# Mitigating Challenges of the Space Environment for Onboard Artificial
Intelligence: Design Overview of the Imaging Payload on SpIRIT

Miguel Ortiz del Castillo Jonathan Morgan Jack McRobbie Clint Therakam Zaher
Joukhadar
Robert Mearns Simon Barraclough Richard Sinnott Andrew Woods Chris Bayliss
Kris Ehinger Ben Rubinstein James Bailey Airlie Chapman Michele Trenti
The University of Melbourne
<EMAIL_ADDRESS>
###### Abstract

Artificial intelligence (AI) and autonomous edge computing in space are
emerging areas of interest to augment capabilities of nanosatellites, where
modern sensors generate orders of magnitude more data than can typically be
transmitted to mission control. Here, we present the hardware and software
design of an onboard AI subsystem hosted on SpIRIT. The system is optimised
for on-board computer vision experiments based on visible light and long wave
infrared cameras. This paper highlights the key design choices made to
maximise the robustness of the system in harsh space conditions, and their
motivation relative to key mission requirements, such as limited compute
resources, resilience to cosmic radiation, extreme temperature variations,
distribution shifts, and very low transmission bandwidths. The payload, called
Loris, consists of six visible light cameras, three infrared cameras, a camera
control board and a Graphics Processing Unit (GPU) system-on-module. Loris
enables the execution of AI models with on-orbit fine-tuning as well as a
next-generation image compression algorithm, including progressive coding.
This innovative approach not only enhances the data processing capabilities of
nanosatellites but also lays the groundwork for broader applications to remote
sensing from space.

##  1 Introduction

Nanosatellites represent a significant advancement in space technology,
offering a compact and efficient alternative to traditional satellite designs
for a growing range of applications. Their design, which often incorporates
Commercial Off-The-Shelf (COTS) components, achieves considerable cost
savings, thereby making space exploration more accessible, at the expense of
higher risk. [21]. However, the lower cost and rapid progress from conceptual
design to flight naturally allows for a greater risk appetite, thus opening
the opportunity to utilize modern compact sensors, even if the hardware is not
explicitly rated for usage in space. Capable of performing a variety of tasks,
these satellites facilitate a wide array of application-oriented
opportunities, from detailed Earth and space observations to agile deployment
of novel missions [26], thereby offering promising prospects to transform the
field.

Recent technological advancements in the miniaturization of computing modules
have significantly expanded the capabilities of nanosatellite payloads. This
breakthrough has facilitated the integration of diverse, computing devices
within nanosatellites, empowering them to execute complex processing tasks
previously thought to be impractical for such compact platforms [10]. This
advancement in payload design opens up new avenues for on-board processing
capabilities, enabling the transition of data processing tasks, once solely
possible on ground systems, to direct execution in-the-loop while in orbit. A
particularly promising opportunity is the deployment of sophisticated AI
systems on these outer-edge devices, leveraging the enhanced computational
power to enable near-real-time data analysis and decision-making directly on
the satellite [14].

Although COTS components on nanosatellites unlock significant potential, they
also present distinct challenges for the successful deployment of AI systems
on-board satellites. The operational environment for these AI solutions is
marked by harsh conditions and a scarcity of resources, notably power (or
often equivalently, ability to dissipate heat), memory, computational capacity
and communication bandwidth [8]. This restricts both the complexity of the
models and their adaptability through retraining and tuning once the satellite
is in orbit. Furthermore, to operate effectively, the AI model requires
robustness in the face of unexpected environmental shifts and data variations,
as well as significant autonomy. The need for autonomy is accentuated by the
communication challenges, characterized by constrained bit rates and limited
opportunities for uplink and downlink of telemetry and telecommands. Moreover,
the hardware design must be well executed to withstand the radiation
environment specific to the target mission’s orbit [13] and to address the
thermal challenges that arise from operating an edge device in the vacuum of
space.

In response to the significant challenges identified in deploying AI systems
on nanosatellites, the Melbourne Space Laboratory, in collaboration with
national and international partners, has recently launched a nanosatellite.
This platform hosts ‘Loris’, a payload that integrates an NVIDIA Jetson Nano
single-board computer with a multi-camera system, specifically engineered to
facilitate AI operations in orbit. This endeavor aims to demonstrate the
viability of sophisticated hardware solutions enabling on-board AI whilst
addressing the complexities and challenges of the space environment. Our goals
are to contribute to the evolving landscape of AI applications on
nanosatellites, to support flexible and adaptable solutions, to enhance real-
time data processing and to improve (in situ) orbital decision-making
capabilities.

In this paper, we outline the design and functionality of our system,
emphasizing the key design choices that have allowed us to address the
challenges inherent in the space environment.

##  2 Related Work

Reduced launch costs have markedly simplified the process of deploying
satellites into orbit, prompting researchers to delve into the potential of
deploying COTS edge processors, with their capacity for low-latency and
distributed computing, in space [8]. A notable milestone in this domain is the
European Space Agency’s $\Phi$-Sat-1 mission, which pioneered the use of on-
board AI for real-time data analysis [12]. Featuring an Intel Movidius Myriad
2 Visual Processing Unit (VPU), $\Phi$-Sat-1 manages to run deep Convolution
Neural Network (CNN) models for precise cloud detection directly on the
satellite, a testament to the potential of low-power COTS components in
executing complex computations with less than 2W of power [17]. Furthermore,
the Myriad 2 has undergone extensive evaluation for its suitability in space
environments, showing resilience to radiation effects. The system experienced
no Single Event Latch-up (SEL) at energies up to 8.8 MeVcm2/mg, and displayed
no evidence of sensitivity to cumulative Cobalt-60 radiation up to 49 krad in
ground Total Ionizing Dose (TID) tests [10], proving the viability of the
Myriad 2 for space missions.

Building on the successful deployment of AI technologies in space missions,
exemplified by $\Phi$-Sat-1 mission, the field is now rapidly progressing [5].
The emergence of compact devices equipped with powerful embedded Graphics
Processing Units (GPUs), such as the ARM Mali and NVIDIA Jetson series,
represents a significant advancement [23]. Notably, the NVIDIA Jetson stands
out as a promising option with low-power, high capability and small form
factor [18]. Recognizing the benefits of incorporating such a module into a
nanosatellite, several studies have assessed the Jetson Nano GPU’s resilience
in space-like environments. A recent experiment conducted at the U.S. Air
Force Research Laboratory with Cobalt-60 irradiation indicates that the Jetson
Nano could exceed a Total Ionizing Dose (TID) of 20 krad [28]. This TID
radation experiment indicated that the Jetson Nano TID provides acceptable
risk levels for a nanosatellite mission lifetime ranging from 1.5 to 2 years
in Low Earth orbits with approximately 3mm of aluminum shielding. Beyond
evaluating the Jetson Nano’s radiation endurance, research has also explored
the radiation impact on micro-SD cards, a key component on some versions of
these modules, revealing a tolerance of up to 40 krad TID [9]. This
combination of hardware resilience and strategic shielding underscores its
capability to meet mission requirements despite the demanding conditions.

The foundation laid by studies such as [11], [30], [19], and [22] has
significantly contributed to the initial understanding of on-board AI
capabilities in space. However, a cohesive and practical approach to system
design, specifically tailored to the harsh space environment, is still
missing. In response, in this paper we present the design of the Loris payload
and the mitigation strategies applied to provide a comprehensive framework for
developing robust hardware and software AI systems suitable for space.

##  3 Loris Payload Design

The Loris payload, showcased in Figure 1, consists of three primary elements:
a Jetson Nano for processing, secured on the Loris carrier frame - a
mechanical mount acting as a custom radiation shield and thermal sink, a
camera multiplexer, and a collection of imaging sensors mounted on custom PCB
adaptors. Central to the system is an NVIDIA Jetson Nano single-board
computer, which enables on-board image processing and compression. This module
interfaces with the Instrument Control Unit (ICU) responsible for coordinating
all payload operations via a differential RS-422 full-duplex communication
protocol. Through this connection, the AI board receives operational commands
and transmits telemetry data, including image files for download.

Figure 1: Loris payload architecture

To address the Jetson Nano’s limitations, specifically its limited number of
camera interfaces, a camera channel multiplexer has been designed. This module
interfaces with up to 16 sensors, significantly expanding Loris’s
observational capabilities and versatility. By leveraging the Jetson Nano’s
native hardware support, the module enhances its capacity through the
integration of additional channels using multiplexers. These are controlled by
an MSP430 microcontroller, facilitating the accommodation of various types of
sensing devices. The control of the cameras is managed through an I2C
interface, offering two methods for receiving image data: either through eight
4-lane MIPI-CSI channels or eight SPI channels. For this mission, the
payload’s imaging array comprises six Sony IMX219 RGB cameras alongside three
FLIR Lepton 3.5 long-wave infrared sensors, offering a diverse imaging
variety, with sensors located on multiple sides of the spacecraft.

