80 | 160
8 | Early K | 0.75 - 0.9 | 36 - 80 | 235
9 | Late G | 0.9 - 0.98 | 0 - 80 | 33
10 | Early G | 0.98 - 1.06 | 0 - 80 | 301
11 | Late G | 0.9 - 0.98 |  $>$ 80 | 203
12 | Early G | 0.98 - 1.06 |  $>$ 80 | 38
Table 1: TOI host stars are divided into 12 different groups according to
their mass and distance. From left to right: number of the group,
corresponding spectral type, mass range, distance range (in pc), and number of
targets within each group. Out of the 2096 target stars, 968 do not fall in
any groups and are therefore not considered. Figure 1: Mass/distance diagram
of the targets from the first two groups. Top and right histogram represent
the distribution of the targets by mass and distance, respectively.

###  2.2 Component characteristics

Since one of this CubeSat’s scientific goal is to observe flares in two
different bands (UV and optical), it needs to embark either two sensors
observing each in one band, or one sensor observing in both bands
simultaneously. In this work we chose to explore the first option. We used for
the following ID4MTVISB-CL111https://en.idule.jp/wp/wp-
content/uploads/2020/07/ID4MTVISB-CL_E_20200715.pdf, a commercial CMOS
manufactured by Gpixel. This backside illuminated CMOS image sensor provides
high sensitivity, low noise, and high dynamic range in both UV and optical,
making it adequate for the scientific purpose of this mission. We give in
Table 2 a few key technical characteristics of this CMOS, mainly the ones that
were used for the calculations. We selected the two wavelength ranges as
follows: UV = [200 nm - 275nm], Optical = [378nm, 555nm]. This UV band
contains emission lines from transition and chromospheric regions (C IV, He II
and Mg II) (Fuhrmeister et al., 2022), and the optical band contains Hα line
profiles (Wu et al., 2022). Data from these emission lines will be extremely
useful to study short- and long-term variability of active M dwarfs, to
provide crucial inputs to stellar models and to understand how flare color
ratios change over flare duration, effective temperature, stellar mass,
stellar rotation period, and stellar age. The optical band contains the exo-
auroral emission lines, increasing the star/planet contrast by orders of
magnitude.

We average the quantum efficiency for each band from the spectral response
curve provided by the manufacturer (Figure 2). This gives us QE${}_{\rm
UV}\approx 0.45$ and QE${}_{\rm optical}\approx 0.90$. We detail in Table 2
the characteristics that will be used for the calculations in Section 2.3.

For the telescope, we considered a 9cm aperture-class telescope, similarly to
other CubeSats in construction with similar goals (Ardila et al., 2018).

Figure 2: The quantum efficiency curve of the ID4MTVISB-CL CMOS image sensor. Name | Meaning | Value | Units
---|---|---|---
$n_{\rm pix}$ | Effective pixel number | $2048(H)\times 2048(V)$ | .
$s_{\rm pix}$ | Pixel size | 11$\mu m\times 11\mu m$ | $\mu m^{2}$
$Q_{\rm E-UV}$ | Average quantum efficiency in UV | 0.45 | .
$Q_{\rm E-opt}$ | Average quantum efficiency in optical | 0.90 | .
$RON$ | Read-out-noise | 0.2 | $e^{-}/pixel$
$DARK$ | Dark current | 1.6 | $e^{-}/s/pixel$
Table 2: CMOS sensor opto-electrical characteristics.

###  2.3 Expected number of observable flares per day

The bolometric energy released by an M dwarf flare is usually estimated by
considering a 9000K blackbody curve (Allred et al., 2015). However, this
method is generally used to estimate the energy produced by very strong flare
events by extrapolating their blackbody in the optical. Arcavi (2022) showed
that this process is prone to large errors if the optical data is not combined
to UV data, because optical bands are mostly sampling the Rayleigh-Jeans tail
of the spectrum at high temperatures. The objective of this work is opposite:
we want to determine what bolometric energy would produce a high enough SNR on
the CubeSat’s sensor. We therefore first re-estimate the temperature of the
weakest recovered flare with the inverse of the Stefan-Boltzmann law:

$T=\left(\frac{R_{e}}{\sigma}\right)^{1/4}=\left(\frac{\partial\phi_{e}}{\partial
A}\frac{1}{\sigma}\right)^{1/4}=\left(\frac{E_{bol}}{A}\frac{1}{\sigma}\right)^{1/4}$
(2)

where $R_{e}$ is the radiant exitance, $\sigma$ is the Stefan-Boltzmann
constant, $\phi_{e}$ is the radiant flux emitted, $A$ is the surface of the
emitting star and $E_{bol}$ is the bolometric energy of the weakest flare
recovered.

We then use the Planck’s law to compute the blackbody radiation corresponding
to this temperature (Kramm and Mölders, 2009):

$L=\frac{2\pi^{4}k^{4}}{15h^{3}c^{2}}T^{4}\qquad W.m^{-2}.sr^{-1}$ (3)

where $L$ is the spectral radiance, $h$ is the Planck’s constant, $c$ is the
speed of light, and $k$ is the Boltzmann’s constant. We also derive from
Equation 3 the total photon irradiance:

$L^{p}=\frac{4\zeta(3)k^{3}}{h^{3}c^{2}}T^{3}\qquad
photon.s^{-1}.m^{-2}.sr^{-1}$ (4)

where $\zeta$ is the Riemann zeta function and $\zeta(3)\approx
1.202056903159594$ (also known as Apéry’s constant).

Naturally, an increase in released bolometric energy (i.e. a flare) will be
translated by an increase in temperature. This will impact the blackbody
radiation by shifting the peak of the emission curve to shorter wavelengths.
As a result, the amount of UV radiation released increases as the bolometric
energy of the flare increases. In Figure 3, we plot three examples of
blackbody radiations for different temperatures and highlight the two
wavelength ranges we consider in this paper to highlight this effect. Even
though the proportion of UV radiation is higher than optical radiation for
high energy flares, the width of the UV band is smaller than that of the
optical band. This will result in a lower SNR in UV compared to optical since
less photons can be captured.

Figure 3: Spectral irradiance curves for black-bodies with temperature of
5000K (red), 7000K (green) and 9000K (blue). We color in shaded red the two
bandwidth considered in this study.

To compute the in-band spectral radiance $F_{e}$ (and by extension the in-band
spectral photon irradiance), we integrate the Planck’s function over a finite
range as follows:

$F_{e}=\int_{\lambda_{1}}^{\lambda_{2}}L_{\lambda}d\lambda=\int_{\lambda_{1}}^{\infty}L_{\lambda}d\lambda-\int_{\lambda_{2}}^{\infty}L_{\lambda}d\lambda\qquad$
(5)

and we use the code provided in Widger Jr and Woodall (1976) to estimate the
two integrals. We then use the inverse square law to compute the number of
photons received ($F_{r}$) at the CubeSat’s entrance pupil, assuming each star
as a perfect sphere emitting equally in every direction:

$F_{r}=\frac{F_{e}}{4\pi d^{2}}\qquad W.m^{-2}.nm$ (6)

where $d$ is the distance between the target star and the CubeSat
(approximated as the distance between the target star and the Earth).

We use the ESO ETC textbook
formula222https://www.eso.org/observing/etc/doc/formulabook/node6.html to
compute the number of photons emitted entering the CubeSat’s optics, similar
to the one used by Gill et al. (2022) :

$N=\frac{F_{r}.\Delta_{\lambda}.t.Q_{E}.S}{P}$ (7)

where $N$ is the number of photons down-converted by the sensor, $F_{r}$ is
the received flux of photons in $W.m^{-2}.nm$, $\Delta_{\lambda}$ is the
wavelength range considered in $nm$, $t$ is the total exposure time in
seconds, $Q_{E}$ is the average quantum efficiency of the band, S is the
telescope surface in $m^{2}$ and $P$ is the energy of one photon. We consider
the solid angle created by the length and width of the sensor as negligible.

Finally, the SNR is calculated with the formula given by the ESO ETC as:

$SNR=\frac{N}{\sqrt{N+n_{pix}.RON^{2}+n_{pix}.DARK.t}}~{}$ (8)

where $n_{pix}$ is the number of pixels of the sensor, RON is the read-out-
noise in $e^{-}/pixel$, $DARK$ is the dark current in $e^{-}/s/pixel$ and $t$
is the exposure time.

The CubeSat will operate following an all-sky scanning law and a
heliosynchronous orbit, with a revisit time of 2 days. We consider an exposure
time of $t=90s$ and a processing time of 30s, meaning that a science image
will be obtained every 2 minutes. The rest of the values used in Equation 7
and Equation 8 can be found in Table 2.

##  3 Results

The bolometric energy of each flare in the TOI catalog corresponds to the
minimum energy for a flare to be observable and not blended in noise. However,
the noise distribution and optical characteristics for our CubeSat will be
different than those for TESS. Thus, we have to be careful when considering
the weakest detectable flare. To address this we fix a threshold on the SNR.
For a flare to be considered as detectable by our CubeSat, it has to produce a
SNR $>$ 10 dB. We compute the SNR corresponding to different flare energies
for each target in Groups 1-4, increasing the energy by $10^{0.5}$ erg
intervals. We plot the results in Figure 4. All flares from Group 1 give an
SNR $>$ 10 and are therefore considered as observable. However, this group
contains drastically less targets as the three others, as can be seen by the
small span of the box-plots. Results from Group 1 might be influenced by a
poor-statistics bias and should therefore be considered with caution.

Figure 4: SNR corresponding to different flare energies for each target in the
first four groups, for our optical band (blue) and UV band (orange).
Horizontal bars correspond to, from bottom to top, statistical minimum, first
quartile, median, third quartile, and statistical maximum. Outliers are
represented by black diamonds. The red horizontal line corresponds to the
value of SNR = 10.

The amount of flares of a given energy over a period of time is determined by
the FFD, as described in Equation 1. Howard (2022) estimates the $\alpha$ and
$\beta$ parameters of each target in the TOI catalog through 200 flare
injection and recovery tests. We then compute the FFD of each target from
Groups 1-4, then crossmatch the data with the results from Figure 4. This
gives us the number of flares per day with enough energy to be observed with a
SNR $>$ 10, for each target. We plot the result in Figure 5.

Figure 5: Number of flares/day observable with a SNR $>$ 10\. Vertical bars
correspond, from left to right, to statistical minimum, first quartile,
median, third quartile, and statistical minimum. The thickness of the box
corresponds to the probability density (i.e. the box is thicker where there is
a lot of data points). Dark shaded boxes corresponds to values for our optical
band, and light shaded regions corresponds to values for our UV band. For
clarity, the color of each group is similar to the one used is Figure 1.

##  4 Discussion

Since Groups 3 and 4 represent nearly 95% of the targets in the first four
groups, we conclude that this set of components would allow our CubeSat to
observe $\sim 10^{-1}-10^{1}$ flares/day. Nearby bright targets from Group 1
drastically improve this value, with some specific targets producing nearly
$10^{4}$ observable flares/day. Assuming the distribution of M dwarfs in the
entire sky is the same as in the TESS Sectors 1 & 2 and considering the
CubeSat’s revisit period of 2 days, we would gather enough UV and optical
flare observations for the realization of the scientific goal in a $\sim$ 1-2
year mission lifetime. However, the CubeSat’s optics have not been confirmed
yet, so we advocate to reproduce similar calculations once the final CMOS and
telescope are chosen.

##  5 Conclusion

In this paper, we used the TOI catalog complemented by injected flares from
Howard (2022) to determine the rate of M dwarfs flares detectable by our
CubeSat concept. We used for the calculations two components likely to be used
for this mission: the ID4MTVISB-CL UV and optical imaging CMOS sensor from
Gpixel and a 9cm aperture-class telescope. We separated M dwarfs in the
catalog according to their mass and distance, before determining the SNR of
the weakest detectable flare for each target. We then used the $\alpha$ and
$\beta$ parameters provided by Howard (2022) to determine the FFD of each
target. We cross-matched the flare’s SNR values and the FFDs to determine the
number of flares detectable per day by our CubeSat with an SNR $>$ 10\. We
conclude that a mission lifetime of $\sim$ 1 - 2 years should provide enough
UV and optical flare observations to accomplish the described scientific
goals.

## Acknowledgements

This work made use of NASA ADS Bibliographic Services. This research has made
use of several public tools developed at CDS, Strasbourg Observatory, France.
OF and JMC acknowledge the support by the Spanish Ministerio de Ciencia e
Innovación (MICINN) under grants PID2019-105510GB-C31 and
PGC2018-098153-B-C33, respectively. OF and JMC acknowledge the support through
the “Center of Excellence María de Maeztu 2020-2023” award to the ICCUB
(CEX2019-000918-M). This work made use of Astropy, a community-developed core
Python package for Astronomy, and the NumPy, SciPy, and Matplotlib Python
modules.