Summary specifications of the Jetson Nano selected for the mission are
provided in Table 1, while the image sensors’ characteristics are outlined in
Table 2. Figure 2 illustrates the Loris Camera Multiplexing submodule,
showcasing the integration of nine cameras and the associated multiplexing
electronics, highlighting the payload’s compact and efficient design, which
includes a deployable arm to extend the cameras outside the nanosatellite once
in orbit.

Figure 2: Loris Camera and Multiplexing Electronics Sub-module Component | Specification
---|---
GPU | 128-core Maxwell
CPU | Quad-core ARM A57 @ 1.43 GHz
Memory | 4 GB 64-bit LPDDR4 25.6 GB/s
Storage | On-board 16 GB eMMC
Table 1: Specifications of the Jetson Nano on Loris.

The adoption of a multiplexing strategy for camera sensors in our payload
mitigate the risk of individual sensor failures, enhancing the overall
resilience of the imaging system. Employing cost-effective COTS sensors, such
as the IMX219 and Lepton 3.5, aligns with the typical budget constraints of
nanosatellite missions although this choice inherently carries a higher risk
of component failure than space-grade cameras. By incorporating multiple
sensors, our design not only mitigates this risk but also facilitates in-orbit
performance validation of the sensors, drawing parallels to terrestrial
testing conducted for the IMX219 [4].

Parameter |  Visible IMX219 |  IR Lepton 3.5
---|---|---
Resolution (px) |  3820 x 2464 |  160 x 120
FoV (deg) |  62.2 x 48.8 |  57 x 44
Pixel Size ($\mu$m) |  1.2 |  12
GSD@500 km (m/px) |  200 |  3,400
Frame-rate (fps) |  15∗ |  8.7
Spectrum ($\mu$m) |  0.4-0.7 |  8.0-14.0
Dynamic Range (°C) |  N/A |  -10–400
Exposure time range |  34$\mu$s-358ms |  Auto

*Full resolution (frame rates vary based on resolution)

Table 2: Loris Sensor Specifications

##  4 Challenges and Mitigation Strategies

Deploying AI systems on nanosatellites poses unique challenges due to the
extreme conditions of space, the inherently limited resources available on
these compact platforms, and the continuously evolving demands characteristic
of modern space missions. This section examines the principal challenges
encountered during the conceptualization and development of the Loris payload,
designed for a mission duration of two years within a 550 km Sun-Synchronous
Orbit (SSO). These challenges include managing thermal constraints, ensuring
radiation resilience, overcoming the limited communication bandwidth,
optimizing scarce computational resources, and maintaining the in-orbit
adaptability of AI algorithms.

(a) Loris payload active

(b) Loris payload idle/inactive

Figure 3: Results from worst case thermal simulation of Loris on board the
host mission (Polar Sun Synchronous Orbit at approx. 500km).

###  4.1 Thermal Management

Considering the Jetson Nano’s power consumption, estimated at 5W, appropriate
thermal management and design are important to prevent both overheating when
running, and overcooling when idle or off. Furthermore, on-orbit thermal
management strategies must accommodate fluctuating thermal environmental loads
encountered during a single orbit (eclipse versus direct sunlight). In vacuum,
traditional convectional cooling strategies, such as finned heat-sinks, are
ineffective, necessitating only conductive and radiative thermal heat
transfer.

Within the Loris payload, the Jetson Nano’s CPU, GPU, and critically, the
power management chip, are all conductively coupled to the Loris carrier
frame, a singular aluminium frame designed to closely follow the contours of
the module. The frame here acts as both a thermal sink for the board,
increasing the thermal inertia of the processors, thereby reducing the
extremes of the Nano’s transient thermal range as the spacecraft enters and
exits eclipse, and as a thermally conductive path from the Loris payload to
the spacecraft heat rejection mechanisms. Sufficient thermal contact between
the Jetson Nano and the Loris carrier frame is ensured via the use of a
compliant, space-rated thermal filler (Laird Tflex). This filler material is
conceptually similar to traditional thermal paste used between a processor and
finned heat-sink, but is suitable for in-orbit use.

To validate Loris thermal performance, thermal simulations were conducted to
assess the Jetson Nano’s temperature extremes using ESATAN-TMS, an industry-
leading space thermal simulation software. It can be used to model a thermal
system with lumped-mass thermal objects (called nodes), and iteratively solves
the Temperature-Time ODEs at each orbital time-step. These simulations produce
both steady-state and transient results under assumptions about environmental
thermal loads, and operational conditions of the subject (power
consumption/dissipation). A thermal model encompassing the entire
nanosatellite was developed for the mission, comprising 200 nodes, of which
only three are attributed to the Loris payload. Nevertheless, the fidelity of
this model, is deemed sufficiently high to assess the temperature range of
Loris.

The results in Figure 3, show that Loris will experience a sinusoidal thermal
profile while in-orbit due to the spacecraft transitioning in and out of
eclipse, and a phase lag of the carrier PCB, while the Nano moves in sync with
the thermal sink. Due to the driving requirements of the primary payload,
SpIRIT has been designed to err on the cold side of the temperature limits of
other payloads (the Jetson Nano included), as can be seen in the idle/inactive
case of Figure 3. The Jetson Nano remains fluctuating between -14 to -21 ∘C in
its inactive state, during the typical cold rest state of the nanosatellite.
Nevertheless, this is above both its non-operational ($T>-40$∘C), and
operational cold limits ($T>-25$∘C). Thus, the Jetson Nano can safely be
powered on at any-time in orbit.

Figure 4: Radiation environment for proton and electron fluxes for Loris

During typical full Loris operations, the simulations predict the Jetson Nano
will reach a maximum temperature of +22 to +29 ∘C over the course of an orbit,
with a difference of approximately 43∘C between the maximums of the active and
inactive cases. The maximum predicted temperatures are well below the Jetson
operational maximum of $T<+97$∘C, with a margin of 68 ∘C. The simulated
positive margin to both the operational maximum and to the non-operational
minimum demonstrates complete operational capability from a thermal
perspective, of the Nano while in orbit. A possible alternative strategy, in
the event that the Loris payload is consistently reaching its maximum
allowable temperatures, is to duty-cycle the system, and therefore reduce the
heat dissipation of the Jetson Nano; however, it is not anticipated that the
onboard Jetson Nano will require duty cycling as the system has been tuned to
the cold end of the allowable temperature envelope.

In addition to the above simulations, Loris has undergone system-level thermal
testing as part of the nanosatellite environmental test campaign. During this
campaign, the spacecraft, and therefore Loris, underwent various thermal tests
in a simulated space environment. During this test campaign, Loris was
subjected to multiple hot and cold cycle extremes in vacuum at predicted
system level maximum and minimum temperature extremes. At these extremes,
short functional test checkouts were conducted to ensure the payload was
behaving nominally - with Loris passing all checkouts. The spacecraft also
underwent thermal balance testing wherein both power dissipation in the
spacecraft and the environment are kept constant, allowing the spacecraft and
all its payloads to reach thermal equilibrium. This steady-state behaviour
allows thermal models used for simulation to be correlated with real-world
results, increasing the confidence in orbital thermal predictions. These
thermal balance tests included running Loris continuously for 10 hours. During
this, Loris performed admirably, reaching a maximum temperature of +43 ∘C. It
should be noted, that this differs from the predicted orbital maximum by
$\sim$20∘C, primarily as a result of the different environmental conditions.
The Thermal balance test lasted for $\sim$10 hours before reaching steady-
state, while a single orbit of the Loris payload will be only 90 mins;
insufficient time to reach thermal equilibrium before the external conditions
change.

From the thermal simulations and physical testing the Loris payload and its
Jetson Nano have undergone, it is evident that the thermal management
strategies employed will be effective in maintaining the Jetson Nano’s
temperature within its operational and non-operational limits.

###  4.2 Radiation Environment

Space missions face the challenge of ionizing radiation, which threatens the
functionality of satellite electronics and data integrity. The LEO radiation
environment is characterized by the presence of both high-energy protons and
lower-energy electrons that can cause critical damage to the spacecraft
operational systems [13]. Therefore, understanding the orbit’s radiation
environment is crucial for safeguarding Loris functionality and mission
success.