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and accretion of diffuse matter. Bayons settled, stars formed, and a
protogalaxy grew into one or the other of the distinct galaxy families
discussed in Section 5.1.

Sidney van den Bergh’s (1976) thinking about galaxy morphologies a half-
century ago was that

> Canonical views on galaxy evolution suggest that the present morphology of
> galaxies is predestined by the genetic heritage provided by initial mass and
> angular momentum. The results discussed above suggest that the evolution of
> galaxies is also substantially affected by environmental factors.

Both thoughts remain empirically well supported. We can add that, if galaxies
grew by gravity out of small primeval Gaussian departures from homogeneity,
then galaxy formation had to have been a bistable process. The point can be
made a little more explicit by recalling the idea of bistable evolution and
its separatrix in classical mechanics.

Suppose the state of a system is completely described by the values of $N$
components of particle positions and their $N$ canonical momenta. Let these
$2N$ parameters be the coordinates in a $2N$ dimension phase space. The
initial condition of the system is represented by its position in this space
at a chosen starting time. Imagine an ensemble of initial conditions spread
across phase space at this starting time. The equation of motion determines
the evolution of the system, its path through phase space, from each initial
position. In a bistable situation paths in phase space from the distribution
of initial conditions arrive at one or the other of two (or more) basins of
attraction. The separatrix is the boundary that separates initial positions in
phase space that end up in one of the basins of attraction from the initial
positions that end up in the other(s). The orbits of stars may have
separatrices (e.g., Yavetz, Johnston, Pearson, Price-Whelan, and Weinberg
2021). The evolution of protogalaxies from their initial conditions is much
more complicated; we must take account of dissipation, for example, and
consider the complexities of stellar formation and its effects on the
evolution of the galaxy. But the example from classical mechanics illustrates
the concept of evolution of protogalaxies from initial conditions without
manifest bimodality to a bimodal final state. It is what seems to have
happened.

So in this way of thinking, what is the separatrix in galaxy formation that
determines the evolution of a protogalaxy to a spiral or elliptical
morphology? It cannot simply be the mass. There are spirals among the most
luminous of galaxies, at $L\sim 10L_{\ast}$. (The distributions of the most
massive spiral and elliptical galaxies relative to the plane Local
Supercluster are shown in Fig. 3.) At least some of these supermassive late
types have the familiar two arms elegantly spiraling out from the center. An
early example is UGC 2885 (Rubin, Ford, and Thonnard 1980); Ogle et al. (2019)
catalogue others. At lower stellar masses there are more spirals than
ellipticals, but both types are observed. Van den Bergh (1976) had good reason
to mention mass as part of the genetic heritage, but the story must be more
complicated.

The disk of stars in a spiral galaxy is supported largely by rotation, while
the stars in an elliptical are supported by a closer to isotropic distribution
of orbits. Thus van den Bergh had good reason to consider that the separatrix
is related to angular momentum. A dimensionless measure of the angular
momentum $L$ of a galaxy is the combination
$\Lambda=L~{}E^{1/2}G^{-1}M^{5/2}$, where $E$ the magnitude of the binding
energy and $M$ is the mass (Peebles 1971). In analytic estimates and numerical
simulations the distribution of $\Lambda$ is not bimodal (e.g., Efstathiou and
Jones 1979). If, despite this, $\Lambda$ is the separatrix, the division
between early and late types would require a sharp sensitivity to the values
of $\Lambda$ and mass. A more likely picture along this line is that
morphology is determined by “the coherent alignment of the angular momentum of
baryons that accrete over time to form a galaxy” (Sales, Navarro, Theuns, et
al. 2012). The investigation of galaxy morphology and halo spin in numerical
simulations by Rodriguez-Gomez, Genel, Fall, et al. (2022) reveals a
systematic difference of angular momentum of models classified as spirals and
as ellipticals plus S0s. It is not yet bimodality in the spin-stellar mass
plane (in their Fig. 1), but perhaps a step in this direction.

Environment matters. The giant $L\sim 10L_{\ast}$ galaxies in rich clusters
likely formed by mergers of cluster members, meaning environment likely is the
separatrix between these giants and ordinary $L\sim L_{\ast}$ galaxies. Maybe
another example follows from the larger ratio of early to late types in denser
regions. For example, one might imagine that all protogalaxies began evolving
toward the spiral morphology, but that violent mergers turned some proto-
spirals into proto-early types. It would have happened more frequently in more
crowded environments. But recall the separate family resemblances of spirals
and ellipticals, which do not seem to be sensitive to environment. And
consider the curious separation of early and late types in the Centaurus group
(Sec. 5.1).

The evidence is that the formation of galaxy morphologies was determined more
by nature than nurture, and it is an interesting challenge to identify the
character of the separatrix. It might be some combination of mass, angular
momentum, and environment, or maybe something completely different. The issue
might be resolved by what is learned from numerical simulations of galaxy
formation, or maybe by semi-analytic considerations of what appears to be
happening. It is a fascinating opportunity for research, provided you bear in
mind that people have been trying to solve the puzzle of the early-late
bimodality for a long time. It means the resolution must be subtle, but surely
it exists.

###  5.3 Bulges and Disks of Spiral Galaxies

Numerical simulations of galaxy formation produce spiral galaxies that are
impressively good approximations to what is observed, but there are three (or
more; I invite suggestions) issues that are persistent enough to merit
attention. One is that the central concentrations of starlight in simulated
galaxies are overly luminous. Another is that the velocity dispersions of the
stars moving in the planes of the disks of model spiral galaxies are
unrealistically large. And a third is that we do not know the separatrix
responsible for the distinct galaxy bimodality. I review these issues in
Peebles (2020b); they are outlined and considered further here.

Early attempts to simulate galaxy formation encountered the problem that a
cloud of baryonic matter — gas and plasma — with the mass and radius typical
of an $L\sim L_{\ast}$ galaxy readily dissipates energy and collapses almost
freely. Observed spiral galaxies must have avoided this overcooling problem,
and it must be avoided in models for otherwise they would have overly
prominent classical bulges or stellar halos. The problem has been tamed by
adjustments of the prescriptions for star formation and models for the effects
of the stars on the distributions of baryonic and dark matter, but the
evidence is that the problem in simulations of galaxy formation persists.

Figure 5 shows the distribution of the ratio of bulge to total luminosities of
the nearby large galaxies. For some galaxies we can add to the hot component
in the bulge the hot stellar halo that spreads out to greater distances away
from the disk. Estimates of the median value of the luminosity fraction of the
stars in the two hot components, bulge plus halo, in spiral galaxies are (from
Peebles 2020b)

$\hbox{simulations: }{B+H\over T}\sim 0.45,\quad\hbox{observations: }{B+H\over
T}\sim 0.18.$ (24)

The rest of the total luminosity, $T$, is assigned to the disk. The median of
the observed fraction is from examinations of ten nearby galaxies by Merritt,
van Dokkum, Abraham, and Zhang (2016) and Harmsen, Monachesi, Bell, et al.
(2017). The hot fraction in simulations is from reports by Grand, Gómez,
Marinacci, et al. (2017) and Garrison-Kimmel, Hopkins, Wetzel, et al. (2018)
of the results of two large research programs. The greater hot fraction in
simulations agrees with my visual impression of images of real and model
spirals. You are invited to check your impression.

A second anomaly is the large dispersion of model disk stars in the direction
of the plane of a simulated spiral galaxy. An illustration uses a simplified
model for a spiral galaxy in which the stars move in the plane of a disk with
a flat rotation curve, constant circular speed $v_{c}$. This is a reasonable
approximation to many observed and model spiral galaxies. I refer to Peebles
(2020b) for the details of the results of computation of stellar orbits. The
orbit of a model star is characterized by a parameter, $\epsilon$, that is a
measure of the orbital angular momentum, with $\epsilon=1$ for a star moving
in a circular orbit and $\epsilon=-1$ for a star in a circular orbit but
moving in the opposite direction from the mean motion of the disk stars.

Numerical solutions give the rms radial velocities at two choices of this
circularity parameter:

$\displaystyle\langle(dr/dt)^{2}\rangle^{1/2}$ $\displaystyle=0.32v_{c}\hbox{
for }\epsilon=0.9;$ $\displaystyle=0.45v_{c}\hbox{ for }\epsilon=0.8.$ (25)

I have not found discussions of disc star velocity dispersions in model disk
galaxies. My estimate is that in recent suites of numerical simulations
(Grand, et al. 2017; Garrison-Kimmel et al. 2018) the most promising of the
distributions in $\epsilon$ for a spiral galaxy have at least a quarter of the
stars at $\epsilon<0.9$, which means that the radial velocity dispersions are
greater than about a third of the circular velocity $v_{c}$ in a quarter of
the stars. A majority of the stars in a promising model have $\epsilon<0.8$,
with radial velocity dispersion greater than about half the circular velocity.
Observations of the distribution and motions of the stars in our neighborhood
of the Milky Way Galaxy (Anguiano, Majewski, Hayes, et al. 2020) indicate the
radial velocity dispersion in the thin plus thick disk stars is about
$\sigma_{r}=43$ km s-1 with $v_{c}\sim 240$ km s-1. The models look much
hotter.

The evidence reviewed here is that the model galaxies that emerge from modern
simulations of cosmic evolution have unacceptably large populations of stars
with large velocity dispersions present in stellar halos, classical bulges,
and disks. This looks quite different from the impression of cool populations
of stars and gas in the common nearby $L\sim L_{\ast}$ pure disk galaxies
(with the small fraction of the stellar mass in hot stars in the halo). I do
not know whether this anomaly has resisted persistent attempts at remediation,
or perhaps it has been put aside pending explorations of how to deal with the
many other complexities in modeling galaxy formation. But since the art of
simulating galaxy formation has a large literature, and the problem with hot
star populations in simulated spiral galaxies remains, it ranks as a serious
anomaly. Perhaps the situation will be resolved by further advances in
numerical simulations based on the $\Lambda$CDM theory. Or again, maybe
something is missing.

###  5.4 Merger Trees and the Cosmic Web

The phrases, “merger tree” and variants, and “cosmic web,” often figure in
discussions of how the galaxies formed. Aspects of both are worth considering
here.

Merging certainly happens; a clear example of a violent merger is the nearby
Antennae Galaxies. Ostriker (1980) introduced considerations of what the
remnant of the merger of two $L\sim L_{\ast}$ galaxies, as in this example,
would look like when it had relaxed to a close to steady state. Let us only
note that the remnant would have a luminous stellar bulge and halo made of
pre-existing stars, which certainly is not seen in the nearby pure disk
galaxies. And if the remnant of merging spirals looked like an elliptical it
would have an unusual mix of chemical elements. If the local galaxies are
close to a fair sample of the situation outside clusters then relaxed remnants
of mergers of $L\sim L_{\ast}$ galaxies are not common, because pure disk
galaxies are common, and I expect we would have heard of it if ellipticals
with odd chemical abundances were common.

A more modest example of merging is the pure disk edge-on galaxy NGC 5907 with
its stellar stream that we may expect eventually will add to the stellar halo
of this galaxy (e.g., van Dokkum, Lokhorst, Danieli, et al. 2020). The ample
evidence of tails and streams of stars around ellipticals and spirals is
suggestive of close passages and mergers (e.g., van Dokkum 2005). And the
stellar halo of the Milky Way is growing by tidal disruptions of dwarf
galaxies (e.g., Belokurov, Zucker, Evans, et al. 2006)

The concept of galaxy formation as a hierarchical merging process grew out of
several considerations. As just noted, galaxies do merge. The distribution of
galaxies on scales from $\sim 0.1$ Mpc to $\sim 10$ Mpc is well approximated
as a scale-invariant clustering hierarchy. It seems natural that the hierarchy
also formed at smaller scales and was erased by merging to form galaxies
(Davis, Groth, Peebles, 1977). And hierarchical growth of clustering is seen
in numerical simulations of cosmic structure formation. But although the
merger tree concept is well motivated by theory and observation it is in the
spirit of empiricism to ask whether, absent simulations but given our
knowledge of the phenomenology, people would have been led to the hierarchical
assembly picture.

Absent the guidance of merger trees people might have settled on the Eggen,
Lynden-Bell, and Sandage (1962) account of the formation of the stellar halo
and disk of the Milky Way spiral galaxy by a closer to monolithic collapse.
The theory would include occasional mergers of galaxies, as observed. It would
include formation of substructure in protogalaxies to account for satellites
and the spreading of baryons across the disks of the Milky Way and other
spiral galaxies, but substructure need not be to the extent of formation of
identifiable halos that merge to form identifiable halos in a merger tree. The
Eggen et al. picture is more in line with the observation that the
distributions of heavy elements in halo stars do not resemble the
distributions in stars in dwarf satellites (e.g., Tolstoy, Hill, and Tosi
2009, Fig. 10). Our stellar halo instead would have formed in the closer to
monolithic collapse Eggen et al. envisoned, and would have been salted by
stars from accreted dwarfs that produced the “field of streams” (Belokurov, et
al. 2006).