The integral flux of protons and electrons along the orbital path of Loris was
simulated using the software SPENVIS [16] and the European Cooperation for
Space Standardization (ECSS-E-ST-10-04) standards. This method provides an
overview of the radiation environment expected during the orbit. Specifically,
Figure 4 integrates the data for proton flux (greater than 0.1 MeV) from
NASA’s AP-8 MIN model and electron flux (greater than 0.04 MeV) from the NASA
AE-8 MAX model. As high-energy particle flux is directly correlated with the
risk of Single Event Effects (SEE), the resulting radiation map highlights
regions where the risk of SEEs, such as bit flips in volatile or non-volatile
memory, is increased. Given its operation in a sun-synchronous orbit, Loris
will be exposed to the intensified radiation at the poles and within the South
Atlantic Anomaly, as compared to an equatorial orbit, increasing the need for
a resilient software architecture to address transient effects which may occur
while traversing those regions.

Figure 5: Loris Software Integrity Monitoring Architecture Figure 6: Shielding
vs TID for Loris calculated for 2 year mission

Loris mitigates SEE that could corrupt its core code and important internal
data by running a dedicated subroutine for error detection and correction.
This approach not only enhances system reliability but also significantly
extends the operational lifespan of the payload by reducing the likelihood
that critical functionalities will be compromised. The monitoring routine
maintains a list of files and their MD5 hash. Periodically, it performs a MD5
hash calculation for both backup and live versions of the files on this list
and compares the outcome to the stored hash values. If the file is found to be
corrupted it is replaced with a backup, provided the backup is not also
corrupted. The program does not distinguish between files in use and backups,
so if a backup is corrupted it will be checked and restored from the live
file. Important files can have increased redundancy by storing multiple
backups, where each backup points to a different copy. Finally, if all copies
of a file are corrupted the program logs the error so a valid copy of the file
can be re-uploaded to the spacecraft. The control flow is shown in Figure 5.
The monitoring software runs every 60 seconds, in an experiment on a similar
device, the Jetson Xavier NX, less than $1\times 10^{-2}$ SEEs were expected
per orbit in low Earth orbit[24], so this is a conservative interval. In
addition to active integrity and consistency checks, Loris adopts operational
strategies to minimize SEE exposure in volatile memory by refraining from
activating the payload while traversing regions known for heightened radiation
flux, specifically the polar areas and the South Atlantic Anomaly, as
illustrated in Figure 4.

Following the identification of critical radiation zones via SPENVIS
simulations, the SHILDOSE-2 model [25] has been utilized to estimate the Total
Ionizing Dose (TID), guiding the optimization of shielding thickness within
the stringent constraints of the mission’s mass budget. This optimisation
seeks to maximize radiation protection with minimal mass increase. Figure 6
delineates the TID for a given shielding thickness, distinguishing three
distinct regions: the red zone indicates expected doses exceeding 20 krad, the
yellow zone represents doses between 20 krad and 2 krad, and the green zone
signifies doses below 2 krad. A derating factor of x10 over thefindings
presented in [28], in which 20krad is provided as a safe upper limit for the
Jetson Nano, has been adopted to ensure ample margin and safeguard against
system degradation. Consequently, a shielding thickness of 3mm was identified
as necessary to achieve a TID of 2 krad throughout the mission’s lifespan (see
Figure 6). The requisite shielding has been incorporated into the design of
the Loris carrier frame.

###  4.3 Limited Bandwidth

(a) 8kb - 1% Preview

(b) 250kb - 30% Preview

(c) 758kb - Full Jpeg-XL File

Figure 7: Progressive Coding Example - Using reference image from [20] Base
Image: 1600kb

One of the foremost challenges in space operations, particularly with
nanosatellites, is the management of transmission bandwidth. The specific
nature of these missions often limits their data transmission and reception
capabilities, to communication with one or a few ground stations with a
handful of short transmission windows a day (depending on orbit and ground
station location). Even when data is downlinked through S-band for a typical
bandwidth of 2Mbits per second rather than UHF (9.600 kbits), modern cameras
generate more data than can be retrieved, when not run at an extremely lowered
duty-cycle. For SpIRIT, the ground segment consists of one UHF ground station
for duplex communication with four available windows with the satellite each
day, each lasting approximately 10 minutes, and one S-band ground station with
simplex (satellite to ground) capabilities. This operational constraint
significantly limits bandwidth, with our estimated uplink capacity set between
100KB and 200KB per day, and downlink capacity for Loris capped at 1MB per day
after accounting for data downlink requirements from other payloads. To
contextualize these figures, an uncompressed image captured by the satellite’s
camera has a resolution of 3820 x 2464 pixels in the RGB format, exceeding the
daily data cap by a factor of 28 for a 24 bit RGB palette. The volume of data
generated by just a single image of this quality highlights the bandwidth
challenge, and underlines the critical need for efficient data management
strategies, including advanced compression techniques and selective
transmission.

To address this bandwidth challenge, Loris implements the JPEG-XL algorithm
for efficient on-orbit compression of image data captured by both RGB and IR
sensors. Choice of image compression algorithms is always a trade off between
compression ratio, speed, and power-usage [3]. Past image compression
applications for nanosatellites have focused on optimising for low power usage
[27] however due to the processing power available in the Jetson Nano for this
mission, Loris compression aims to prioritise bandwidth limitations instead.
Our aim is to test in orbit the use of the JPEG-XL compression for space
applications due to its high compression ratio at ‘visually lossless’ settings
and the progressive coding feature [1]. JPEG-XL is an advanced image coding
system based on a novel colour-space transform, variable sized discrete cosine
transform and adaptive quantization and prediction steps [1]. To the best of
our knowledge Loris’ implementation is the first system that executes this
algorithm in-orbit for space applications.

####  4.3.1 Lossless vs Lossy Compression

When choosing a compression algorithm the first factor to consider is lossless
or lossy compression. In lossless compression the original data can be
perfectly reconstructed from the compressed data, whereas for lossy
compression, the uncompressed data differs from the original, such that some
information is lost. As Loris’ cameras are not designed for high-fidelity
scientific data collection but rather for technology, scientific
demonstration, and public outreach, perfect reconstruction is not necessary.
Thus, we use lossy compression for all images to achieve higher compression
ratios. An advantage of JPEG-XL is that it can perform both lossy and lossless
compression, so combined with Loris’s re-configurable software architecture it
is still possible to use lossless compression on an as-needed basis.

####  4.3.2 Progressive Coding

Progressive coding encodes the compressed image bit-stream such that it can be
decoded from partial transmission. As more of the image data is received the
quality of the decoded image increases. This feature is particularly useful
for nanosatellites as it allows efficient use of the limited bandwidth, as
image transmissions can be stopped once the downlinked image is of sufficient
quality [29]. JPEG-XL allows the use of progressive coding including placing
the DC components of the discrete-cosine transform at the start of the bit-
stream, allowing for decoding of the image with as little as 1% of the image
data, demonstrated in Figure 7. During early in-orbit operations, this Loris
feature has demonstrated its value by allowing evaluation of image acquisition
using thumbnails of just 2kB in size, allowing tens of thumbnails to be
downloaded per day.

####  4.3.3 Comparison with CCSDS Standard

The Consultative Committee for Space Data Systems (CCSDS) produced an image
data compression standard in 2017 that describes the recommended
specifications for two-dimensional spatial data from payload instruments [6].
The CCSDS standard is based on the JPEG2000 format with reduced complexity to
enable easier implementation on limited spacecraft hardware [7]. A key
difference between JPEG-XL and the CCSDS standard is the colour space - the
CCSDS standard supports only a single colour channel (i.e. grayscale images),
whereas JPEG-XL uses a novel colour space, XYB, modelled on the human visual
system [7] [1]. The mapping of the RGB colour space to XYB allows efficient
encoding of redundant data between the colour channels, whereas the CCSDS
standard would require encoding of each channel separately. As JPEG-XL targets
a human visual system it is ideally suited for the RGB inspection cameras used
by Loris, while the single channel approach of CCSDS is more suited to
scientific instruments that may have a single channel [2]. The benefits of the
CCSDS Standard, namely implementation ease, low-algorithmic complexity and
memory efficiency, are not required on general purpose hardware such as the
Jetson Nano.