How are we to interpret the description of the formation of early type
galaxies by dry mergers and the late type by wet mergers, those rich in
diffuse hydrogen? It calls to mind formation of morphology by nature rather
than nurture: protogalaxies that have dry or wet natures. That could happen in
a merger tree, but more simply in a monolithic collapse.

Cowie, Songaila, Hu, and Cohen (1996) pointed out that lower mass galaxies on
average formed the bulk of their stars later. This downsizing effect does not
naturally follow from a hierarchical merger tree in which less massive halos
formed earlier. The discrepancy need not be serious because galaxy formation
is complicated, but it does call to mind a picture similar to Eggen et al.
(1962).

Madau and Dickinson (2014) concluded that “galaxies formed the bulk (75%) of
their stellar mass at $z<2$.” The growth of the stellar mass of a pure disk
galaxy in the manner described by Madau and Dickinson cannot have been by the
merging of subhalos, or galaxies, that contained many stars, because the stars
would have ended up in stellar bulges or halos, which are not prominent in
these galaxies. The stars in pure disk galaxies had to have formed out of gas
or plasma that had settled to the disk, as in cool streams (e.g. Kretschmer,
Dekel, and Teyssier, 2022). This has the flavor of the Eggen, Lynden-Bell, and
Sandage picture.

The phrase, “cosmic web,” also often figures in discussions of galaxy
formation. Bond, Kofman, and Pogosyan (1996) introduced the concept as an
evocative description of the distribution of dark matter in numerical
simulations: large and small concentrations of dark matter are connected by
filaments of dark matter in a pattern that calls to mind a web. It also
resembles the observed galaxy distribution. Bond et al. pointed out that the
filaments in simulations might be observable by detection of atomic hydrogen
along the filaments. One might imagine that the filaments also are threaded by
a magnetic field, and maybe even cosmic strings.

Detection of HI streams would be particularly interesting because the
filaments are expected to be present, connecting collapsing concentrations of
dark matter, if the dark matter is adequately well approximated as a
continuous fluid with no pressure or viscosity and the initial conditions are
continuous. Dark matter consisting of black holes would be expected to form
streams if the masses were small enough, and separate dark matter halos if the
masses were large enough.

Instrument arrays capable of detecting 21-cm radiation from the hydrogen in
primeval filaments of matter connecting dark matter halos may be becoming
available (e.g., Tudorache, Jarvis, Heywood, et al., 2022; Greene, Bezanson,
Ouchi, et al., 2022). It will be interesting to see the nature of the HI
distribution between mass concentrations, and the constraint that places on
the black hole mass in a black hole model of the dark matter.

###  5.5 Massive Black Holes

The large luminosities and compact natures of quasars led to the thought that
these objects are powered by the energy released by the collapse of matter
onto black holes with masses of perhaps a million solar masses (Salpeter 1964;
Lynden-Bell 1969). The clear evidence now is that large galaxies contain
central compact objects with masses in the range of $10^{5}$ to
$10^{10}M_{\odot}$. The objects in the centers of the elliptical M 87 and our
Milky Way spiral galaxy certainly are compact (Event Horizon Telescope
Collaboration et al., 2019; 2022). It makes a good case that these two
objects, and the ones in other galaxies, are supermassive black holes of the
kind predicted by Einstein’s general theory of relativity.

It was natural to suppose that matter would settle to the center of a galaxy
and perhaps accumulate to the point of relativistic gravitational collapse.
But that picture is complicated by the extreme difference between the density
characteristic of an $L\sim L_{\ast}$ galaxy, perhaps $\sim 10^{-24}$ g cm-3,
and the density characteristic of a $10^{9}M_{\odot}$ black hole, $\sim
c^{6}G^{-3}M^{-2}$, roughly $1$ g cm-3. Feeding the growth of a supermassive
black hole by dissipative settling of diffuse baryonic matter certainly is
conceivable, but one might instead expect that the settling would result in
multiple fragmentation and the formation of star clusters, as in the formation
of the first stars (e.g., Abel, Bryan, and Norman, 2002). Statistical
relaxation of the star cluster would in time produce core collapse to a
central black hole surrounded by a nuclear star cluster. But this is only one
of the several current lines of thought that are reviewed by Greene, Strader,
and Ho (2020), along with a discussion of how these black holes are detected.
Issues that seem particularly relevant are discussed here.

A clue to the formation of these central black holes is the relation between
the black hole mass and properties of the galaxy such as the bulge or spheroid
mass or stellar velocity dispersion (e.g., Magorrian, Tremaine, Richstone, et
al., 1998). We need more than one relation, because some of the pure disk
$L\sim L_{\ast}$ galaxies that are common nearby have massive central black
holes with at most modest classical bulges. The familiar example is the Milky
Way Galaxy with its central bar, little starlight in a classical bulge, and
clear evidence of a central black hole with mass $4\times 10^{6}M_{\odot}$.
Another is the galaxy NGC 4945 (Gaspar, Díaz, Mast, et al. 2022 and references
therein). This galaxy is seen nearly edge-on, it looks wonderfully flat, and
there is little indication of a concentration of starlight in a classical
stellar bulge rising out of the disk. (You can see the image of this galaxy at
https://apod.nasa.gov/apod/ap220226.html.) The evidence is that this galaxy
contains an active galactic nucleus operating around a black hole with mass
comparable to the one in the center of our Milky Way galaxy.

If evidence accumulates that every $L\sim L_{\ast}$ galaxy has a central
supermassive black hole it will invite the thought that galaxies formed around
black holes, whether supermassive or collections of less massive black holes
that seeded their formation (e.g., Silk and Rees 1998; Carr and Silk 2018).
The thought is encouraged by the observations of quasars at redshifts $z\sim
7$. These quasars presumably depended on the presence of massive black holes,
at a cosmic time when the stellar masses of galaxies were much smaller than
now.

In the Local Void (discussed in Sec. 4) galaxy formation seems to have been
suppressed. The thought that galaxies formed around black holes suggests that
the Local Void contains black holes, seed or supermassive, that are centered
on galaxies that are unusually small for their black hole masses. Maybe closer
examinations of the space distributions and redshifts of the stars in the two
void dwarfs at the top and to the left in Figure 4 could determine whether
they contain unusually massive black holes for such small galaxies. There are
other void galaxies to examine, and there is a considerable area of sky and
range of redshifts in the Local Void for deeper surveys for HI sources, star
clusters, and maybe even gravitational lensing by primeval black holes without
stars, any of which could be a valuable clue to the origin of massive black
holes.

Seth, van den Bosch, Mieske, et al. (2014) present evidence of an ultra-
compact dwarf galaxy with an exceptionally massive central compact object,
maybe a black hole. It may be near the large elliptical galaxy M 60. Maybe
this dwarf is the remnant of a galaxy whose growth around a particularly
massive primeval massive black hole was interrupted by tidal stripping. It is
easy to invent such scenarios, sometimes difficult to test them, but perhaps
an essential part of the search for the explanation of these objects.

Are there normal-looking $L\sim L_{\ast}$ galaxies that do not have a central
massive black hole? The relatively nearby and face-on spiral galaxy M 101 has
lanes of dust that spiral in toward the center, ending at a star cluster with
mass $\sim 4\times 10^{6}M_{\odot}$ (Kormendy et al 2010). It is not yet known
whether there is a massive central black hole inside the star cluster. A
detection, maybe from the shapes of integrated Doppler-broadened stellar
lines, would be interesting, and a seriously tight upper bound on the mass of
a central black hole would be even more interesting.

The normal-looking spiral galaxy M 33, the third largest galaxy in the Local
Group, does not have a central black hole more massive than about $2\times
10^{3}M_{\odot}$ (Gebhardt, Lauer, Kormendy, et al., 2001; Merritt, Ferrarese,
and Joseph, 2001). It is difficult to imagine how a merger of two galaxies
could have driven both black holes out of the remnant while leaving the pure
disk morphology of this galaxy. The more likely interpretation is that the
formation of M 33 did not require a primeval black hole. It would mean that
the massive black holes in other galaxies need not have served as seeds for
galaxy formation, but instead grew together with the galaxies.

In the coevolution picture the accumulation of mass in a growing central black
hole would be by dissipative settling and merging at rates that might be
expected to differ from galaxy to galaxy. This could be compared to the
formation of stellar bars that run across the centers of spiral galaxies: some
dominate the shape of the spiral, some are less conspicuous, and others are
not noticeable. So it might be with the formation of supermassive black holes.
The correlation of mass with host galaxy properties argues against a broad
scatter of massive black hole masses at given galaxy mass, but it will be
helpful to see the scatter of central black hole masses as a function galaxy
properties in larger samples. It might serve as a test of the coevolution
picture. And it is to be noted that the coevolution picture does not seem
promising for M 33, because there is no evidence of a central massive black
hole.

The LIGO detection of gravitational waves from the merging of black holes with
masses $\sim 66$ and $85M_{\odot}$ (the event GW190521 reported by Abbott,
Abbott, Abraham, et al. 2020) was unexpected because the masses are
intermediate between the black holes produced by the relativistic collapse of
stars and the supermassive black holes in the centers of galaxies. Maybe they
are in line with the idea that black holes in this intermediate mass range
were seeds for the formation of supermassive black holes. There is a long span
of logarithmic time from the end of inflation, or whatever saved us from the
spacetime singularity of the standard cosmology, to the formation of the
isotopes of hydrogen and helium. During this time cataclysmic events of some
sort might have produced massive black holes or their seeds. The favorite
thought is directed to the disturbances to the mass distribution as the
universe expanded and cooled through first-order cosmic phase transitions.
These transitions might have been violent enough to have produced seed black
holes, maybe with a broad range of masses set by the variety of cosmic first-
order transitions in standard particle physics (e.g., Cappelluti, Hasinger,
and Natarajan, 2022). Another thought is that supermassive black holes or
their precursors formed during cosmological inflation (e.g., Kallosh and Linde
2022). Yet another is that seed mass black holes formed by collapse of the
first generation of gravitationally bound clouds of hydrogen and helium with
mass $\sim 10^{5}M_{\odot}$ set by the baryon Jeans length (Silk and Rees
1998).

Considerable research on the theory and observations of supermassive black
holes in the centers of galaxies has not yet produced a convergence to the
theory the origin of these objects. Their presence remains an anomaly.

###  5.6 Why the Characteristic Galaxy Luminosity?

The frequency distribution of optical luminosities of galaxies has a
characteristic value, $L_{\ast}$. There are far more galaxies with
luminosities less than $L_{\ast}$, but the $L\sim L_{\ast}$ galaxies produce
most of the cosmic mean optical luminosity density. The largest known galaxies
have luminosities $L\sim 10L_{\ast}$. That factor of ten is a curiously abrupt
cutoff compared to the broad range of luminosities of galaxies that are less
luminous than $L_{\ast}$. What accounts for the value of $L_{\ast}$ and the
cutoff at greater luminosities?

The abrupt cutoff was anticipated by Schechter’s (1976) functional form for
the galaxy luminosity function with its exponential cutoff. It grew out of a
Press and Schechter (1974) argument that “contains no ad hoc information about
an initial spectrum of long-wavelength density perturbations.” The
counterargument in Peebles (1974) agrees with the more recent demonstrations
that the formation of cosmic structure is sensitive to the form of the
spectrum of primeval departures from homogeneity. The Press and Schechter
argument nevertheless produced an analytic form for the luminosity function
that remains broadly useful.

In pure dark matter numerical simulations of the growth of cosmic structure in
the standard cosmology the halo mass function is not as abruptly truncated at
the high mass end as the galaxy luminosity function (e.g., Garrison,
Eisenstein, Ferrer, et al., 2018, Fig. 7). That need not be an anomaly; we
must bear in mind the complexities of how mass was apportioned to dark matter
halos and the baryons to stars. But is the existence of the characteristic
luminosity $L_{\ast}$ and the sharp upper cutoff in galaxy luminosities an
accidental result of these complexities, or might both be more readily
understandable in an improved cosmology?

###  5.7 Why MOND is Successful but Unpopular

The rotation speed $v_{c}$ of the stars and gas in the outer parts of the disk
of a spiral galaxy typically is close to independent of radius. The standard
interpretation is that the spherically averaged mass density in the outer
parts of the galaxy varies with the distance $r$ from the galaxy as
$\rho\propto r^{-2}$, which translates to gravitational acceleration $g\propto
r^{-1}\propto v_{c}^{2}/r$, satisfying the condition that the speed $v_{c}$ is
independent of distance from the galaxy. This is the flat rotation curve
observed in many spiral galaxies. The starlight density in the outer parts of
a typical spiral galaxy falls off more rapidly then $r^{-2}$. The standard
remedy is the postulate that the mass in the outer parts of a galaxy is the
nonbaryonic dark matter of the $\Lambda$CDM theory, the dark matter halo.