###  4.4 Computational Resources Limitations

The Nvidia Jetson Nano equipped with a 128-core Maxwell GPU hosted on Loris
does not match the computational power of terrestrial AI GPUs such as the A100
or H100. Yet, the inclusion of the Maxwell GPU represents a significant
advancement in space computing technology, transitioning from predominantly
CPU-based computations to more parallelizable GPU-enabled processing. Still,
we note that the Jetson Nano model comes with its limitations, specifically,
4GB of RAM and 16GB of embedded Multi-Media Card (eMMC) storage, table 1.
Furthermore, the Linux operating system and housekeeping functions consume a
significant portion of this storage, effectively leaving approximately 2GB
free for operational use. Consequently, while on-board data processing
benefits from enhanced computational capabilities, it still faces substantial
constraints in terms of available storage space relative to the uncompressed
size of an image collection from the cameras.

These limitations significantly influence the range of machine-learning models
deployable on this hardware framework. For instance, lightweight models such
as MobileNet can be used for real-time inference due to their efficient
architecture and lower computational demands. MobileNet, specifically designed
for mobile and edge devices, requires approximately 569 million operations for
a single forward pass and can fit within the memory constraints of the Jetson
Nano [15]. In contrast, larger models with billions of parameters, common in
advanced AI applications, exceed the Jetson Nano’s processing and storage
capabilities, necessitating a careful selection of algorithms that strike a
balance between performance and resource consumption. This limitation
necessitates innovative approaches to model optimization and compression to
leverage the available computational resources effectively while navigating
the storage constraints inherent to nanosatellites.

###  4.5 In Orbit Adaptability

As described above, one of the most significant constraints imposed on an
imaging system on board a nanosatellite is management of transmission
bandwidth. Therefore, accurate labeling of archived on-board data is extremely
valuable to efficiently allocate downlink resources. As a proof of concept,
Loris implements a cloud detection model and labels images autonomously,
thereby providing an indication of an image’s utility (whether it contains
clouds or not).

One challenge with this approach is model fine-tuning and retraining. Loris
leverages an innovative approach known as the Ground Truth (GT) Factory,
situated at the ground station. During its mission, Loris will gather metadata
for each captured image, such as UTC time and GPS coordinates. Since direct
image download is not feasible, the GT Factory utilizes the GPS data and time
stamps from the captured images to infer estimated labels through correlation
with data from alternative satellite sources or ground-based observations.
These inferred labels, processed on the ground, are then relayed back to the
satellite. This process facilitates dynamic, in-orbit refinement of the AI
model, exemplifying a method for enhancing AI model accuracy through remote
fine-tuning.

##  5 Conclusion and Future Work

In this paper, we presented the Loris imaging and onboard AI payload that was
successfully launched on SpIRIT in December 2023. We examined the challenges
of acquiring and processing images on a nanosatellite, particularly focusing
on radiation and thermal management issues, limited downlink bandwidth,
storage constraints for AI models, and innovative approaches for labeling
images in orbit using metadata provided by the satellite. By implementing
targeted solutions to these critical challenges, our payload design addresses
the operational complexities associated with deploying AI in space and
presents a framework for future missions to enhance AI deployment in space
environments efficiently.

The payload, alongside the satellite platform, is currently in the
commissioning phase on-orbit. To date, all sensors have successfully undergone
initial checkouts, and preliminary images have been successfully downloaded,
indicating effective operation and demonstrating the first use of JPEG-XL in
orbit. Additionally, the Jetson Nano has demonstrated great performance,
reinforcing its capability for advanced processing in space. These initial
accomplishments provide a strong basis for future in-depth testing and
operational endeavors, signaling a positive trajectory for the mission’s
progress.

## Acknowledgment

This research was partially funded by the Office of National Intelligence -
National Intelligence and Security Discovery Research Grant program for
NI220100072 and funded by the Australian Government.

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#  MS-TP-21-24 Hidden sectors and a multi-temperature universe

Amin<EMAIL_ADDRESS>, Wan-Zhe<EMAIL_ADDRESS>, Pran<EMAIL_ADDRESS>and Zhu-Yao
<EMAIL_ADDRESS>

aInstitut für Theoretische Physik, Westfälische Wilhelms-Universität Münster,
Wilhelm-Klemm-Straße 9, 48149 Münster, Germany
bCenter for Joint Quantum Studies and Department of Physics,
School of Science, Tianjin University, Tianjin 300350, PR. China
cDepartment of Physics, Northeastern University, Boston, MA 02115-5000, USA

###### Abstract

A variety of supergravity and string based models contain hidden sectors which
can play a role in particle physics phenomena and in cosmology. In this note
we discuss the possibility that the visible sector and the hidden sectors in
general live in different heat baths. Further, it is entirely possible that
dark matter resides partially or wholly in hidden sectors in the form of dark
Dirac fermions, dark neutralinos or dark photons. A proper analysis of dark
matter and of dark forces in this case requires that one deals with a multi-
temperature universe. We discuss the basic formalism which includes the multi-
temperature nature of visible and hidden sectors in the analysis of phenomena
observable in the visible sectors. Specifically we discuss the application of
the formalism for explaining the velocity dependence of dark matter cross
sections as one extrapolates from galaxy scales to scales of galaxy clusters.
Here the dark photon exchange among dark fermions can produce the desired
velocity dependent cross sections consistent with existing galactic cross
section data indicating the existence of a new fifth (dark) force. We also
discuss the possibility that the dark photon may constitute a significant
portion of dark matter. We demonstrate a realization of this possibility in a
universe with two hidden sectors and with the visible sector and the hidden
sectors in different heat baths which allows a satisfaction of the constraints
that the dark photon have a lifetime larger than the age of the universe and
that its relic density be consistent with Planck data. Future directions for
further work are discussed.

Submitted to the Proceedings of the US Community Study

on the Future of Particle Physics (Snowmass 2021)

###### Contents

  1. 1 Hidden sectors in supergravity and strings
  2. 2 Equations that govern a multi-temperature universe
  3. 3 Evolution of hidden sector temperatures
  4. 4 A dark force and galaxy structure anomalies
  5. 5 Dark photon as dark matter
  6. 6 Hidden sectors and the BBN constraint
  7. 7 Future directions
  8. 8 Conclusion

##  1 Hidden sectors in supergravity and strings

Most modern model building based on supergravity and strings involve hidden
sectors which arise in a natural way in a variety of higher dimensional
supergravity and string compactifications. Hidden sectors first arose in the
context of gravity mediated breaking of supersymmetry and were subsequently
identified in string model building (for a review see [1]). While the hidden
sectors are neutral under the Standard Model (SM) gauge group they can still
communicate with the visible sector via a variety of portals such as the Higgs
portal [2] and via kinetic mixing [3] or Stueckelberg mass mixings [4] or both
[5] if the hidden sectors are charged under extra $U(1)$ gauge groups.
Further, the hidden sectors may contain matter [4, 6, 5]. Because of feeble
couplings between the hidden and the visible sectors, the hidden sectors may
reside in heat baths which are significantly colder than that of the visible
sector. The feeble coupling between the hidden and the visible sectors would
tend to thermalize the two sectors over time as long as the two sectors are
coupled chemically and kinetically. However, such a thermalization in the
early universe is not instantaneous and thus thermal evolution of the coupled
visible and hidden sectors must be taken into account in the study of the
early universe and of the particle physics phenomena that carry signatures of
physics of the early universe.

A coupled evolution of the visible and the hidden sectors brings in
significant new constraints [7, 8]. First, the entropy conservation holds only
for the sum of all entropies including that of the visible and of the hidden
sectors. Some of the early works ignored this constraint and used separate
entropy conservations for the visible and the hidden sectors which is invalid
in the presence of coupling between the sectors. Second, the Friedman
equations are modified since the energy density and the pressure density
appearing there include those from the visible and from the hidden sectors
which consequently also affect the evolution of the Hubble parameter. Because
of this, cosmology of the early universe is affected by the presence of hidden
sectors. Since the visible sector and the hidden sectors may reside in
different heat baths, a multi-temperature nature of the universe must be
implemented for the proper understanding of the cosmological and particle
physics phenomena. We address this issue in this note.

Figure 1: A schematic diagram exhibiting the SM extended by various hidden
sectors, indicated by grey circles. There might be multiple hidden sectors
beyond the SM that have either direct couplings or indirect couplings with the
SM. In general these hidden sectors will evolve separately and live in their
own heat baths.