Milgrom (1983) introduced an influential alternative: modified Newtonian
gravity, or MOND. Instead of the hypothetical dark matter Milgrom proposed
that the rotation curve is flat in the outer parts of a galaxy because at
gravitational acceleration less than a characteristic value, $a_{0}$, Newton’s
law is modified to gravitational acceleration $g=\sqrt{GMa_{0}}/r$. In this
limit, and assuming most of the mass is within the radius $r$, then the speed
in a circular orbit is $v_{c}=(GMa_{0})^{1/4}$. If the luminosity $L$ of the
stars in the galaxy is proportional to the mass $M$ in baryons, then MOND
predicts that the value of the circular velocity $v_{c}$ in the outer flat
part of the galaxy rotation curve scales with the luminosity of the galaxy as
the universal form $v_{c}\propto L^{1/4}$. This is close to the empirical
Tully and Fisher (1977) relation. It is even closer to the power law relation
$v\propto M^{1/4}$ observed when $M$ is the mass in interstellar atomic
hydrogen added to the mass in stars (McGaugh 2020).

MOND was proposed after the discovery of the Tully-Fisher relation, but it is
reasonable to count the observed $v_{c}\propto M^{1/4}$ relation as a MOND
prediction that passes a tight test. One may ask why this successful
prediction receives so little community attention.

Let us note first that in the standard $\Lambda$CDM cosmology the observed
$v_{c}\propto M^{1/4}$ relation does not challenge the theory. It is instead
is a property of galaxies, along with the other family traits. The challenge
is to explore in this theory how these family resemblances among galaxies grew
as the universe expanded. It will be a crisis for $\Lambda$CDM if an
explanation for the observed traits cannot be found within the theory. We know
far too little about how galaxies formed to hope for a judgement on this point
any time soon.

An argument for MOND is the considerable literature on how the properties of
galaxies, and groups and clusters of galaxies, can be understood in this
picture. It is reviewed by Diaferio and Angus (2016) and Banik and Zhao
(2022). If in an alternative world all our present phenomenology of cosmic
structure were known but nothing was known about the evidence of a
relativistic evolving universe, MOND likely would be a community favorite. But
in our world there are two serious reasons for limited interest in MOND.

First, the well-tested $\Lambda$CDM theory with its cold dark dark matter
offers a ready and promising framework for development of a theory of the
formation of cosmic structure, galaxies and all. It has attracted the
attention of active and productive research groups. I have argued for problems
with the results, but they are details that have not discouraged the research
groups and I am hoping might guide us to adjustments that improve
$\Lambda$CDM.

Second, Milgrom’s (1983) MOND does not offer a ready framework for development
of a viable cosmology. The approach explored by Angus (2009) and Diaferio and
Angus (2016) follows thoughts about alternative gravity physics by Bekenstein
and Milgrom (1984) and Milgrom (2010). A starting postulate is that there is
dark matter, in the form of thermal sterile neutrinos with rest mass 11 eV.
The dark matter density parameter is close to the standard model. Gravity
physics in this model is enough like general relativity at redshifts $z\lower
2.15277pt\hbox{$\;\buildrel>\over{\sim}\;$}1000$, and the warm dark matter is
enough like the cold dark matter of the standard cosmology, that the acoustic
oscillation pattern imprinted on the CMB is close to the standard prediction
and the measurements. This is an important result. At low redshift the
neutrino hot dark matter would have largely escaped galaxy potential wells,
and gravity physics would have become enough like Milgrom’s original MOND that
galaxy rotation curves fit measurements without dark matter in halos around
galaxies and with the weaker gravity of MOND. This is viable, within the
notions of the gravity physics in this picture, though contrived. It is not
demonstrated in a theory that allows computations of predictions. Diaferio and
Angus (2016) conclude that

> It remains to be seen whether [in the adopted gravity physics] gravitational
> instability in a universe filled with baryonic matter and one species of
> sterile neutrino with 11 eV mass can form the observed cosmic structure at
> the correct pace.

The neutrino dark matter might be trapped in growing clusters of galaxies,
which could be a helpful feature for the application of MOND to clusters. But
Diaferio and Angus caution that

> the ability to explain the cluster mass discrepancy does not directly imply
> that MOND combined with 11-eV sterile neutrinos can form clusters in a
> cosmological context.

To my mind it is exceedingly unlikely that an alternative gravity physics and
cosmology without cold dark matter, or something that acts much like it, can
fit the array of tests passed by the standard general theory of relativity
applied to the $\Lambda$CDM cosmology. But good science seeks to replace
intuition with worked predictions of adequately specified theories. As
Diaferio and Angus conclude, it remains to be seen whether this can be done
for a generalization of Milgrom’s MOND.

##  6 Summary Remarks

To prevent misunderstandings I repeat the conclusion in Section 1.1.2, that
the empirical tests give excellent reason to expect that a more advanced
physical cosmology will look much like the theoretical $\Lambda$CDM universe,
because many well-checked tests show that the $\Lambda$CDM universe looks much
our universe. But the great progress in cosmology and the other physical
sciences has left anomalies, some of which have been troubling for a long
time.

A century ago Pauli and Jordan understood the vast difference between the
vacuum mass density allowed by the relativistic theory and the density
suggested by quantum physics (Sec.2.8). Applications of quantum physics have
grown far broader, giving compelling evidence that this physics is a broadly
useful approximation to reality, but I am not aware of a significant advance
in resolving the quantum energy density problem, apart from the anthropic
argument (in Sec. 1.2).

A century ago Öpik (1922) turned earlier thoughts that the spiral nebulae
might be other galaxies of stars into a quantitative demonstration. The
progress from there to a promising physical basis for analyses of how the
galaxies formed was slower than the development of quantum physics, but we
have now a well-tested cosmology that might be expected to be an adequate
basis for a secure understanding of these objects. The starting fundamental
goals for a theory of the galaxies are to understand galaxy stellar masses,
the spatial distributions of the stars in galaxies, and the stellar motions.
Modern numerical simulations have made encouraging progress to this end, but
there are anomalies. The evidence I have seen is that, despite careful
attention to the many details required for the numerical simulations, disk
star velocity dispersions in the planes of model spiral galaxies are
unrealistically large (Sec. 5.3). The overcooling problem remains, resulting
in unrealistically large classical bulges and stellar halos (Sec. 5.3). Many
of the nearby $L\sim L_{\ast}$ are strikingly flat, unlike model spirals.