The outline of the rest of the paper is as follows: In section 2 we discuss
the basic cosmological constraints that govern coupled visible and hidden
sectors. Here we assume an arbitrary number of hidden sectors coupled to the
visible sector (see Fig. 1). We assume that each of the hidden sectors
possesses a $U(1)$ gauge group which has kinetic mixing and Stueckelberg mass
mixing with the hypercharge field and with each other. In section 3 we discuss
the dynamical equations that allow one to evolve the hidden sectors and the
visible sector and compute the temperatures of the hidden sectors as a
function of a reference temperature. Here we discuss two explicit examples. In
the first example, we have one hidden sector and only one temperature ratio
needs to be evolved, while in the second example we consider two hidden
sectors and we have two temperature ratios that need to be evolved. In section
4, we consider a hidden sector with a dark fermion and a dark photon where the
dark fermion is the dark matter and the dark photon acts as a force mediator
between the dark fermions. Assuming the mass of the mediator to be much
smaller than the mass of the dark fermion, we fit the velocity dependent cross
sections of dark fermionic dark matter from galaxy scales to scales of galaxy
clusters. In section 5, we discuss the possibility of a dark photon being dark
matter. This possibility is difficult to realize with just one hidden sector,
since the twin constraints that the dark photon relic density be consistent
with the Planck data and the constraint that the lifetime of the dark photon
be larger than the age of the universe are difficult to satisfy in this case.
For this reason in this section we consider two hidden sectors and show that a
dark photon as dark matter can be realized in this framework. In section 6 we
discuss the $\Delta N_{\text{eff}}$ constraint on the hidden sectors. In
section 7 we discuss future directions and conclusions in section 8.

##  2 Equations that govern a multi-temperature universe

If hidden sectors exist they contribute to the pressure and the energy density
of the universe and enter in the Friedman equations. Thus in the presence of
several hidden sectors which in general are at different temperatures, the
Friedman equations read

$\displaystyle H^{2}$ $\displaystyle=\frac{8\pi
G_{N}}{3}\left[\rho_{v}(T)+\sum_{i}\rho_{i}(T_{i})\right],$ (2.1)
$\displaystyle\frac{\ddot{a}}{a}$ $\displaystyle=-\frac{4\pi
G_{N}}{3}\left[(\rho_{v}+3p_{v})(T)+\sum_{i}(\rho_{i}+3p_{i})(T_{i})\right],$
(2.2)

where $a$ is the scale factor in an FRW universe, $H$ is the Hubble parameter,
$G_{N}$ is Newton’s gravitational constant, $p_{v},\rho_{v}$ are the pressure
density and the energy density for the visible sector which are functions of
the visible sector temperature $T$, and $p_{i},\rho_{i}$ are the pressure
density and the energy density for the $i^{\rm th}$ hidden sector and are
functions of the hidden sector temperature $T_{i}$. Further, in the presence
of couplings between the visible and the hidden sectors, it is only the total
entropy $S$, where $S=a^{3}s$ with $s$ being the entropy density and $a$ the
scale factor, which is conserved, i.e., $\rm{d}(sa^{3})/\rm{d}t=0$ leads to

$\displaystyle{\rm d}s/{\rm d}t+3Hs=0,$ $\displaystyle
s=\frac{2\pi^{2}}{45}\left(h^{v}_{\rm eff}(T)T^{3}+\sum_{i}h_{\rm
eff}^{h_{i}}(T_{i})T_{i}^{3}\right),$ (2.3)

where $h^{v}_{\rm eff}(T)$ is the effective entropy degrees of freedom for the
visible sector at temperature $T$ and $h_{\rm eff}^{h_{i}}(T_{i})$ is the
effective entropy degrees of freedom for the $i^{\rm th}$ hidden sector at
temperature $T_{i}$. Further, the total energy density satisfies the
conservation equation,

$\displaystyle\frac{d\rho}{dt}+3H(\rho+p)=0.$ (2.4)

One may also exhibit the equations of motion satisfied by the individual
energy density in each sector so that

$\displaystyle\frac{d\rho_{v}}{dt}+3H(\rho_{v}+p_{v})=j_{v},$
$\displaystyle\frac{d\rho_{i}}{dt}+3H(\rho_{i}+p_{i})=j_{i},(i=1\cdots n),$
(2.5)

where $j_{v},j_{i}$ are the corresponding source functions which are
determined by the couplings among the visible and the hidden sectors. They are
discussed in detail in [7, 8]. In order to study the correlated temperature
dependence in the evolution equations it is then convenient to write the
evolution equations in terms of temperature rather than time. The equation
relating the two is given by

$\displaystyle\frac{dT}{dt}=-\frac{4\lambda\rho}{d\rho/dT}H.$ (2.6)

Here $\lambda=\frac{3}{4}(1+p/\rho)$ and where $\lambda=1$ is for the
radiation dominated era and $\lambda=3/4$ for the matter dominated universe.
Since the coupled equations involve different temperatures, the temperature
evolution of the hidden sectors relative to the visible sectors is determined
by the functions

$\displaystyle\xi_{i}=\frac{T_{i}}{T},~{}i=1\cdots n,$ (2.7)

which requires that one generate evolution equations for $\xi_{i}$ or
equivalently for $\eta_{i}\equiv\xi_{i}^{-1}$. In deriving the evolution
equations one needs to choose a temperature clock, which is a reference
temperature, in terms of which all other temperatures are measured. This
reference temperature can be either the visible sector temperature or the
temperature of one of the hidden sectors. Thus if $T$ is chosen as the clock
then one needs $n$ number of evolution equations for the quantities
$d\xi_{i}/dT~{}(i=1\cdots n)$.

As indicated in Fig. 1, in general the universe can have a large number of
hidden sectors, some of which have direct coupling with the SM while others
have indirect or no coupling with the SM. For the case of additional $U(1)$’s,
each hidden sector may have matter fermions and gauge bosons. The total
Lagrangian is given by

$\mathcal{L}=\mathcal{L}_{\rm vis}+\mathcal{L}_{\rm hid}+\mathcal{L}_{\rm
vh}\,,$ (2.8)

where $\mathcal{L}_{\rm vis}$ is the SM Lagrangian, $\mathcal{L}_{\rm hid}$ is
the Lagrangian for the hidden sector and $\mathcal{L}_{\rm vh}$ is the
Lagrangian which involves the couplings between the visible sector and the
hidden sector. In general the hidden sector involving $n$ number of hidden
sectors and invariant under $n$ $U(1)$ gauge transformations is given by

$\mathcal{L}_{\rm
hid}=-\frac{1}{4}\sum_{i}F_{i\mu\nu}F^{\mu\nu}_{i}-\frac{1}{i}\sum_{i}\bar{\chi}_{i}\gamma_{\mu}(\partial^{\mu}-ig_{i}Q_{i}C^{\mu}_{i})\chi_{i}-\sum_{i}m_{i}\bar{\chi}_{i}{\chi}_{i}\,,$
(2.9)

where we sum over all hidden sectors, and $\chi_{i}$ indicates the $i$th
fermion from the $i$th hidden sector with mass $m_{i}$.

Finally, $\mathcal{L}_{\rm vh}$ contains interactions between the visible
sector and hidden sectors, as well as interactions among the hidden sector
gauge bosons via kinetic mixing and via Stueckelberg mass mixing and is given
by

$\mathcal{L}_{\rm
vh}=-\sum_{i}\frac{\delta_{i}}{2}B_{\mu\nu}F^{\mu\nu}_{i}-\sum_{i<j}\frac{\delta^{h}_{ij}}{2}F_{i\,\mu\nu}F^{\mu\nu}_{j}-\frac{1}{2}\left(M_{B}B^{\mu}+\sum_{i}M_{i}C^{\mu}_{i}+\sum_{i}\partial_{\mu}\sigma_{i}\right)^{2}\,,$
(2.10)

where $\delta_{i}$ is the kinetic mixing parameter between the $i$th hidden
sector with the hypercharge, $\delta^{h}_{ij}$ is the kinetic mixing parameter
among the $i$th and the $j$th hidden sectors. In Eq. (2.10), $\sigma_{i}$ are
axionic fields which have appropriate transformations under the $U(1)_{Y}$ and
$U(1)_{X_{i}}$ to guarantee the gauge invariance of Eq. (2.10) and we drop
them when working in the unitary gauge. As noted earlier, in general both
kinetic mixing and Stueckelberg mass mixing between the visible sector and the
hidden gauge fields play a role in the dynamics involving the visible and the
hidden sectors [7, 8].