A century ago Wolf (1908) reviewed evidence of what proves to be the bimodal
natures of galaxies. The far richer evidence we have now (Sec. 5.1) presents
us with an interesting opportunity: identify the separatrix that determines
whether a protogalaxy evolves into a spiral or an elliptical (Sec. 5.2). How
are we to understand the cool motions of stars in the wonderfully thin
galaxies seen nearby, so very different from the motions of stars in
elliptical galaxies? The problem has been known for a century, aspects of the
situation are the subjects of many papers, but identification of the
separatrix remains an open challenge.

Less familiar anomalies tend to be less secure because less thought has been
given to the theory and observation, and we can add that it is natural to give
less thought to what is contrary to accepted thinking. We have an example in
Section 3, on the large-scale distributions of astronomical objects. In the
standard cosmology clusters of galaxies formed where the primeval upward mass
density fluctuations were unusually large. Within available accuracy this
agrees with numerical simulations of cosmic structure formation. But why would
the primeval mass distribution in the $\Lambda$CDM universe be so arranged
that upward mass fluctuations capable of evolving into the clusters that at
distances less than about 85 Mpc are present only near the extended plane of
the Local Supercluster (Fig. 1 in Sec. 3.1)? Why are the most massive
elliptical galaxies within 85 Mpc close to this plane, while comparably
massive spirals are not noticeably correlated with the plane (Fig. 3)? The
powerful radio sources present in some galaxies are thought to be associated
with massive central black holes. Many large galaxies contain these black
holes. So why are the powerful radio sources within 85 Mpc present in a select
few of the large galaxies, those near this plane? Is there something special
about these black holes? Tully and Shaver knew aspects of this situation
thirty years ago (Sec. 3.1). To judge by the sparse citations to Shaver’s key
point these phenomena have not captured the general attention of the
community. But the phenomena surely are real, and interesting, and not likely
to have grown out of the Gaussian, adiabatic, and near scale-invariant initial
conditions of the present standard cosmology.

On larger scales, the applications of scaling relations to convert cluster
luminosities to distances for estimates of peculiar velocities yield
indications of unreasonable bulk flows relative to the rest frame defined by
the CMB (Sec. 3.2.3). This disagrees with observations of the effect of the
motion of intracluster plasma on the CMB. This kinetic SZ effect indicates a
reasonably small cluster bulk flow. Maybe the situation is confused by subtle
systematic errors, though the peculiar cluster velocity measurements have been
carefully checked. If the anomalous peculiar velocities are confirmed it means
the luminosities of first-ranked cluster members, and the properties of the
intracluster plasma, are not well constrained by other cluster properties that
are not sensitive to distance, maybe even that cluster properties depend on
parameters that are not in the standard cosmology. The thought is speculative,
but recall that there are cosmic magnetic fields, and maybe cosmic strings,
which might connect clusters and perhaps set hidden parameters.

On scales comparable to the Hubble length the heliocentric dipole anisotropies
of quasars and radio galaxies are about in the direction expected from the
kinematic effect of our motion relative to the CMB, but the dipole amplitude
is unacceptably large. If this were because of a real unexpectedly large
dipole anisotropy in the mass distribution on the scale of the Hubble length
then the standard cosmology would predict an unacceptably large local peculiar
velocity. But recall that at distances $\lower
2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}85$ Mpc the curious distributions
of radio galaxies, massive elliptical and spiral galaxies, and clusters of
galaxies encourage the thought that the positions of radio galaxies, and so
likely quasars, are only weakly related to the mass distribution traced by
$L\sim L_{\ast}$ galaxies. So we have a mystery: what would have caused the
anomalous large-scale distributions of massive ellipticals, quasars, radio
galaxies and clusters of galaxies? The evidence is that all these objects
contain massive black holes. Establishment of the theory of how these black
holes formed might help.

The standard $\Lambda$CDM theory passes demanding well-checked tests that
reenforce the expectation that some if not all of the curious phenomena
discussed here will prove to be results of systematic errors and/or
statistical fluctuations. But consider one example, the distributions of the
clusters of galaxies and the most luminous galaxies at distances less than
about 85 Mpc. The $\Lambda$CDM theory offers a good account of the number
density of mass concentrations similar to rich clusters. This adds to the
argument for this theory and against the proposed anomalies. But does the
distribution of these mass concentrations that grow into the clusters shown in
Figure 1 in Section 3.1 look reasonable? It certainly looks real. Luminous
radio galaxies and the most massive elliptical galaxies also tend to be close
to this plane. They are related, but identified and cataloged in different
ways. The consistent case for alignment of these object with the extended
plane of the Local Supercluster is convincing. The odd thing is that the most
massive spirals, and the galaxies that are most luminous at $60\mu$, are not
noticeably concentrated to the plane.This curious situation is difficult to
reject and maybe suggestive of something interesting to be discovered.

Let us not blame the messengers for the problems with the properties of
galaxies reviewed in Section 5 and the distributions of galaxies discussed in
Sections 3 and 4; research groups are doing the best they can with the theory
they have. It has not escaped community attention that the extreme simplicity
of the dark sector of the standard $\Lambda$CDM cosmology seems unlikely to be
better than a crude approximation to reality, maybe crude enough to be an
impediment to progress in understanding cosmic structure.

##  7 Acknowledgements

I am grateful to colleagues for guidance to issues arising. They include Jean
Brodie and Elaina Tolstoy for advice about dwarf galaxies; Antonaldo Diaferio
and Garry Angus or advice on the generalization of MOND; Simon Driver and
Samir Salim for education about galaxy morphologies; Mike Hudson, Tod Lauer,
and Kostas Migkas for explanations of cluster bulk flow measurements; Manoj
Kaplinghat for discussions of supermassive black holes; Roya Mohayaee and
Subir Sarkar for discussions of the kinematic dipole; Dylan Nelson for
discussions of simulations of galaxy formation; Patrick Ogle for instruction
on supermassive spiral galaxies; and Xavier Prochaska for comments on
observations of extragalactic magnetic fields. I am particuarly indebted to
Michael Strauss for guidance to the phenomena and Neil Turok for guidance to
the theory. Turok encouraged me to write this considerable revision of the
draft in Peebles (2021).

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