##  3 Evolution of hidden sector temperatures

As was noted above, the temperatures of the visible and the hidden sectors
could be different [7, 8] (for earlier literature see [10, 11, 12]). We
discuss now the explicit evolution of the temperatures in the hidden sector vs
the visible sector for two cases: one for the case of a single hidden sector
and the other when there are two hidden sectors. First we discuss the case of
a single hidden sector where we choose for convenience our reference
temperature to be the hidden sector temperature $T_{h}$ and a direct
computation gives [7]

$\frac{{\rm d}\eta}{{\rm
d}T_{h}}=-\frac{A_{v}}{B_{v}}+\left(\frac{\lambda\rho_{v}+\rho_{h}(\lambda-\lambda_{h})+j_{h}/(4H)}{\lambda_{h}\rho_{h}-j_{h}/(4H)}\right)\frac{d\rho_{h}/dT_{h}}{B_{v}},$
(3.1)

where

$\displaystyle A_{v}$ $\displaystyle=\frac{\pi^{2}}{30}\left(\frac{{\rm
d}g_{\rm eff}^{v}}{{\rm d}T}\eta^{5}T_{h}^{4}+4g_{\rm
eff}^{v}\eta^{4}T_{h}^{3}\right),$ (3.2) $\displaystyle B_{v}$
$\displaystyle=\frac{\pi^{2}}{30}\left(\frac{{\rm d}g_{\rm eff}^{v}}{{\rm
d}T}\eta^{4}T_{h}^{5}+4g_{\rm eff}^{v}\eta^{3}T_{h}^{4}\right).$ (3.3)

Here $\lambda$ is as defined after Eq. (2.6) and
$\lambda_{h}=\dfrac{3}{4}\left(1+\dfrac{p_{h}}{\rho_{h}}\right)$, where
$\rho_{h}$ and $p_{h}$ are determined in terms of the density of hidden sector
particles. We implement this for the specific model given by the Lagrangian

$\displaystyle\mathcal{L}=$
$\displaystyle-\frac{1}{4}C^{\mu\nu}C_{\mu\nu}-g_{X}\bar{D}\gamma^{\mu}DC_{\mu}-m_{D}\bar{D}D$
$\displaystyle-\frac{\delta}{2}C^{\mu\nu}B_{\mu\nu}-\frac{1}{2}(M_{1}C_{\mu}+M_{2}B_{\mu}+\partial_{\mu}\sigma)^{2},$
(3.4)

where $C_{\mu}$ is the gauge field of the hidden sector associated with the
$U(1)_{X}$ gauge group, $D$ is a Dirac fermion which is charged under
$U(1)_{X}$ and $\delta$ is the kinetic mixing parameter. We assume that
initially the hidden sector is colder than the visible sector but they begin
to thermalize with time and eventually attain thermal equilibrium. However, as
shown in the left panel of Fig. 2, the rate at which they thermalize varies
depending on the size of the couplings. As expected the thermalization is
slower for smaller $\delta$ and becomes faster as $\delta$ increases.

Case of one hidden sector
---
| Model |  $m_{D}$ (GeV) |  $M_{1}$ (MeV) | $g_{X}$ |  $\delta~{}(\times 10^{-9}$)
| (a) | 1.50 | 1.20 | 0.016 | $28$
| (b) | 2.0 | 1.22 | 0.014 | $4.0$
| (c) | 2.16 | 1.13 | 0.015 | $4.7$

Case of two hidden sectors
---
Model | $m_{D}$ | $M_{1}$ | $M_{3}$ | $M_{4}$ | $\delta_{1}$ | $\delta_{2}$ | $m_{Z^{\prime}}$ | $m_{\gamma^{\prime}}$ | $\Omega h^{2}$
(a) | 1.00 | 4.50 | 0.0 | 0.43 | $4.0\times 10^{-10}$ | 0.40 | 4.90 | 0.43 | 0.124
(b) | 0.50 | 4.50 | 0.0 | 0.47 | $6.5\times 10^{-11}$ | 0.40 | 4.90 | 0.47 | 0.103
(c) | 0.05 | 4.50 | 0.0 | 0.45 | $5.6\times 10^{-12}$ | 0.40 | 4.91 | 0.45 | 0.102
(d) | 0.62 | 4.50 | -5.0 | 0.45 | $4.0\times 10^{-10}$ | 0.05 | 6.76 | 0.30 | 0.108

Table 1:  Upper table: Benchmarks for the case when there is only one hidden
sector. Lower table: Benchmarks for the case when there are two hidden sectors
where $g_{X}=0.95$ and masses are in MeV except $m_{D}$ which is in GeV. Taken
from [7, 8].

Figure 2: Left panel: Evolution of $\xi$ for the case of one hidden sector
with the visible sector temperature for three values of the gauge kinetic
mixing $\delta$ as given in the upper Table 1. One may note that the
thermalization of the hidden and the visible sector is slower more feeble the
coupling between the sectors is. Right panel: Evolution of
$\kappa=T_{2}/T_{1}$ as a function of the visible sector temperature $T$ for
three benchmarks (a), (b) and (c) as given in the lower Table 1. Figures from
[7, 8].  Figure 3: Schematic diagram of the visible sector interacting with
two hidden sectors. Hidden sector 1 has a dark $Z^{\prime}$ and a dark fermion
$D$ and has direct coupling with the visible sector. Hidden sector 2 has a
dark photon $\gamma^{\prime}$ but no dark fermion and direct coupling with
hidden sector 1 and only indirect coupling with the visible sector via hidden
sector 1.

Next we consider the case of two hidden sectors which together have an
extended gauge invariance $U(1)_{X_{1}}\times U(1)_{X_{2}}$ where hidden
sector 1 with gauge invariance $U(1)_{X_{1}}$ has the gauge field $C^{\mu}$
and a Dirac fermion $D$ charged under $U(1)_{X_{1}}$ and has kinetic coupling
$\delta_{1}$ to the visible sector. The hidden sector 2 with gauge invariance
$U(1)_{X_{2}}$ has a gauge field $D^{\mu}$ and a kinetic coupling $\delta_{2}$
and a Stueckelberg mass mixing via the mass parameter $M_{3}$ with the hidden
sector 1. However, it has no direct coupling with the visible sector, see Eq.
(3.5) and Fig. 3. Thus the Lagrangian involving the fields of the hidden
sectors is given by

$\displaystyle\mathcal{L}_{\text{h}}+\mathcal{L}_{\text{hv}}=$
$\displaystyle-\frac{1}{4}C^{\mu\nu}C_{\mu\nu}-\frac{1}{4}D^{\mu\nu}D_{\mu\nu}-\frac{\delta_{1}}{2}B^{\mu\nu}C_{\mu\nu}-\frac{\delta_{2}}{2}C^{\mu\nu}D_{\mu\nu}$
$\displaystyle-\frac{1}{2}(M_{1}C_{\mu})^{2}-\frac{1}{2}(M_{3}C_{\mu}+M_{4}D_{\mu})^{2}-m_{D}\bar{D}D+g_{X}\bar{D}\gamma^{\mu}DC_{\mu}.$
(3.5)

The total Lagrangian
$\mathcal{L}=\mathcal{L}_{\text{v}}+\mathcal{L}_{\text{h}}+\mathcal{L}_{\text{hv}}$
must be canonically normalized and its mass eigenstates in the neutral vector
boson sector consist of $\gamma^{\prime},Z^{\prime},Z,\gamma$. Here $Z$ and
$\gamma$ reside in the visible sector, $Z^{\prime}$ is the neutral massive
gauge boson in hidden sector 1 and $\gamma^{\prime}$ is the dark photon which
resides in hidden sector 2. In this case we evolve temperatures $T_{1}$ of
hidden sector 1 and $T_{2}$ of hidden sector 2, and $T$ for the visible sector
in a correlated fashion. We define two functions that allow us to accomplish
this

$\displaystyle\eta=\frac{T}{T_{1}}~{}~{}\text{and}~{}~{}\zeta=\frac{T_{1}}{T_{2}}.$
(3.6)

It is then straightforward to deduce the following evolution equations for
$\eta$ and $\zeta$ [8]

$\displaystyle\frac{d\eta}{dT_{1}}=$
$\displaystyle-\frac{\eta}{T_{1}}+\left(\frac{4H\rho_{v}+j_{1}+j_{2}}{4H\rho_{1}-j_{1}}\right)\frac{d\rho_{1}/dT_{1}}{T_{1}\frac{d\rho_{v}}{dT}},$
(3.7) $\displaystyle\frac{d\zeta}{dT_{1}}=$
$\displaystyle-\frac{\zeta}{T_{1}}+\left(\frac{4H\rho_{2}-j_{2}}{4H\rho_{1}-j_{1}}\right)\frac{d\rho_{1}/dT_{1}}{T_{1}\frac{d\rho_{2}}{dT_{2}}},$
(3.8)

where we used $T_{1}$ as the clock. Solution to these equations allows us to
compute the temperatures in the hidden sectors 1 and 2 in terms of the visible
sector temperature. To exhibit this numerically we consider a set of
benchmarks as given in the lower Table 1. In this case the hidden sector 1
evolves similar to the left panel of Fig. 2 and the hidden sector 1 and the
visible sector thermalize. However, the temperature in the hidden sector 2
evolves more slowly and the hidden sector 2 does not fully thermalize with the
visible sector as exhibited in right panel of Fig. 2. Here we end up with the
ratio $T_{2}/T\leq 0.1$ for the model points exhibited. This ratio has direct
implications for $\Delta N_{\rm eff}$ at BBN time as will be discussed later.

##  4 A dark force and galaxy structure anomalies

In this section we discuss how hidden sectors can affect cosmology in
significant ways. Here one area where hidden sectors could have direct impact
is dark matter. Thus currently the standard $\Lambda$CDM is seen to work well
at large scales. However, at galaxy scales there seem to appear some
anomalies. Often these are described as the missing satellite, cusp-core and
the too-big-to-fail anomalies. It is possible they could be resolved by more
comprehensive analyses using complex dynamics and baryons along with CDM [13].
However, other alternatives have also been proposed such as self-interacting
dark matter [14] which has attracted attention [15, 16, 17, 18, 19, 20, 21,
22, 23, 24, 25, 26, 27, 28, 29]. Thus in this picture dark matter is self-
interacting and collisional at galaxy scales, but collision-less at the scale
of galaxy clusters. Currently there exist data on dark matter cross sections
over the range of scales mentioned above [30, 31, 32, 33] and we will refer to
it as ‘data from Dwarf Galaxy scales to galaxy Clusters (DGC)’. The data
indicates $\sigma/m=O(1){\rm cm}^{2}/{\rm g}$ at small galaxy scales and
appears to exhibit a velocity dependence of dark matter cross sections. Such a
velocity dependence does not arise from conventional WIMP scattering. In
previous works, Yukawa potentials have been used to fit the data [15, 31].
However, within this setup it is difficult to compute the relic density of
dark matter.

We discuss now a hidden sector model to accomplish that, i.e., satisfy the
relic density and give a fit to DGC. The model we use is the first one
discussed in section 3 (see Eq. 3.4)), where we have one hidden sector with a
dark fermion and a dark photon. In the analysis we assume that dark matter is
constituted of dark fermions ($D$ and $\bar{D}$) and their self-interactions
are generated via the exchange of dark photons. The dark photons, however, are
unstable and decay before BBN and do not contribute to the relic density. In
the analysis we assume that the dark particles are produced by the freeze-in
mechanism [34, 35, 36, 37, 38]. Here even with feeble couplings to the visible
sector it is possible to generate $D$ and $\bar{D}$ in sufficient amounts to
saturate the dark matter relic density [7].

To fit the galactic cross section data, we compute the self-interaction cross-
section

$\frac{d\sigma}{d\Omega}=\sum_{i=1}^{3}\frac{\overline{|\mathcal{M}_{i}|^{2}}}{64\pi^{2}s},$
(4.1)

where $i=1\cdots 3$ sums over the three processes $D\bar{D}\to D\bar{D}$,
$DD\to DD$, and $\bar{D}\bar{D}\to\bar{D}\bar{D}$ and using the Lagrangian of
Eq. (3.4), one can compute $\sigma v/m_{D}$ where $v$ is the Moller velocity.
The explicit forms of $\mathcal{M}_{i}$ are given in [7]. A set of benchmarks
which satisfy all of the current dark matter constraints are given in upper
Table 1. A plot of $\sigma v/m_{D}$ is given in Fig. 4 and shows that a fit to
DGC occurs for $\langle v\rangle$ from (10$-$3000) km/s.

Figure 4: A plot of the theory prediction of $\sigma v/m_{D}$ versus $\langle
v\rangle$ (the average relative velocity of the DM particles in the halo)
based on the model with one hidden sector with dark fermions self-interacting
via exchange of dark photons with $m_{\gamma^{\prime}}<<m_{D}$, where the band
represents the range of model points presented in [7] and the DGC data is
taken from the analysis of [39, 31].

##  5 Dark photon as dark matter

As discussed above it is likely that dark matter resides partially or wholly
in the hidden sector (for early work see, e.g., [40]). Here we discuss the
possibility that the dark photon constitutes a significant portion of dark
matter. In order for this to occur, two important constraints need to be
satisfied. First, the dark photon must have a lifetime larger than the age of
the universe and second, it must be produced copiously enough to constitute a
significant portion of the dark matter relic density consistent with the
Planck data [41], i.e.,

$\Omega h^{2}=0.1198\pm 0.0012.$ (5.1)

It appears difficult to satisfy both these constraints with one hidden sector.
This is so because for the dark photon to be long lived the kinetic mixing
needs to be extremely small. On the other hand to generate a significant
amount of relic density we need the kinetic mixing larger than what is
required to obtain a long lived dark photon. This tension between the lifetime
and the relic density constraints is relaxed by invoking two hidden sectors,
see Eq. (3.5). We note in passing that the case of two hidden sectors was
discussed in a different context in [42]. In this case we have two kinetic
mixings $\delta_{1}$ and $\delta_{2}$, and a mass mixing $M_{3}$ which allows
for a relaxation of the tension between the lifetime and the relic density
constraints. In Fig. 5 we exhibit the region of the parameter space where a
dark photon with a lifetime greater than the age of the universe and a relic
density consistent with Eq. (5.1) can be achieved. The excluded regions of the
parameter arise from constraints from experiments which include BaBar [43],
CHARM [44, 45], NA48 [46], NA64 [47, 48], E141 [49] and $\nu$-CAL [50, 51,
45], electron and muon $g-2$ [52], and E137 [53, 54]. For a dark photon mass
less than 1 MeV the strongest constraints arise from the decay
$\gamma^{\prime}\to 3\gamma$ [55, 56], from Supernova SN1987A [57], and from
stellar cooling [58]. The regions excluded by the BBN constraint are in pink.
In the analysis we have used the code darkcast [59] to obtain most of the
above mentioned limits. We note that in addition to the mechanism for
production of the dark photon in the early universe discussed in the analysis
here, one also has pure gravitational production of dark photons [60, 61, 62].
The gravitational production is dependent on the dark photon mass and on the
reheat temperature. For the parameters in the analysis of Fig. 5 with a dark
photon mass of $\sim 1$ MeV, gravitational production will be suppressed if
the reheat temperature lies below $10^{11}$ GeV.

Figure 5: An exhibition of the allowed region in the $\delta_{1}$ vs
$m_{\gamma^{\prime}}$ parameter space where a dark photon is long lived with a
lifetime larger than the age of the universe and can contribute a substantial
portion of the dark matter relic density. Here $\delta_{2}=0.4$ and
$m_{Z^{\prime}}=(5-20)m_{\gamma^{\prime}}$. The regions where a dark photon
can exist as dark matter are indicated by four colored vertical regions
corresponding to the four ranges of $m_{D}$ indicated in the legend on the
lower left hand corner. Taken from [8]. The description of the various
experimental constraints on the model are discussed in the text.

Regarding the lifetime of the dark photon there are two main decay channels:
$\gamma^{\prime}\to 3\gamma$ and $\gamma^{\prime}\to\nu\bar{\nu}$. The decay
width of $\gamma^{\prime}\to 3\gamma$ is given by [63, 64]

$\displaystyle\Gamma_{\gamma^{\prime}\to 3\gamma}$
$\displaystyle=\frac{17\alpha^{3}\alpha^{\prime}}{2^{7}3^{6}5^{3}\pi^{3}}\frac{m_{\gamma^{\prime}}^{9}}{m_{e}^{8}}\approx
4.70\times
10^{-8}\alpha^{3}\alpha^{\prime}\frac{m_{\gamma^{\prime}}^{9}}{m_{e}^{8}}.$
(5.2)

Here $\alpha=e^{2}/4\pi$, $\alpha^{\prime}=(ke)^{2}/4\pi$,
$k=-\delta_{1}(\delta_{2}-\sin\beta)\cos\theta_{w}$, where $\theta_{w}$ is the
weak angle, and $\beta$ is defined such that $\tan\beta=M_{3}/M_{4}$ where
$M_{3}$ and $M_{4}$ are as given in Eq. (3.5). For the parameters of model (d)
at the bottom of Table 1, the decay lifetime is $\tau_{\gamma^{\prime}\to
3\gamma}\sim 5.3\times 10^{15}$ yrs. For $\gamma^{\prime}\to\nu\bar{\nu}$ the
decay width is given by

$\displaystyle\Gamma_{\gamma^{\prime}\to\nu\bar{\nu}}$
$\displaystyle=\frac{g_{2}^{2}\delta_{1}^{2}(\delta_{2}-\sin\beta)^{2}\epsilon_{\gamma^{\prime}}^{4}}{8\pi}m_{\gamma^{\prime}}\tan^{2}\theta_{w}\,,$
(5.3)

where $\epsilon_{\gamma^{\prime}}=m_{\gamma^{\prime}}/m_{Z}$. In this case the
dark photon lifetime for the illustrative model (d) is
$\tau_{\gamma^{\prime}\to\nu\bar{\nu}}\sim 8.4\times 10^{21}$ yrs. Thus the
dominant decays of the dark photon have lifetime much larger than the age of
the universe. Also as can be seen from Table 1 one can generate a relic
density consistent with the Planck data.

##  6 Hidden sectors and the BBN constraint

Hidden sectors bring in new degrees of freedom while BBN constraints strongly
limit the extra neutrino degrees of freedom. Thus the SM predicts $N_{\rm
eff}=3.046$ at BBN time while the analysis using data from BBN, CMB and BAO
[41] gives a deviation from the SM of $\Delta N_{\rm eff}=0.22$.
Theoretically, if there are extra $\Delta n_{b}$ relativistic bosonic degrees
of freedom beyond those of the SM they contribute an extra amount to $\Delta
N_{\rm eff}$ so that

$\displaystyle\Delta N_{\rm eff}\simeq\frac{4\Delta
n_{b}}{7}\left(\frac{11}{4}\right)^{\frac{4}{3}}\left(\frac{T_{h}}{T_{\gamma}}\right)^{4},$
(6.1)

where $T_{h}$ is the hidden sector temperature where the new degrees of
freedom reside. Thus it is clear that if the hidden sector is very feebly
coupled to the visible sector, it is likely that it may be far from thermal
equilibrium with the visible sector at the BBN time. Thus suppose
$T_{h}/T_{\gamma}=0.2$. In this case the constraint $\Delta N_{\rm eff}=0.22$
implies that $\Delta n_{b}$ could be as large as about 60. While this is an
extreme example, it illustrates the importance of evolving in an accurate
fashion the temperature of the hidden sector temperature relative to that of
the visible sector.

##  7 Future directions

Hidden sectors and their implications for particle physics and for cosmology
can be tested in a number of current and future experiments which we discuss
below. Thus hidden sector dark matter, specifically light dark matter in the
MeV$-$GeV range and below, would be explored in a number of dark matter
detectors both via direct detection and via indirect detection. An example of
this is the Xenon-1T detector which is sensitive to dark matter in the sub-GeV
mass range and provides a testing ground for specific models of hidden sector
with dark fermions down scattering from bound electrons in xenon in an
inelastic exothermic process [65] (for theoretical analyses of these see [66]
and the references therein). Further improvements in experiment with Xenon-nT
will lead to greater sensitivity to hidden sector dark matter. PandaX-II
liquid xenon detector [67] also measures scattering cross section between the
dark matter and electrons and has placed the most stringent limits in the dark
matter range of 15$-$30 MeV and a corresponding DM-electron cross section from
$2\times 10^{-37}-3.1\times 10^{-38}$ cm2. PandaX-II also explored constraints
specifically for self-interacting dark matter with mass range of 1$-$100 GeV
with a light mediator mass from 1 MeV to 1 GeV [68]. Further, much smaller
mass ranges for the hidden sector dark matter will be explored by future dark
matter detectors. Thus dark matter-electron scattering from aromatic organic
targets [69, 70] presents a new area of dark matter detection for light dark
matter. Here scattering events involve dark matter interactions with electrons
which reside in molecular orbitals which have excitation energies of a few eV.
Such detectors are sensitive to dark matter which are as light as a few MeV.

Another dark matter experiment suitable for hidden sector dark matter is
CDEX-10 [71] at the China Jinping Underground Laboratory which uses a
germanium detector and has already put direct detection constraints on dark
photons. Thus it sets stringent limits on the kinetic mixing parameter
$\delta$ in the mass range of 0.1$-$10 KeV. The superCDMS experiment [72]
constraints the dark photon kinetic mixing parameter $\delta$ in the mass
range (1.2$-$50) eV. Hidden sector dark matter can also be detected via
indirect means. Thus, for example, hidden sector dark fermions $\chi$ can
annihilate via the process $\bar{\chi}\chi\to\gamma\gamma$. For light hidden
sector dark matter in the sub-GeV range, the $X$-ray and $\gamma$-ray spectrum
will be typically soft which, however, can be detectable by e-ASTROGAM [73]
which is an observatory space mission dedicated to the study in the photon
energy range from 0.3 MeV to 3 GeV [73] which is an energy range with
sensitivity not accessible to other $X$-ray and $\gamma$-ray searches such as
Fermi-LAT, EGRET, COMPTEL and SPI.

As noted, models of hidden sector dark matter are very sensitive to the
relative temperature of the hidden sector in which they reside vs that of the
visible sector. For this reason accurate thermal evolution of the hidden
sector and of the visible sector heat baths are essential. The formalism
discussed here allows one to accomplish that and thus relevant for further
study as analyses along these lines would be needed to test hidden sector
models of the dark photon and of other astrophysical phenomena with data in
the future.

##  8 Conclusion

Modern theories of particle physics and cosmology based on supergravity and
strings necessarily involve hidden sectors needed for breaking of
supersymmetry. However, the hidden sectors needed in supersymmetry breaking
are not the only ones that appear in supergravity and string
compactifications. In general there can be additional hidden sectors many of
them endowed with gauge groups. While neutral under the SM gauge groups, the
hidden sector can communicate with the visible sector in a variety of ways
such as via Higgs portals and via kinetic mixing and Stueckelberg mass mixing
between the hidden sectors and the visible sector if the hidden sectors posses
$U(1)$ gauge symmetries. In this work we point out that an accurate treatment
of a visible sector coupled to hidden sectors leads to a multi-temperature
universe with the visible sector and the hidden sector residing in different
heat baths. A proper treatment of the coupled system then involves correlated
evolution of the temperatures for the coupled sectors. In this work we have
discussed the general formalism for accomplishing that. We also discussed two
specific cases of multi-temperature evolution where the first one involves one
hidden sector and the second two hidden sectors. For the first case one needs
only one evolution parameter for the simultaneous evolution of the two
temperatures, i.e., $\xi=T_{1}/T$ where $T_{1}$ is the temperature of the
hidden sector and $T$ is the temperature of the visible sector. For the case
of two hidden sectors we need in addition the evolution of the parameter
$\zeta=T_{2}/T_{1}$. The evolution equations for $\xi$ and $\zeta$ were
discussed in section 3.

Applications of the formalism were given in sections 4 and 5. In section 4, we
discuss a model based on one hidden sector where the hidden sector contains a
dark fermion which acts as dark matter and the dark photon which mediates the
interaction between the dark fermions. This model leads to self-interacting
dark matter which has a velocity dependent cross section and allows one to fit
the galactic data from galaxy scales where the dark matter appears to behaves
collisional to the scale of galaxy clusters where the data indicates that dark
matter is collision-less. In section 5 we discussed the possibility that the
dark photon constitutes the bulk of dark matter in the universe. Here it is
shown that to generate the desired relic density and also satisfy the
constraint that the dark photon lifetime exceeds the lifetime of the universe,
one needs two hidden sectors. It is shown in this case that while the hidden
sector thermalizes with the visible sector at BBN time, this is not the case
for hidden sector 2 for which the ratio $T_{2}/T$ is smaller than unity and is
helpful in the satisfaction of the BBN constraint on the degrees of freedom.
The formalism discussed here is helpful in building realistic particle physics
which include dark particles and dark forces as well as in cosmology studies
which include hidden sectors in the analysis.

Acknowledgments:  The research of AA was supported by the BMBF under contract
05H18PMCC1. WZF was supported in part by the National Natural Science
Foundation of China under Grant No. 11905158 and No. 11935009. The research of
PN and ZW was supported in part by the NSF Grant PHY-1913328.

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